Momentum
Forces and Motion

Momentum and Newton's second law

for 14-16

There are two teaching approaches to Newton’s second law used in early physics teaching: 

  • the approach through using forces to produce acceleration with different masses leading to F ∝ ma
  • the approach through momentum and force x time = change of momentum (in symbols Ft = Δmv ), which was Newton’s choice.  

Students often confuse energy and momentum. It may help for teachers to have at the back of their minds, when introducing these ideas, that change of energy is the space integral (ΔE = ∫ F ⋅ Δs) and change of momentum is the time integral (Δmv = ∫ F ⋅ Δt).

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Force of impact on a floor

Momentum
Forces and Motion

Force of impact on a floor

Practical Activity for 14-16

Demonstration

This demonstration models a student jumping from a table to the floor. The force which the floor must exert to stop a ball of Plasticine quickly is measured.

Apparatus and Materials

  • For step 1
  • Ball of Plasticine, 250 g
  • Domestic balance, 50 N
  • For step 2
  • Demonstration spring balance, 50 N
  • Metal sphere, 2 cm
  • Retort stands, 2
  • Bosses, 4
  • Extra retort stand rod
  • Ball of pPlasticine, 250 g
  • Pivoted table
  • Steel rods, 2

Health & Safety and Technical Notes

Read our standard health & safety guidance


Set up a length of wood about 25 cm long, 7.5 cm wide and not more than 1 cm thick. Its weight will be neglected so it should not be heavy. Screw hooks fixed into one end pivot around a length of 5 mm steel rod held horizontally in a boss. This forms the pivot for the table.

Towards the other end of the beam use another screw hook to support the table from a demonstration spring balance fixed above it.

Position a second steel rod, R , held by a boss, so that the table is secured against it whilst the spring balance is under tension. Tie about 7.5 cm of twine to the metal sphere and trap about 5 cm of the end of the twine between the steel rod and the table. This sphere acts as a signal ball which will fall when the table moves downward and there is no longer a reaction between table and rod.

By adjusting the height of the demonstration spring balance, the tension can be altered within wide limits, a suitable value being 30 N.

Procedure

  1. Drop a ball of Plasticine onto the domestic balance.
  2. Drop a ball of Plasticene onto the table from various heights until a height is found at which the signal ball is released. Take care to drop the Plasticine as near to the hook attached to the spring balance as possible and always on the same point on the table.

Teaching Notes

  • Step 1 gives a quick idea of the forces involved.
  • Step 2 shows that the force to release the platform is much greater than the weight of the Plasticine ball.
  • When the table is pushed down, releasing the sphere, there is no reaction between the rod R and the table and the force of impact P must exceed the tension T in the spring balance (neglecting the weight of the beam).
  • Students need practice in using the concept of momentum before they go on to conservation of momentum. Examples of using a small force for a long time, such as crumple zones in cars and bending knees when jumping from a great height, are helpful in discussion.

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Force used to kick a football

Momentum
Forces and Motion

Force used to kick a football

Practical Activity for 14-16

Demonstration

Using impact time and change of momentum of a football to measure the force needed to kick the ball.

Apparatus and Materials

  • Scaler or electronic timer accurate to 0.001 s
  • Round football (rugby type not suitable)
  • 30 cm flexible leads with crocodile clips, 2
  • Stopwatch or stopclock
  • Balance (to measure mass of ball)
  • Aluminium foil square, 15 cm by 15 cm
  • Aluminium foil square, 7.5 cm by 7.5 cm
  • Sellotape
  • Plasticene

Health & Safety and Technical Notes

Take care that the football is aimed so that it does not cause damage, and there is no danger of the timer being knocked off the bench.

Read our standard health & safety guidance


The large foil is Sellotaped to the football: the small foil is taped to the toe of the kicker’s foot.

Connections to the foil are made with crocodile clips. The other ends of the leads should be a loose fit in the ‘timer input’ sockets so that they will come out easily in the event of an accident. It is sensible to have a student holding the timer on the bench.

Providing that the flexible leads are arranged so that the period of contact takes place before the ball pulls the foil away from the crocodile-clip contact, no difficulties should arise. You should obtain consistent results.

It is possible to get a value for the time of flight of a ball kicked with medium force down a 10 m corridor (or even a 5 m laboratory).

Procedure

  1. Place the ball on a laboratory table, using three small lumps of Plasticene to stabilize it.
  2. Kick the ball in a horizontal direction from a standing position, with only medium force. More vigorous kicks can be used out of doors to show the longer time of contact.
  3. Find the time of contact of the ball with the foot from the scaler or timer, t , seconds.
  4. Find the mass of the ball, m kg, using a balance.

