Trolley and falling mass

Class practical

Measuring the energy stored gravitationally transferred so as to be stored kinetically in 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
• Thread
• 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.

Read our standard health & safety guidance

Procedure

1. 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

2. 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.
3. 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

4. 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.
5. Estimate the value of v from the ticker-tape. Measure the mass of the trolley on the balance.
Calculate 1/2 mv².
6. Compare this with the change in energy of the load stored gravitationally, Δ E = m × g{Δ{h}

Teaching Notes

• The energy stored gravitationally in the load end up being stored kinetically in the trolley. Students should consider the start point of the load at its lowest point and end point of the load at its highest point. At the end point the load itself will be moving, so there will be some energy stored kinetically in the load and in the trolley. However, if the mass of the load is very small compared to the mass of the trolley then the energy stored kinetically will be (almost) negligble.
• Students are likely to be disappointed when they find that the values for 1/2 mv² and Δ E = m × g{Δ{h} 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 stored thermally s, e.g. warming the pulley, and the wheel bearings, the air.
• It is impossible to demonstrate the principle of conservation of energy for thermodynamic reasons. As a result of friction, energy will always be stored thermally in the surroundings. 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.
• 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 decrease in the energy stored kinetically is compared to energy stored gravitationally.
• 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-tested in August 2007