A ball of mass 2 kg moving with velocity 3 ~m / s , collides with spring of natural length 2 m and force constant 144 ~N / m . What will be length of compressed spring?

Step-by-step solution

Let spring is compressed by a length x . Kinetic energy of ball = Potential energy of spring i e, 1 2 m v^2= 1 2 k x^2 Given, m=2 ~kg , v=3 ~m / s , k=144 ~N / m 1 2 2 (3)^2= 1 2 144 x^2 x= 9 72 = 1 2 2 ~m Hence, length of compressed spring =2- 1 2 2 = 4 2 -1 2 2 =1.5 ~m