Demonstration

A trolley experiences an acceleration when an external force is applied to it. The aim of this datalogging experiment is explore the relationship between the magnitudes of the external force and the resulting acceleration.

Apparatus and Materials

• Light gate, interface and computer
• Dynamics trolley
• Pulley and string
• Slotted masses, 400 g
• Mass, 1 g
• Clamp
• Ruler
• Double segment black card (see diagram)

Health & Safety and Technical Notes

Take care when masses fall to the floor. Use a box or tray lined with bubble wrap (or similar) under heavy objects being lifted. This will prevent toes or fingers from being in the danger zone.

Read our standard health & safety guidance

Pass a piece of string with a mass hanging on one end over a pulley. Attach the other end to the trolley so that, when the mass is released, it causes the trolley to accelerate. Choose a length of string such that the mass does not touch the ground until the trolley nearly reaches the pulley. Fix a 1 kg mass on the trolley with Blu-tack to make the total mass (trolley plus mass) of about 2 kg . This produces an acceleration which is not too aggressive when the maximum force (4 N) is applied.

The force is conveniently increased in 1 newton steps when slotted masses of 100 g are added. Place the unused slotted masses on the trolley. Transfer them to the slotted mass holder each time the accelerating force is increased. This ensures that the total mass experiencing acceleration remains constant throughout the experiment.

Fit a double segment black card on to the trolley. Clamp the light gate at a height which allows both segments of the card to interrupt the light beam when the trolley passes through the gate. Measure the width of each segment with a ruler, and enter the values into the software.

Connect the light gate via an interface to a computer running data-logging software. The program should be configured to obtain measurements of acceleration derived from the double interruptions of the light beam by the card.

The internal calculation within the program involves using the interruption times for the two segments to obtain two velocities. The difference between these, divided by the time between them, yields the acceleration.

A series of results is accumulated in a table. This should also include a column for the manual entry of values for force in newtons. It is informative to display successive measurements on a simple bar chart.

Procedure

Data collection

1. Select the falling mass to be 100 g. Pull the trolley back so that the mass is raised to just below the pulley. Position the light gate so that it will detect the motion of the trolley soon after it has started moving.
2. Set the software to record data, then release the trolley. Observe the measurement for the acceleration of the trolley.
3. Repeat this measurement from the same starting position for the trolley several times. Enter from the keyboard '1' (1 newton) in the force column of the table (see below).
4. Transfer 100 g from the trolley to the slotted mass, to increase it to 200 g. Release the trolley from the same starting point as before. Repeat this several times. Enter '2' (2 newtons) in the force column of the table.
5. Repeat the above procedure for slotted masses of 300 g and 400 g.

Analysis

1. Depending upon the software, the results may be displayed on a bar chart as the experiment proceeds. Note the relative increase in values of acceleration as the slotted mass is increased.
2. The relationship between acceleration and applied force is investigated more precisely by plotting an XY graph of these two quantities. (Y axis: acceleration; X axis: force.) Use a curve-matching tool to identify the algebraic form of the relationship. This is usually of the form 'acceleration is proportional to the applied force'.
3. This relationship is indicative of Newton's second law of motion.

Teaching Notes

• This is a computer-assisted version of the classic experiment. The great advantage of this version is that the software presents acceleration values instantly. This avoids preoccupation with the calculation process, and greatly assists thinking about the relationship between acceleration and force. Each repetition with the same force gives a similar acceleration. If the force is doubled, this results in a doubling of the acceleration, and so on. The uniform increases in the acceleration can be confirmed by using cursors to read off corresponding values from the graph.
• The resulting straight line fit on the graph should be scrutinized for sources of error. The quality of the fit is reduced if the suggested procedure for maintaining the total mass constant is ignored. Also, a common outcome is a very small intercept near the graph origin. The most likely cause of this is neglect of the effect of friction on the motion of the trolley.
• The gradient of the line may be correlated with 1/mass of the system (trolley and slotted masses).
• There is a variation of this experiment, in which the force is held constant but the mass of the trolley is altered by attaching further masses. This may be conducted to provide data for the complementary relationship indicated by Newton's second law: for a given applied force, the acceleration of the trolley is inversely proportional to its mass.

