You raise a 1200-N piano a distance of 5.00 m using a set of pulleys. You pull in 20 m of rope while exerting a force of 340 N.

a) what is the work output?

b) what is work input

c) what is the mechanical advantage of this machine?

d) what is the efficiency of this machine?

(a) 6000 J

(b) 6800 J

(c) 3.53

(d) 88.23%

Explanation:

(a) Work output: This is the work done by the pulley.

W₁ = L * x ... Equation 1

Where W₁ = work output, L = weight of the load or force required by the pulley to lift the load, x = distance moved by the load.

Given: L = 1200 N, x = 5.00 m

Substituting these values into equation 1,

W₁ = 1200*5

W₁ = 6000 J

Thus the work output = 600 J

(b) Work input: This is the work done by the person pulling the rope in the pulley.

W₂ = E * y ... Equation 2

Where W₂ = work input, E = force applied to the pulley or Effort, y = length of the rope.

Given: F₂ = 340 N, d₂ = 20 m

Substituting these values into equation 2

W₂ = 340*20

W₂ = 6800 Joules

Thus the work input = 6800 J

(c) Mechanical advantage: This is the ratio of load to effort of a machine.

M. A = L/E ... Equation 3

Where M. A = mechanical advantage, L = load, E = effort

Given: L = 1200 N, E = 340 N

Substituting into equation 3

M. A = 1200/340

M. A = 3.53.

Thus the mechanical advantage of the machine = 3.53

(d) Efficiency of a machine: This is the ratio of work output to work input expressed in percentage.

E (%) = (W₁/W₂) * 100

E (%) = (6000/6800) * 100

E (%) = 88.23%

Thus the percentage efficiency of the machine = 88.23%