Jo lifts a 330 N cement block 3.6 m (using a system of pulleys) by pulling 16 m of rope with a force of 121 N.

a. What is the mechanical advantage of the pulley system?

b. What is the work input?

c. What is the work output?

d. What is the efficiency of the machine?

a) Mechanical advantage: 2.7 b) Work input: 1,936J c) Work ouput: 1,188J d) Efficieny: 0.61

Explanation:

a. Mechanical advantage

The mechanical advantage of a system of pulleys is the ratio of the ouput force (weight of the object) to the input force (pulling force):

Mechanical advantage = output force / input force

Mechanical advantage = 330N / 121N = 2.727 ≈ 2.7

b. Work input

Work is the product of the force applied by the distance traveled in the same direction:

Work input = Input force * input distance = 121N * 16m = 1,936J

c. Work output

Using the law of conservation of energy, the work output is equal to the change in the potential energy of the block:

ΔPotential energy = mass * g * height

ΔPotential energy = weight * height = 330N * 3.6m = 1,188J

Work output = 1,188J

d. Efficiency

The efficiency is the ratio of the work output to the work input:

Efficiency = Work input / Work output

Efficiency = 1,188J / 1,936J = 0.61

You can check that the efficiency is also the ratio of the mechanical advantage to the ideal mechanical advantage

The ideal mechanical advantage is equal to the ratio of the input distance (pulling distance) to the output distance (lift distance):

Ideal mechanical advantage = 16m/3.6m = 4.444

Efficiency = mechanical advantage / ideal mechanical advantage

Efficiency = 2.727 / 4.444 = 0.61