School Science Lessons
(UNPh17)
2024-07-25
Collisions, Momentum, Viscosity
Contents
17.4.0 Collisions, one dimension
17.5.0 Collisions, two dimensions
17.8.0 Conservation of linear momentum
17.1.0 Friction, static friction and rolling friction
17.6.0 Linear momentum
16.4.0 Momentum, seat belts
17.7.0 Rockets and thrust
17.3.0 Viscosity, Stokes' law
17.1.0 Friction, static friction and rolling friction
Experiments
17.0.0 Friction, static friction, rolling friction
17.1.1 Angle of repose of an inclined plane
17.1.2 Capstans
17.1.3 Friction blocks on inclined plane
17.1.4 Interleaved telephone books, finger lock, "pycrete"
17.1.5 Low friction surfaces, Teflon
17.1.6 Raisin cake
17.1.8 Sliding friction
17.1.9 Stabbed rice, gripping rice, suspended rice (friction, pile driver action)
17.1.10 Static friction and rolling friction
17.1.11 Static friction vs sliding friction
17.1.12 Toothbrush friction
17.2.1 Reduce friction with air streams, balloon hovercraft
17.2.2 Reduce friction with ball bearings, marble bearings
17.2.3 Reduce friction with liquids, lubricants
17.3.0 Viscosity, Stokes' law
Viscosity, derived unit, 1 poise (P) = 10-1 NM-2s
17.3.01 Stokes' law
17.3.1 Viscosity, Stokes' law, fluid friction, falling ball in liquid
17.3.2 Ball bearing falling in liquid, Stokes' Law
17.3.3 Electrorheological fluid (ER fluid), cornflour and vegetable oil
17.3.4 Newtonian fluids
17.3.5 Non-Newtonian fluids, dilatancy, thixotropy
17.3.6 Pulling an aluminium plate
17.3.7 Stir-thickening cornflour mixture, cornstarch
17.3.8 Stir-thinning tomato sauce
17.3.9 Syringe water velocity
17.3.10 Terminal velocity coffee filters
17.3.11 Terminal velocity drop balls and specific gravity
17.3.13 Time to empty the funnel, viscosity
17.3.14 Uniform pressure drop
17.3.15 Viscosity and temperature
17.3.16 Viscosity bubble race
17.3.17 Viscosity disc
17.3.18 Viscous drag
17.3.19 Viscosity of engine oil
17.3.20 Viscosity of honey
17.3.21 Viscosity of thick and thin liquids
17.3.9 Viscosity pipe
17.4.0 Collisions in one dimension
Experiments
17.4.1 Air track collision gliders
17.4.2 Bouncing dart
17.4.3 Double ball drop, tennis ball over basketball
17.4.4 Double air glider bounce
17.4.5 High bounce paradox
17.4.6 Pendulum collisions
17.4.1.1 Equilibrium of forces, Suspended block
17.5.0 Collisions in two dimensions
Experiments
17.5.1 Air table collisions, equal mass, unequal mass
17.5.2 Lost momentum
17.5.3 Shooting pool (billiards, snooker)
17.5.4 Super ball bouncing
17.6.0 Linear momentum, stream impulse
17.6.1 Linear momentum and collisions, impulse and thrust, conservation of linear momentum
17.4.1 Air track collision gliders
17.4.2 Bouncing dart
17.6.5 Bulbous bow
17.6.6 Catapult a ball from cart to cart
17.6.7 Catch an egg in a sheet
17.6.8 Centre of mass of see-saw (teeter-totter)
17.6.9 Change of force direction
17.6.10 Collisions, elastic and inelastic collisions
17.4.4 Double air glider bounce
17.4.3 Double ball drop, tennis ball over basketball
17.6.14 Exploding pendulums
17.4.5 High bounce paradox
17.5.2 Lost momentum
17.6.17 Motion on a rolling board
17.6.18 Move coin without touching
17.8.4 Newton's cradle, colliding balls, counting balls
17.4.6 Pendulum collisions
17.6.21 Pile driver with foam rubber
17.6.22 Shoot a ballistic air glider
17.5.3 Shooting pool (billiards, snooker)
17.5.4 Super ball bouncing
17.6.25 Throw ball on a blackboard, deform clay
17.6.26 Velocity of a softball
17.6.1.1 Water stream impulse
17.7.0 Rockets and thrust
Experiments
17.7.1 Rockets
17.7.2 Ball bearing rocket cart
17.7.3 Blow rocket
17.7.4 Carbon dioxide cartridge rocket
17.7.5 Fire extinguisher cart
17.7.6 Necessity of seat belts in a motor car
17.7.7 Seat belts, car crashes
17.7.8 Seat belts, Instructions for using seat belts
17.7.9 Water jet reaction force
17.7.10 Water rocket
17.8.0 Conservation of linear momentum
Experiments
17.6.8 Centre of mass of see-saw (teeter-totter)
17.6.14 Exploding pendulums
17.6.17 Motion on a rolling board
17.6.19 Newton's cradle, colliding balls, counting balls
17.8.6 Spring apart air track gliders
16.4.0 Momentum, seat belts
Momentum is a vector quality with direction the same as the velocity of the object.
p = mv, where p = momentum, kg m s-1, m = mass, kg, and v = velocity, ms-1
From Newton's second low of motion, a resultant force acting on an object causes a change in momentum.
The rate of change of momentum is proportional to the size of the resultant force and takes place in the direction of the resultant force.
F = change in mv / change in t, where F= resultant force in newtons, and change in time is the time when the force acts.
Assuming mass m is constant, change in mv = m(v-u), a = (v-u) / change in t, So F = ma.
17.7.6 Necessity of seat belts in a motor car
17.7.7 Seat belts, car crashes
17.7.8 Seat belts, Instructions for using seat belts
38.5.18 Seat belts warning, (electronics)
17.0.0 Friction, static friction, rolling friction
The direction of friction is such as to oppose motion.
When a force is applied to a body and the body is about to move or is moving the friction is called limiting friction.
Limiting friction
Limiting friction F = muR, where mu is the coefficient of friction and R is the normal reaction at right angles to the surfaces.
The frictional force opposes the motion of one surface in contact with another.
Walking is difficult on a surface covered by ice, so the lack of friction can be an inconvenience.
Machines are lubricated to reduce friction to allow the machine to do its work.
1. Friction is a force emerging in the relative motion of two objects in contact.
When two surfaces are in contact and one surface moves relative to the other, they produce a frictional force that opposes the motion.
Two types of friction are possible, depending on the nature of the relative displacement of solid objects in contact:
* Sliding friction occurs when an object is sliding over the surface of another object.
* Rolling friction occurs when an object rolls over the surface of another object.
Sliding friction
The sliding friction force is directed along the contact surface of objects against the displacement.
For the same solid objects, sliding friction is nearly proportional to the force with which one object is pressed against the other, i.e. to the force of pressure of one object on the other.
This force is normal to the contact surface between the objects, f = N.
The proportionality factor is called the coefficient of sliding friction, = f / N.
Sliding friction, kinetic friction, is the force needed to be applied to an object to keep it sliding across a surface.
Static friction
Static friction is the force that prevents an object from sliding across a surface when a force is applied to it, so it is the friction between two objects in contact that are not moving.
Static friction is usually greater than sliding friction, kinetic friction, and must be overcome before an object can be set in motion.
2. Coefficients of friction
Between solid surfaces, friction acts parallel to the surfaces and in the opposite direction to the motion, or the attempted motion.
Sliding friction depends on the materials in contact and their degree of smoothness, is usually less than static friction, is independent of speed of motion and is not dependent on area of contact.
Friction is directly proportional to the normal reaction of the surface.
For sliding friction, examples of coefficients of friction are as follows:
Tyre on dry road = 0.7, Tyre on wet road = 0.5, Steel on steel = 0.6, Wood on wood = 0.3.
Newton's second law of motion state F = ma, where F is the resultant accelerating force, but the acceleration will be less than expected, due to friction.
Friction appears not only when one surface slides over another surface, but also when you attempt to cause such a slip by applying a force to an object.
If the size of the external the force is less than N, no slip occurs between the objects, because the force is balanced by static friction that automatically assumes a value equal to the size of the force.
When the force attains a value equal to N, the object starts to slide over the surface of the other object, and static friction becomes sliding friction.
Static friction may assume values between zero and N.
The coefficient of friction depends on the force n and the velocity of slippage.
You can assume that the coefficient is constant.
3. Direction of friction
The direction of friction is that friction always opposes the motion.
This statement is often heard or read and, indeed, friction does oppose the motion in very many situations.
In the following situation, with a block sitting on top of another block and the system moving to the right under the action of an applied force.
