Edexcel M1 — Question 1

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
TopicMoments

  1. In a safety test, a car of mass 800 kg is driven directly at a wall at a constant speed of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The constant force exerted by the wall on the car in bringing it to rest is 60 kN .
    1. Calculate the magnitude of the impulse exerted by the wall on the car.
    2. Find the time it takes for the car to come to rest.
    3. Show that the deceleration of the car is \(75 \mathrm {~ms} ^ { - 2 }\).
    \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{2def617f-3c25-4458-8500-8e20ba7c1e53-2_531_661_678_539} \captionsetup{labelformat=empty} \caption{Fig. 1}
    \end{figure} Figure 1 shows an aerial view of a revolving door consisting of 4 panels, each of width 1.2 m and set at \(90 ^ { \circ }\) intervals, which are free to rotate about a fixed central column, \(O\). The revolving door is situated outside a lecture theatre and four students are trying to push the door. Two of the students are pushing panels \(O A\) and \(O D\) clockwise (as viewed from above) with horizontal forces of 70 N and 90 N respectively, whilst the other two are pushing panels \(O B\) and \(O C\) anti-clockwise with horizontal forces of 80 N and 60 N respectively.
  2. Calculate the total moment about \(O\) when the four students are pushing the panels at their outer edge, 1.2 m from \(O\).
    (3 marks)
    The student at \(C\) moves her hand 0.2 m closer to \(O\) and the student at \(D\) moves his hand \(x \mathrm {~m}\) closer to \(O\). Given that the students all push in the same directions and with the same forces as in part (a), and that the door is in equilibrium,
  3. find the value of \(x\).