A machine is driven by a 100 kg mass that falls 8m in 4*0s. 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*0m. (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*0s.

A machine is driven by a 100 kg mass that falls 8m in 4*0s. it lifts a

1.	A machine is driven by a 100 kg mass that falls 8m in 40s. 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 80m. (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*0s.
Answer» Solution :Given: `m=100kg,d=80m,t=40s,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` `=1000xx80=8000J` (c) Power input`=("work done on machine")/("time")` `=(8000J)/(40s)=2000W` (d) Given, EFFICIENCY=60%=`06` power input=? SINCE efficiency=`("power input")/("power input")` `therefore`Power output=power input`xx`efficiency `=2000Wxx06=1200W` (E) Work done by the machine is `40`s =power output `xx` time `=1200Wxx40s=4800J`.