Question

question 11
1 pts
a small box is placed on an adjustable ramp. the ramps angle is slowly increased until the object is just about to move. the maximum angle the object can reach before it starts to move is 13 degrees. what must be the coefficient of static friction for the box?
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Explanation:

Step1: Analyze the forces

When the box is on the verge of moving, the force of static friction \(f_s=\mu_s N\) balances the component of the gravitational force along the ramp \(mg\sin\theta\). The normal force \(N = mg\cos\theta\).

Step2: Set up the equation

Since \(f_s = mg\sin\theta\) and \(f_s=\mu_s N=\mu_s mg\cos\theta\), we can equate \(mg\sin\theta=\mu_s mg\cos\theta\). Canceling out \(mg\) (mass and gravity terms), we get \(\mu_s=\tan\theta\).

Step3: Calculate the coefficient

Given \(\theta = 13^{\circ}\), then \(\mu_s=\tan(13^{\circ})\). Using a calculator, \(\tan(13^{\circ})\approx0.23\).

Answer:

\(0.23\)