# Large trolley investigations of acceleration

##### 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.

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

**a** 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.

**b** 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.

**c** Measure the distances between the cards. Use *average velocity = distance/time* to obtain values for average velocity.

**d** Use these figures to plot a velocity-time graph.

**e** Measure the gradient of the graph to obtain a value for the acceleration of the trolley.

**f** Repeat the measurement with larger applied force, and see what effect that has on the acceleration.

**g** Repeat the measurement with a second student on the trolley.

####

Teaching notes

**1** 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.

**2** 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.

**3** 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-checked in December 2004*