An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy ? If the object is allowed to fall, find its kinetic energy when it is half - way down.

Explanation

Here, Mass, m = 40 kg
Acceleration due to gravity, `g = 10 m//s^(2)`
And Height, h = 5 m
So, Potential energy `m xx g xx h`
(at 5 m height) `= 40 xx 10 xx 5 J`
= 2000 J `" "` (or 2000 joules)
Initial, the object is at a height above the ground will be half of 5 m (and has a potential energy of 2000 J). When this object is allowed to fall and it is half way down, its height above the ground will be half of 5 m which is `(5)/(2) = 2.5 m`. Now, the potential energy of this object of 40 kg when it is at a height of 2.5 m will be :
Potential energy `= m xx g xx h`
(at 2.5 m height) `= 40 xx 10 xx 2.5 J`
= 1000 J `" "` (or 1000 joules)
Now, according to the law of conservation of energy :
Total potential energy = Potential energy at half way down + Kinetic energy at half way down
or 2000 = 1000 + Kinetic energy at half way down
So, Kinetic energy at = 2000 - 1000
half way down = 1000 J `" "` (or 1000 joules)