In: Physics
Calculate the final speed of an object dropped on Earth from altitude of 8 times the radius of Earth. (hint: neglect friction
due to atmosphere and use expression of gravitational potential energy and principle of conservation energy. Answer =
10.6 km/s).
The gravitational potential energy at a point is defined as the workdone to move a body from infinity to that point and if a body is falling towards earth the gravitational potential energy of the body at a distance r from the earth surface is given by,
Where
M= mass of earth=
m=mass of the body.
So if the body is falling from a hight
to a hight
the change in gravitational potential energy is given by
If the velocity of the body is
, the change in kinetic energy from velocity 0 to
is given by
According to conservation of energy,
For earth surface radius of earth is
Here