Answer to Question #231039 in Physics for Ian

Question #231039
Two masses collide on a frictionless horizontal floor and in perfectly inelastic collision. Mass 1 is 4 times that of mass 2. Velocity of mass 1 = 10 m/s to the right while the velocity of mass 2 = 20 m/s to the left. What is the velocity and direction of the resulting combined mass?
1
Expert's answer
2021-08-30T15:05:35-0400

Let's choose the rightwards as the positive direction. Then, we can find the velocity and direction of the resulting combined mass from the law of conservation of momentum:


m1v1m2v2=(m1+m2)vc,m_1v_1-m_2v_2=(m_1+m_2)v_c,vc=m1v1m2v2m1+m2.v_c=\dfrac{m_1v_1-m_2v_2}{m_1+m_2}.

Since m1=4m2m_1=4m_2 we get:


vc=4m2v1m2v24m2+m2=m2(4v1v2)5m2=4v1v25,v_c=\dfrac{4m_2v_1-m_2v_2}{4m_2+m_2}=\dfrac{m_2(4v_1-v_2)}{5m_2}=\dfrac{4v_1-v_2}{5},vc=410 ms20 ms5=4 ms.v_c=\dfrac{4\cdot10\ \dfrac{m}{s}-20\ \dfrac{m}{s}}{5}=4\ \dfrac{m}{s}.

The sign plus means that the velocity of the resulting combined mass directed to the right.


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