Question

Assuming that the gravitational potential energy at infinity is zero the change in potential energy of an object of mass m,when taken to a height h from the surface of earth of radius R is given by,

Answer 1

Answer:

Climbing stairs and lifting objects is work in both the scientific and everyday sense—it is work done against the gravitational force. When there is work, there is a transformation of energy. The work done against the gravitational force goes into an important form of stored energy that we will explore in this section

Answer 2

Answer:

The change in potential energy = m g h

Explanation:

Mass of object = m

Mass of earth = M

Radius of earth =R

We know that gravitational force at distance r given as

$F=-G\dfrac{mM}{r^2}$

We also know that

F= -dU/dr

U= - ∫ F.dr

So U= -GmM/r

Given that potential at infinite is zero.

So change in potential energy at height h

ΔU = Uf - Ui

ΔU= -GmM/(R+h) -  (-GmM/R)

ΔU= -GmM/(R+h) +  GmM/R

Now

1/(R+h) = 1/[R(1+h/R)] = (1/R) x (1 - h/R)

R is large and h is small  then

ΔU = -GmM/R + GmMh/R² + GmM/R = GmMh/R²

ΔU =  GmMh/R²  

We know that

g = GM/R²  

So by putting the value

ΔU =  GmMh/R²  = m g h

The change in potential energy = m g h