Teaching Notes

  • Measure how far the ball travels horizontally before it hits the floor, s , then s = vT.
  • The time of flight, T , can be found from the height of the table, h = 1/2 gT 2 .
  • The acceleration due to gravity = 10 m s-2 T 2 = 2h /g T = √2 h /g
  • Substituting in the equation v = s /T gives a value for the initial velocity of the ball.
  • Therefore using Ft = Δ( mv) the force, F, on the ball can be calculated.
  • Alternatively, film the flight of the ball using a camcorder, and use frame-by-frame playback mode to calculate its speed.
  • Once students have learnt about the conservation of momentum in a collision then a different method can be used to calculate the force. The football is kicked into a cardboard box which is fixed to roller-skates or a skateboard.
  • The box should be made massive so that it moves slowly enough for the time of motion to be measured with a stopwatch. The flaps on the box should trap the ball. All the momentum of the ball is shared with the box.
  • The momentum of the box is calculated from its mass and velocity (= distance travelled in the measured time). This is equal to the initial momentum of the ball after it is kicked. Using Ft = Δmv then the force can be calculated if the time of contact is measured on the scaler.

Up next

Elastic collision of trolleys

Momentum
Forces and Motion

Elastic collision of trolleys

Practical Activity for 14-16

Class practical

Students investigate what happens when two trolleys collide and no energy is lost in the collision.

Apparatus and Materials

Per student pair

  • Dynamics trolleys, 3
  • Runway
  • Ticker-tape vibrator

Health & Safety and Technical Notes

The runways are heavy and long. They need to be handled with care to avoid damage to students on nearby equipment. Runways are best lifted into position by 2 people. Place a barrier to ensure the trolleys do not roll off the end of the bench.

Read our standard health & safety guidance


Two vibrators can be used, one for each tape, if desired.

Multiflash photographs can be taken of the collision or use a camcorder and play back frame by frame. A dowel covered in aluminium foil is attached to the trolleys. The light should point down the track. Position the camera (with mechanical strobe if needed) opposite where the collision will take place.

Procedure

  1. Set up the trolley board and compensate it for friction. It can only be compensated if the trolleys continue to move in the same direction.
  2. Put two trolleys on the board, each with a ticker-tape attached. Run both tapes under the same vibrator, but with a separate carbon paper for each. Place one trolley at rest about halfway along the runway. Hold the other trolley at the beginning of the runway.
  3. Give the trolley at the top of the runway an initial push, leaving it to run with constant velocity until it collides with the other trolley.
  4. Use the ticker-tapes to calculate the speed of the moving trolley before the collision, and of each of the speeds of the two trolleys after collision.
  5. Calculate the total forward momentum before and after the collision.

Teaching Notes

  • You could have the following discussion before or after the experiment:
  • "Here are two things which are going to collide. If during the collision A pushes B to the right and B pushes A to the left with equal and opposite forces, then B receives that force F from A and has a change in momentum (F)t and A has a change of momentum given by this force (-F)t."
  • "The time during which A pushes B must be just the same as the time during which B pushes A. So we have changes in momentum of Ft and –Ft. The total change in momentum is Ft +(-Ft) = 0 = (mv) B + (mv) A . The total momentum in any kind of interaction, in a closed system, is therefore always the same. We say momentum is conserved. This is an application of Newton's third law."
  • "Of course all participants must be included. When a car comes to rest it loses a lot of momentum and that momentum seems to disappear but the Earth gains an equal amount of momentum carried off by friction. The accounting is harder to do and so in elementary physics this momentum loss is rarely calculated but is discussed as part of the complete system. Even momentum in electromagnetic fields needs to be included."
  • If the trolleys have equal masses and are arranged with spring buffers so that the collision is elastic, the moving trolley is brought practically to rest and the stationary trolley picks up the full motion. It is probably better to start with a collision of unequal masses – otherwise velocities are confused with momenta. The trolley that is used as a projectile should be loaded up with an equal trolley so that it has twice the mass of the stationary trolley.
  • The relative masses on the trolleys can be varied either by piling up more trolleys or loading them with weights and weighing the trolley and weights on a balance.
  • On collision the trolleys do not stick together, but the lighter one bounces forward with greater speed while the original one moves more slowly after the collision. Ticker-tape records are obtained of the motion both before and after the collision and these are analyzed to see whether momentum is conserved or not.
  • In these experiments, if the friction compensation is well done, the colliding bodies have constant speeds before collision and constant speeds (of different size) after collision. Before the experiment, make it clear to students that they are to measure speeds, not accelerations. The main concern is whether momentum is conserved in the collision.
  • Either hard collisions or collisions using the spring-loaded rod on the trolley can be used. Both types of collision should be tried, to see whether the time of collision makes any difference to the conservation.
  • Results:
    • A double trolley mass, 2 M collides with a single trolley mass M.
    • The same force F causes the first trolley to slow down and the second trolley, originally stationary, to speed up while the spring is in contact with both of them. The speed of both trolley sets is determined by their masses.
    • A single trolley collides with a stationary single trolley. In this case their masses are the same and the moving trolley slows down and stops and the originally stationary one speeds up until its velocity is the same as the one which was originally moving
    • Avoid using a single trolley colliding with a double trolley, because the single trolley bounces back and tangles the ticker-tape whilst the double trolley moves off at a slow velocity.
    • Hard collisions, without the spring extended, show what happens when the time of interaction is reduced.