If you think about the forces on the system, you indeed find that friction that friction between the lower block and the table is opposing the motion.
What about the upper block
What is causing it to move
In this case, the upper block is moving, because of friction between it and the lower block.
Friction is in the same direction as the motion! In fact, you often meet this question.
The simple act of walking is a demonstration of friction acting in the direction of motion.
Push back on the earth and the friction force between your feet and the earth moves you forward.
17.1.1 Angle of repose of an inclined plane
See diagram 21.3.1: Inclined plane
Lift one end of an inclined plane until a block begins to slide.
1. Put the following different objects at one end of a smooth tray
1.1 Cubes of different substances
1.2 Knife fork and spoon
1.3 Identical packets of salt with,
1.3.1 smallest area down,
1.3.2 medium-sized area down,
1.3.3 largest area down.
Slowly lift the tray by raising the end where the objects are placed.
Note the angle or height of that end of the tray when the objects start to slide.
Note the sequence of objects starting to slide.
2. Repeat the experiment with another tray with a different surface or attach a new surface to the first tray, e.g. a sheet of sand paper or emery paper.
The objects will start to slide at a greater height than before, but note whether the sequence of objects starting to slide is the same.
3. Place a block on an adjustable inclined plane and adjust the angle of repose of the inclined plane until the block slides with uniform velocity.
The tangent of the angle of repose gives the coefficient of friction between the surface of the block and the surface of the inclined plane.
17.1.2 Capstans
Examine the frictional force vs the number of turns around a rod.
Falling flask capstan: Attach a 4 litre round bottom flask at the other end of a ball on a string and drape the flask around a horizontal rod 1 m high.
Falling keys capstan:
Hang a set of keys from a string draped around a pencil and when the string is released the keys don't hit the floor.
Friction experiments with the cord wrapped around a cylinder.
17.1.3 Friction blocks on inclined plane
See diagram 17.183: Friction block
See diagram 17.184 Body on an inclined plane
See diagram 17.185 Force to pull body up an incline
1. Pull a block along different surfaces with a spring scale, e.g. Teflon, wood sandpaper, and rubber.
2. Make a sliding friction machine by attaching a spring scale is attached to an object on a rotating table.
3. Observe the weight dependence of friction by pulling a friction block with a spring scale add a second equal block to the first and repeat the observation.
4. Observe the area dependence of friction by using a friction block with rectangular shape with one side twice as big as the other.
The friction block is pulled along the bench top while resting on either the narrow or wide face.
5. Observe friction blocks down an incline.
A loaded cart rolls down an incline and hits a barrier.
The load continues sliding on a second incline until it stops.
The mass on the slider is varied to show stopping distance is independent of mass.
6. Observe cross friction.
Push a block across the slope of an incline and the block will move with a straight line trajectory.
Knock a coin across and it will move in a curved path
17.1.4 Interleaved telephone books
1. Put two identical telephone books on the table side by side, push them to touch then interleave the pages, i.e. any page of one book has a page of the other book above it and below it.
After interleaving, push the books together to maximize contact between the pages.
Place a heavy weight on the interleaved telephone books then later remove the weight and try to pull the books apart.
A considerable force is needed to pull the books apart and even heavy machinery may be needed.
2. The considerable friction between the pages of the telephone book is augmented by "Chinese finger lock".
It is used by police to restrain suspects before "patting down" to detect weapons or other objects.
Finger lock techniques are also used in ju-jitsu, (jiu-jitsu), Japanese unarmed combat contests.
3. Pycrete
A mixture of 14% wood pulp and water can be frozen to produce "pycrete" that is much stronger than the same volume and shape of a piece of ice.
The pycrete should contain no air bubbles.
The friction between the particles of wood pulp causes the extra strength of pycrete.
4. If the edge of a piece of paper cuts your finger the cut is very painful, because of the multitude of jagged edges from the wood fibres in the paper.
17.1.5 Low friction surfaces, Teflon
Teflon surface: Cut up a Teflon coated cookie sheet for an inexpensive Teflon surface.
Teflon pulley: Teflon sheet bent around corner replaces a pulley.
Dylite beads on a rimmed glass surface window pane provide a low friction surface.
17.1.6 Raisin cake
Coat raisins with flour before adding them to a batter to make a raisin cake.
The flour increases the surface friction of the raisins so that not all of them will fall down to finish at the bottom of the cake, but be more equally distributed throughout the cake.
17.1.8 Sliding friction
See diagram 17.183: Friction blocks
Sliding friction between solids, reducing friction with oil, walking, skid, slippery floor, sewing, wear and tear
Experiments
1. Wrap a house brick in newspaper.
Attach the brick to a spring scale with string.
Put the brick on a uniform table surface with the largest area down on the table.
Practice pulling the spring scale to move the brick with constant velocity while another person reads and records the spring scale measurement.
If you pull the house brick horizontally at constant velocity, the applied force equals the frictional force.
2. Friction and different surfaces
Record the frictional force with different kinds of wrapping on identical house bricks, e.g. newspaper, plastic from a plastic bag, sandpaper.
3. Friction and the area of a surface
Turn the wrapped house brick so that a smaller area is down on the table.
Adjust the attached string and measure the frictional force.
4. Compare starting motion friction with maintaining motion friction
Measure the frictional force needed to start the brick moving.
Compare the force with 2. 5. Friction and speed of motion
Measure the frictional force necessary to move the brick at different constant velocities.
5. Friction and force pressing the surfaces together
Measure sliding friction with stacks of two to five bricks.
6. Attach a string from a heavy box to a spring balance.
Move the box across the table by pulling it with the spring balance.
Record the force needed to pull the box at constant slow speed.
The force of friction opposes the motion.
The friction between the bottom of the box and the table is called sliding friction.
7. Put a sheet of glass on the table.
Record the force needed to pull the box at a slow constant speed.
If the surface of the glass is smoother than the surface of the table, the sliding friction is less.
8. Use chalk or water or oil to lubricate the surface of the table.
Record the force needed to pull the box at a slow constant speed.
9. Bind a thick book with string.
Place the book on a smooth tabletop, and, on a rough wood, then attach the string to the hook of the spring balance and pull the spring balance to make the book move with uniform velocity.
Compare the reading on the spring balance and note when friction is the smallest.
10. Prevent squeaky chalk.
You don't have to break chalk to eliminate squeaking, because if you use friction you can hold the chalk at an angle that eliminates it.
11. Observe a sliding chain.
Hang a chain over the edge of the table until the weight of the chain makes it slide.
This simulates the action of a siphon.
17.1.9 Stabbed rice, gripping rice, suspended rice
A pile driver used in civil engineering construction pushes a pile down.
It can do this, because the pile pushes earth particles to the side.
1. Almost fill a narrow neck plastic jar with rice.
Note the level of the rice in the jar.
Stab down into the rice with a sharpened pencil.
Keep stabbing down, sometimes deeply to the bottom of the plastic jar and sometimes shallowly.
When the rice starts to grip the rice, slowly, with great force. push the pencil down to touch the bottom of the plastic jar.
The conical end of the pencil pushes rice sideways when the pencil is pushed into the jar.
When the pencil is raised and removed from the jar, rice falls into the space left by the pencil, so the level of rice in the jar decreases slightly.
The action of the repeated stabbing with the pencil is to pack the rice more closely.
Eventually, the rice is so closely packed to increase friction between the rice grains that you cannot raise the pencil without the jar of rice also being raised.
If enough chains of rice grains wedge themselves against the blade and the top of the jar, when the knife is lifted the entire jar will cling to it. 2. Use a jar with a narrowing neck.
Fill the jar to the brim with rice.
Push a pencil into the rice.
The pencil should easily slides through the rice.
Grip the pencil firmly and start stabbing the rice repeatedly in the centre of the jar, stabbing occasionally to the bottom.
The rice begins to form a crater.
After about forty stabs, the pencil begins to grip the rice, so it is more difficult to push the pencil down.
The conical tip of the pencil pushes rice sideways when the pencil is forced into the jar.
The rice packs more closely in the jar causing the level to rise slightly.
When the rice is packed more tightly, the friction between each grain increases and the friction between the pencil, rice and jar becomes so strong to prevent the pencil slipping through the rice. 3. Use a jar that is wider than its opening.
Almost fill the jar with uncooked white rice and stab down into it with a knife using short jabs.
Some rice has moved aside to let the knife blade descend.
Add more rice to the jar, pull the knife up and stab down again.
After repeating this action a few times.
Stab the rice down to the bottom.
When you pull up the knife slowly, the jar and packed rice rises as well, because of the pressure between the knife, rice grains and wall of the jar.
The pressure from the sharp knife is enough to force the rice grains apart, but then they settle back into place and lock into each other and hold the knife in place.
