Statics of rigid bodies

Sample questions

Original practice questions written in the style of the exam.

1. Question 16 marks

   A uniform ladder $AB$, of length $4\,\text{m}$ and mass $15\,\text{kg}$, rests with $A$ on rough horizontal ground and $B$ against a smooth vertical wall. The ladder makes an angle $\theta$ with the ground, where $\tan\theta = \tfrac{4}{3}$, and lies in a vertical plane perpendicular to the wall. The coefficient of friction between the ladder and the ground is $0.5$.

   A man of mass $75\,\text{kg}$ climbs the ladder. Modelling the man as a particle, find how far up the ladder from $A$ he can climb before the ladder slips.

   Mark scheme

   • B1 Resolve vertically: $R = 90g$ (1)
   • B1 Limiting friction: $F = 0.5 \times 90g = 45g$ (1)
   • B1 Resolve horizontally: wall reaction $$ (1)