Up next

Head on collision between trolleys with magnets attached

Momentum
Forces and Motion

Head on collision between trolleys with magnets attached

Practical Activity for 14-16

Demonstration

"Invisible" collisions: collisions when objects do not touch.

Apparatus and Materials

  • Dynamics trolleys, 2
  • Horseshoe magnets, Alnico, 2
  • Sellotape
  • 0-Gauge railway track with trucks (OPTIONAL)

Health & Safety and Technical Notes

Read our standard health & safety guidance


Fix the strong magnets onto the ends of the dynamics trolleys. The magnets are repelling each other. Use Sellotape to secure them satisfactorily.

Alternatively, you could use trucks on a gauge-0 railway track or gliders on an air track.

Procedure

Show collisions between these trolleys when they are pushed gently towards each other.

Teaching Notes

  • The collision is silent as the trolleys/trucks do not physically collide. When the magnets on the trolleys/trucks come in range their magnetic fields interact and the trolleys/trucks are repelled. Momentum is transferred to the magnetic field.
  • You could say: "This demonstration is important as a reminder that in collisions we do not need to have contact. Is there really any contact at the atomic level? In fact all that happens is that forces rise steeply to big repulsions as the atoms move closer. The repulsions grow so large that, even though they have a very short time to act during the collision, they are able to bring the colliding bodies to a stop and push them apart again. There is always a distance of closest approach. This grows smaller and smaller as the collisions become more violent when colliding bodies are projected towards each other at higher and higher speeds."
  • The attractions between atoms or molecules are short range electrical forces extending out a few molecular diameters at the most. See the experiment Soap film; the tension remains constant for thin films:

    Soap film


    There must also be repulsions or else solids and liquids would collapse under the attraction. These are very short range, a small fraction of an atomic diameter.
  • We think of the repulsive forces as not appearing until one atom goes ‘smack’ against another in a collision. There is no real ‘smack’, only a very sudden slowing and stopping and starting away again of an atom in the strong force field of another atom’s repulsion.
  • Considering only one atom the equilibrium position in which it should settle down is:
    • At point X where the two forces just balance (where the resultant force is zero)
    • Where the potential energy is minimum at point Z.
  • In practice the atom does not settle down but remains in oscillation about the equilibrium point.

Up next

Inelastic collision of trolleys

Momentum
Forces and Motion

Inelastic collision of trolleys

Practical Activity for 14-16

Class practical

Collisions when objects stick together.

Apparatus and Materials

Per student pair

  • Dynamics trolleys, 2
  • Runway, friction-compensated
  • Ticker-tape vibrator
  • Cork
  • Needle or large pin

Health & Safety and Technical Notes

The runways are heavy and long. They need to be handled with care to avoid damage to students or nearby equipment. Runways are best lifted into position by 2 people. Place a barrier to ensure the trolleys do not roll off the end of the bench.

Read our standard health & safety guidance


The method by which the cork and pins are attached to the trolley will depend on the particular make used. With most, it is easy to wedge a pin so that it sticks out from the trolley. It may be easier to fix a pin on both trolleys and stick a cork on one of them rather than to fix the cork directly on the trolley.

Another way to get the trolleys to stick together after collision is to fix a block of Plasticine onto one trolley with strong insulating tape at the edges. For the other trolley, another piece of Plasticine can be used or a series of drawing pins can be poked through a strip of insulating tape, before that too is attached to the trolley.

Yet another method is to attach double sided adhesive pads to the trolleys.

