Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 7 - Linear Momentum - Problems - Page 193: 31

Answer

(a) The velocity of the target ball is 1.7 m/s in the direction that the first ball was moving initially. (b) The mass of the target ball is 1.2 kg.

Work Step by Step

Let $m_B$ be the mass of the target ball which is initially at rest. Let $v_A$ be the initial velocity of the ball of mass $0.220~kg$. Since the collision is elastic, we can use Equation 7-7 to set up an equation. $v_A - 0 = v_B' - v_A'$ $v_B' = 5.5~m/s + (-3.8~m/s)$ $v_B' = 1.7~m/s$ The velocity of the target ball is 1.7 m/s in the direction that the first ball was moving initially. Now, we use conservation of momentum to set up an equation.: $m_A~v_A + 0 = m_A~v_A' + m_B~v_B'$ $m_B = \frac{(0.220~kg)(5.5~m/s) - (0.220~kg)(-3.8~m/s)}{1.7~m/s}$ $m_B = 1.2~kg$ The mass of the target ball is 1.2 kg.
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