Question

The person in the figure is standing on crutches. Assume that the force exerted on each crutch by the ground is directed along the crutch. The coefficient of static friction between the crutch and the ground is $0.90$. 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

Answer: 0.90

$N=F\cos \theta$
$F\sin \theta =\mu N$
$\frac{\sin \theta }{\cos \theta }=\mu$
$\tan \theta =0.9$
$\theta ={\tan }^{-1}(0.9)$