Procedure

  1. Fix a needle on the front of the moving trolley and a cork on the back of the second trolley, so that the trolleys stick together on collision. They will then move on as one unit after collision.
  2. Use a single ticker-tape attached to the back of the first trolley and pulled through a ticker-tape vibrator, to record the motion before and after collision.
  3. Make a moving trolley collide with an identical trolley at rest.
  4. Make a moving trolley collide with a trolley double the mass (one trolley stacked on top of another).
  5. Analyze the tapes to see if momentum is conserved.

Teaching Notes

  • In these experiments the colliding bodies have constant speeds before collision and constant speeds (of different size) after collision. Make it clear beforehand that the students are to measure speeds, not accelerations, before and after impact. They then calculate momentum = mass x velocity. A reminder that velocity is a vector, so the direction of motion should be indicated by choosing a positive direction and giving the momenta a positive or negative value.
  • A lot of kinetic energy will be dissipated in this inelastic collision, up to 50%, but hopefully it will demonstrate that momentum is conserved.
  • You could say: "Elastic has a special meaning in science. A spring is termed 'elastic' if, when stretched and released the spring goes back in exactly the same way and to exactly the same length as it was originally. It shows no sign of fatigue or of permanent stretch. Springs of good, hardened steel are elastic over a large range of stretches. Rubber cords are not perfectly elastic. They show a little fatigue and after-effects so it is unfortunate that we call them 'elastic'".
  • "In a collision, the objects approach each other, come to rest momentarily then move apart. If they end up with the same total energy stored kinetically as they started with, then we say that the collision has been 'perfectly elastic'".
  • The collision is inelastic if the total energy stored kinetically is much less after collision than before. Some of the original energy stored kinetically has been transferred elsewhere; often to warm up the colliders. If two lumps of sticky clay are thrown at each other so that they stick together then the collision is completely inelastic. If the two masses were equal and the velocities were equal in magnitude but opposite in direction, the combined lump would be at rest. All the energy stored kinetically will now be stored thermally. However, momentum is a vector quantity (energy is not) and the two equal and opposite lots of momentum before the collision add up to zero before and after the collision. Conservation of momentum always holds.

Up next

Adding mass to a moving system

Momentum
Forces and Motion

Adding mass to a moving system

Practical Activity for 14-16

Class practical

Another example of an inelastic interaction.

Apparatus and Materials

For each student pair

  • Dynamics trolleys, 2
  • Runway, friction-compensated
  • Ticker-tape vibrator

Health & Safety and Technical Notes

The runways are heavy and long. They need to be handled with care to avoid damage to nearby students or equipment. Runways are best lifted into position by 2 people. Place a barrier to ensure the trolleys do not roll off the end of the bench.

Read our standard health & safety guidance


The sudden placing of the second trolley on top of the moving one requires some practice. It is probably better to tie a cradle of string around the second trolley and lower it by a single string attached to the cradle.

If a second trolley is not available, use a brick instead; but then the mass of the brick and trolley must be known.

Procedure

  1. Attach ticker-tape to a trolley. Push the trolley so that it runs along the runway at constant velocity.
  2. About halfway along the track gently drop a second trolley, which has been held at rest in mid-air onto the moving trolley from just above. Use the ticker-tape to obtain estimates of speeds.
  3. Calculate the momentum before and after the addition, to see whether it is conserved.

Teaching Notes

Although the added trolley brings in and loses some vertical momentum, it contributes no horizontal momentum but only changes the mass of the moving system. Where does the vertical momentum go? It is transferred to the Earth.

Up next

Explosion of two trolleys

Momentum
Forces and Motion

Explosion of two trolleys

Practical Activity for 14-16

Class practical

Another example of an inelastic interaction.

Apparatus and Materials

  • Dynamics trolleys, 2
  • Blocks of wood (to act as stops), 2

Health & Safety and Technical Notes

Read our standard health & safety guidance


Runways are not required for this experiment. Use the normal bench-top. A block of wood at each end of the bench acts as a stop. Position the blocks so that each trolley moves the same distance after the explosion before hitting its stop.

The buffer rods in the trolleys are pushed in against the built-in compression springs.

Procedure

  1. Put two dynamics trolleys together in the middle of the bench.
  2. Release one of the buffer rods by a smart tap on the vertical release rod. The trolleys will fly apart.

