CAIE M1 2005 November — Question 4

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2005
SessionNovember
TopicNewton's laws and connected particles

4
\includegraphics[max width=\textwidth, alt={}, center]{2026cad4-8494-4139-ad21-d8a17ac2b955-3_276_570_264_790} A stone slab of mass 320 kg rests in equilibrium on rough horizontal ground. A force of magnitude \(X \mathrm {~N}\) acts upwards on the slab at an angle of \(\theta\) to the vertical, where \(\tan \theta = \frac { 7 } { 24 }\) (see diagram).
  1. Find, in terms of \(X\), the normal component of the force exerted on the slab by the ground.
  2. Given that the coefficient of friction between the slab and the ground is \(\frac { 3 } { 8 }\), find the value of \(X\) for which the slab is about to slip.