Reading a force-time graph

Problem

Graph reading: $F(t)$. A graph shows $F(t)$ during a collision: triangular shape with $F_\text{max} = 200\;\text{N}$ and base $\Delta t = 4\;\text{ms}$. Calculate the impulse transferred and the change in velocity of a $50\;\text{g}$ ball.

Solution

Impulse = area under the curve $F(t)$ (triangle of base $\Delta t$ and height $F_\text{max}$): $J = \tfrac{1}{2}\,\Delta t\,F_\text{max} = \tfrac{1}{2}\cdot 4\cdot 10^{-3}\cdot 200 = 0{,}40\;\text{N}\cdot\text{s}$

Change in velocity ($J = m\,\Delta v$, with $m = 0{,}050\;\text{kg}$): $\Delta v = \frac{J}{m} = \frac{0{,}40}{0{,}050} = 8{,}0\;\text{m/s}$

$\ev{J = 0{,}40\;\text{N}\cdot\text{s}, \quad \Delta v = 8{,}0\;\text{m/s}}$

Links

Topics: Quantità di moto e urti Concepts: Impulso · Quantità di moto Skills: Lettura dei grafici