OCR MEI M1 2013 June — Question 7

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2013
SessionJune
TopicNewton's laws and connected particles

  1. Represent the forces acting on the object as a fully labelled triangle of forces.
  2. Find \(F\) and \(\theta\). Show that the distance between the object and the vertical section of rope A is 3 m . Abi then pulls harder and the object moves upwards. Bob adjusts the tension in rope B so that the object moves along a vertical line. Fig. 7.2 shows the situation when the object is part of the way up. The tension in rope A is \(S \mathrm {~N}\) and the tension in rope B is \(T \mathrm {~N}\). The ropes make angles \(\alpha\) and \(\beta\) with the vertical as shown in the diagram. Abi and Bob are taking a rest and holding the object stationary and in equilibrium. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{83e69140-4abf-4713-85da-922ce7530e47-5_383_360_534_854} \captionsetup{labelformat=empty} \caption{Fig. 7.2}
    \end{figure}
  3. Give the equations, involving \(S , T , \alpha\) and \(\beta\), for equilibrium in the vertical and horizontal directions.
  4. Find the values of \(S\) and \(T\) when \(\alpha = 8.5 ^ { \circ }\) and \(\beta = 35 ^ { \circ }\).
  5. Abi's mass is 40 kg . Explain why it is not possible for her to raise the object to a position in which \(\alpha = 60 ^ { \circ }\).