Kick and impulse

Problem

Summary: kick and impulse. A $0{,}45\;\text{kg}$ ball, at rest, is kicked and leaves at $25\;\text{m/s}$. The foot is in contact with the ball for $8\;\text{ms}$. Calculate: (a) impulse, (b) average force on the foot, (c) energy transferred.

Solution

(a) Impulse (equal to the change in momentum): $J = m\,\Delta v = 0{,}45\cdot 25 = 11{,}25\;\text{N}\cdot\text{s}$

(b) Average force ($J = F\,\Delta t$, with $\Delta t = 8\cdot 10^{-3}\;\text{s}$): $F = \frac{J}{\Delta t} = \frac{11{,}25}{8\cdot 10^{-3}} \approx 1{,}4\cdot 10^{3}\;\text{N}$

(c) Energy transferred (kinetic energy gained by the ball): $E = \tfrac{1}{2}m v^2 = \tfrac{1}{2}\cdot 0{,}45\cdot 25^2 \approx 141\;\text{J}$

$\ev{J = 11{,}25\;\text{N}\cdot\text{s}, \quad F \approx 1{,}4\cdot 10^{3}\;\text{N}, \quad E \approx 141\;\text{J}}$

Links

Topics: Momentum and collisions Concepts: Impulse · Momentum · Kinetic energy