A-level · Moments

Non-uniform rods and tiltingExam-style questions

Beams whose weight does not act at the centre — finding the weight or the position of the centre of mass by taking moments — and "on the point of tilting" problems, where the reaction at the support about to be left is zero.

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14 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4

1
A non-uniform plank $AB$ has length $6$ m and mass $20$ kg. Its centre of mass is at the point $G$ , where $AG = 2.5$ m. The plank rests horizontally on two supports at $C$ and $D$ , where $AC = 1$ m and $AD = 4.5$ m. Take $g = 9.8$ m s⁻².(a) Find the magnitudes of the reactions at $C$ and $D$ . (5 marks)
(b) A child stands at $B$ , and the plank is on the point of tilting about $D$ . Modelling the child as a particle, find the child's mass. (4 marks)
(c) A different child, of mass $40$ kg, walks along the plank from $D$ towards $B$ . Find how far from $A$ they can walk before the plank starts to tilt. (3 marks)
Level 4 · 12 marksTry it