Question

The person in the figure is standing on crutches. Assume that the force exerted on each cructh by the ground is directed along the crutch. the coefficient of static friction between the crutch and the ground is \(0.9\) . If the largest angle that the crutch can have just before it begins to slip on the floor is \(\theta ^{max}=\tan^{-1}(n)\), then find \(n\).

Answer 1

Draw a FBD of crutch.

Diagram

Find the value of \(n\).

Normal reaction will act perpendicular to surface.
Force exerted by man on the ground at angle \(\theta\)
So, we have to resolve force into vertical and horizontal directio as shown in diagram,
\(N=F\cos\theta~~~~~\ldots(i)\\
F\sin\theta=\mu N~~~~~~\ldots (ii)\)
Divided both the equations,
\(\dfrac {\sin\theta}{\cos\theta}=\mu\\
\tan\theta=\mu\\
\theta=\tan^{-1}(0.9)\)

Final Answer : 0.9