Question

question 17
1 pts
an object of mass \m\ is placed on a ramp which has an angle of 55 degrees. the object has a coefficient of kinetic friction equal to 0.43. the objects slides down the ramp. what must be the acceleration of the object down the ramp? your answer should be a positive number.
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Explanation:

Step1: Analyze forces along the ramp

The gravitational force component along the ramp is \(F_{g\parallel}=mg\sin\theta\), and the frictional force is \(F_f = \mu_k N\). The normal force \(N = mg\cos\theta\). According to Newton's second law \(F_{net}=ma\), so \(mg\sin\theta-\mu_kmg\cos\theta=ma\).

Step2: Solve for acceleration \(a\)

Divide the equation \(mg\sin\theta-\mu_kmg\cos\theta=ma\) by \(m\) (since \(m
eq0\)). We get \(a = g(\sin\theta-\mu_k\cos\theta)\). Substitute \(g = 9.8\ m/s^2\), \(\theta = 55^{\circ}\), and \(\mu_k=0.43\).

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Answer:

\(5.61\ m/s^2\)