A body of mass 10 kg is raised to a height of 10 m with an upward force of 196 N . Find the work done by the upward force and the work done against gravitation. Show that the total energy in this case is equal ot the work done by the upward force .
`[g=9.8 m*s^(-2)`]

Explanation

Work done by the upward force,
W = force `xx` displacement
`=196 N xx 10m =1960 N*m= 1960 J`
Upward acceleration of the body in absence of gravity,
`a^. =("upward force")/("mass") =(196)/(10) =19.6 m*s^(-2)`
`therefore ` Effective upward acceleration ,
`a=a^.-g=19.6-9.8= 9.8 m*s^(-2)`
If the body starts from rest, and attains a velocity v at the height of 10m , then from `v^2=u^2+2as`,
`v^2=2xx9.8xx10 m^2*s^(-2)`
`therefore` Kinetic energy of the body at this height,
`K =1/2 mv^2=1/2 xx10xx2xx9.8xx10=980J`
Work done against gravitational force,
`W^.` = force due to gravity `xx` displacement
= mass `xx` acceleration due to gravity `xx` displacement
`=10xx9.8xx10=980J`
This work done against gravitational pull gets stored as potential energy V of the body . Hence, V =980 J.
`therefore` Total mechanical energy of the body at a height of 10 m `=V+K =980 +980 =1960 J=W`
So, a part of the work done by the upward forces changes into kinetic energy of the body , and the other part transforms itself into the stored potential energy . thus , the total energy and work done by the upward force are equal.