Question

a 5.2 - kg ball rolling at 2.6 m/s bumps into a pillow and stops in 0.60 s. part a find the force exerted by the pillow. express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Calculate the initial momentum

The formula for momentum is $p = mv$. Given $m = 5.2\ kg$ and $v=2.6\ m/s$, so $p_{i}=5.2\times2.6 = 13.52\ kg\cdot m/s$. The final momentum $p_{f}=0$ since the ball stops.

Step2: Use the impulse - momentum theorem

The impulse - momentum theorem is $J=\Delta p = F_{avg}\Delta t$. $\Delta p=p_{f}-p_{i}=0 - 13.52=- 13.52\ kg\cdot m/s$. We know $\Delta t = 0.60\ s$. Then $F_{avg}=\frac{\Delta p}{\Delta t}=\frac{-13.52}{0.60}\approx - 22.53\ N$. The magnitude of the force is considered here, so $F\approx23\ N$.

Answer:

$23\ N$