Work-energy theorem test answers and mark scheme for AP Physics 1 (free PDF download)

The questions are on the work-energy theorem test. Take it under real conditions before reading the mark scheme.

Quick answer: Work is the energy a force transfers when it acts through a displacement: W = F d cosθ, in joules. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 1 test on work-energy theorem, from definition and theorem to gradient meaning, with the equivalent answers to accept.

Work-energy theorem test answers and mark scheme for AP Physics 1 (free PDF download)

Model answers with a marking guide. Give credit for correct methods even when an arithmetic slip follows, and check that every work value carries the right sign and unit.

Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 3

Contents

Question 1 Definition and theorem (2 marks)

The net work done on an object equals its change in kinetic energy (W_net = ΔK). 1 J = 1 kg m²/s².

Marking: 1 mark for the theorem, 1 mark for kg m²/s².

Question 2 Arrow in a target (3 marks)

K = ½ × 0.040 × 55² = 60.5 J.
F = K ÷ d = 60.5 ÷ 0.12 = 5.0 × 10² N.
K is four times larger, so d = 4 × 0.12 = 0.48 m.

Marking: 1 mark per part.

Question 3 Variable force on a block (4 marks)

Rectangle: 10 × 3.0 = 30 J; triangle: ½ × 2.0 × 10 = 10 J; total 40 J.
½ m v² = 40, so v = √(2 × 40 ÷ 4.0) = 4.5 m/s.

Marking: (a) 1 for each area; (b) 1 for the theorem, 1 for the value.

Question 4 Hauling firewood (4 marks)

W = 90 × 25 × cos 30° = 1.9 × 10³ J (1949 J).
W = −55 × 25 = −1375 J.
W_net = 574 J; v = √(2 × 574 ÷ 40) = 5.4 m/s.

Marking: (a) and (b) 1 mark each; (c) 1 for net work, 1 for the speed.

Question 5 Satellite in orbit (3 marks)

The gravitational force on the satellite always points toward the centre of the circle, while its displacement over a short time is along the tangent. These directions are perpendicular, so cosθ = 0 and gravity does no work. With zero net work, the work-energy theorem gives ΔK = 0, so the speed stays constant.

Marking: 1 mark for perpendicular directions, 1 for zero work, 1 for linking to ΔK = 0.

Question 6 Lifting two ways (2 marks)

The work done by gravity is the same in both: −m g h, because it depends only on the height change. On the ramp the displacement is longer but only the component along the vertical counts.

Marking: 1 mark for equal work, 1 mark for the justification based on height.