Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 7 - Impulse and Momentum - Problems - Page 191: 3

Answer

The force exerted on the roof is $-1.8N$, which is consistent with the conclusion reached in Conceptual Example 3.

Work Step by Step

The impulse-momentum theorem states that $$\sum \vec{F}\Delta t=m\vec{v}_f-m\vec{v}_0$$ $$\sum\vec{F}=\frac{m\vec{v}_f-m\vec{v}_0}{\Delta t}=\frac{m}{\Delta t}(\vec{v}_f-\vec{v}_0)$$ We have $\frac{m}{\Delta t}=0.06kg/s$, $\vec{v}_0=-15m/s$ and $\vec{v}_f=+15m/s$ $$\sum \vec{F}=+1.8N$$ Since we neglect the hail's weight, $\sum \vec{F}$ is the force the roof exerts on the hail. According to Newton's 3rd law, the force the hail exerts on the roof has the same magnitude but opposite direction, so the force exerted on the roof is $-1.8N$. This force has double the magnitude as the force exerted by the rain, so the answer is consistent with the conclusion.
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