A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length i

Question

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N / m . The block is pushed such that the length of the spring becomes 1 m and then released. At distance xm ( x < 2 ) from the wall. the speed of the block will be :

TestHub · Accepted Answer

Given, Natural length of spring = 2 m Initial compression in spring ( x i ​ ) = 1 m Final compression in spring ( x f ​ ) = ( 2 − x ) m Using energy conservation ​ K i ​ + U i ​ = K f ​ + U f ​ 0 + 2 1 ​ Kx i 2 ​ = 2 1 ​ mv 2 + 2 1 ​ Kx f 2 ​ 2 1 ​ mv 2 = 2 1 ​ K ( x i 2 ​ − x f 2 ​ ) 2 1 ​ × 2 × v 2 = 2 1 ​ × 200 × ( 1 2 − ( 2 − x ) 2 ) v 2 = 100 [ 1 − ( 2 − x ) 2 ] v = 10 [ 1 − ( 2 − x ) 2 ] 1/2 ​

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