OCR MEI M2 2006 June — Question 1

Exam BoardOCR MEI
ModuleM2 (Mechanics 2)
Year2006
SessionJune
TopicMomentum and Collisions 1

1
  1. Two small spheres, \(P\) of mass 2 kg and \(Q\) of mass 6 kg , are moving in the same straight line along a smooth, horizontal plane with the velocities shown in Fig. 1.1. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{31c38a58-e9d5-4d01-90af-3b41213a9c7d-2_252_647_404_708} \captionsetup{labelformat=empty} \caption{Fig. 1.1}
    \end{figure} Consider the direct collision of P and Q in the following two cases.
    1. The spheres coalesce on collision.
      (A) Calculate the common velocity of the spheres after the collision.
      (B) Calculate the energy lost in the collision.
    2. The spheres rebound with a coefficient of restitution of \(\frac { 2 } { 3 }\) in the collision.
      (A) Calculate the velocities of P and Q after the collision.
      (B) Calculate the impulse on P in the collision.
  2. A small ball bounces off a smooth, horizontal plane. The ball hits the plane with a speed of \(26 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(\arcsin \frac { 12 } { 13 }\) to it. The ball rebounds at an angle of \(\arcsin \frac { 3 } { 5 }\) to the plane, as shown in Fig. 1.2. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{31c38a58-e9d5-4d01-90af-3b41213a9c7d-2_238_545_1695_767} \captionsetup{labelformat=empty} \caption{Fig. 1.2}
    \end{figure} Calculate the speed with which the ball rebounds from the plane.
    Calculate also the coefficient of restitution in the impact.
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