Question

If the linear momentum of a dynamic object increases by 10%, What is the rate of change in its kinetic energy?

Answer 1

L = mv ; KE = 1/2 m v^2

if L is increased by 10%

new L = L + 10% of L

or, L' = mv + 0.10 mv = 1.1 mv = 1.1 L

As KE = 1/2 m v^2

we can write KE = 1/2m m^2 v^2

or, KE = 1/2m L^2

so, new KE = 1/2m (1.1 L)^2 = 1/2m 1.21L^2

or, KE' = 1.21 × (1/2m L^2) = 1.21 KE

1.21 KE = KE + 0.21 KE

So, KE will increase by 21 % .