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A machine is driven by a 100 kg mass tha...

A machine is driven by a 100 kg mass that falls `8m` in `4*0`s. it lifts a load of mass 500 kg vertically upwards. Taking `g=10ms^(-2)`. Calculate:
(a) the force exerted by the falling mass.
(b) the work done by the falling mass in its displacement by `8*0`m.
(c) the power input to the machine.
(d) the power output of the machine if its efficiency is 60%, and
(e) the work done by the machine is `4*0`s.

Text Solution

Verified by Experts

Given: `m=100kg,d=8*0m,t=4*0s,L=500kg`
(a) Force exerted by the falling mass=mg
`=100xx10=1000N`
(b) Work done by the falling mass
=force exerted by the falling mass`xx`displacement
`=mgxxd`
`=1000xx8*0=8000J`
(c) Power input`=("work done on machine")/("time")`
`=(8000J)/(4*0s)=2000W`
(d) Given, efficiency=60%=`0*6`
power input=?
Since efficiency=`("power input")/("power input")`
`therefore`Power output=power input`xx`efficiency
`=2000Wxx0*6=1200W`
(e) Work done by the machine is `4*0`s
=power output `xx` time
`=1200Wxx4*0s=4800J`.
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