Edexcel M1 — Question 1

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
TopicMomentum and Collisions

  1. Two particles \(P\) and \(Q\), of mass \(m\) and \(k m\) respectively, are travelling in opposite directions on a straight horizontal path with speeds \(3 u\) and \(2 u\) respectively. \(P\) and \(Q\) collide and, as a result, the direction of motion of both particles is reversed and their speeds are halved.
    1. Find the value of \(k\).
    2. Write down an expression in terms of \(m\) and \(u\) for the magnitude of the impulse which \(P\) exerts on \(Q\) during the collision.
      (3 marks)
    \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{54642aff-2042-494e-ba4a-8332bd47a751-2_222_1170_790_372} \captionsetup{labelformat=empty} \caption{Fig. 1}
    \end{figure} Figure 1 shows a plank \(A B\) of mass 40 kg and length 6 m , which rests on supports at each of its ends. The plank is wedge-shaped, being thicker at end \(A\) than at end \(B\). A woman of mass 60 kg stands on the plank at a distance of 2 m from \(B\).
  2. Suggest suitable modelling assumptions which can be made about
    1. the plank,
    2. the woman. Given that the reactions at each support are of equal magnitude,
  3. find the magnitude of the reaction on the support at \(A\),
  4. calculate the distance of the centre of mass of the plank from \(A\).