Answer to Question #169786 in Mechanics | Relativity for Mae

Question

an inclined plane as shown in figure 1 is used to raise an object of mass 30 kg. if the plane is inclined 5° above the horizontal and the coefficient of friction is 0.20, calculate the ideal mechanical advantage, actual mechanical advantage, and the efficiency of this machine.

Answer 1

Ideal mechanical advantage of an incline(IMA) $=\dfrac{length\space of\space incline}{vertical\space rise}=\dfrac{1}{sin\theta}=\dfrac{1}{sin5\degree}=11.47$

Since the coefficient of friction for horizontal surface = 0.20

Actual mechanical advantage(AMA) = $\dfrac{1}{sin\theta(1+\mu)}=\dfrac{1}{sin5\degree(1+0.20)}=3.48$

Efficiency, $\eta=\dfrac{AMA}{IMA}\times100=30.34\%$