OCR MEI M2 2013 January — Question 1

Exam BoardOCR MEI
ModuleM2 (Mechanics 2)
Year2013
SessionJanuary
TopicMomentum and Collisions 1

1
  1. Fig. 1.1 shows the velocities of a tanker of mass 120000 tonnes before and after it changed speed and direction. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{42b6ee17-f0ae-4687-8392-281ba724a607-2_237_917_360_577} \captionsetup{labelformat=empty} \caption{Fig. 1.1}
    \end{figure} Calculate the magnitude of the impulse that acted on the tanker.
  2. An object of negligible size is at rest on a horizontal surface. It explodes into two parts, P and Q , which then slide along the surface. Part P has mass 0.4 kg and speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Part Q has mass 0.5 kg .
    1. Calculate the speed of Q immediately after the explosion. State how the directions of motion of P and Q are related. The explosion takes place at a distance of 0.75 m from a raised vertical edge, as shown in Fig. 1.2. P travels along a line perpendicular to this edge. \begin{figure}[h]
      \includegraphics[alt={},max width=\textwidth]{42b6ee17-f0ae-4687-8392-281ba724a607-2_238_1205_1366_429} \captionsetup{labelformat=empty} \caption{Fig. 1.2}
      \end{figure} After the explosion, P has a perfectly elastic direct collision with the raised edge and then collides again directly with Q . The collision between P and Q occurs \(\frac { 2 } { 3 } \mathrm {~s}\) after the explosion. Both collisions are instantaneous. The contact between P and the surface is smooth but there is a constant frictional force between Q and the surface.
    2. Show that Q has speed \(2.7 \mathrm {~ms} ^ { - 1 }\) just before P collides with it.
    3. Calculate the coefficient of friction between Q and the surface.
    4. Given that the coefficient of restitution between P and Q is \(\frac { 1 } { 8 }\), calculate the speed of Q immediately after its collision with P .