You wish to lift a 400 lb car engine a vertical distance of 3 ft using a strong rope. Unfortunately, your hand crank winch can only generate 100 lb of tension in your rope. In order to overcome this obstacle, you use a multiple pulley system (block and tackle) to lift the engine.

a)What is the mechanical advantage of this system?

b) What length of rope is required to complete the work?

a) Mechanical Advantage is defined as the ratio of the load to the effort applied to an object. Mechanical advantage occurs when we can use a minimal effort to overcome a much larger load.

Mathematically; Mechanical advantage = Load/ Effort

Load = 400 lb car engine

Effort applied = Tension generated by the hand crank in the rope = 100lb

Mechanical Advantage = 400lb/100lb

MA = 4

b) Assuming the efficiency is 100%

Efficiency = Workdone by the machine/Work put in the machine * 100%

Workdone by the machine = work output = Force * distance moved by load

= 400*3

= 1200lbft

Work put in the machine = Work input = Force * distance moved by effort

Work input = 100*d

substituting into the equation;

100% = 1200/100d * 100%

1 = 1200/100d

100d = 1200

d = 1200/100

d = 12ft

The length of the rope required to complete the work is 12ft