Chapter 8, Problem 10A

If the time of impact in a collision is extended by four times, how much does the force of impact change?

To determine

The change in the force of impact if the time of impact in collision is extended by four times.

Answer to Problem 10A

Force will reduce by four times.

Explanation of Solution

Introduction:

Impulse on an object is given by,

  $F\Delta t=\Delta p$

Where,

  $F=$ force exerted on an object

  $\Delta t=$ time taken to change its momentum

  $\Delta p=$ change in momentum of the object

Now, the change in momentum during the impact will be same. Thus, using above-mentioned formula,

  $\begin{array}{l}F\Delta t=\text{constant}\\ \Rightarrow F=\frac{\text{constant}}{\Delta t}\end{array}$

Thus, if the time of impact is extended by four times, then force of impact will reduce by four times.

Conclusion:

Hence, force will become one-fourth of its initial value.