Quick answer: Work is the energy a force transfers when it acts through a displacement: W = F d cosθ, in joules. This AP Physics 1 lab on work-energy theorem gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
A hanging mass pulls a cart along a track and a light gate measures its speed. By comparing the work done on the system with its gain in kinetic energy over several distances, you test whether the net work equals the change in kinetic energy.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 3
Aim
Test the work-energy theorem by comparing the work done on a cart-and-mass system with its gain in kinetic energy.
Equipment
- Dynamics cart (mass 0.500 kg) and a level track with a pulley at one end
- Hanging mass of 0.050 kg on a light string
- Light gate and timer, or a phone recording at 120 frames per second
- Metre rule, balance, small wooden block to tilt the track
Safety
Place a soft stop at the pulley end of the track and keep feet away from the falling mass. Do not let the cart hit the pulley or fall off the bench.
Method
- Raise the far end of the track a little until the cart, given a gentle push, rolls with constant speed. This cancels friction.
- Connect the string over the pulley to the 0.050 kg hanging mass.
- Release the cart from rest. Place the light gate at d = 0.20 m and record the speed through the gate.
- Repeat for d = 0.40, 0.60, 0.80 and 1.00 m, with three trials each, and keep the average.
- Calculate the work done on the system, M g d, and its kinetic energy ½ (m + M) v².
Results
Sample averages (cart 0.500 kg, hanging mass 0.050 kg, g = 9.81 N/kg):
| Distance d (m) | Speed v (m/s) | Work M g d (J) | Kinetic energy ½(m+M)v² (J) | K ÷ W |
|---|---|---|---|---|
| 0.20 | 0.59 | 0.098 | 0.096 | 0.98 |
| 0.40 | 0.85 | 0.196 | 0.199 | 1.01 |
| 0.60 | 1.03 | 0.294 | 0.292 | 0.99 |
| 0.80 | 1.19 | 0.392 | 0.389 | 0.99 |
| 1.00 | 1.32 | 0.491 | 0.479 | 0.98 |
Analysis questions
Question 1 Check one row
Show how the last two columns were found for d = 0.60 m.Question 2 Why the total mass
Explain why the mass in the kinetic energy is m + M and not m alone.Question 3 Plotting
Plot kinetic energy (vertical axis) against work (horizontal axis) and describe the graph.Question 4 Gradient
Calculate the gradient through the origin and state what the theorem predicts.Question 5 Percentage uncertainty
The speed is uncertain by ±0.02 m/s at d = 0.20 m. Find the percentage uncertainty in K there.Question 6 Friction effect
Predict, with a reason, what the K ÷ W values would be if the track were not tilted.Question 7 Improvement
Suggest one improvement that would allow a better test over a wider range.
