Answer to Question #277150 in Physics for Lili

Question #277150

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.

1
Expert's answer
2021-12-08T10:00:19-0500

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


m1v1i+m2v2i=m1v1f+m2v2f,m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f},m1v1i+0=0+m2v2f,m_1v_{1i}+0=0+m_2v_{2f},v2f=m1v1im2=0.50 kg×12 ms0.50 kg=12 ms.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:


m1v1i+m2v2i=m1v1f+m2v2f,m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f},m1v1i+0=m1v1f+m2v2f,m_1v_{1i}+0=m_1v_{1f}+m_2v_{2f},v2f=m1(v1iv1f)m2,v_{2f}=\dfrac{m_1(v_{1i}-v_{1f})}{m_2},v2f=0.50 kg×(12 ms2.4 ms)0.50 kg=9.6 ms.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:


m1v1i+m2v2i=m1v1f+m2v2f,m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f},m1v1i+0=m1v1f+m2v2f,m_1v_{1i}+0=m_1v_{1f}+m_2v_{2f},v2f=m1(v1iv1f)m2,v_{2f}=\dfrac{m_1(v_{1i}-v_{1f})}{m_2},v2f=0.50 kg×(12 ms0.3 ms)0.50 kg=11.7 ms.v_{2f}=\dfrac{0.50\ kg\times(12\ \dfrac{m}{s}-0.3\ \dfrac{m}{s})}{0.50\ kg}=11.7\ \dfrac{m}{s}.

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