Question

A body of mass 10 kg is moving with a velocity 20 m s^-1. If the mass of the body is doubled and its velocity is halved, find:

1. the initial kinetic energy, and
2. the final kinetic energy.

Answer 1

Given:

Let initial Mass, 

m₁= 10 kg and velocity, v₁ = 20 m/s

Final mass,

m₂ = 2 × 10 = 20 kg and velocity, v₂ = `20/2` = 10 m/s

Formula:

Kinetic energy = `1/2 × mv^2`

Solution:

Initial kinetic energy, K₁= `1/2 × mv^2`

= `1/2 ×10 ×(20)^2`

= `1/2 × 10 × 20 × 20`

= 2000 J

Final kinetic energy, K₂ = `1/2 × mv^2`

= `1/2 × 20 ×(10)^2`

= `1/2 × 20 ×10 ×10`

= 1000 J

`"K"_1/"K"_2 = 2000/1000`

= `2/1`

= 2 : 1