The efficiency of a pulley system is 64 percent. The pulleys are used to raise a mass of 78 kg to a height of 4.0 m. What force is exerted on the rope of the pulley system if the rope is pulled for 24 m in order to raise the mass to the required height

The force exerted on the rope of the pulley system if the rope is pulled for 24 m in order to raise the mass to the required height is 81.6 N

Explanation:

Efficiency, γ = 64%

mass, m = 78 kg

height, h = 4 m

Force, F = ?

distance of the rope pulled, x = 24 m

We know,

Acceleration due to gravity, g = 9.81 m/s²

Potential energy, PE = mgh = (78) X (9.81) X (4) = 3060.72 joules

Work, W = F X x

F = W/d = (3060.72) / (24) = 127.53 N

However, the efficiency of the pulley system is 64%.

The real force required is F (net) = (127.53) X (0.64) = 81.6 N

Therefore, the force exerted on the rope of the pulley system if the rope is pulled for 24 m in order to raise the mass to the required height is 81.6 N