This experiment was safety-tested in November 2006

Demonstration

This demonstration is rather fussy to set up, but produces good results.

Apparatus and Materials

• Carbon dioxide cylinder (Syphon type)

• CO₂ pucks kit, including glass plate and pucks
• Dry ice attachment for cylinder
• Camera and multiflash system
• Lamp, bright, up to 500W
• Elastic cord, to accelerate puck

Health & Safety and Technical Notes

When using CO₂ and dry ice it is essential to have good ventilation to the room.

Remember to wear heat-insulating gloves when handling dry ice.

Read our standard health & safety guidance

Read this guidance note for general hints and detail of specific methods:

Multiflash Photography

The magnetic puck is a small metal ring magnet, of the kind used as field magnets in television sets. It has a metal or card lid. When it is filled with solid carbon dioxide, the puck floats on the sublimed gas.

A kit is available from scientific suppliers. Four pucks are provided, two magnetic, two non-magnetic and made of brass. They are, however, all of the same size and mass and you can stack them one on top of the other.

Polish the glass plate using a duster and methylated spirit or window cleaning fluid. Carefully level it using the wedges supplied.

The lengths of elastic used with trolleys are not suitable because a smaller force is needed here. Instead, use a longer length, with one end attached to the top of the puck with sticky tape. The stretch on this must be kept uniform. Here is a convenient technique. Hold the end against a half-metre rule. Ensure that it is always the same distance from the puck. With practice you can produce a fairly steady force.

The start of the motion does not necessarily coincide with an exposure or with an image. A high frequency of exposure is required. This reduces any error in identifying the time of the start of the motion, relative to later images.

For further information about making dry ice see the apparatus entry:

carbon dioxide cylinder

Three-quarter length blackout is essential for good photographs.

Procedure

Making the image

1. Attach a bright pointer to the centre of a magnetic puck.
2. Set a camera alongside the glass plate, so that it can photograph the pointer as the puck moves across the plate. Illuminate the pointer with the lamp. Align the stroboscope slit with the camera lens, as shown.

3. Put 2-3 cm3 of solid CO2 underneath one of the magnetic pucks, and place the puck on the plate.
4. Attach an elastic cord to the puck and apply a force.
5. With the multiflash system active, open the camera shutter on the B setting. Release the puck and accelerate it with a small near-constant force.

Analyzing the image

1. Measure the distances between the puck positions. Use the multiflash frequency (time = 1/frequency) to determine the time between each position.
2. To find out if the acceleration was uniform, plot distance against (time)2.

Teaching Notes

• Discussion points arising from the experiment:
• The time between images is constant.
• Spacing between images of a body increases with speed.
• A constant force on a body produces constant acceleration.
• For constant acceleration, and provided that the starting velocity of the measured motion is zero, the graph will be a straight line passing through the origin.
• By stacking pucks on top of each other, up to a maximum of four, and applying the same force in each case, you can show that acceleration decreases as mass increases.

This experiment was safety-tested in April 2006

This detailed experiment involves measurement of acceleration.

Apparatus and Materials

For each student groups

• Dynamics trolleys, up to 3
• Rods for stacking trolleys
• Elastic cords, 3
• Runway
• Ticker-tape
• Ticker-timer with power supply unit
• String

Health & Safety and Technical Notes

Long runways or heavy shorter ones should be handled by two persons. In operation, ensure that a string is tied across the bottom of the runway, to prevent the trolley falling onto the floor (or someone's foot).

Read our standard health & safety guidance

It might not be possible for every group to have three trolleys, and so groups may need to share.

To ensure the elastic cords (given to one group of students) all stretch by the same amount for the same force, set up a testing rig as shown in the diagram.

Oil the bearings on the trolley wheels. Do not use trolleys with bent axles (through dropping). Ensure the runway and the trolley wheels are clean.

