Mechanical advantage, Efficiency and WO WI

Simple machines

Work output, work input

• W = Fd

• Using a block and tackle, you supply an effort force of 250N and move the rope 3m. The load being lifted is 750N and moves a distance of 1m. What is the work input and work output?

• W = Fd; 250N x 3m = 750J

• W = Fd; 750N x 1m = 750J

Efficiency of a machine

• Efficiency = Work Output ÷ work input x 100

• Express as a percentage (%)

• A force of 1200N is needed to move a box up a ramp. The ramp is 4m long. The ramp raises the 3200N resistance (load) to a height of 1 m. What is the work output, the work input and the efficiency of the ramp?

• Work input: W = Fd; 1200N x 4m = 4800J

• Work output: W = Fd; 3200N x 1m = 3200J

• Efficiency: 3200J ÷ 4800J x 100 = .67 x 100 = 67%

Mechanical Advantage for a lever or inclined plane

• MA = Resistance force ÷ Effort force

MA = R ÷ E

• MA = Effort distance ÷ Resistance distance (length of ramp ÷ height of ramp)

MA = ED ÷ RD

• MA = Effort arm ÷ Resistance arm

MA = EA ÷ RA

Mechanical advantage for a pulley

• Count the number of strands of rope that support the load or resistance force

• 1 fixed pulley – 1

• 1 moveable pulley – 2

• 2 fixed and one moveable pulley – 3

• 2 fixed and 2 moveable pulleys – 4