Irodov Problem 1.207

Problem Statement

A ball of mass m moving at speed v₀ hits a wall and bounces back with speed v₀ (perfectly elastic). Find the impulse delivered to the wall.

Given

m, v₀ before and after (reversed direction). Elastic bounce off wall.

Concepts & Formulas

Impulse = change in momentum of ball (in magnitude, wall receives equal and opposite).

Step-by-Step Solution

Step 1: Initial momentum: +mv₀ (toward wall).
Step 2: Final momentum: −mv₀ (away from wall).
Step 3: Δp_ball = −mv₀ − mv₀ = −2mv₀.
Step 4: Impulse on wall = +2mv₀.

Worked Calculation

J_wall = 2mv₀.

Boxed Answer

Impulse on wall = 2mv₀

Physical Interpretation

The impulse is twice the ball’s momentum — because the ball reverses direction, the wall must absorb the initial momentum and supply the return momentum.