Teaching Notes

  • As the trolleys will be moving in opposite directions, it is not possible to compensate for friction. Therefore, it is not worthwhile to use ticker-tape for this experiment. Instead, blocks of wood are used to act as stops at measured distances along the bench. Since this experiment deals with speeds (for momenta) rather than accelerations, this method of comparing distances travelled will suffice. With trolleys of equal masses, the trolleys hit their stops simultaneously.
  • The experiment can be repeated by doubling the mass of one trolley (put an extra trolley on top). Students now decide for themselves how to rearrange the blocks (or the starting point) so that the trolleys again hit the blocks simultaneously. They can find, from the masses and distances, whether the trolleys acquired equal and opposite amounts of momentum.
  • This is an interesting experiment because the total momentum before the explosion is zero. Because of the vector nature of momentum, the total momentum after the explosion is also zero.
  • Give some other examples which use the idea of recoil, e.g.:
    • Firing a cannon ball
    • Firing a bullet from a rifle
    • Pushing a boat away from a bank.

Up next

Inverse explosion: trolley practical

Momentum
Forces and Motion

Inverse explosion: trolley practical

Practical Activity for 14-16

Class practical

Trolleys colliding inelastically.

Apparatus and Materials

  • Dynamics trolleys, 2
  • Runway
  • Elastic cords, 2
  • Corks
  • Needle or large pin

Health & Safety and Technical Notes

The runways are heavy and long. They need to be handled with care to avoid damage to students or nearby equipment. Runways are best lifted into position by two people. Place a barrier to ensure the trolleys do not roll off the end of the bench.

Read our standard health & safety guidance


The method by which the cork and pins are attached to the trolley will depend on the particular make used. With most, it is easy to wedge a pin so that it sticks out from the trolley. It may be easier to fix a pin on both trolleys and stick a cork on one of them rather than to fix the cork directly on the trolley.

Another way to get the trolleys to stick together after collision is to fix a block of Plasticine onto one trolley with strong insulating tape at the edges. For the other trolley, another piece of Plasticine can be used or a series of drawing pins can be poked through a strip of insulating tape, before that too is attached to the trolley.

Yet another method is to attach double-sided adhesive pads to the trolleys.

Procedure

  1. Hold a pair of trolleys some distance apart with two elastic cords stretched between them, trying to pull them together.
  2. Release the trolleys simultaneously and watch what motion is left after impact.
  3. Repeat the experiment with one trolley made twice as massive, by placing an extra trolley on top.

Teaching Notes

  • When two equal masses with the same momentum but in opposite directions collide then after the collision the combined masses will be stationary.
  • Two unequal masses, colliding inelastically, will continue to move in the direction that the mass with the greatest momentum was moving before the collision.

Up next

Collisions on an air-track

Momentum
Forces and Motion

Collisions on an air-track

Practical Activity for 14-16

Alternative experiments to show momentum interchanges.

Apparatus and Materials

  • Air-track and accessories
  • Air blower
  • Multiflash equipment
  • Xenon strobe or regularly flashing light
  • Camera
  • Background

Health & Safety and Technical Notes

Avoid flash frequencies between 15-20 Hz and avoid red flickering light, which makes some people feel unwell. Rarely, some people can experience photosensitive epilepsy.

Read our standard health & safety guidance


A good matt-black background is essential.

The air-track comes with an accessories kit and an instruction booklet. Many momentum experiments done with trolleys can be done with an air-track.

The track should be carefully levelled and tested by running the vehicle along the track.

The air-track vehicles are lighter than trolleys; in some experiments this is a critical factor. Ticker-tape is not suitable, but multiflash photography or light gates can be used to measure the time intervals.

For multiflash photography, shine the xenon strobe along the track and place the camera halfway along the track pointing at right angles to it. See the guidance note:

Multiflash photography


With light gates, a cardboard mask will need to be attached to the vehicle to measure the time, t, for which the light is cut off. Using the length of the mask, s, then the speed of the vehicle can be calculated as v = s/t.

An aluminium foil-covered rod needs to be attached vertically to a vehicle to reflect the light so that the multiflash photograph can mark the position of the vehicle at time intervals decided by the strobe.

An alternative method for illuminating the vehicle is to build a flashing light system and attach it to the vehicle. Then take photographs with an open camera.

Procedure

  1. Show what happens when vehicles of equal mass collide
    • One initially at rest
    • Travelling at the same speed but in opposite directions
  2. Show what happens in a collision when one vehicle is more massive than the other.

Up next

Investigating momentum during collisions

Momentum
Forces and Motion

Investigating momentum during collisions

Practical Activity for 14-16

Demonstration

A moving glider on a linear air track collides with a stationary glider, thus giving it some momentum. This datalogging experiment explores the relationship between the momentum of the initially moving glider, and the momentum of both gliders after the collision.