Rice grains have wedged themselves against the blade and the top of the jar.
The experiment may work better if you stab at an angle, not vertically.
17.1.10Static friction and rolling friction
See diagram 17.260: Static friction and rolling friction
1. Put a box on the bench or table.
Use a spring balance to record the force needed to start the box moving - static friction.
Use a spring balance to record the force needed to pull the box at the same slow constant speed - sliding friction
2. Put ball bearings or marbles under the box.
Use a spring balance to record the force needed to pull the box at the same slow constant speed - rolling friction.
Compare the values of rolling friction and sliding friction
3. Put the box on a sheet of glass on the table.
Repeat the above experiments. The sliding friction is less than the sliding friction on the bench or table.
4. Put round pencils under a box to act as rollers.
Pull the spring balance to make the book move with uniform velocity.
When the book moves off the most back pencil, put it under the book again from the front of the book.
Compare the reading on the spring balance with and without pencils under the book.
5. Attach a spring balance to a box on the table.
Record the force needed to pull the box at a slow constant speed.
Put ball bearings or marbles under the box.
Record the force needed to pull the box at a slow constant speed.
Pour oil on the ball bearings or marbles.
Record the force needed to pull the box at a slow constant speed.
This may be the least force needed to pull the box.
Repeat the experiment with a sheet of glass on the table.
Record the force needed to pull the box at a slow constant speed.
If the surface of the glass is smoother than the surface of the table, the sliding friction is less.
17.1.11 Static friction vs sliding friction
See diagram 17.183: Friction block
Kinetic friction is the friction experience by two surfaces sliding against each other with a known relative speed.
Static friction has values from zero to a maximum value.
Friction coefficients are dimensionless.
1. Measure static friction by noting the scale reading just before the block slides.
Measure sliding friction by pulling the block at a constant speed.
Compare the two readings.
Change the surface materials and note the different friction.
If reading on spring scale = F, and force of static friction = fs, then F = fs, until block starts to move and fs has maximum value.
Once the block starts moving the friction is kinetic friction, fk, i.e. sliding friction.
2. Measure sliding friction by continuing to pull the block at constant speed.
3. Change the rough surface and note the different values for static friction and sliding friction.
(Table 17.5.7)
Friction coefficients
 Kinetic friction, k
 Static friction, s
Steel on steel
 0.57
 0.74
Glass on steel
 0.40
 0.94
Steel on ice
 0.06
 0.10
17.1.12 Toothbrush friction
See diagram 17.6.01: Toothbrush friction
Hold two toothbrushes vertically, one handle up (above), and the other handle down (below).
Push the brushes together by pushing horizontally.
Attach a string and a weight to the end of the handle of the lower toothbrush.
Pick up the end of the handle of the upper toothbrush.
The weight can be raised, because of the friction between the bristles of the two toothbrushes.
17.2.1 Reduce friction with air streams, balloon hovercraft
See diagram 17.265: Reduce friction with air stream A Balloon, B Cotton reel, C Cardboard
The hovercraft blows air below itself so that the hovercraft floats on a cushion of air between itself and the ground.
So there is no contact with the ground and almost no friction with the ground.
Then the hovercraft can move easily by sending out little spurts of air parallel to the ground so that it moves in the opposite direction.
Cut out a disc of cardboard about 10 cm in diameter.
With a red-hot pin, burn a hole through the centre.
Saw a small cotton reel in half and glue the original end of one half over the middle of the disc.
Find a piece of bamboo or another tube that just fits the hole in the reel.
Push this into the neck of a small balloon, using cotton or a rubber band to secure the joint.
Blow up the balloon, pinch the neck, and insert the tube into the hole in the cotton reel.
Place the disc on the table and release the air.
The expanding air, escaping through the hole in the disc, will lift the card so that, given a flick, it will shoot across the table with practically no friction.
This experiment illustrates the principle of the hovercraft.
2. Drill a hole in the centre of a plastic bottle cap the same diameter as the hole in the centre of a disused CD-ROM disc.
Glue the bottle cap to the centre of the CD-ROM disc with the holes aligned.
Inflate a balloon and twist the inlet tightly, but do not tie it closed.
Roll the lip of the balloon inlet over the plastic bottle cap.
Place the apparatus on a smooth table and release the twisted balloon inlet.
The apparatus slides over the table top just like a hovercraft.
3 Observe air friction by dropping the same size pieces of paper crumpled and flat sheets of paper.
17.2.2 Reduce friction with ball bearings, marble bearings
See diagram 17.264: Ball bearings, marbles
1. Use two paint pots with a deep groove around the lid.
Put marbles in one groove and invert the other paint pot over the marbles to form a ball bearing race.
Put a book on top of the paint pots and note how you can easily move the top paint pot around.
Add oil to the marbles and the top paint pot turns more easily.
2. Mount a box on wheels.
Record the force needed to pull the box at a slow constant speed.
Has the rolling friction decreased
Put ball bearings or marbles under the box.
Record the force needed to pull the box at a slow constant speed.
Pour oil on the ball bearings or marbles.
Record the force needed to pull the box at a slow constant speed.
This may be the least force need to pull the box.
3. Use two same round iron boxes.
There is a shallow trough near the rim of each cover, e.g. iron cans containing biscuits or milk powder.
Remove the cover of the box and place some steel balls or glass marbles in the trough on the cover.
Pile the other box on the cover with steel balls or glass marbles.
Place a heavy book on the box and make them move together.
You may feel how easy it is.
If you drop a bit of lubrication oil or cooking oil on the balls, they rotate more easily.
17.2.3 Reduce friction with liquids, lubricants
The friction acting on an object in a fluid, and the friction between two solid surfaces, is always directed against the motion of the object and depends on velocity.
When an object moves in a fluid, a force appears that hampers the motion of the object.
The fluid particles exert this force on the moving object.
The resistance of the fluid medium differs from the friction between two solid surfaces in that no static friction exists, because the weakest possible force can displace an object floating in a liquid.
Experiments
1. Place a large block of glass on a desk.
Use small block of glass, for example, the glass on a small picture frame.
Place the small block of glass under the large one.
Push the small glass with your fingers to make it move under the large one.
Experience the magnitude of the force you exert.
Wet the contact surface between two blocks of glass.
Make sure the surface completely wet.
Then push the small glass again and experience the magnitude of the force you exert.
2. Repeat the experiment, but using oil instead of water.
Which is easier
If wipe oil on your hand then push the small glass.
Note what you feel. Compare the experiences.
3. Reduce friction with oil.
Lay two panes of glass side by side and place a few drops of oil on one.
Feel the difference when you rub a finger back and forth on the unoiled pane and on the oiled pane.
Repeat the experiment by substituting other liquids for oil.
4. Lay two sheets of glass side by side and place a few drops of oil on one sheet.
Feel the difference when you rub a finger back and forth on the unoiled pane and on the oiled sheet.
5. Use chalk or water or oil to lubricate the surface of the table.
Record the force needed to pull a box at a slow constant speed.
17.3.01 Stokes' law
See diagram 17.3.01: Dropped ball bearings
Stokes' law (George Stokes 1851) describes the frictional force on a spherical ball falling through liquid, force = 6 × π × radius × velocity × viscosity of liquid.
A falling ball accelerates until it reaches a constant terminal speed, settling velocity.
F = gravitational force on the spherical ball less the upthrust.
Stokes' law can be applied to liquid and gas mediums.
The falling sphere viscometer uses Stokes' law to calculate viscosity of a fluid from the size and density of a sphere falling in it, the density of the liquid and the terminal velocity of the sphere.
Experiments
1. Drop ball bearings or a sphere with known density and weight into treacle or glycerine to determine their viscosity.
2. To demonstrate Stokes law, that when a body moves through a fluid the viscous resistive force is proportional to the radius a and its velocity v.
Arrange a series of steel ball bearings with different sizes so that they can be released balls simultaneously to fall through a liquid.
The smaller balls take a longer time to fall than the larger balls.
As a consequence of Stoke's law, the terminal velocity is proportional to the square of the ball radius.
Hence a ball of diameter "x" will take 4 times as long to fall a given distance than a ball of diameter "2x".
If x = 5, and small ball takes 25 seconds, then large ball takes 100 seconds to reach terminal velocity.
17.3.1 Viscosity, Stokes' law, fluid friction, falling ball in liquid
Fluid friction, ball bearing falling in a liquid
1. Viscosity is the property of a fluid that resists the force tending to cause the fluid to flow.
Viscosity is the property of a fluid that tends to prevent the movement of one portion of the fluid relative to an adjacent portion, or prevent the motion of any body through the liquid.
