A 2 kg block is attached to a spring of natural length 2 m and spring constant 200 N/m on a frictionless horizontal table. The spring is compressed to length 1 m and released. When the block is at distance x m from the wall, with x < 2, its speed is:
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Question

A 2 kg block is attached to a spring of natural length 2 m and spring constant 200 N/m on a frictionless horizontal table. The spring is compressed to length 1 m and released. When the block is at distance x m from the wall, with x < 2, its speed is:

Options

G1 Physics · Accepted Answer

Natural spring length is 2 m. Initially the spring length is 1 m, so initial compression is xᵢ = 2-1 = 1 m. When the block is at distance x from the wall, spring compression is x f x_f x f ​ = 2-x. Mechanical energy is conserved: ½kxᵢ² = ½mv² + ½k x f 2 . x_f². x f 2 ​ . Therefore, mv² = k(xᵢ² - x f 2 ) . x_f²). x f 2 ​ ) . Substitute m = 2 kg, k = 200 N/m, xᵢ = 1: 2v² = 200[1 - (2-x)²] ⇒ v² = 100[1 - (2-x)²]. Hence, v = 10√[1 - (2-x)²] m/s. Correct option: B.

A 2 kg block is attached to a spring of natural length 2 m and spring constant 200 N/m on a frictionless horizontal table. The spring is compressed to length 1 m and released. When the block is at distance x m from the wall, with x &lt; 2, its speed is:

A 2 kg block is attached to a spring of natural length 2 m and spring constant 200 N/m on a frictionless horizontal table. The spring is compressed to length 1 m and released. When the block is at distance x m from the wall, with x < 2, its speed is: