A ball of mass 4 kg , moving with a velocity of 10 m s - 1 , collides with a spring of length 8 m and force constant 100 N m - 1 . The length of the compressed spring is x m . The value of x , to the nearest integer, is ___ .

Step-by-step solution

Let's say the compression in the spring by: y . So, by work-energy theorem we have ⇒ 1 2 m v 2 = 1 2 k y 2 ⇒ y = m k · v ⇒ y = 4 100 × 10 ⇒ y = 2   m ⇒ Final length of spring, = 8 - 2 = 6   m .