Viscosity is the internal friction of a fluid, produced by the movement of its molecules against each other, the result of the diffusion of atoms or molecules inside an amorphous material.
Viscosity causes the fluid to resist flowing.
A viscous material, e.g. honey, resists shear flow and strain linearly with time when a stress is applied.
2. Absolute viscosity, η is a measure of this resistance, equal to the tangential stress on a liquid undergoing streamline flow divided by its velocity gradient.
It is measured in newton seconds per metre2.
3. Dynamic viscosity, the coefficient of velocity of a fluid at a given temperature, has symbol η (eta) and (mu).
Dynamic viscosity measures the resistance to flow of a liquid under shear stress in pascal seconds.
The SI unit is the pascal.second, Pa.s, in newton.second / metre2. 1 Pa.s = 1.00 g.cm-1.s-1.
Dynamic viscosity of water at 20oC = 0.001001 Pa.s.
The CGS (cgs) unit of dynamic viscosity is the poise, P (for some technologies centipoise, cP).
Dynamic viscosity of water at 20oC = 1.002.0 cP.
Viscosity: Pa s: Pascal second, N s m-2, a measure of viscosity replacing the c.g.s. unit, poise = 0.1 Pa s.
4. Kinetic viscosity (kinematic viscosity), ν (nu) is the ratio of the viscosity of a liquid to its density ρ (rho).
The SI unit, ν = / ρ, where is measured in m2 / s, and is measured in kg / m3.
The CGS (cgs) unit is stokes, St, or centistokes, cSt.
Kinetic viscosity of water = 1 cSt.
5. At 20oC the viscosity of water is 1.002 mPas and its kinematic viscosity (ratio of viscosity to density) is 1.0038 mm2 / s.
Lubricating oil may be classified using a Viscosity index (VI) for change of viscosity with temperature.
When a liquid flows slowly through a pipe, the rate of flow depends on the viscosity of the liquid.
However, when velocity exceeds a critical velocity, ν, the flow becomes turbulent and the rate of flow depends on the density of the liquid and not the viscosity.
Critical velocity, ν = k η ρ r, where k = constant. (Let water = 1000), η (eta) = coefficient of velocity of a fluid at a given temperature, ρ (rho) = density of liquid, r = radius
17.3.3 Electrorheological fluid (ER fluid), cornflour and vegetable oil
Mix 3 parts of vegetable oil with 1 part of cornflour (maize flour, cornstarch) to produce a colloidal mixture.
Leave the mixture to chill in a refrigerator, then remove the mixture to warm until it starts to flow.
Rub wool or hair on a block of polystyrene or PVC or a rubber ball to give the object a negative charge.
Place the charged object near the flowing mixture.
The mixture stops flowing and pieces of mixture may break off.
The mixture is an electrorheological fluid (ER fluid), i.e. a mixture of small non-conducting particles in an electrically insulating fluid.
Under the electric field, electrorheological fluids form fibrous structures, which are parallel to the applied field so the fluid increases in viscosity.
The dielectric cornflour particles separated by the oil form positive to negative chains aligned with the applied electric field.
The ER fluid gets thicker, because the charged dielectric cornflour particles in the chains attract due to positive negative attraction.
Similarly, melted chocolate may stop flowing in an electric field.
ER fluids are used in brakes and shock absorbers.
17.3.4 Newtonian fluids
Deformation occurs when a force is applied to a volume of material.
If two plates, area A, are separated by a fluid distance apart, separation height H, are moved relative to each other at velocity V, by a force F, the shear stress, force divided by area parallel to the force, F / A, is proportional to the shear strain rate, V / H.
An example of shear strain rate is the rate of stirring.
The proportionality of shear stress to shear strain rate follows Newton's laws.
So you can refer to Newtonian fluids, which follow this law of proportionality.
In a Newtonian fluid. the velocity gradient is directly proportional to the shear stress, the analogue for gooey materials of Hooke's Law for springs.
17.3.5 Non-Newtonian fluids
1. For dilatant (shear thickening) fluids, the faster the liquid moves, the more viscous it becomes, shear viscosity increases with applied shear stress, the viscosity increases with the rate of shear strain, e.g. mixture of cornstarch and water (oobleck).
When walking on wet sand the sand immediately below the foot is dry due to rearrangement of the grains from a close packed to a less close packed structure.
Dilatancy is the property of increasing in volume when pressure is applied.
2. For thixotropic fluids, the faster the liquid moves, the less viscous it becomes, the material becomes more fluid with increasing time of applied force, e.g. quicksand.
Struggle in "quicksand", it becomes "quicker" and you will sink into it, so do not struggle to get out of quicksand!
The proportionality constant is called the dynamic viscosity η (eta).
Viscosity is the tendency of a fluid to resist flow.
Viscosity increases, "becomes thicker", with increase in concentration or increase in molecular weight of a solute.
17.3.6 Pulling an aluminium plate
Use a string and pulley to a mass to pull an aluminium plate out of a viscous fluid, e.g. silicone fluid.
17.3.7 Stir-thickening cornflour mixture, cornstarch
Isotropy is the property of a fluid to become firm when agitated, e.g. walk slowly on wet sand and your feet sink into the sand, but run over the sand and it feels firm.
Thixotropy is the property of a fluid mixture to become more fluid, when agitated, e.g. strike the end of a ketchup bottle, the ketchup become "runny" and flows more easily.
Cornflour is powdery starch synthesized from maize and used as a cooking thickener, (in USA "cornstarch"), (in Australia "wheaten starch").
A cornflour mixture is called a stir-thickened mixture, shear-thickened liquid, and non-Newtonian liquid, because it does not follow the laws of Newtonian physics.
Experiments
1. Put cornflour into a plastic container.
Slowly add water to make a thick sludge and mix with your fingers.
Add a few drops of food colouring, e.g. cochineal.
Stop mixing when all the cornflour powder is wet.
Tap the surface of the mixture with your index finger.
The mixture is correct if it feels hard, although when mixing it felt wet.
If you add too much water the mixture will be too thin.
If the mixture is too powdery add more water.
Let the cornflour mixture run through your fingers and observe how fast it runs.
Slap the mixture with your fist.
Let the cornflour mixture run through your fingers and observe how fast it runs.
Note whether it is still "runny".
Take a handful and add a force to it so that it forms into a ball.
Stop the force and note that the mixture will snap like a solid.
The cornflour mixture is a stir-thickening substance.
The viscosity increases when a force of stirring or thumping is applied.
Repeat the experiment with cream.
2. Place a cup of cornstarch, corn flour, in a bowl.
Add 1/4 cup of water.
Keep adding water until the mixture appears thicker than pancake batter.
Take a handful and knead the mixture, like kneading bread dough, into a ball.
As the mixture is squeezed, it will become firm during the continuous pressure of kneading.
When the pressure stops, the "batter" returns to its original form and can pour through the fingers.
3. Make kinetic sand with a 50 lb bag of sand, 6 cups of cornstarch, 2 tablespoons of soap, water.
17.3.8 Stir-thinning tomato sauce
Stir-thinning liquids get thinner, decrease in viscosity, when you add force to them by stirring or shaking.
1. Pick up a bottle of tomato sauce and without shaking it.
Try to pour it out and observe what happens.
2. Shake the bottle of tomato sauce ten times.
Try to pour it out and observe what happens.
3. Leave the tomato sauce bottle to stand still for 20 minutes.
Try to pour it out and observe what happens.
4. Shake the bottle of tomato sauce ten times.
Try to pour it out and observe what happens.
After tomato sauce has fallen on food and stopped moving it becomes thick again
5. Repeat the experiment using hair gel.
17.3.9 Syringe water velocity
Squirt water out of a syringe.
The water moves faster through the constriction.
17.3.10 Terminal velocity coffee filters
Drop a coffee filter and it falls with low terminal velocity.
Crumple a coffee filter, drop it and it falls with a greater terminal velocity.
17.3.11 Terminal velocity drop balls and specific gravity
Drop steel, glass and lead balls of different diameters in a tall cylinder filled with glycerine.
Use a precision ball in a precision tube.
Measure the terminal velocity in water and glycerine.
Drop steel balls in large 1 metre test-tubes or graduated cylinders filled with water and filled with glycerine.
Drop four balls of the same diameter with different specific gravity into glycerine.
Drop Styrofoam balls in a 5 m tall glycerine cylinder.
Use Dylite beads reach to attain terminal velocity quickly in water and when expanded by heating in boiling water.
Also, use Dylite bead to show terminal velocity in air.