Procedure

The relationship between acceleration and force

1. In this part, you will vary the force and measure different accelerations. Mass must stay the same.
2. Set up the runway and compensate for friction, as in the experiment Compensating for friction.
3. Set up the ticker-timer at the higher end of the runway.
4. Accelerate a single trolley by a single strand of elastic cord. Use a ruler to help you to stretch the cord by a fixed amount, or extend the cords the full length of the trolley.

5. Use the tape to find out the trolley's acceleration. Use the method described here:

   Finding average acceleration with a ticker-timer

6. Repeat using two cords in parallel, stretched by the same amount as before. Measure and record the new acceleration.
7. Repeat with three cords.
8. Plot a graph of acceleration (y axis) against force (x axis). Simply use the number of cords, 1, 2 or 3, as a way of measuring force.

The relationship between acceleration and mass

Repeat steps 1 to 8, but this time apply the same force in all cases. Vary the mass by stacking up to three trolleys. (Two cords in parallel helps when pulling more trolleys.) For simplicity, you can use a trolley mass as a unit of mass (instead of mass in kilograms).

Teaching Notes

• Students gain a great deal from feeling the effect of a constant force on increasing masses, and the sluggish effect on their motion.
• The degree of necessary compensation varies with number of trolleys. Students will obtain best results if they readjust the slope of the runway when they increase the number of trolleys, so that they are still compensating for friction.
• The graphs each have three points. High precision of measurement is not possible. This can give rise to discussion. For example can a small number of measurements of modest precision yield valid conclusions? What is the nature of uncertainty and error here?
• The two investigations may take more than one lesson. You could save time by arranging for half the class to investigate the effect of force, F , and the other half to investigate the effect of mass, m . Then combine the results to arrive at a = F/m.
• How Science Works Extension: This experiment is designed specifically to avoid a pitfall present in other experiments looking at F = ma. In some experiments (such as Investigating Newton's second law of motion) the force accelerating the mass is provided by hanging masses; their weight provides the force. However, this assumes that weight is proportional to mass, and so the relationship that the experiment is designed to show is already assumed in the design of the experiment.
• You might discuss with your class how this experimental design overcomes this. The elastic cords are shown to be identical; if they are stretched the same amount, they provide the same force (although we don’t know what that force is in newtons). Similarly, the three trolleys are identical so their masses are equal.
• In principle, we can only say from this experiment that F is proportional to ma. In the SI system of units, we define the newton so that F = ma.
• For an example of some real ticker-tape charts, click here.

This experiment was safety-checked in March 2005

Class practical

Students can quickly see that force and mass have opposite effects on acceleration.

Apparatus and Materials

For each student group

• Dynamics trolleys, up to 3
• Rods for stacking trolleys
• Elastic cords, 3
• Runway
• Stopwatch or stopclock
• String

Health & Safety and Technical Notes

Long runways or heavy shorter ones should be handled by two persons. In operation ensure that a string is tied across the bottom of the runway, to prevent the trolley falling onto the floor (or someone's foot).

Read our standard health & safety guidance

It might not be possible for every group to have three trolleys at all times, and so groups may need to share.

Procedure

1. Set up the runway and compensate for friction, as in the experiment:

   Compensating for friction


2. Accelerate a single trolley using a single strand of elastic cord.
3. Measure the time taken to travel a marked distance along the runway.
4. Predict how this time will change if you double the force by using two elastic cords in parallel, stretched by the same amount as before. Try it out to test your prediction.

5. Predict how the time will change if you double the mass (approximately) by stacking another trolley on top of the first one. Test your prediction.

6. Predict how the time will change, compared with your first measurement, if you double both the force and the mass. Test your prediction.
7. Predict how the time will change if you treble both the force and the mass.
8. If a ticker-timer is used then the acceleration can be measured. See the experiment:

   Finding average acceleration with a ticker-timer

Teaching Notes

• The degree of necessary compensation varies with the number of trolleys. Students will obtain the best results if they readjust the slope of the runway when they increase the number of trolleys, so that it is still compensated for friction.
• Make sure that students understand that the time is a reliable indication of acceleration. The shorter the time, the greater the acceleration.
• When the mass of a moving object is changed, students are apt to find the interpretation more difficult. For them, mass is more artificial and less familiar than force. The reciprocal relationship between F and m for a constant acceleration is itself a barrier.
• The ratio of force/mass is constant if the acceleration is kept constant.

