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Edexcel A-Level Mathematics A2 M2.5.2 Equilibrium of Rigid Bodies Questions

Practise combining moments with force resolution for rods, beams and ladders, finding resultant support forces, and applying limiting-equilibrium conditions on rough or smooth supports.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • combine moments with vertical or horizontal resolution to solve for loads and reactions
  • find resultant hinge or support forces from perpendicular components
  • apply limiting equilibrium to rods or ladders on rough or smooth supports

Edexcel A-Level Mathematics A2 M2.5.2 Equilibrium of Rigid Bodies Questions question 1

[Maximum number: 6]
Figure 4

Figure 4

A uniform rod⁡AB\operatorname{rod} A B has length 8 a and weight W.
The end A of the rod is freely hinged to a fixed point on a vertical wall.
A particle of weight 14W\frac{1}{4} W is attached to the rod at B.
A light inelastic string of length 5 a has one end attached to the rod at the point C, where A C=5 a.

The other end of the string is attached to the wall at the point D, where D is above A and A D=5 a, as shown in Figure 4.

The rod rests in equilibrium.
The tension in the string is T.

Find, in terms of W, the magnitude of the force exerted on the rod by the hinge at A.

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