17.3.13 Time to empty the funnel, viscosity
1. Collect liquids from the home, e.g. oil, honey, sauce, water, milk.
2. Put your finger over the bottom end opening of a small kitchen funnel and fill the funnel with one of the liquids.
3. Hold the funnel over a larger container, remove your finger and observe the time taken for the funnel to empty.
Note which liquid takes the longest to leave the funnel.
You can measure viscosity by how easily things move through a liquid or how easily the liquid flows.
In the more viscous liquids, the molecules are sticking together more making it harder for them to pass quickly through a narrow space.
17.3.14 Uniform pressure drop
Make water flows in a horizontal glass tube with three pressure-indicating stand pipes fitted with wooden floats.
17.3.15 Viscosity and temperature
Invert tubes filled with motor oil and silicone oil at room temperature and after cooling.
Rotate a cylinder of castor oil in a water bath on a turntable at different temperatures.
Increase of temperature in a liquid increases the kinetic energy of the molecules, increasing attractive inter-molecular forces, e.g. van der Waal's forces, to increase the mobility of the molecules and decrease viscosity.
Increasing the temperature of gases increases the molecular interchange, which increases the viscosity of gases.
Viscosity of gases is proportional to square root of the absolute temperature.
17.3.16 Viscosity bubble race
Use a bubble race to compare viscosity in different tubes of different liquids when inverted.
Almost fill identical test-tubes, or plastic tubes with stoppers, with the same volume liquids having different viscosity, e.g. cooking oil, lubricating oil, dishwashing detergent, glycerol, water, methylated spirit.
The height of liquids in the test-tubes must be identical.
Put corks in the test-tubes.
Put the test-tubes in a test-tube stand and attach them to it so that when the test-tube stand is inverted the test-tubes will not fall down.
Quickly invert the test-tube stand and note the speed of the bubbles passing up through the liquids.
Note the sequence of the bubbles hitting the bottom of the inverted test-tubes.
The liquid that wins the bubble race is the least viscous.
17.3.17 Viscosity disc
Hang a horizontal disc on a single thread and spin a second disc below it to cause deflection.
Spin a disc between two parallel plates of a platform balance and note the deflection.
A horizontal disc is hung on a single thread and a second is spun below it causing deflection.
Mount a metal sheet and a disc parallel in a container of fluid, rotate the disc and observe the displacement of the sheet.
17.3.18 Viscous drag
Mount 2 coaxial cylinders are separated by a fluid.
As you rotate the outer cylinder, you can observe the drag induced motion of the inner cylinder.
17.3.19 Viscosity of engine oil
1. Viscosity index
The viscosity change is called the viscosity index.
The higher the viscosity index the less change in viscosity as the temperature rises.
The SAE (Society of Automotive Engineers) classification is an unbiased way of classifying the viscosity of "light", "medium" and "heavy" engine oils.
For example, SAE 10 W is a "thin" oil that you use to start engines in cold weather and SAE 30 is a "thick" oil that you use to start worn engines in hot weather.
2. Centistokes
The common denominator for Kinematic Viscosity measurement is "Centistokes", measured at 40oC, and 100oC, and at sub zero temperature, e.g. SAE 15W40 engine oil measures 13 to 15 Centistokes at 100oC, but above 16.3 Centistokes you rate the oil as SAE 50 Grade.
3. Engine oil additives
Additives to engine oil include the following: oxidation and / or corrosion inhibitors to retard engine deposits, detergent dispersers to keep dirty oil soluble, rust preventives, anti-wear agents to retard wear of moving parts, foam inhibitors to reduce froth, pour point depressants to allow oil to flow at low temperatures, and viscosity index improvers to reduce difference of viscosity of hot and cold oil.
4. Friction and wear
Engines rely on moving parts to function.
The surfaces that move over each other wear with use.
Friction is the resulting force encountered at the common boundary between two bodies when, under the action of an external force, one body moves, or tends to move, relative to the surface of the other.
Wear is progressive damage, involving material loss, which occurs to the surface of a component, because of relative motion at the surface of that component.
Wear is a gradual process, so the associated costs and inconvenience are not as apparent as failure due to brittle fracture or fatigue.
Lubrication is the application of lubricants to reduce friction and wear.
Boundary lubrication mode is reached every time machinery comes to a standstill.
Most of the wear takes place at start-up.
Hydrodynamic lubrication is reached within moments of the machinery starting up.
The oil pump begins to push the oil in circulation.
The oil pressure lifts each movable component into operational relationship with the mating component.
Low viscosity oils (light oils), flow freely, and high viscosity oils, (heavy oils), flow slowly.
5. Viscosity index
Viscosity changes with temperature, the higher the temperature the lower the viscosity.
The Viscosity Index is an empirical numbering system that describes the rate of change of viscosity of an oil within a given temperature range.
A low Viscosity Index signifies a relatively large change, while a high viscosity index shows a relatively small change, i.e. the higher the Viscosity Index the less oil thins out with increasing temperature and vice versa.
Fluid lubricants include specially formulated Engine Oils, Transmission Oils (Manual and Automatic), Heavy Duty Gear Oils suitable for differentials, Hydraulic Fluids, Compressor Oils.
6. Engine greases
Greases are semi-solid lubricants.
A variety of viscosity ranges are produced.
The Load Bearing Capacity is linked to both the viscosity (or thickness) and adherence or retention characteristics.
The speed of rotation (RPM) of the journal in a bearing will dictate the viscosity needs of the grease.
The same factors apply in gearboxes or transmission.
The rule is as follows:
The faster the movement of the components, the lighter the viscosity of the gear / transmission oil, and the slower the movement of the components, the heavier the lubricant needs to be.
If you use a heavy viscosity oil, e.g. SAE 25W60, in winter condition, the engine may not start without being preheated.
Engines usually need much lighter viscosity oil, e.g. SAE 5W30, to enable easy cold starting.
If you use SAE 5W30 oil in tropical conditions where pavement temperatures may be above 55oC, premature, wear may occur, because it is too thin or "light" for such high temperature conditions.
7. "Speciality oils"
The OEMs (Original Equipment Manufacturers) are asked to produce engines with finer tolerances, because the lighter viscosity engine oils will result in less internal fluid friction and diminish the amount of fuel required.
A survey of over 100 major transport companies in USA established that 80% of power is used initially in overcoming friction.
"Speciality oils" can minimize friction by increasing the film strength of the lubricants.
An interstate heavy transport operator who has used ordinary brand lubricants until recently decided to try a "speciality" brand gear oil in the differential of his prime mover to reduce the operating temperature.
The result was lower operating temperature, because of the higher load carrying capability of the gear oil by comparison with the oil previously used.
In another example, a used car given an oil change oil at 10 000 km was given a "speciality" brand of engine of the same viscosity (SAE 15W40).
After the oil change, it was travelling 120 km further on every tankful of fuel, so saving over 15% of the fuel costs.
In both of these examples less fuel is being burnt, so less harmful exhaust gas emissions pollute the atmosphere.
Experiment
Compare the viscosity of two engine oils by shaking two identical bottles at the same temperature by the same amount.
Invert the bottles and compare the speed bubbles rise.
The higher the speed the lower the viscosity.
17.3.20 Viscosity of honey
1. Dip a knife into a jar of honey at room temperature.
Lift the knife out and keep lifting to make a stream of honey.
Observe the stream of honey as the knife gets higher and higher.
2. Raise the temperature of the honey by standing it in a bowl of warm water for 15 minutes.
Dip a knife into a jar of honey at room temperature.
Lift the knife out and keep lifting to make a stream of honey.
Observe the stream of honey as the knife gets higher and higher.
Observe how high can you raise the knife before the stream of honey becomes drips
Note the direction the stream of honey coils.
17.3.21 Viscosity, thick and thin liquids
(After Donna Bennett, The Queensland Science Teacher, Volume 24, No. 2)
Heating a liquid makes it thinner, less viscous, because the spaces between the molecules get bigger and the molecules can slide over one another more easily.
17.3.22 Viscosity pipe
Make a series of small holes in a long water pipe or gas pipe to show pressure drop due to friction.
Run a water pipe around the laboratory with pressure gauges at the top and bottom of each side and examine the difference between static pressure and kinetic pressure.
17.4.1.1 Equilibrium of forces, Suspended block
See diagram 17.4.15: Suspended block
1. Forces parallel and perpendicular to the plane will support the block in mid-air when the plane is removed.
The components of force of a block on an inclined plane are countered by weights.
Then remove the inclined plane.
A 1.5 kg block rests on the slope of a 3: 4: 5 triangle.
When the three blocks are stable the triangle can be moved to the left and removed leaving the block suspended by the 0.9 kg and 1.2 kg blocks.
2. Hanging the plank.
Suspend a heavy plank from three spring scales in several configurations.