This experiment was safety-tested in March 2005

Demonstration or Class practical

This activity demonstrates that inertia depends on mass and not on any other interpretation of size. Force, mass and acceleration are inter-related quantities.

Apparatus and Materials

• Mass, brass or lead, 1 kg
• Mass, aluminium, 1 kg
• Dynamics trolleys, 2
• Elastic cords for accelerating trolleys, 2
• Stopclock
• Balance, able to measure or compare two 1kg masses
• Long weak spring or rubber thread
• Runway, if necessary

Health & Safety and Technical Notes

A trolley runway requires two persons to carry it and set it up on the bench.

Read our standard health & safety guidance

Procedure

1. Use a balance to show that the two (gravitational) masses are equal even though their sizes are not.
2. Put each mass in turn on a dynamics trolley and accelerate it with a standard force using elastic cord. Show that the time to travel a measured distance is the same in each case.
3. Repeat this, applying a larger force.
4. Place two equal trolleys far apart on a level runway. Put one of the masses on each trolley. Stretch a weak spring or long rubber thread between them to accelerate them towards each other.
5. Repeat all of the previous exercises, but with unequal masses.

Teaching Notes

• You can use the activity to review ideas about inertia, and as an introduction to work on force, mass and acceleration, and their relationship. It shows that the three quantities are interdependent, and provides a basis for further work to determine the nature of the relationship.
• Step 2 : This shows that the two inertial masses are the same.
• Step 3 : The times are still equal to each other but shorter than before. Force affects acceleration, directly.
• Step 4 : When you release the trolleys, they travel equal distances to the point of collision.
• Step 5 : The two masses show different degrees of inertia. They experience different accelerations when subject to the same forces. Acceleration is inversely proportional to mass.
• At a sophisticated level, there are, in Newtonian physics, two independent definitions of mass - gravitational mass and inertial mass. Steps 1 and 2 in the above procedure relate to this and are suitable for able students only. Gravitational mass determines a body's ability to exert and experience gravitational force. Inertial mass determines a body's resistance to change in its motion (acceleration).
• The fact that mass requires two separate definitions is an unsatisfactory aspect of Newtonian physics that is resolved by Einstein's general relativity. According to Newton it is just an incredible coincidence that the two types of mass, gravitational and inertial, are equal in size. According to Einstein, this equivalence is not coincidence but fundamental. These two types of mass become one and the same.
• You could use timing techniques, such as use of ticker-timers, for quantitative work. You could then discuss good experimental practice: keeping one variable fixed, varying another, and watching the related changes in the third.

This experiment was safety-tested in March 2005

Demonstration

This provides an active way to vary measurement of distances, velocities and acceleration.

Apparatus and Materials

• Trolley, demonstration (or skateboard)
• Demonstration forcemeter, 50 N
• Additional forcemeter if measuring frictional force
• Springs, large, 3
• Card, small pieces of
• Stopwatch or stopclock

Health & Safety and Technical Notes

Clearly, there are dangers of collisions or of students falling off skateboards. The activity should be done in a reasonably large, clear space, on a level floor or surface.

If a skateboard is used, head, knee and elbow protection should be worn by the skater.

Read our standard health & safety guidance

Commercial trolleys are ideal. They have an attachment so that a wheel drives a dynamo attached to a meter, which acts as a speedometer. This is valuable, but is not essential.

If trolleys are not available, it is possible to use a skateboard.

So that trolleys can be accelerated with fairly constant force, put a strong spiral spring between the spring balance and the trolley. This smooths out jerkiness of motion.

