Chapter 5, Problem 12TE

In the preceding question, in which case is the greatest impulse required?

To determine

The greatest impulse required in the given conditions.

Answer to Problem 12TE

The baseball will undergo the greatest impulse if it is caught and then thrown back.

Explanation of Solution

Write the expression for the change in momentum.

$\Delta P=P_f-P_1$

Here,

P_f is the final momentum

P_i is the initial momentum

Substitute mv for P_f and mv₂ for P_i in the above equation.

$\Delta P=m{v}_2-m{v}_1$ …… (I)

From previous question, consider the third case in which the baseball is first caught and then thrown back with an initial velocity v and final velocity is -v .

Substitute v for v_i and -v for v₂ in equation (I).

$\begin{array}{l}\Delta P=-mv-m\times 0\text{m}/\text{s}\\ \Delta P=-2mv\end{array}$

From the above results, it is clear that the ball will undergo the greatest change in momentum if it is caught and then thrown back, which is twice as much as the change in momentum when ball is either caught or thrown.

Impulse is equal to change in momentum. So, the maximum impulse will be required to impart greatest change in momentum of the baseball. Therefore maximum impulse needs to be imparted to the baseball when it is caught and then thrown back.

Conclusion:

Therefore, the baseball will undergo the greatest impulse if it is caught and then thrown back.