Apparatus and Materials

  • Light gates, interface and computer, 2
  • Linear air track with two gliders, each fitted with a black card
  • Glider accessories: magnetic buffers, pin and Plasticine
  • Clamps for light gates, 2
  • Electronic balance

Health & Safety and Technical Notes

The most significant hazard is that of setting up the linear air track on the bench, especially if it is stored on a high shelf. Two people may be needed to achieve this safely.

Read our standard health & safety guidance


Photograph courtesy of Mike Vetterlein

Set up the linear air track in the usual manner, taking care to adjust it to be perfectly horizontal. A stationary glider should not drift in either direction when placed on the track.

Select two air track gliders of equal mass. Attach to each a magnetic buffer at one end, and a black card in the middle.

Prepare each card accurately to a width of 5.0 cm, and enter this value into the software.

The mass of the gliders must also be measured and entered into the software to prepare for the calculations (see below). If magnets are not available, crossed rubber band catapults are an acceptable alternative.

Connect the light gates via an interface to a computer running data-logging software.

The program should be configured to obtain measurements of momentum, derived from the interruptions of the light beams by the cards.

The internal calculation within the program uses the interruption times from each light gate to obtain two velocities. These are multiplied by the appropriate glider masses to give two values of momentum, one before the collision, and one after. This assumes that the measurements for the width of the card and the masses of the gliders have been entered into the program correctly.

For the elastic collision (first part), the momentum measured at A depends upon the mass of the moving glider only. The momentum measured at B depends upon the mass of the initially stationary glider only.

For the inelastic collision (second part), the momentum measured at A depends upon the mass of the moving glider, whereas the momentum measured at B depends upon the combined mass of both gliders.

Students accumulate a series of results in a table with two columns, showing the momentum before and after each collision. It is informative to display successive measurements on a simple bar chart.

Procedure

Data collection

    Part 1: Elastic Collisions
  1. Position the light gates A and B either side of the midpoint of the track as shown.
  2. Place one glider at the left hand end of the track, and the second between the light gates, with the magnetic buffers facing. The second glider should remain stationary.
  3. Give the first glider a short push so that it passes through light gate A. It then collides with the stationary glider. This then moves and passes through light gate B. If necessary, adjust the positions of the light gates to make sure that the sequence is correct. (As the magnetic buffers approach each other they repel so that there is no real contact between the two gliders. This creates the condition for 'elastic' collisions.)
  4. Return the gliders to their starting positions, set the software to record data, and repeat the sequence. Observe the measurements of momentum before and after the collision. Repeat this whole process several times to obtain measurements for a series of collisions.
  5. Part 2: Inelastic collisions
  6. Replace the magnetic buffers with a pin on one glider and a lump of Plasticine on the other. (This will cause the gliders to stick together after the collision, making it an 'inelastic' collision.) The black card may be removed from the initially stationary glider.
  7. Reset the program so that the measurements at B use the combined mass of both gliders.
  8. Use the same procedure as for Part 1 to obtain measurements for a series of inelastic collisions.
  9. Analysis
  10. Depending upon the software, the results may be displayed on a bar chart as the experiment proceeds. Note the very similar values for momentum before and after each collision of either type.
  11. The results can be displayed as a graph of 'momentum before collision' against 'momentum after collision'. A straight line graph would demonstrate that the relationship does not depend upon the magnitude of the initial momentum. If the graph is at 45°, this confirms the conservation of momentum.

Teaching Notes

  • This is a computer-assisted version of the classic experiment, using light gates and electronic timers. The great advantage of this version is the instant presentation of momentum values using the software. This avoids preoccupation with the calculation process and allows attention to focus on the results.
  • It is unusual for the measured values of momentum before and after each collision to be identical. It is wise to limit the number of decimal places displayed, so that the discrepancy does not appear exaggerated. Note how small the discrepancy is, compared with the magnitude of each value. A bar chart display makes this comparison very plain to see. Thus it can be argued that momentum is conserved in each case.
  • A discussion of the measurement errors must consider the residual friction affecting the motion of the gliders. Errors may be kept to a minimum by strategically placing the light gates so that they capture the motion as close as possible to before and after a collision.

This experiment was safety-tested in June 2007

Up next

Speed of a rifle pellet measured with a scaler or timer

Momentum
Forces and Motion

Speed of a rifle pellet measured with a scaler or timer

Practical Activity for 14-16

Demonstration

A direct measurement of the speed of a rifle pellet.

Apparatus and Materials

  • Strips of metal, about 5 mm x 5 cm, with a small nick cut in them at their middle
  • Mounted air rifle and pellets
  • Circuit breakers, 2
  • Scaler or timer accurate to 0.001 s
  • Safety screens

Health & Safety and Technical Notes

Make absolutely certain the rifle is unloaded before setting up or adjusting the experiment.

