Takeshi raises a 1050 N piano a distance of 5.00 m using a set of pulleys. He pulls in 19.5 m of rope. (a) How much effort force would Takeshi apply if this were an ideal machine? (b) What force is used to balance the friction force if the actual effort is 340 N? (c) What is the output work? (d) What is the input work? (e) What is the mechanical advantage?

a) 269.23 N

b) Fr = 70.77 N

c) Work output = 5250 J

d) Work Input = 6630 J

e) Mechanical Advantage

- ideal mechanical advantage = 3.9

- Actual Mechanical Advantage = 3.09

Explanation:

a) In an ideal machine, all the work input is converted to work output.

Work output = F₀ × d₀ = 1050 × 5 = 5250 J

Work input = Fᵢ × dᵢ = 19.5 Fᵢ

19.5 Fᵢ = 5250

Fᵢ = 269.23 N

b) Real effort = 340 N

Since 269.23 N is the force required to lift the 1050 N load in this pulley system, the rest of the 340 N force services frictional forces.

Frictional force = 340 - 269.23 = 70.77 N

c) Output work = Work done by the load = F₀ × d₀ = 1050 × 5 = 5250 J

d) Input Work = Work done by the Effort = Fᵢ × dᵢ = 340 × 19.5 = 6630 J

e) Ideal Mechanical advantage = distance travelled by effort/distance travelled by load

ideal mechanical advantage = 19.5/5 = 3.9

Actual Mechanical Advantage = Load/Effort = 1050/340 = 3.09

Efficiency = Work output/Work input = 5250/6630 = 0.792