Work, Energy, Power – Question and solution

A body of mass 20 kg is projected vertically upwards with a velocity of 20m/s.
Find –

(a) its potential energy at the starting point         
(b) its kinetic energy at the starting point         
(c) its potential energy at the highest point          
(d) its kinetic energy at the highest point.

Answer –

(a) its potential energy at the starting point         
We know that –
Potential energy = mgh
m= 20 kg
g=10m/sec²
h=0 m
Therefore,
Potential energy of the body= 20×10×0=0 joules

(b) its kinetic energy at the starting point
Kinetic energy = 1/2 mv²
Here,
m=20 kg
v = 20m/s
Therefore,
Kinetic energy of the body = 0.5×20×20×20=4000 joules

(c ) Potential energy at the highest point

We know that the kinetic energy at the starting point will be converted to potential energy at the highest point as per the principle of conservation of energy.

The kinetic energy (in red color) decreases with height while the potential energy in green color increases with height which is by application of the law of conservation of energy.Therefore, the potential energy at the highest point is equal to the kinetic energy at the starting point = 4000 joules.

We can find the height of the object from this .

Here, Potential energy = 4000 joules
m = 20 kg
g = 10m/sec²
Therefore, Height h= 4000/20×10 = 20m

(d) its kinetic energy at the highest point.

Kinetic energy at highest point will be zero as the velocity is zero at the highest point.
Therefore, Kinetic energy = 0, at the highest point.