A safety screen should be used, with students standing at a distance behind the rifle.

All present should wear eye protection.

Absorbing material should be used to catch stray pellets.

The rifle and target holders must remain fixed to the board at all times. You should check whether a licence is needed. (In the UK you will need a licence if the muzzle energy of the pellet exceeds 16.25 J.)

Read our standard health & safety guidance


The rifle is aimed so that the pellet passes through two small strips of metal foil a measured distance apart, breaking each strip in turn. The timer is connected to the strips in such a way that the timer starts counting millisecond pulses when the first strip is broken and stops when the second strip is broken. Thus the timer measures the time taken by the pellet to travel the measured distance between the strips.

Even with a pellet as slow as the pellet from an air rifle, the time to travel one metre will be only a dozen or so milliseconds. The strips should therefore be placed as far apart as is convenient for aiming. The length of the flight is short and so the result will not be very accurate.

Two circuit breakers can be made with wood or hardboard frames. Each of these should have two terminals with spring clips to hold the aluminium foil strips. Set up two circuit breakers a metre apart on the board to which the air rifle is mounted.

If thin pencil leads as used for mechanical pencils are available, these serve well instead of strips of foil. They break more sharply.

Since the metal strips must be broken by the pellet, they must be set up very carefully in the line of fire. Making that adjustment might waste a lot of time and spoil the demonstration by a series of misses. Therefore, a scheme such as the following for aligning the metal strips reliably beforehand is essential.

Place a small sheet of paper at each of the positions where metal strips are to be placed. With the rifle clamped in position, fire a pellet through these two sheets of paper. Then position the strips of metal (which are about 5 mm across and 5 cm long with a small nick cut in them at the middle) over the pellet-holes in those pieces of paper on the side away from the rifle in both cases. (A laser beam could also be used for alignment.)

The rifle should be loaded immediately before firing as any delay may produce inconsistent results due to leaking of air or weakening of the spring.

Some teachers find it difficult to aim the pellet and break the foil. An alternative arrangement illustrated above. This uses a card in a stand, which falls over breaking the contact when struck by the pellet. There is then less difficulty in aiming, but there is a danger of great inaccuracy.

Procedure

  1. Fire a pellet and note the time taken for the pellet to travel between the two circuit breakers, t.
  2. Calculate the pellet velocity, v , using v = s/t where s is the distance between the foil strips.

Teaching Notes

  • This experiment is a direct method of measuring the speed of a rifle pellet. This can be confirmed by using the conservation of momentum to calculate the velocity of the pellet. See the experiment:

    The speed of a rifle pellet by momentum


  • The length of the flight is short and so the timing is only a few milliseconds, which will not be very accurate. The result should, however, give a good order of magnitude value, within about 10%.

Up next

The speed of a rifle pellet by momentum

Momentum
Forces and Motion

The speed of a rifle pellet by momentum

Practical Activity for 14-16

Demonstration

A practical application of the law of conservation of momentum to measure the speed of a fast-moving object.

Apparatus and Materials

  • Air rifle and pellets
  • Lengths of gauge 0 straight railway track, 5
  • Flat truck, gauge 0
  • Metre rule
  • Stopclock or stopwatch
  • Plasticince, 300g

Health & Safety and Technical Notes

Make absolutely certain the rifle is unloaded before setting up or adjusting the experiment.

A safety screen should be used, with students standing at a distance behind the rifle.

All present should wear eye protection.

Absorbing material should be used to catch stray pellets.

The rifle must remain fixed to the board at all times. You should check whether a licence is needed. (In the UK you will need a licence if the muzzle energy of the pellet exceeds 16.25 J.)

Read our standard health & safety guidance


The rifle is securely bolted on its side to a board near to one end. It is mounted on two blocks of wood of suitable height to ensure the pellet will hit the centre of a 200-300 gramme mass of Plasticine on the truck. The bolts go through the two blocks of wood which act as spacers. The barrel of the gun must be parallel to the track; and the assembly should be such that the loading mechanism can be pulled out sideways.

The straight railway track is laid along the trolley board to take the flat truck with its Plasticine load. The board should be inclined slightly to compensate for friction so that the truck runs down the track at constant speed when given a start. The truck is placed a few centimetres from the muzzle. A metre rule is placed on the board parallel to the track with its end 7-10 centimetres along the track from the end of the truck.

There must be a safety stop at the end of the range to catch pellets. This may be a large block of Plasticine or clay or a large block of polystyrene with wooden backing (at least 2 cm thick). It would be wise to add a metal plate behind that. Alternatively, a large box of sand can be used.

