Quick answer: Work done by a variable force is the integral W = ∫F dx, the area under the force–position graph. This AP Physics C test on work energy theorem has 8 questions worth 20 marks, to do in 45 minutes: conservative force, variable force and energy diagram. The mark scheme is on a separate page; free printable PDF.
This test covers work as an integral, the work–energy theorem, potential energy curves and equilibrium. Use g = 9.81 m/s² and G = 6.67 × 10⁻¹¹ N·m²/kg². Show your integrals and substitutions, and give units in all final answers. You have 45 minutes and may use a calculator.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 3
Question 1 Conservative force (2 marks)
- State what is meant by a conservative force. (1 mark)
- Write the relation between a conservative force and its potential energy in one dimension. (1 mark)
Question 2 Variable force (3 marks)
A force F = 2.0x + 3.0x² newtons acts on a 1.5 kg block along the x-axis from x = 0 to x = 2.0 m. The block starts from rest.- Calculate the work done by integration. (2 marks)
- Calculate the final speed. (1 mark)
Question 3 Energy diagram (4 marks)
A 0.50 kg particle moves in the potential U = 2.0(x − 3.0)² joules.- State the stable equilibrium position. (1 mark)
- Find the turning points. (1 mark)
- Calculate the maximum speed. (1 mark)
- Calculate the force at x = 4.0 m. (1 mark)
Question 4 Equilibrium (3 marks)
A potential is U = 3.0x² − 2.0x³ joules.- Find the equilibrium positions. (1 mark)
- Use the second derivative to classify each one. (2 marks)
Question 5 Spring launcher (2 marks)
A spring with k = 300 N/m is compressed 0.12 m and launches a 0.20 kg block on a frictionless table.- Calculate the stored energy. (1 mark)
- Calculate the launch speed. (1 mark)
Question 6 Leaving the Moon (2 marks)
The Moon has mass 7.35 × 10²² kg and radius 1.74 × 10⁶ m.- Calculate the work to take 1.0 kg from the surface to infinity. (1 mark)
- Calculate the escape speed. (1 mark)
Question 7 Turning points (2 marks)
Explain why a particle with total energy E cannot be found at positions where U > E, and what happens at a position where U = E. (2 marks)Question 8 Engine power (2 marks)
A car engine delivers 15 kW to the wheels at a constant speed of 25 m/s.- Write the relation between power, force and speed. (1 mark)
- Calculate the resistive force. (1 mark)
