The questions are on the impulse momentum test. Take it under real conditions before reading the mark scheme.
Quick answer: Momentum is the product of mass and velocity, p = m v, measured in kg m/s. This mark scheme gives the model answers and the marks for the 8 questions of the Physics 11-12 test on impulse momentum, from definitions to kinetic energy and sticking, with the equivalent answers to accept.
The model answers show the method and the final result in bold. Marks are given for the working as well as the result, so write each step. Check the sign of every velocity and the unit of every answer.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB A.2
Question 1 Definitions (2 marks)
- Impulse is force multiplied by the time for which it acts; it equals the change in momentum.
- The total momentum of a system is constant if no external resultant force acts on it.
Marking: 1 mark each; accept F Δt = Δp for (a).
Question 2 Hammer and nail (3 marks)
- Δp = 0 − 2.0 × 5.0 = −10 kg m/s, a loss of 10 kg m/s.
- F = Δp ÷ Δt = 10 ÷ 0.0040 = 2500 N.
Marking: (a) 1 mark; (b) 1 mark for the formula, 1 mark for the result.
Question 3 Pucks sticking together (3 marks)
- 0.30 × 4.0 = 0.90 v, so v = 1.2 ÷ 0.90 = 1.3 m/s.
- Before: ½ × 0.30 × 16 = 2.4 J. After: ½ × 0.90 × 1.33² = 0.80 J. Lost = 1.6 J.
Marking: (a) 1 mark for conservation equation, 1 for result; (b) 1 mark.
Question 4 Elastic collision (3 marks)
- Before: 3.0 × 4.0 = 12 kg m/s. After: 3.0 × 2.0 + 1.0 × 6.0 = 12 kg m/s. Conserved.
- Approach 4.0 m/s; separation 6.0 − 2.0 = 4.0 m/s. Equal.
- Before: ½ × 3.0 × 16 = 24 J. After: ½ × 3.0 × 4 + ½ × 1.0 × 36 = 6 + 18 = 24 J. Conserved.
Marking: 1 mark for each part.
Question 5 Force-time graph (3 marks)
- Impulse = area = ½ × 0.010 × 600 = 3.0 N s.
- v = J ÷ m = 3.0 ÷ 0.50 = 6.0 m/s.
- F = 3.0 ÷ 0.010 = 300 N.
Marking: 1 mark for each part.
Question 6 Rocket in space (2 marks)
The rocket expels exhaust gas backwards, giving the gas backward momentum. The total momentum of rocket and gas stays constant, so the rocket gains an equal forward momentum and accelerates forwards.Marking: 1 mark for gas gaining momentum backwards; 1 mark for conservation giving forward momentum to the rocket.
Question 7 Pucks at right angles (3 marks)
- px = 0.60, py = 0.80, so p = √(0.60² + 0.80²) = 1.0 kg m/s.
- v = 1.0 ÷ 0.40 = 2.5 m/s.
- tan θ = 0.80 ÷ 0.60, so θ = 53° north of east.
Marking: 1 mark for each part.
Question 8 Kinetic energy and sticking (1 mark)
No. In a perfectly inelastic collision, kinetic energy is transferred to thermal energy and deformation, so it is not conserved.Marking: 1 mark for no, with a correct reason.
