# Trolley and falling mass

##### Class practical

Measuring the gravitational potential energy transferred to kinetic (motion) energy with a dynamics trolley.

#### Apparatus and materials

Ticker-tape

Pulley, single, on clamp

Dynamics trolley

Runway

Ticker-timer

Mass hanger and slotted masses (100 g)

Balance, 5 kg

Knitting needle or length of glass tube

#### Health & Safety and Technical notes

Long runways or heavy shorter ones should be handled by two persons. Ensure that a buffer is tied across the bottom of the runway, to prevent the trolley falling onto anyone.

#### Procedure

Photo courtesy of Mike Vetterlein

a Clamp the pulley to the end of the runway. Compensate it for friction in the normal way. Do this by raising one end of the board so that the trolley, once started, will continue at constant speed as judged by the equal spacing between ticker-tape dots. (See the experiment Compensating for friction.)

b Attach a length of thread to the trolley. Thread it over the pulley and tie it to the mass hanger. The length of thread must be long enough for the mass hanger to hit the ground well before the trolley reaches the end of the runway.

c Attach a length of ticker-tape to the trolley. Pass the other end through the ticker-timer. See also the experiment Using the ticker-timer to measure time.

d Release the trolley, so that the falling mass accelerates it until the mass hits the ground. After this, the trolley will move with constant velocity v.

e Estimate the value of v from the ticker-tape. Measure the mass of the trolley on the balance.

Calculate 1/2 mv2.

Compare this with the gravitational potential energy transferred by the falling load, E = mgh.

#### Teaching notes

1 The falling load gives kinetic (motion) energy to the trolley, but it also gains some kinetic energy itself. Allowing for the latter energy would spoil the clear story at this introductory stage; so it should be neglected. Therefore, the mass of the pulling load must be only a very small fraction of the mass of the trolley.

2 Students are likely to be disappointed when they find that the values for 1/2 mv2 and mgh do not agree. You will need to discuss the results. How reliable is the experiment? Where do students think that the energy might have been transferred to? Some energy will be transferred thermally, e.g. warming the pulley, and the wheel bearings.

It is impossible to demonstrate the principle of conservation of energy for thermodynamic reasons. As a result of friction, energy will always be transferred to the surroundings as thermal energy. However, if the demonstration is carried out slowly, and as many 'energy losses' as possible are accounted for, then the two values should be close enough to satisfy the students.

3 The experiment can be repeated but in reverse, using the trolley to raise the load.

Compensate the runway for friction the opposite way round. The thread should be attached to the trolley and carry a 100 g weight hanger as before. This time start the trolley at the end of the trolley board nearest the pulley, with the thread slack. Because the thread is slack it will not stay in a pulley groove, and so a length of glass tube or knitting needle should be used as a roller. The ticker-tape is also fixed to the reverse end of the trolley so that it runs out behind the trolley and passes through the ticker-timer.

This time when the trolley is given a push, it travels with constant velocity v down the compensated runway until halfway down. Then the thread goes taut and the load is raised a distance d as the trolley comes to rest. The kinetic energy lost is compared with the gravitational potential energy gained.

4 This experiment could be extended into a series of readings for different loads and different distances of fall. This would provide different values of v in 1/2 mv2. The mass of the trolley, m, could also be changed. Students could plot graphs to show relationships between d and v2, and graphs for different masses.

This experiment was safety-checked in August 2007