Question

in order to reduce thesting in catching a hard ball one usually,
a. increase the contact time
b. increases the contact force
c. increases the impulse
d. increases momentum change

Explanation:

Step1: Recall the impulse - momentum theorem

The impulse - momentum theorem is given by \(J = F\Delta t=\Delta p\), where \(J\) is the impulse, \(F\) is the average force, \(\Delta t\) is the time of contact, and \(\Delta p\) is the change in momentum.

Step2: Analyze the effect of contact time on force

When catching a ball, the change in momentum \(\Delta p\) of the ball is fixed (assuming the ball comes to rest relative to the hand). From \(F=\frac{\Delta p}{\Delta t}\), if we increase the contact time \(\Delta t\) (by moving the hand backward while catching), for a fixed \(\Delta p\), the average force \(F\) exerted on the hand (which causes the'sting') will decrease.

• Option b: Increasing the contact force will increase the'sting', so this is wrong.
• Option c: The impulse \(J=\Delta p\) (change in momentum) is fixed for a given ball - catching situation (initial and final momentum of the ball), so we cannot increase the impulse, this is wrong.
• Option d: The change in momentum \(\Delta p = m(v - u)\) is fixed as the mass \(m\) of the ball, initial velocity \(u\) (before catching) and final velocity \(v\) (after catching, \(v = 0\) relative to the hand) are fixed, so this is wrong.

Answer:

A. Increase the contact time