Procedure

1. One student sits on the trolley. Another holds it still and releases it when ready. A third attaches the forcemeter to the trolley and pulls with a constant force of, say, 10 N. A fourth ‘catches’ the trolley to slow it down gently at the end of its run.
2. The student on the trolley counts seconds, and drops a card at the same position relative to the trolley at each count. The count could be assisted by a fifth student with a watch or clock.
3. Measure the distances between the cards. Use average velocity = distance/time to obtain values for average velocity.
4. Use these figures to plot a velocity-time graph.
5. Measure the gradient of the graph to obtain a value for the acceleration of the trolley.
6. Repeat the measurement with larger applied force, and see what effect that has on the acceleration.

7. Repeat the measurement with a second student on the trolley.

Teaching Notes

• Students are actively involved with this demonstration. It illustrates that an increase in applied force results in an increase in acceleration. Precision is not high, but concepts of velocity and acceleration are reinforced, and the experiment provides an introduction to the relationship between force and acceleration.
• It is possible to go further, and try to show that acceleration changes by the same proportion as net force, but this requires consideration of the influence of friction.
• Accelerate the trolley using a spring balance with a force of, say, 30 N. Plot velocity against time. Repeat this with a backward drag applied by a student pulling backward on the trolley with another spring balance and spring. This student maintains a constant force of, say, 10 N while moving forward with the trolley. Once again, produce a velocity-time graph. Repeat this with different applied backwards forces, but the same forwards force, until you obtain a graph that is as flat (zero gradient) as possible.
• For a flat graph, we know that net force on the trolley is zero, since its acceleration is zero. Frictional force is then equal to the difference between the applied forward force and the applied backward force.
• Assuming that the frictional force is always the same, you can obtain velocity-time graphs using different applied forwards force, and no applied backwards force. Then subtract the frictional force from each applied forwards force to find the net force.
• Obtain values of acceleration from the gradients of the velocity-time graphs. Plot net force (on the x axis since it is the input variable) against acceleration (on the y axis since it is the output variable). If assumptions and estimations that you have made are reasonable then this graph should be a simple shape – a straight line passing through the origin, revealing the simple nature of the relationship between force and acceleration.
• By using students of different mass, and constant force, you can also demonstrate that an increase in mass results in a decrease in acceleration.

This experiment was safety-tested in December 2004

Demonstration

This experiment illustrates a fundamental point about the nature of measurement, as well as providing a way of measuring the speed of a trolley.

Apparatus and Materials

• Demonstration trolley
• Meter attachment, including wheel contact, small DC dynamo, and millivoltmeter

Health & Safety and Technical Notes

Clearly there are dangers of collisions. The activity should be done in a reasonably large, clear space, on a level floor or surface.

Read our standard health & safety guidance

The meter attachment is a special device, recommended not for general use but for the learning involved in setting it up and calibrating it.

Procedure

1. One wheel of the trolley drives a small DC dynamo. Connect the dynamo to a millivoltmeter which will show a reading that depends on velocity.
2. Calibrate the system. Move the trolley at constant velocity, as closely as you can. Drop cards at 1-second intervals and use the distances between them to calculate the velocity of the trolley. Do this at several speeds. Match these measured velocities with the readings on the millivoltmeter.

Teaching Notes

• Once calibrated, you can now use the system for further investigations on velocity and hence also on acceleration. Measurements taken from the meter at 1-second intervals can, for example, substitute for the cards used in the previous experiment.
• Measuring acceleration: Instead of connecting directly to the millivoltmeter, you can feed the output to the primary coil of a small transformer; the secondary of the transformer is connected to the millivoltmeter. The voltage across the secondary coil will be roughly proportional to the rate-of-change of the primary current, so that the meter gives a measure of acceleration. Once again, students could test whether the meter measures this quantity and can attempt a rough calibration.
• Since this activity is linked with work on acceleration, we refer to velocity rather than speed. It would, however, be correct to say that the meter measures speed.

This experiment was safety-tested in December 2004

Demonstration

You can use the formula F = ma to calibrate a forcemeter without using gravity. It is difficult to do with precision.

Apparatus and Materials

• Lightweight forcemeter, 0-10 N, with scale markings concealed by paper (this is to be written on)
• Dynamics trolley
• Runway
• Stopclock
• Balance, 5 kg
• String

Health & Safety and Technical Notes

A trolley runway requires two persons to carry it and set it up on the bench.

