AP Physics 1 Unit 4 FRQ Practice: Linear Momentum Free Response

Free-Response Question · Unit 4

Scenario: A ball of mass m₁ = 0.5 kg moves east at v₁ = 4 m/s on a horizontal frictionless surface. It collides with a stationary block of mass m₂ = 1.5 kg. The ball and block stick together after the collision (a perfectly inelastic collision).

— AP Physics 1 style problem · Topics 4.3, 4.4

Using conservation of momentum, calculate the velocity of the combined ball-and-block immediately after the collision.

✓ Model answer (earns the points)

The surface is frictionless, so no net external horizontal force acts on the ball-block system. Therefore total momentum is conserved.

Before: p_i = m₁v₁ + m₂v₂ = (0.5)(4) + (1.5)(0) = 2 kg·m/s east

After (stuck together, mass = m₁ + m₂ = 2 kg):

p_f = (m₁ + m₂) · v_f

Conservation: p_i = p_f

2 = (2) · v_f → v_f = 1 m/s

Answer: The combined object moves east at 1 m/s.

Why it scores: (1) States conservation of momentum and the condition for it (no net external force / frictionless surface). (2) Sets up p_i = p_f with correct values. (3) Uses combined mass (m₁ + m₂) for the final state since they stick. (4) Reports the answer with units and direction.

Determine how much kinetic energy is lost in the collision.

✓ Model answer (earns the points)

Kinetic energy before:

K_i = ½m₁v₁² + ½m₂v₂² = ½(0.5)(4)² + 0 = 4 J

Kinetic energy after (using v_f = 1 m/s from part A, combined mass = 2 kg):

K_f = ½(m₁ + m₂)v_f² = ½(2)(1)² = 1 J

Energy lost:

ΔK = K_f − K_i = 1 − 4 = −3 J

Answer: 3 J of kinetic energy is lost in the collision.

This energy was converted to heat, sound, and deformation as the ball and block stuck together.

Why it scores: (1) Calculates K_i correctly (only the moving ball has KE; the stationary block contributes 0). (2) Calculates K_f using the COMBINED mass and the answer from part A. (3) Reports the magnitude of energy lost. (4) Optionally identifies where the energy went (heat, sound, deformation).

A student says: "Since this collision is inelastic and kinetic energy is lost, the momentum must also have decreased during the collision." Is the student correct? Justify your answer.

✓ Model answer (earns the points)

The student is incorrect. Momentum and kinetic energy are different quantities, and they're conserved under different conditions.

Momentum is conserved in ALL collisions when there is no net external force on the system (regardless of whether the collision is elastic or inelastic). The forces between the colliding objects are internal — by Newton's third law they come in equal and opposite pairs, so they can't change the system's total momentum.

Kinetic energy is conserved ONLY in elastic collisions. In inelastic collisions (like this one), some kinetic energy is converted into other forms — heat, sound, or deformation of the objects. Energy is still conserved overall (no energy is destroyed), but mechanical KE drops.

Verify with the numbers:

p_i = (0.5)(4) + (1.5)(0) = 2 kg·m/s

p_f = (2)(1) = 2 kg·m/s ✓ Momentum is the same.

K_i = 4 J, K_f = 1 J. KE dropped by 3 J. So momentum is conserved even though KE is not.

Why it scores: (1) Clearly states the student is incorrect. (2) Explains that momentum is conserved in ALL collisions (when no external force). (3) Explains that KE is conserved ONLY in elastic collisions. (4) Identifies where the lost KE went (heat, sound, deformation). (5) Bonus points for numerical verification showing p is conserved.

How to score points on AP Physics 1 momentum FRQs

Always state conservation of momentum explicitly AND identify why it applies (no net external force, frictionless surface, internal-only forces during collision).
Set up the equation symbolically first. p_i = p_f is the universal start.
Watch your signs — momentum is a vector. Pick a positive direction and use it consistently.
For perfectly inelastic collisions, use COMBINED mass (m₁ + m₂) after — both objects move together at the same velocity.
Don't confuse momentum and KE. In ANY collision, p is conserved (with no external force). KE is conserved only in ELASTIC collisions.
Where does the "lost" KE go? In inelastic collisions, KE becomes heat, sound, deformation, internal energy. It's NOT destroyed.
Units, units, units. "1" is not a complete answer; "1 m/s east" is.