About this chapter
Momentum and impulse deals with collisions: trucks that join, balls that rebound from walls, strings that jerk taut, and a pile driver hitting a post. Almost every mark depends on directions, so a before-and-after diagram with a positive direction is the first line of every good answer.
This chapter covers momentum, impulse as change in momentum, conservation of momentum, directions and signs, particles that join or are jerked into motion, equal and opposite impulses, units, the motion before and after a collision, and conditions such as a particle reversing its direction.
The ten questions
- Q1 (6 marks): two railway trucks collide and join: their speed and direction, and the impulse on one with units.
- Q2 (6 marks): a ball rebounding from a wall: the impulse, the average force, and the impulse on the wall.
- Q3 (6 marks): two particles collide head on: the speed and direction of one after, and the impulse.
- Q4 (6 marks): a slack string jerks taut: the common speed and the impulse on the second particle.
- Q5 (6 marks): an impulse λmu on a particle: find λ, and the range of λ that reverses its direction.
- Q6 (10 marks): a particle slows on a rough table, collides, and the second particle then slides to rest.
- Q7 (10 marks): three particles in a line, with two collisions one after the other.
- Q8 (10 marks): a pile driver falls, strikes a pile, and drives it into the ground against resistance.
- Q9 (10 marks): a collision, then a rebound from a wall and whether the particles meet again.
- Q10 (11 marks): a collision where P reverses, the impulse on it, and the condition on k for Q's direction.
Key skills tested
Momentum. Momentum is mass × velocity, measured in N s. It has a direction, so choose a positive direction and give each velocity a sign.
Impulse. Impulse is the change in momentum, mv − mu, measured in the direction of the impulse. For a constant force, impulse = force × time.
Conservation of momentum. Total momentum before equals total momentum after, when the only impulses are between the two particles.
Directions. Draw before and after diagrams. A negative answer for a velocity means the particle moves the opposite way.
Joining and jerks. Particles that join, or are connected by a string that becomes taut, move with a common velocity afterwards.
Equal and opposite. The impulse on P equals the impulse on Q in size, in the opposite direction. Use whichever particle you know most about.
Magnitudes and units. A speed and the magnitude of an impulse are positive. Impulse is in N s, and there is no g in an impulse.
Before and after. Use suvat or F = ma to find the speed just before a collision, then again for the motion after it.
Conditions. "P reverses direction" means its new velocity has the opposite sign, which gives an inequality, such as k < 8.
Worked example
Question 1 from this chapter. Trucks A (25 tonnes) and B (15 tonnes) move towards each other at 3 m/s and 1 m/s, collide and join. Find (a) their speed and direction afterwards, and (b) the magnitude of the impulse on B, with units.
(a) Take A's direction as positive and work in kilograms: 25 000 × 3 − 15 000 × 1 = 40 000v, so 60 000 = 40 000v and v = 1.5 m/s, in A's original direction.
(b) B's velocity changes from −1 to 1.5, so the impulse on B is 15 000 × (1.5 − (−1)) = 37 500 N s.
Using 1.5 − 1, and so ignoring B's change of direction, scores nothing, and the units N s are required.
Seen on real papers
Every question in our booklets is original. These are the recent papers where each question type has appeared.
- January 2025, Q3: an impulse found from a change in momentum, then motion against friction, and a collision using conservation of momentum, as in Q5 and Q6.
Where marks are lost
- A missing factor in the impulse. In January 2025 the mass or one of the speeds was sometimes left out of the impulse-momentum equation.
- The wrong starting speed. After an impulse, many used 0 instead of the new speed as u in the next stage of motion.
- Mixing up the masses. Some put 3m on one side of an equation of motion and m on the other, or carried the impulse into F = ma as if it were a force.
- The speed before the collision. A few used the speed from an earlier moment instead of the speed just before impact.
Common questions
What are the units of impulse?
N s, which is the same as kg m/s.
How do I know the direction after a collision?
Take one direction as positive. If a velocity comes out negative, the particle moves the other way; say so in words.
Can I use the impulse on either particle?
Yes. The impulses are equal in size and opposite in direction, so work with whichever particle's velocities you know.
Where this chapter leads
- Mechanics 1 Chapter 5: Forces and Friction: the friction that slows particles between collisions.
- Mechanics 1 Chapter 2: Constant Acceleration: suvat for the motion before and after an impact.