Ensure that a string is tied across the bottom of the runway to prevent the trolley falling onto anyone.

Read our standard health & safety guidance

It is important that the balance is lightweight, so that it does not add to the mass. It is also better if the balance is not too precise.

Procedure

1. Set up a runway that is compensated for the effect of friction, as described in the experiment:

   Compensating for friction

2. Load the trolley, so that its total mass is a whole number of kilograms. Check this by putting the trolley and load on the balance.

3. Attach the forcemeter to the trolley by a length of string.
4. With the forcemeter, apply a force to the trolley to accelerate it from rest.

5. Measure the time, t , for the motion over a measured distance, x .
6. Use the formula x = 1/2 at ² to calculate the acceleration, a.
7. Use F = ma, where m is the measured mass, to find force F in absolute units.
8. Mark the paper over the forcemeter scale with this force. For the forcemeter, you also know where to mark zero.
9. Assume that the meter acts in a linear way. That is, that equal changes in force are represented on the scale by equal distances.
10. Make a complete scale for the forcemeter, on the paper.
11. Compare this with the scale provided by the forcemeter manufacturer.

Teaching Notes

• Newton's laws of motion define the concept of force. A scale of forces in newtons is essentially derived from measurements of mass and acceleration.
• Students often suppose that the manufacturer has access to some unknown means of providing a scale of absolute reliability. They may have little awareness that calibration is an important process of inherent uncertainty, however it is done. Invite them to discuss which is more reliable, the scale made by themselves or by the manufacturer.
• It is essential to keep the logic straight: force is calculated from Newton's second law once the acceleration produced by the forcemeter has been found experimentally.

This experiment was safety-tested in March 2005

Demonstration

You can use the formula F = ma to calibrate a forcemeter without using gravity.

Apparatus and Materials

• Trolley, demonstration (or skateboard)
• Leightweight forcemeter, 0-10 N, with scale markings concealed by paper (this is to be written on)
• Bathroom scales, calibrated in kg (or N)
• Stopclock

Health & Safety and Technical Notes

A trolley runway requires two persons to carry it and set it up on the bench.

Ensure that a string is tied across the bottom of the runway to prevent the trolley falling onto anyone.

Read our standard health & safety guidance

Procedure

1. Measure the mass of a student and add it to the mass of the trolley.
2. Seat the student safely on the trolley. Attach the forcemeter to the trolley by a length of string.
3. With the forcemeter, apply a constant force to the trolley to accelerate it from rest.
4. Measure the time, t , for the motion over a measured distance, x .
5. Use the formula x = 1/2 at ² to calculate the acceleration, a.
6. Use F = ma, where m is the measured mass, to find force F .
7. Mark the paper over the forcemeter scale with this force. For the forcemeter, you also know where to mark zero.
8. Assume that the meter acts in a linear way. That is, that equal changes in force are represented on the scale by equal distances.
9. Make a complete scale for the forcemeter, on the paper.
10. Compare this with the scale provided by the forcemeter manufacturer.

Teaching Notes

• To allow for friction, first use the spring balance to pull the trolley with whatever force is needed to maintain constant speed. Mark the reading of the pointer for constant speed on the paper that covers the scale. Then do an acceleration experiment, keeping the pointer at another mark for the larger force that is used. Remove the paper and read off the places of both marks on the scale. Compare the force calculated by using F = ma with the difference between those scale readings.
• Newton's laws of motion define the concept of force. A scale of forces in newtons is essentially derived from measurements of mass and acceleration.
• Students often suppose that the manufacturer has access to some unknown means of providing a scale of absolute reliability. They may have little awareness that calibration is an important process of inherent uncertainty however it is done. Invite them to discuss which is more reliable, the scale made by themselves or by the manufacturer.
• It is essential to keep the logic straight: force is calculated from Newton's second law once the acceleration produced by the forcemeter has been found experimentally.

This experiment was safety-tested in March 2005