#### Question

A fixed pulley is driven by a 100 kg mass falling at a rate of 8.0 m in 4.0s. It lifts a load of 500 kgf.

(a) Calculate the power input to the pulley taking the force of gravity on 1 kg as 10 N.

(b) If the efficiency of the pulley is 75%, find the height to which the load is raised in 4.0s.

#### Solution

Load = 500 kgf

Mass of falling object = 100 kg

Displacement of effort = 8.0 m

Time taken = 4.0s

(a) Effort = 100 X 10 = 1000 kgf

Power Input = `"πππ πππππππππ‘ ×ππππππ‘ "/"π‘πππ"` = `8 ×1000/4` = 2000 W

(b) The efficiency of the pulley is = 75% = 0.75

Mechanical advantage of this system M.A =`" πΏπππ"/"πΈπππππ‘"`=`500/100` =5 Velocity ratio of this system V.R = `"π.π΄"/"π"`= `5/0.75`= `20/3`

Displacement of load D= `"πππ πππππππππ‘ ππ ππππππ‘"/"π.π
"`= `(3×8)/20` = 1.2π