OCR MEI M2 2014 June — Question 3

Exam BoardOCR MEI
ModuleM2 (Mechanics 2)
Year2014
SessionJune
TopicMoments
3
  1. Fig. 3.1 shows a framework in equilibrium in a vertical plane. The framework is made from 3 light rigid rods \(\mathrm { AB } , \mathrm { BC }\) and CA which are freely pin-jointed to each other at \(\mathrm { A } , \mathrm { B }\) and C . The pin-joint at A is attached to a fixed horizontal beam; the pin-joint at C rests on a smooth horizontal floor. BC is 2 m and angle BAC is \(30 ^ { \circ }\); BC is at right angles to \(\mathrm { AC } . \mathrm { AB }\) is horizontal. Fig. 3.1 also shows the external forces acting on the framework; there is a vertical load of 60 N at B , horizontal and vertical forces \(X \mathrm {~N}\) and \(Y \mathrm {~N}\) act at A ; the reaction of the floor at C is \(R \mathrm {~N}\). \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{334b2170-3708-46db-bff7-bcad7d5fab00-4_323_803_571_580} \captionsetup{labelformat=empty} \caption{Fig. 3.1}
    \end{figure}
    1. Show that \(R = 80\) and find the values of \(X\) and \(Y\).
    2. Using the diagram in your printed answer book, show all the forces acting on the pin-joints, including those internal to the rods.
    3. Calculate the forces internal to the rods \(\mathrm { AB } , \mathrm { BC }\) and CA , stating whether each rod is in tension or thrust (compression). [You may leave your answers in surd form. Your working in this part should correspond to your diagram in part (ii).]
  2. Fig 3.2 shows a non-uniform rod of length 6 m and weight 68 N with its centre of mass at G . This rod is free to rotate in a vertical plane about a horizontal axis through B , which is 2 m from A . G is 2 m from B . The rod is held in equilibrium at an angle \(\theta\) to the horizontal by a horizontal force of 102 N acting at C and another force acting at A (not shown in Fig. 3.2). Both of these forces and the force exerted on the rod by the hinge (also not shown in Fig 3.2) act in a vertical plane containing the rod. You are given that \(\sin \theta = \frac { 15 } { 17 }\). \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{334b2170-3708-46db-bff7-bcad7d5fab00-4_396_314_1747_852} \captionsetup{labelformat=empty} \caption{Fig. 3.2}
    \end{figure}
    1. First suppose that the force at A is at right angles to ABC and has magnitude \(P \mathrm {~N}\). Calculate \(P\).
    2. Now instead suppose that the force at A is horizontal and has magnitude \(Q \mathrm {~N}\). Calculate \(Q\).
      Calculate also the magnitude of the force exerted on the rod by the hinge.
This paper (4 questions)
View full paper
Q1 Q2 Q3 Q4