The questions are on the conservation of energy test. Take it under real conditions before reading the mark scheme.
Quick answer: Conservation of energy says the total energy of an isolated system stays constant: energy changes form, such as gravitational or spring potential energy becoming kinetic energy, but is never created or destroyed. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 1 test on conservation of energy, from power and energy to hoist with losses, with the equivalent answers to accept.
Model answers with the mark scheme. Award marks for correct method even where the final number is wrong by a slip, and apply the unit mark in every calculation.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 3
Question 1 Power and energy (2 marks)
a. Power is the rate at which energy is transferred (or work is done), P = ΔE/t.
b. t = 2.0 × 3600 = 7200 s; E = Pt = 60 × 7200 = 4.3 × 10⁵ J (432 000 J).
Marking: 1 mark for the definition including the idea of rate; 1 mark for correct substitution and result with unit.
Question 2 Book on a shelf (2 marks)
a. ΔU = mgh = 2.4 × 9.81 × 1.6 = 38 J (37.7 J).
b. mgh = ½mv², v = √(2gh) = √(2 × 9.81 × 1.6) = 5.6 m/s.
Marking: 1 mark for each part, with unit.
Question 3 Playground swing (3 marks)
a. mgh = ½mv², v = √(2 × 9.81 × 0.80) = √15.7 = 4.0 m/s.
b. K = mgh = 40 × 9.81 × 0.80 = 3.1 × 10² J (314 J).
Marking: (a) 1 mark for setting U equal to K, 1 mark for the speed; (b) 1 mark.
Question 4 Dart gun (2 marks)
a. Us = ½kx² = ½ × 300 × (0.040)² = 0.24 J.
b. ½mv² = 0.24 J, v = √(2 × 0.24 ÷ 0.015) = √32 = 5.7 m/s.
Marking: 1 mark for each part, with unit.
Question 5 Sliding crate (3 marks)
a. ΔU = 8.0 × 9.81 × 1.5 = 118 J.
b. ΔK = ½ × 8.0 × (3.0)² = 36 J.
c. Eint = 117.7 − 36 = 82 J.
Marking: 1 mark for each part; accept 81.7 J.
Question 6 Pump power (2 marks)
a. ΔU = mgh = 200 × 9.81 × 15 = 29 430 J ≈ 2.9 × 10⁴ J.
b. P = ΔU/t = 29 430 ÷ 120 = 245 W.
Marking: 1 mark for each part.
Question 7 Two ramps (3 marks)
a. The speeds are equal. Each block loses the same mgh (same mass, same height) and no friction acts, so all of it becomes kinetic energy and v = √(2gh) in both cases.
b. Block B takes longer: its acceleration along the gentle ramp is smaller, so it reaches the same speed over a longer distance in more time.
Marking: (a) 1 mark for equal loss of potential energy, 1 mark for equal speeds; (b) 1 mark for B with the reason.
Question 8 Hoist with losses (3 marks)
a. F = mg = 150 × 9.81 = 1471.5 N; P = Fv = 1471.5 × 0.40 = 589 W.
b. Pin = 588.6 ÷ 0.60 = 981 W.
Marking: (a) 1 mark for the force, 1 mark for the power; (b) 1 mark.
