why potential energy will be positive when we move the body above the surface of earth
Answers
Answer:
We defined work and potential energy in Work and Kinetic Energy and Potential Energy and Conservation of Energy. The usefulness of those definitions is the ease with which we can solve many problems using conservation of energy. Potential energy is particularly useful for forces that change with position, as the gravitational force does over large distances. In Potential Energy and Conservation of Energy, we showed that the change in gravitational potential energy near Earth’s surface
Explanation:
Gravitational potential energy of mass m at any point at a distance r from the centre of earth is
U=−
r
GMm
At the surface of earth r=R,
∴U
s
=−
R
GMm
=−mgR(∵g=
R
2
GM
)
At the height h=nR from the surface of earth
r=R+h=R+nR=R(1+n)
∴U
h
=−
R(1+n)
GMm
=−
(1+n)
mgR
Change in gravitational potential energy is
△U=U
h
−U
s
=−
(1+n)
mgR
−(−mgR)
=−
1+n
mgR
+mgR
=mgR(1−
1−n
1
)=mgR(
1+n
n
).