100 balls each of mass $\mathrm{m}$ moving with speed $v$ simultaneously strike a wall normally and reflected back with same speed, in time $\mathrm{t ~s}$. The total force exerted by the balls on the wall is
Solution
When the balls strike the wall, the change in momentum of each ball is given by:
<br/><br/>$\Delta p = mv - (-mv) = 2mv$
<br/><br/> Since there are 100 balls, the total change in momentum of all the balls is $\Delta P = 2m(100v) = 200mv.$ The time taken for all the balls to strike the wall is $\mathrm{t}$ seconds. Therefore, the average force exerted on the wall is given by:
<br/><br/>$$F = \frac{\Delta P}{\mathrm{t}} = \frac{2m(100v)}{\mathrm{t}} = \frac{200mv}{\mathrm{t}}$$
<br/><br/>Therefore, the total force exerted by the balls on the wall is $\boxed{F = \frac{200mv}{\mathrm{t}}}$
About this question
Subject: Physics · Chapter: Rotational Motion · Topic: Torque and Angular Momentum
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