The rifle should be loaded immediately before firing as any delay may produce inconsistent results due to air escaping or weakening of the spring.

Procedure

  1. Friction compensate the board. Otherwise the truck may not travel one metre.
  2. Pull back and then close the loading mechanism in order to insert a pellet and cock the rifle.
  3. Fire the rifle, after a count-down.
  4. Start the stop clock when the truck reaches the beginning of the metre rule and stop it when the truck has travelled one metre.
  5. Use this time to calculate the velocity of the loaded truck assuming the conservation of momentum.
  6. Calculate the initial kinetic energy of the pellet and the final kinetic energy of the pellet and truck
  7. The velocity of the pellet can be confirmed by a time-of-fight method.

Teaching Notes

  • It is tempting to place the beginning of the metre rule at the truck before firing, and start the stopwatch when the rifle is fired. That procedure, however, is likely to make students associate the measurement with an acceleration from rest. You want the constant velocity of the truck (and pellet) after impact. Therefore, it is better for the sake of appearances to let the impact occur first and then make a measurement of speed at a stage that is clearly later.
  • Students can calculate the velocity of the pellet assuming the conservation of momentum. The loaded truck is weighed and the average mass of a pellet is also found by weighing, say, a group of 10 or 20 of them.

Up next

Multiflash photography

Conservation of Energy
Energy and Thermal Physics | Forces and Motion

Multiflash photography

Teaching Guidance for 14-16

Multiflash photography creates successive images at regular time intervals on a single frame.

Method 1: Using a digital camera in multiflash mode

You can transfer the image produced direct to a computer.

Method 2: Using a video camera

Play back the video frame by frame and place a transparent acetate sheet over the TV screen to record object positions.

Method 3: Using a camera and motor-driven disc stroboscope

You need a camera that will focus on images for objects as near as 1 metre away. The camera will need a B setting, which holds the shutter open, for continuous exposure. Use a large aperture setting, such as f3.5. Digital cameras provide an immediate image for analysis. With some cameras it may be necessary to cover the photocell to keep the shutter open.

Set up the stroboscope in front of the camera so that slits in the disc allow light from the object to reach the camera lens at regular intervals as the disc rotates.

Lens to disc distance could be as little as 1 cm. The slotted disc should be motor-driven, using a synchronous motor, so that the time intervals between exposures are constant.

You can vary the frequency of ‘exposure’ by covering unwanted slits with black tape. Do this symmetrically. For example, a disc with 2 slits open running at 300 rpm gives 10 exposures per second.

The narrower the slit, the sharper but dimmer the image. Strongly illuminating the objects, or using a light source as the moving object, allows a narrower slit to be used.

Illuminate the object as brightly as possible, but the matt black background as little as possible. A slide projector is a good light source for this purpose.

Method 4: Using a xenon stroboscope

This provides sharper pictures than with a disc stroboscope, provided that you have a good blackout. General guidance is as for Method 3. Direct the light from the stroboscope along the pathway of the object.

In multiflash photography, avoid flash frequencies in the range 15-20 Hz, and avoid red flickering light. Some people can feel unwell as a result of the flicker. Rarely, some people have photosensitive epilepsy.

General hints for success

You need to arrange partial blackout. See guidance note

Classroom management in semi-darkness


Use a white or silver object, such as a large, highly polished steel ball or a golf ball, against a dark background. Alternatively, use a moving source of light such as a lamp fixed to a cell, with suitable electrical connections. In this case, place cushioning on the floor to prevent breakage.

Use the viewfinder to check that the object is in focus throughout its motion, and that a sufficient range of its motion is within the camera’s field of view.

Place a measured grid in the background to allow measurement. A black card with strips of white insulating tape at, say, 10 cm spacing provides strong contrast and allows the illuminated moving object to stand out.

As an alternative to the grid, you can use a metre rule. Its scale will not usually be visible on the final image, but you can project a photograph onto a screen. Move the projector until the metre rule in the image is the same size as a metre rule held alongside the screen. You can then make measurements directly from the screen.

Use a tripod and/or a system of clamps and stands to hold the equipment. Make sure that any system is as rigid and stable as possible.

Teamwork matters, especially in Method 3. One person could control the camera, another the stroboscope system as necessary, and a third the object to be photographed.

  • Switch on lamp and darken room.
  • Check camera focus, f 3.5, B setting.
  • Check field of view to ensure that whole experiment will be recorded.
  • Line up stroboscope.
  • Count down 3-2-1-0. Open shutter just before experiment starts and close it as experiment ends.
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