Answer to Question #277150 in Physics for Lili

Question

3. Each croquet ball in a set has a mass of 0.50 kg. The green ball, traveling at 12.0 m/s, strikes the blue ball, which is at rest. Assuming that the balls slide on a frictionless surface and all collisions are head-on, find the final speed of the blue ball in each of the following situations:

a. The green ball stops moving after it strikes the blue ball.

b. The green ball continues moving after the collision at 2.4 m/s in the

same direction.

c. The green ball continues moving after the collision at 0.3 m/s in the

same direction.

Answer 1

(a) Let's apply the law of conservation of momentum:

$$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f},$$ $$m_1v_{1i}+0=0+m_2v_{2f},$$ $$v_{2f}=\dfrac{m_1v_{1i}}{m_2}=\dfrac{0.50\ kg\times12\ \dfrac{m}{s}}{0.50\ kg}=12\ \dfrac{m}{s}.$$

(b) Let's apply the law of conservation of momentum:

$$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f},$$ $$m_1v_{1i}+0=m_1v_{1f}+m_2v_{2f},$$ $$v_{2f}=\dfrac{m_1(v_{1i}-v_{1f})}{m_2},$$ $$v_{2f}=\dfrac{0.50\ kg\times(12\ \dfrac{m}{s}-2.4\ \dfrac{m}{s})}{0.50\ kg}=9.6\ \dfrac{m}{s}.$$

(c) Let's apply the law of conservation of momentum:

$$m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f},$$ $$m_1v_{1i}+0=m_1v_{1f}+m_2v_{2f},$$ $$v_{2f}=\dfrac{m_1(v_{1i}-v_{1f})}{m_2},$$ $$v_{2f}=\dfrac{0.50\ kg\times(12\ \dfrac{m}{s}-0.3\ \dfrac{m}{s})}{0.50\ kg}=11.7\ \dfrac{m}{s}.$$