By how many times will the kinetic energy of a body increase if it's speed is tripled? Show by calculation.
Mass,m = m
Velocity,v = v
K.E[1] = 1/2 x m x [v]^2
K.E.[1] = 1/2 m v^2
When velocity,v is tripled then,
Mass,m = m
Velocity,v = 3v
K.E [2].= 1/2 x m x [v]^2
K.E.[2] = 1/2 x m x [3v]^2
K.E.[2] = 1/2 x m x 9v^2
K.E.[2] = 1/2 m 9v^2
Ratio of K.E. [1] and [2],
1/2 x m x v^2 / 1/2 x m x 9v^2
v^2 / 9v^2
1 /9 or 1 : 9
Hence, K.E. will increase by 9 times if it's speed is tripled.
Velocity,v = v
K.E[1] = 1/2 x m x [v]^2
K.E.[1] = 1/2 m v^2
When velocity,v is tripled then,
Mass,m = m
Velocity,v = 3v
K.E [2].= 1/2 x m x [v]^2
K.E.[2] = 1/2 x m x [3v]^2
K.E.[2] = 1/2 x m x 9v^2
K.E.[2] = 1/2 m 9v^2
Ratio of K.E. [1] and [2],
1/2 x m x v^2 / 1/2 x m x 9v^2
v^2 / 9v^2
1 /9 or 1 : 9
Hence, K.E. will increase by 9 times if it's speed is tripled.