PhysicsIntroductory PhysicsHigh school

Momentum

Impulse and conservation of momentum in collisions.

Momentum is mass times velocity, $p = mv$ , a vector measured in kg·m/s. A heavy truck and a fast bullet can have similar momenta. A force applied over time changes momentum; this impulse $J = F\Delta t = \Delta p$ explains why airbags and crumple zones reduce injuries by stretching out the collision time.

In any collision or explosion with no outside net force, total momentum is conserved. In elastic collisions kinetic energy is also conserved; in inelastic collisions some is turned into heat and sound, and in perfectly inelastic collisions the objects stick together.

Key terms

Momentum: Mass times velocity.
$p = mv$

Key ideas

Conservation: $m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2'$ .
Choose a positive direction; velocities in the other direction are negative.
Perfectly inelastic: $(m_1 + m_2)v' = m_1 v_1 + m_2 v_2$ .
Impulse equals the area under a force-time graph.

Worked example

A 1000 kg car moving at 20 m/s hits a stationary 1500 kg car and they stick together. Find their speed just after.

Total momentum before: $1000 \times 20 + 0 = 20000$ kg·m/s.
After: $(1000 + 1500)v' = 20000$ .
$v' = \frac{20000}{2500} = 8$ m/s.
Kinetic energy drops from 200 kJ to 80 kJ, so the collision is inelastic.

Answer: $8$ m/s

Common mistakes

Ignoring direction signs in head-on collisions.
Assuming kinetic energy is conserved in every collision.
Adding speeds rather than momenta.

Practice questions

Try each one, then open the answer. Numerical answers on this page are verified by an automated calculation check.

1.Find the momentum of a 0.15 kg ball at 40 m/s.
Show answer
$6$ kg·m/s
2.A 50 N force acts for 0.2 s. What is the impulse?
Show answer
$10$ N·s
3.A 60 kg skater pushes a 40 kg skater from rest; the 40 kg skater moves at 3 m/s. How fast does the 60 kg skater recoil?
Show answer
$2$ m/s

Key terms

Key ideas

Worked example

Common mistakes

Practice questions

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