Rod hinged to wall with strut or direct force support

A rod freely hinged at one end to a wall and held in equilibrium by a strut, direct applied force, or contact with another surface (not a string), requiring calculation of the support force and hinge reactions.

3 questions · Standard +0.3

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Edexcel M2 2009 June Q4
11 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8e220b8a-46f1-4b9b-88a4-f032c7fbda50-05_568_956_205_516} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A uniform rod \(A B\), of length 1.5 m and mass 3 kg , is smoothly hinged to a vertical wall at \(A\). The rod is held in equilibrium in a horizontal position by a light strut \(C D\) as shown in Figure 1. The rod and the strut lie in the same vertical plane, which is perpendicular to the wall. The end \(C\) of the strut is freely jointed to the wall at a point 0.5 m vertically below \(A\). The end \(D\) is freely joined to the rod so that \(A D\) is 0.5 m .
  1. Find the thrust in \(C D\).
  2. Find the magnitude and direction of the force exerted on the \(\operatorname { rod } A B\) at \(A\).
Edexcel M1 Q3
9 marks Standard +0.3
3. A lump of clay, of mass 0.8 kg , is attached to the end \(A\) of a light \(\operatorname { rod } A B\), which is pivoted at its other end \(B\) so that it can rotate smoothly in a vertical plane. A force is applied to \(A\) at an angle of \(60 ^ { \circ }\) to the vertical, as shown, the magnitude \(F \mathrm {~N}\) of this force being just enough to hold the lump of clay in equilibrium with \(A B\) inclined \includegraphics[max width=\textwidth, alt={}, center]{31efa627-5114-4797-9d46-7f1311c18ff8-1_309_335_1453_1590}
at an angle of \(30 ^ { \circ }\) to the upward vertical.
  1. Find the value of \(F\),
  2. Find the magnitude of the force in the \(\operatorname { rod } A B\).
  3. State the modelling assumption that you have made about the lump of clay.
    (6 marks)
    (2 marks)
    (1 mark)
OCR M2 2009 June Q3
10 marks Standard +0.3
3 \includegraphics[max width=\textwidth, alt={}, center]{e85c2bf4-21a8-4d9a-93c5-d5679b2a8233-2_497_951_1123_598} A uniform beam \(A B\) has weight 70 N and length 2.8 m . The beam is freely hinged to a wall at \(A\) and is supported in a horizontal position by a strut \(C D\) of length 1.3 m . One end of the strut is attached to the beam at \(C , 0.5 \mathrm {~m}\) from \(A\), and the other end is attached to the wall at \(D\), vertically below \(A\). The strut exerts a force on the beam in the direction \(D C\). The beam carries a load of weight 50 N at its end \(B\) (see diagram).
  1. Calculate the magnitude of the force exerted by the strut on the beam.
  2. Calculate the magnitude of the force acting on the beam at \(A\).