3. Tension in a string.
Compare the weight of a mass hung from a single spring scale to the weight shown on a spring scale between two masses over pulleys.
Suspend a spring scale between strings running over pulleys to equal weights.
4. Rope and three weights.
Suspend a rope over two pulleys with masses on the ends and hang another mass from the centre to deflect the rope.
Measure the deflection rope and three weights.
5. Rope and three students.
Two large strong students pull on the ends of a rope and a small student pushes down in the middle.
The small student can easily deflect the rope if it is held very tightly by the large students.
6. Weight on a clothesline.
Hang a 1 newton weight from a clothes line and pull on one end of the line with a spring scale.
7. Break wire with hinge.
Suspend a 1 kg mass from a length of wire.
Break a length of similar wire by placing the same mass on the back of a large hinge.
Pushing down on a slightly bent hinge will break the wire fastened to the ends.
8. Hang a weight on a string suspended between two spring scales in front of the blackboard.
Start with the strings vertical then increase the angle.
9. Sit on a chair that hangs from a chain attached to loads on each end of the chain in front of the blackboard.
17.4.1 Air track collision gliders
1. Two sets of air track carts one with springs and the other with "Velcro" give elastic and inelastic collision.
Air gliders have springs on one end and the post / clay on the other.
Place a metre stick on two carts and lift it up before one hits an end bumper.
Use a metre stick resting on top of two air track carts to give equal velocities then after one hits the end bumper you have equal and opposite velocities.
A small cart with bumper springs hits a big cart elastically placed so that after the collision both carts hit the ends simultaneously then the carts will again collide at the original place.
Mount a plunger on one air track and a cylinder packed with modelling clay on the other.
2. Shoot a stream of balls at a moving air cart until the cart stops.
17.4.1.9 Rubber band scale, spring scale
Calibrate rubber bands or springs for force vs length then predict the mass of an object hung in a non-collinear configuration.
17.4.2 Bouncing dart
A dart hits a block of wood with a thud, inelastic collision, but, when thrown with the pointer removed, elastic collision, the dart knocks the block over showing greater impulse associated with elastic collisions.
17.4.3 Double ball drop, tennis ball over basketball
17.4.3 Double ball drop, tennis ball over basketball
1. Drop a small ball from chin height and record the height it bounces.
Hold a small ball, e.g. ping-pong ball, just above a large ball, e.g. a basket ball, with the small ball at chin height, h.
Drop the balls simultaneously.
The balls have velocity V near the ground.
The large ball hits the ground first, bounces and hits the still falling small ball.
The small ball bounces off the large ball with velocity 3V to about nine times the original height, h.
Kinetic energy is proportional to V2, 32 = 9.
2. Separately drop two balls with different mass, m and M and note how high they bounce.
Hold the light ball to sit directly over the centre of the heavy ball, i.e. m over M.
Drop the combination, weighing (m + M), and note how high the balls bounce.
The light ball, m, bounces much higher than the heavy ball, and higher than its former separate bounce.
The bouncing is an example of conservation of momentum.
The combination of two balls hits the ground with momentum (m + M) X V1.
The larger ball bounces up with momentum MV2 and velocity V2.
The smaller ball bounces up with momentum mV3, and velocity V3.
However, m is much smaller than (m +M) so V3 is much greater than V2.
3. Hold a basketball and the tennis ball next to each other at about shoulder height.
Drop both balls at the same time.
Observe how high each ball bounces.
Hold the tennis ball on top of the basketball at shoulder height.
Drop both balls at the same time.
Observe how high each ball bounces.
If momentum in a system is conserved, as the mass decreases, the velocity increases.
In this tennis ball and basketball system, when the two balls are dropped on top of each other, the mass of the system is the combined mass of the balls.
When the balls hit the floor only the tennis ball bounces up, the mass of the system decreases to only the mass of the tennis ball, so the velocity of the tennis ball increases.
Observe how high each ball bounces.
When the basketball hits the ground, it quickly bounces back up and hits the small ball, which is still falling.
When the balls collide, the basketball transfers a lot of its energy to the smaller ball, so the small ball bounces very high.
When the two balls are held above the ground, they have potential energy, mgh, which changes into kinetic energy, mv2, when they begin to fall.
When the balls collide on the rebound, kinetic energy is transferred from the basketball to the tennis ball, so it bounces high into the air.
On the rebound most of the energy of the basketball is transferred to the tennis ball.
Its mass remains the same, so to conserve energy it moves faster and bounces high into the air.
The basketball has transferred some of its kinetic energy to the tennis ball so it does not bounce as high as when falling by itself. 4. Repeat the activity with the balls reversed, so the basketball falls on top of the tennis ball.
The tennis ball does not have much energy to transfer to the basketball, because its mass is much less.
So the tennis ball is squashed under the weight of the heavier basketball.
17.4.4 Double air glider bounce
Let two air gliders accelerate down 30 cm of track and measure the rebound as the mass of the leading glider is increased.
17.4.5 High bounce paradox
Flip a half handball inside out and drop on the floor then it bounces back higher than the height from which it was dropped.
17.4.6 Pendulum collisions
Release simultaneously two pendulums of equal mass, one of steel and the other of clay, from equal height to strike low friction carts and note greater momentum transfer during the elastic collision is observed
17.3.2 Ball bearing falling in liquid, Stokes' Law
1. Use household liquids with different viscosity, e.g. honey, petroleum oil, vinegar, water, olive oil, fruit juice cordial concentrate.
Drop a large ball bearing into the liquids and note the time to fall a certain distance.
The relative times is one method of calculating viscosity based on Stokes' Law.
17.5.1 Air table collisions, equal mass, unequal mass
See diagram 17.6.6.4: Air table collisions
1. Inelastic collisions between equal and unequal mass air pucks.
Use a video tape or video capture to obtain data. Elastic collisions can also be done with this apparatus.
2. Vary the angle of impact between a moving and stationary air puck.
The path left by liquid air pucks on a table sprinkled with Lycopodium powder shows the 90o scattering law for particles of equal masses.
Use unequal dry ice pucks to do two-dimensional collisions.
17.5.2 Lost momentum
Modify the air pucks so the line of force during the collision passes through the centre of mass.
17.5.3 Shooting pool (billiards, snooker)
Use a framework to allow a billiard ball pendulum to strike another on an adjustable tee.
Let ink-coated balls roll down chutes onto a stage placed on the overhead projector.
Use a pool-shooting box with a soapy glass surface and plans for a ball shooter.
17.5.4 Super ball bouncing
Analyse the trajectory of a super ball from the floor to the underside of a table and back to the hand.
[A "Super Ball" is made from polybutadiene with small amounts of sulfur to reinforce the material and serve as a vulcanizing agent.]
The ball is moulded under very high pressure and temperature and is said to have a 92% resiliency, about three times the resiliency of a tennis ball.
It can continue to bounce for about a minute after being dropped from a short height.]
17.6.1 Linear momentum and collisions, impulse and thrust, conservation of linear momentum
See diagram 16.4.0: Forces
AstroBlaster, high bounce balls, conservation of momentum (toy product)
From Newton's second law, force, F time rate of change of momentum.
When the change of momentum is uniform, F time rate of change of momentum / t, so Ft change of momentum, Ft = constant × change in momentum.
If the constant = 1, Ft = change on momentum = mv - mu.
Ft is called the impulse of the force.
The conservation of linear momentum states that if there is no external force acting on a body or system in a given direction, the total momentum of the body or system will be constant.
If there is a force acting on a body or system in a given direction, the change of momentum in that direction will be equal to the impulse of the force.
It follows that if two bodies moving in the same direction collide, the momentum gained by one body will equal the momentum lost by the other body.
Impulse and momentum
Impulse = force × time, newton second, Impulse (newton.sec) = change in momentum (kg.m / sec).
Momentum = mv, kg m / second, Conservation of momentum m1v1 + m2v2 = m3v3
17.6.5 Bulbous bow
The bulbous bow reduces the overall ships drag by reducing the severity of the bow wave both in amplitude and in water displaced.
It allows the ship to better push water clear of it without creating a significant wake resulting in higher resistance and greater fuel consumption.
17.6.6 Catapult a ball from cart to cart
1. Catapult a ball of equal mass as the cart into a catcher in the second cart.
Conservation of momentum of a thrust producing a stream of water is shown by two carts on a track, one with a nozzle and the other a bucket to catch the water.
2. Thrust carts.
Pull the plug on a container of water on a cart to show conservation of momentum by reaction to discharging water stream.
3. Drop a sandbag on a cart.
A cart passes by a device that drops a sandbag of equal mass on a cart then use timers to measure the velocity before and after the transfer.
Two people on roller carts push against each other.
