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# Solution for 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) I - ICSE Class 10 - Physics

#### 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

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 = "𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 ×𝑒𝑓𝑓𝑜𝑟𝑡 "/"𝑡𝑖𝑚𝑒" = 8 ×1000/4 = 2000 W
(b) The efficiency of the pulley is = 75% = 0.75

Mechanical advantage of this system M.A =" 𝐿𝑜𝑎𝑑"/"𝐸𝑓𝑓𝑜𝑟𝑡"=500/100 =5 Velocity ratio of this system V.R = "𝑀.𝐴"/"𝜂"= 5/0.75= 20/3
Displacement of load D= "𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑒𝑓𝑓𝑜𝑟𝑡"/"𝑉.𝑅"= (3×8)/20 = 1.2𝑚

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Solution 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) I Concept: Concept of Pulley System.
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