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Question 2.6.7: The force in example question 6 is assumed to vary with time...

The force in example question 6 is assumed to vary with time as shown in Figure 6.7.
Deduce the maximum force that acted on the ball.

A second, harder, ball of identical mass to the first also bounces off the wall with the same initial and final speed, but since it is harder it stays in contact with the wall for only 0.125 s. What is the maximum force exerted by the wall on this ball?

 

6.7
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The area under the curve is the total change in the ball’s momentum, which we found to be Δp = 2.25 N s. The area is a triangle and so

\frac{1}{2} \times F_{\max } \times 0.150=2.25

 

\Rightarrow F_{\max }=30 N

The area under the force-time graph in the case of the harder ball will be the same. Thus

\frac{1}{2} \times F_{\max } \times 0.125=2.25

 

\Rightarrow F_{\max }=36 N

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