Question

6.4 bouncing

1. which undergoes the greatest change in momentum if all of the baseballs have the same speed just before being caught and just after being thrown? explain.

a. a baseball that is caught.
b. a baseball that is thrown.
c. a baseball that is caught and then thrown back.

1. in the preceding question, which case requires the greatest impulse?

Explanation:

Step1: Calculate momentum change for each case

Let the mass of the baseball be \(m\) and speed be \(v\).

• Case a: Initial momentum \(p_{i}=mv\), final momentum \(p_{f} = 0\). Change in momentum \(\Delta p_{a}=0 - mv=-mv\)
• Case b: Initial momentum \(p_{i}=0\), final momentum \(p_{f}=mv\). Change in momentum \(\Delta p_{b}=mv - 0=mv\)
• Case c: Initial momentum \(p_{i}=mv\), final momentum \(p_{f}=-mv\). Change in momentum \(\Delta p_{c}=-mv - mv=- 2mv\)

Step2: Compare the magnitudes

\(\vert\Delta p_{a}\vert = mv\), \(\vert\Delta p_{b}\vert=mv\), \(\vert\Delta p_{c}\vert = 2mv\)

Answer:

1. The baseball that is caught and then thrown back (case c) undergoes the greatest change in momentum.
2. The case that requires the greatest impulse is the baseball that is caught and then thrown back (case c) because impulse \(J=\Delta p\) (impulse - momentum theorem) and \(\vert\Delta p_{c}\vert\) is the largest.