Question

you place a sneaker on a wooden plank to tests its coefficient of static friction. the shoe starts to slip at an angle of 53 degrees. what is the coefficient of static friction between the shoe and the wooden surface? a 0.6 b 0.8 c 1 d 1.33 e 53

Explanation:

Step1: Analyze forces at slipping point

When the shoe is on the verge of slipping, the component of gravitational force along the incline \(mg\sin\theta\) is equal to the maximum static - friction force \(F_f=\mu_sN\). The normal force \(N = mg\cos\theta\).

Step2: Derive formula for \(\mu_s\)

From \(mg\sin\theta=\mu_smg\cos\theta\), we can cancel out \(mg\) (since \(m
eq0\) and \(g
eq0\)). Then \(\mu_s=\tan\theta\).

Step3: Calculate \(\mu_s\)

Given \(\theta = 53^{\circ}\), and \(\tan53^{\circ}=\frac{\sin53^{\circ}}{\cos53^{\circ}}\). We know that \(\sin53^{\circ}\approx0.8\) and \(\cos53^{\circ}\approx0.6\), so \(\tan53^{\circ}=\frac{0.8}{0.6}\approx1.33\).

Answer:

D. 1.33