Question

A 200 kg body is pulled up an inclined plane 15 m long and 5 m high. The force required to pull the body up the plane at a slow uniform speed is 976 N. Compute the ideal mechanical advantage, the actual mechanical advantage and the efficiency of the plane under these conditions.

Answer 1

Answer: mechanical advantage = 2.0081

velocity ratio = 3, efficiency = 66.94%.

Explanation:

From the question, mass of object = 200kg, force (effort) = 976N.

Mechanical advantage = load /effort

the load is simply the weight of the object which w=mg, where m is mass of object and g = acceleration due gravity = 9.8 m/s²

Hence, load = 200* 9.8 = 1960 N

M.A = 1960/976 = 2.0081.

Velocity ratio = distance traveled by effort / distance traveled by load.

It can be seen that the object is meant to move up the height of 5m and the applied force is to move along the plane of 15m.

Hence distance traveled by effort = 15m, distance traveled by load = 5m

V.R = 15/3 = 5.

Efficiency = (M.A/V.R) * 100

Efficiency = 2.0081/5 * 100

Efficiency = 0.6694 * 100

Efficiency = 66.94%