4. Vertical catapult from a moving cart.
Shoot a ball of equal mass from a moving cart into a catcher and time to find the velocity before and after the transfer.
Run at constant velocity and jump on a roller cart.
5. Floor carts and medicine ball.
See diagram 17.6.3.2: Carts and heavy ball, (medicine ball)
Two people on roller carts throw a heavy ball, (medicine ball), to each other.
17.6.7 Catch an egg in a sheet
See diagram 17.6.1.6m: Catch an egg in a sheet
Throw an egg into a slightly-draped sheet held by two students.
This is an example of impulse and thrust, linear momentum and collisions.
17.6.8 Centre of mass of see-saw (teeter-totter)
Let two carts magnetically repel each other on a see-saw (teeter-totter).
Let identical weight magnet carts on a balanced board repel when a constraining string is burned then repeat with carts loaded unequally.
Burn a string holding two carts with opposing horseshoe magnets and observe if they remain balanced on a board as they repel.
17.6.9 Change of force direction
Use a cylindrical cardboard map container with a removable end.
Lightly push a broomstick handle inside the container to push off the removable end.
Pour coarse salt into the container.
Again, lightly push the broomstick handle inside the container to push off the removable end.
Much more force is needed to push off the removable end, because the salt crystals have deflected the force from the broomstick handle against the walls of the cardboard container.
17.6.10 Collisions, elastic and inelastic collisions
See diagram 17.6.01: Elastic collisions on an air track
Collisions, elastic collisions involving kinetic energy and momentum conservation, inelastic collisions
In an elastic collision the paths of the colliding objects are the same for coming together or moving apart, momentum is conserved and the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
In a head on, elastic collision, with a stationary object all the momentum and kinetic energy are transferred to the stationary mass.
In an inelastic collision, some kinetic energy is lost during the collision.
Experiments
1. Elastic collisions of gliders
Two gliders on an air track are fitted with clock spring steel loops at each end so that they make elastic collisions when they collide.
Propel the gliders so that they travel carrying the same or different weights and travel with the same or different velocities.
Observe the directions and relative motions of the two gliders.
2. Time of contact
Let a ball swing against a plate to complete an electrical circuit allowing an oscillator to feed a counter to measure the collision time.
3. Six billiard balls are mounted on bifilar suspensions.
Use a large frame to hold seven bowling balls on quadfilar supports.
Use billiard balls in a V track.
Roll a ball down an incline into a trough with five other balls.
Use identical steel balls on bifilar suspensions and insert wax for inelasticity.
Many collisions occur in a 3: 1: 1 system, elastic and inelastic collisions.
4. Focussing collisions.
Suspend balls from one string and spaced at a distance of 3r.
Depending on the angle the collision is initiated, the collisions will either focus or defocus.
5. Golf ball collisions.
Suspend two golf balls from a ring then take a time lapse photograph of the collision after you pull one golf ball to the side and release it.
17.6.14 Exploding pendulums
Let two large pendulums of unequal mass hold between them a compressed spring tied with cord and note the maxima of the pendulums when the spring is released.
17.6.17 Motion on a rolling board
Start and stop a radio-controlled car on a board on rollers.
Use a straight train track mounted on a movable board and change the weight of the train to change the relative velocities of the train and track.
Use a circular toy train track for conservation of angular momentum.
17.6.18 Move coin without touching
See diagram 17.6.2.4: Move coin without touching
Put 3 coins, A, B, and C on the table.
Move coin A without moving coin B. Press finger down on coin B so it cannot move.
Use another finger to move coin C quickly towards coin B, but release it before it strikes coin B.
Coin C hits coin B.
Force is transmitted through coin B to coin A.
Coin A moves away.
17.6.19 Newton's cradle, colliding balls, counting balls
See diagram 8.6.2.7: Newton's cradle
See diagram 8.5.2.7.1: Collision balls
1. One ball raised and let go on one end will give one ball launched out from the other.
Try different numbers of balls.
If it doesn't work well, there is probably an alignment problem.
Make sure the threads are straight and the balls are in a perfect line.
2. Suspend seven identical steel balls, balls 1 to 7, by a bifilar suspension from a frame, with the balls just touching along a horizontal line.
Pull out ball 1 at one end and let it swing as a pendulum, so that it hits ball 2.
Then ball 7 at the other end is knocked away with the same speed initial speed as ball 1, while steel balls 3 to 6 remain nearly at rest.
Pull out balls 1 and 2 and let them strike the other balls.
Then balls 6 and 7 are knocked away from the other end, and balls 3 to 5 remain nearly at rest.
The system shows conservation of momentum and energy.
For small displacements, the motion of the balls is linear so they show conservation of momentum and with the conservation of energy law, following the collision if x balls give an impulse to the system, then, x balls leave the system following the collision.
Just after impact, all balls are in contact with the next ball or balls and compression occurs at their interfaces to store potential energy and produce interface elastic forces.
The line of balls moves at nearly the same speed affected by slight differences due to elastic compression and relaxation.
When all the balls are in contact, the kinetic energy of the system is less than the kinetic energy of the initially moving ball, some kinetic energy is temporarily stored as potential energy of compression.
The motions of any variations of the system, e.g. 3 balls, unequal balls or suspended bells, are very difficult to analyse.
3. The "Mythbusters" used a Newton's cradle of five one inch diameter steel balls to obtain a 98% transfer of energy measured by the difference in vertical height of the first ball and the fifth ball.
The efficiency dropped slightly with an increase in size of balls, 2 inch and 6 inch diameter, but dropped to 30- 45% efficiency with one ton balls. (1 US ton = approx. 907 kg)
17.6.21 Pile driver with foam rubber
Break a bar of Plexiglas supported on two blocks with a pile driver then add foam to a second bar and it doesn't break.
A pile driver breaks a plastic sheet supported at the sides, but add a piece of form rubber, and the plastic does not break.
17.6.22 Shoot a ballistic air glider
Shoot a 0.22 bullet into a wood block mounted on an air glider and use a timer to find the velocity.
17.6.25 Throw ball on a blackboard, deform clay
Throw a silicone ball at a dirty blackboard then measure the diameter of the mark and place weights on the silicone ball until it is squashed to the same diameter.
Compare the imprint of a sponge ball thrown against a dirty blackboard with the force required to get an equal size deformation and calculate the interaction time.
Drop a 50 g mass on a blob of softened clay then add masses slowly to another identical blob of clay until the depression is equal.
.17.6.26 Velocity of a softball
Throw a softball into a box, inelastic collision, and find the velocity of the box from the recoil distance.
17.6.27 Water stream impulse
Let the impulse supplied by a counterweight equal the loss of horizontal momentum of a jet of water then calculate the exit velocity of the water jet and check by measuring the range.
Measure the vertical height of a water jet, collect the water to find the flow and match the deflection of the nozzle by hanging weights with the flow turned off.
17.7.1 Rockets
Rockets move forward, because of the conservation of linear momentum, m1v1 = m2v2.
The mass being expelled to the rear x its velocity = mass of the rocket x its forward velocity.
When an octopus wants to escape quickly, it uses its muscles to quickly expel water to the rear in a jet resulting in its forward motion.
A space rocket expels a mass of fuel m1 with velocity v1 resulting in the rocket mass m2 moving forward with velocity v2, because m1v1 = m2v2.
A rocket in space does not have to push against anything external to it, because it can push against its own fuel.
The ejected fuel exerts a thrust force on the space rocket.
The momentum increase of the space rocket = mass of burned fuel x its velocity.
17.7.2 Ball bearing rocket cart
A cart is propelled down a track by ball bearings rolling down a chute attached to the cart.
4.1 Use 15 large steel ball bearings to fall through a chute to propel a cart so that the last ball moves in the same direction as the cart.
4.2 A cart on a 6 metres track bears 12 large ball bearings, held in place with a metal gate.
If the gate is removed, the ball bearings roll out the rear of the cart to cause the cart to accelerate down the track.
17.7.3 Blow rocket
See diagram 16.6.4.1 Blow rocket
Insert a short piece of glass tubing into a one-hole stopper and fix the stopper into the mouth of a sidearm test-tube.
Use two threads to suspend the sidearm test-tube from a bar.
Attach the end of a piece of rubber tubing to the sidearm, suspend it from the bar with two threads, and blow into the other end of the tubing.
The sidearm test-tube moves away from you while you are blowing as air escapes from the piece of glass tubing, acting as a jet.
17.7.4 Carbon dioxide cartridge rocket, "rocket to the moon"
Do not use carbon dioxide soda syphon bulbs in science teaching activities.
Be careful! Dangerous experiment!
Carbon dioxide cylinders should not be used as a source of propellant gases!
