Question

question 9
1 pts
an object of mass \m\ is placed on a frictionless ramp at an incline of 33 degrees. what must be the acceleration of the object down the ramp?

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Explanation:

Step1: Resolve the gravitational force

The gravitational force acting on the object is \(F = mg\). When resolved along the ramp, the component of the force is \(F_{parallel}=mg\sin\theta\), where \(\theta = 33^{\circ}\)

Step2: Apply Newton's second law \(F = ma\)

Since \(F_{parallel}=ma\) (because there is no friction, so net force along the ramp is \(F_{parallel}\)), we substitute \(F_{parallel}=mg\sin\theta\) into \(F = ma\). Then \(mg\sin\theta=ma\). Canceling out the mass \(m\) (since \(m
eq0\)) gives \(a = g\sin\theta\)

Step3: Calculate the value

Taking \(g = 9.8\ m/s^{2}\) and \(\theta = 33^{\circ}\), we have \(a=9.8\times\sin(33^{\circ})\). Using a calculator, \(\sin(33^{\circ})\approx0.5446\), so \(a = 9.8\times0.5446\approx5.34\ m/s^{2}\)

Answer:

\(5.34\ m/s^{2}\)