Chapter 15, Problem 15.1CYU

Check Your Understanding Why would it hurt more if you snapped your hand with a ruler than with a loose spring, even if the displacement of each system is equal?

To determine

The reason for hand to get hurt more if one snapped hand with a ruler than with a loose spring, even if the displacement of each system is equal.

Answer to Problem 15.1CYU

The ruler will hurt more as ruler will have more impulsive force than a loose spring.

Explanation of Solution

Introduction :

Impulse is defined as the change in momentum.

Also, Impulse force is defined as time take to change momentum

$\text{Force}=\frac{\text{Impulse}}{\text{Time}}$

When hand is snapped with ruler or spring, both will have same impulse, that is both stop after hitting.

Given that the displacement of hand in both system − ruler and spring is same.

Now the same displacement of spring will take more time as compared to the displacement of ruler. Thus, time taken to change impulse is more in spring than in ruler.

Because force is indirectly proportional to time taken, the impulsive force is less in spring as compared to ruler.

Conclusion:

Thus, ruler will hurt more than the loose spring.