Momentum and Collisions

Grade 11 · Science · Study Guide

Master linear momentum, impulse, conservation laws, and the analysis of elastic and inelastic collisions.

Momentum (p) is the product of an object's mass and velocity: p = mv. It is a vector quantity with both magnitude and direction. The law of conservation of momentum states that the total momentum of an isolated system (no external forces) remains constant before and after any collision or interaction.

Impulse (J) is the change in momentum: J = Δp = FΔt. This impulse-momentum theorem tells us that a large force applied over a short time produces the same change in momentum as a smaller force over a longer time — the principle behind airbags and crumple zones.

Collisions are classified by whether kinetic energy is conserved. In elastic collisions, both momentum AND kinetic energy are conserved. This gives us two equations to solve for two unknowns (usually final velocities). The special case of equal masses exchanging velocities is a classic result. In perfectly inelastic collisions, the objects stick together after impact; momentum is conserved but kinetic energy is not — the maximum kinetic energy is lost.

For a 1D elastic collision: v1' = ((m1-m2)/(m1+m2))v1 and v2' = (2m1/(m1+m2))v1. In 2D collisions, x- and y-components of momentum are conserved independently.

The center of mass of a system moves at a constant velocity when no external net force acts, regardless of internal collisions between objects.

Key terms

Linear Momentum (p)
The product of mass and velocity: p = mv; a vector quantity conserved in isolated systems.
Impulse (J)
The change in momentum; J = FΔt = Δp. The area under a force-time graph.
Conservation of Momentum
In the absence of external forces, the total momentum of a system remains constant.
Elastic Collision
A collision in which both kinetic energy and momentum are conserved; objects bounce off without energy loss.
Perfectly Inelastic Collision
A collision in which objects stick together; momentum is conserved but kinetic energy loss is maximized.
Center of Mass
The weighted average position of mass in a system; its velocity is constant when no external net force acts.

Flashcards

Momentum Formula
p = mv; momentum equals mass times velocity; SI units are kg·m/s.
Impulse-Momentum Theorem
J = Δp = FΔt; the impulse equals the change in momentum.
Conservation of Momentum
p_total_before = p_total_after for any isolated system with no net external force.
Elastic Collision Conditions
Both momentum (Σp) and kinetic energy (ΣKE) are conserved; no energy is converted to heat or deformation.
Inelastic Collision
Momentum is conserved but kinetic energy is NOT conserved; some KE converts to heat, sound, or deformation.
Coefficient of Restitution
e = (relative speed after)/(relative speed before); e=1 is elastic, e=0 is perfectly inelastic.
Explosion (Internal Forces)
Reverse of inelastic collision; objects initially at rest fly apart. Total momentum remains zero if system was at rest.
2D Momentum Conservation
Each component (x and y) of total momentum is independently conserved in 2D collisions.

Questions

  1. A 2 kg ball moving at 5 m/s collides and sticks to a 3 kg stationary ball. What is the final velocity of the combined mass?

    1. 1 m/s
    2. 2 m/s
    3. 3 m/s
    4. 5 m/s
    Show answer

    Answer: 2 m/s

    Conservation of momentum: p_before = p_after. (2)(5) + (3)(0) = (2+3)v_f. 10 = 5v_f. v_f = 2 m/s.

  2. In a perfectly elastic collision between equal masses where one mass is initially at rest, the moving mass comes to a complete stop after impact.

    Show answer

    Answer: True

    For equal-mass elastic collisions, the formulas give v1' = 0 and v2' = v1. The moving object stops completely and the stationary one moves at the original speed.

  3. The impulse-momentum theorem states that impulse equals the _____ in momentum.

    Show answer

    Answer: change

    The impulse-momentum theorem: J = Δp = FΔt. Impulse equals the change (Δ) in momentum.

  4. Two objects collide elastically. Mass 1 (2 kg) moves at 6 m/s and Mass 2 (2 kg) is stationary. What is the velocity of Mass 1 after the collision?

    1. 6 m/s
    2. 3 m/s
    3. 0 m/s
    4. 12 m/s
    Show answer

    Answer: 0 m/s

    For equal masses in elastic collisions: v1' = ((m-m)/(m+m))v1 = 0. Mass 1 stops completely and Mass 2 moves at 6 m/s.

  5. Kinetic energy is always conserved in any type of collision.

    Show answer

    Answer: False

    Kinetic energy is only conserved in elastic collisions. In inelastic collisions, kinetic energy is converted to heat, sound, or deformation energy.

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