Examples of experiments:
1. Carbon dioxide-powered car accelerates across the bench.
2. Small carbon dioxide-powered rocket rides a wire across the classroom.
3. Carbon dioxide cartridge in the back of a model plane may be used to propel it around in circles.
17.7.5 Fire extinguisher cart
See diagram 16.6.4.0: Fire extinguisher cart
Mount a fire extinguisher on a cart and take a ride!
Remove the expansion nozzle from a fire extinguisher and replace it with a length of pipe.
Sit on a low-friction cart and face the nozzle away from you.
Make sure the extinguisher is well braced and wear a crash helmet.
Only use a fire extinguisher about to be replaced!
17.7.6 Necessity of seat belts in a motor car
The Volvo car company had investigated for the effect of seat belt in Sweden.
They analyse 50 thousand car accidents, half of them involved the use of a seat belt.
The data analysis shows that among 25 thousand of no seat belt 37 persons died, 263 persons had severe injuries, but among the people who used seat belts in same numbers with the above, only 6 died, 161 had severe injuries.
The results of the analysis shows that the seat belt can effectively decrease the degree of the hurt in car accidents.
For a fixed change in momentum, if the time during which the change takes place is increased the impulsive force will be decreased.
If the opposite happens and the time is decreased, the impulsive force will be increased.
Equipment A 1.5 m long, 30 cm wide wooden board used for ramp, a small piece of wood used for a barrier, a toy car, a piece of Plasticine, (modelling clay), a piece of chalk, a metre ruler, masking tape and sheets of graph paper.
Mark 20 cm intervals on the ramp, starting from the bottom 0, 20, 40.
Support one end of wooden board by some books about 40 cm in height, the end of 0 marked is downward to construct a ramp.
Put the small piece of wood on bottom of the ramp about 30~40 cm from 0, tape it firmly on the table or ground.
Form the Plasticine (modelling clay) into a cube with side 1 cm, put it on the cover of the engine (in front of driver).
Put the car on the place of 20 cm of the ramp, release it, it moves along the ramp.
As the car crashes into the wooden block, observe what happens to the Plasticine cube.
Mark with a piece of chalk where it hits on the table and measure the distance between the marked point and impact point, accurately to cm.
Record the data in a table.
Repeat the above experiment twice, each time operate as consistently as possible.
Then calculate the average of the distances that the Plasticine was compressed for the three times.
Put the car on a higher place in ramp, e.g. 60 cm, repeat the above experiment, three times in one height, calculate the average.
Do the experiment at 3 heights.
Graph by using the data from the experiment on graph paper, the horizontal axis is the height of the car's original place, the vertical axis is the distance of Plasticine compressed.
Analyse according to the graph what is the relation between the distance of Plasticine compressed and the speed of the car when it crashes.
You can see through your analysis that as the mass of the Plasticine is fixed, the more the car's speed is, the more the impact violently and so the variation of the momentum of the Plasticine is greater, the distance it is compressed is greater.
As the car crashes with the barrier in certain speed, it is acted on by a large impact force to stop it in a very short time.
This rapid change in momentum means the Plasticine is acted on by a very strong push in a very short time intervals.
If the Plasticine was replaced by a car driver the driver would be seriously hurt.
The seat belt not only stops the crash with the barrier in front of him, but also as the body of the car crumples lengthens the time interval for the change in momentum and so decreases the impact force.
17.7.7 Seat belts, car crashes
Roll a cart down an incline to smash beverage cans.
Vary the bumpers to change the impulse.
Roll a cart rolls down an incline and smash a beverage can against a brick wall.
To study car safety on the air track use models of a person with a head seat belt and a head rest placed on an air track cart.
17.7.8 Seat belts, Instructions for using seat belts
1. Seat belt and vehicle speed
The higher the speed and the greater the weight, the greater the energy to be released if there is an accident.
Passengers not wearing seat belts are not connected to the vehicle.
If a frontal collision occurs, they will continue to move forward at the same speed at which the vehicle was travelling before impact, until something stops them.
When passengers are not restrained by seat belts, the kinetic of the body will only be released at the point of impact against the interior of the vehicle, e.g. the steering wheel, dash panel, or windscreen, or against the road if ejected from the vehicle.
At speeds of 30 km / h to 50 km / h, the forces acting on the body during an accident can easily exceed one tonne, 1, 000 kg.
Some people believe that the occupants can brace their weight with their hands in a minor collision.
However, even at low speeds, the forces acting on the body in a collision are so great that bracing oneself with arms and hands is not possible.
Rear passengers not wearing seat belts endanger themselves, the driver, and other people in the vehicle.
Seat belts, if fastened properly, hold the vehicle occupants in the correct sitting positions during an accident or braking manoeuvre, prevent uncontrolled movements, and reduce the danger of being thrown from the vehicle.
Seat belts reduce the kinetic energy as do front crumple zones and the airbag system.
Wearing a seat belt is required by law in most countries.
2. Airbags in vehicles
The airbag system is not a substitute for the seat belts, because triggered airbags provide only additional protection and airbags are not triggered in all kinds of accidents.
The front airbags will not be triggered during minor frontal collisions, minor side collisions, rear collisions, rolls or accidents in which the airbag trigger threshold in the control unit is not exceeded.
3. Maintenance of seat belts
Regularly check the condition of all seat belts.
Keep the seat belts clean.
Never let any foreign bodies and liquids get on to the seat belt, the latch plate or into the slot for the seat belt buckle.
Do not allow the belt webbing to become jammed, damaged or to rub on any sharp edges.
Do not trap or damage the seat belt and latch plate, when closing the door.
Never remove, modify or repair the seat belt or any part of the belt fixture system.
Always fasten the seat belt correctly before any journey and wear it properly while the vehicle is in motion.
4. Fastening seat belts
Fasten seat belts before every trip and adjust the front seat and head restraint correctly with the rear seat backrests in an upright position.
Take hold of the latch plate and pull across your chest and pelvis, but do not twist the belt in the process.
Insert the latch plate securely into the buckle belonging to the occupied seat.
Pull on the seat belt to ensure that the latch plate is securely locked in the buckle.
The shoulder part of the seat belt must always lie on the centre of the shoulder and between the breasts, never across the neck, or over or under the arm of behind the back.
The lap part of the seat belt must always be across the pelvis, never across the stomach, especially with pregnant women.
The seat belt must always lie flat and snugly on the body.
Tighten the belt when necessary.
5. Unfastening and removing seat belts
When unfastening seat belts, the belt has been completely removed when a "clicking" sound can be heard as the seat belt is being rolled up.
A locked seat belt must be released when a vehicle occupant uses the seat belt.
Unfasten seat belts only when the vehicle is stationary.
Press the red button in the buckle.
The latch plate is released and springs out.
Guide the belt back by hand so that it rolls up easily, without twisting the seat belt and without damaging the trim.
If removing the seat belt from the belt guide is difficult, the seat belt may have become twisted if it were returned too quickly into the side trim.
Take hold of the latch plate then slowly and carefully pull out the seat belt.
Untwist the seat belt and guide it back slowly by hand.
Fasten the seat belt even if you are unable to undo the twist.
However, the twist should not be in part of the seat belt that comes into direct contact with the body.
The twist should be corrected immediately by a qualified workshop.
17.7.9 Water jet reaction force
Tie one end of a rubber hose to a spring and turn on the water, then cut the string.
17.7.10 Water rocket
See diagram 34.7.1: Water rocket
A water rocket uses water as its reaction mass.
The pressure vessel, the engine of the rocket, is usually a used plastic soft drink bottle.
The water is forced out by a pressurized gas, compressed air.
As the water is ejected, the mass of the rocket mass becomes less so less force is needed to maintain acceleration.
However, as the gas expands its pressure becomes less and can provide less force.
The Asia-Pacific Regional Space Agency Forum (APRSAF) hosts an annual Water Rocket event in a student between 12 and 16 years of age, and an accompanying teacher, is selected for a competition where the rocket must hit a 4m diameter target at a range of 60 m.
1. Pump a toy water rocket the same number of times first with only air and then with water.
2. Fill the rocket 1/3 with water.
Pump it a specific number of times (your specification) and launch the rocket (you will probably get wet).
Repeat the launch with the rocket filled with air to show the difference in range.
17.8.1 Exploding basketballs
Explode a firecracker between a light and heavy basketball are suspended near the ceiling.
Explode a firecracker in a cart on model railroad track.
17.8.6 Spring apart carts
See diagram 17.6.2.5: Spring apart carts
Two carts or air track gliders, are fixed together with a spring in between them.
The trigger is tripped and the spring pushes the carts apart.
Different masses in the carts give different exit velocities.
Burn a string holding a compressed spring between two unequal mass air gliders.