Momentum & Collisions — Practice · Grade 12 Science

Chapter: Work, Energy & Momentum

What this practice covers

By the end of Momentum & Collisions you should be able to:

9 questions, numeric, multiple choice and written answer, each with a worked explanation.

Vocabulary used: momentum, impulse, conservation of momentum, elastic collision, inelastic collision.

Problem 1

Find the momentum of a 0.50 kg ball moving at 4.0 m/s.
Answer and explanation

2 kg·m/s

p = mv = 0.50 × 4.0 = 2.0 kg·m/s.

Problem 2

A 0.50 kg ball, initially at rest, is struck and leaves at 20 m/s. Find the impulse delivered to it.
Answer and explanation

10 kg·m/s

Impulse equals the change in momentum: J = Δp = m(v_f − v_i) = 0.50 × (20 − 0) = 10 kg·m/s.

Problem 3

A 3.0 kg cart moving at 4.0 m/s collides with and sticks to a 1.0 kg cart at rest. Find their common velocity afterward.
Answer and explanation

3 m/s

Conservation of momentum: 3.0 × 4.0 + 1.0 × 0 = (3.0 + 1.0)v′, so 12 = 4.0v′ and v′ = 3.0 m/s.

Problem 4

In a perfectly inelastic collision, which quantity is always conserved?
  1. Momentum only
  2. Kinetic energy only
  3. Both momentum and kinetic energy
  4. Neither momentum nor kinetic energy
Answer and explanation

Momentum only

Momentum is conserved in every collision with no external force. In an inelastic collision, some kinetic energy is converted to heat, sound, and deformation, so only momentum is conserved.

Problem 5

A 50 kg astronaut floating at rest throws a 2.0 kg wrench at 15 m/s. Find the astronaut's recoil speed.
Answer and explanation

0.6 m/s

Total momentum starts at 0, so 50 × v + 2.0 × 15 = 0, giving 50v = −30 and v = −0.6 m/s. The astronaut recoils at 0.6 m/s in the opposite direction.

Problem 6

A 1 kg cart at 4 m/s sticks to a stationary 3 kg cart. Find shared velocity. Show the reasoning, not just the conclusion.
Hints

Initial KE=9 J and final KE=6 J; sticking need not conserve kinetic energy.

Answer and explanation

Initial momentum=4; final mass=4; velocity=1 m/s.

Problem 7

Why must signs be included for head-on collision velocities?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Momentum is a vector; opposite directions contribute opposite signed components.

Problem 8

Collision names classify kinetic energy and final motionCollision names classify kinetic energy and final motionCollision modelMomentumKinetic energyElastic, isolatedConservedConservedInelastic, isolatedConservedMay decreasePerfectly inelasticConservedBodies share finalvelocityKinetic decrease becomes other forms, not destroyed energy.
Original classification table assumes an isolated collision system for its momentum column.
Interpret the supplied visual. For the initial A+B case sticking together, what final velocity follows?
Answer and explanation

vf=ptotal/(mA+mB)=2/3≈+0.667 m/s.

An elastic collision conserves total kinetic energy as well as momentum in the isolated system. An inelastic collision has a kinetic-energy decrease into deformation, thermal changes or other forms; perfectly inelastic means the bodies remain together after impact. “Perfectly” does not mean all kinetic energy disappears. Use momentum first for a shared final velocity, then calculate kinetic energy before and after to determine the change.

vf=ptotal/(mA+mB)=2/3≈+0.667 m/s.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the physical or environmental relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 9

A 3 kg cart at 4 m/s sticks to a 1 kg cart initially at rest. Neglect external impulse. Find final velocity and kinetic-energy decrease.
Answer and explanation

Initial momentum=12 kg·m/s, so vf=3 m/s. Ki=24 J and Kf=18 J;6 J leaves the kinetic category through other energy forms.

Initial momentum=12 kg·m/s, so vf=3 m/s.

Ki=24 J and Kf=18 J;6 J leaves the kinetic category through other energy forms.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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