A 1.6 kg block slides with a speed of .95 m/s on a frictionless, horizontal surface until it encounters a spring with a spring constant of 902 N/m. A) How much does the spring compress when the block comes to rest?

B) When the block has compressed the spring 1.8 cm how fast is the block moving?

(a) the compression of the spring when the block comes to rest is 4cm

(b) speed of the block is 0.427 m/s

Explanation:

Given;

mass of the block, m = 1.6 kg

spring constant, k = 902 N/m

initial speed of the block, v₀ = 0.95 m/s

(a) the compression of the spring when the block comes to rest

when the block comes to rest, the final speed, vf = 0

Apply the law of conservation of energy;

¹/₂kx² = ¹/₂mv₀²

kx² = mv₀²

x = 4 cm

(b)  speed of the block

Apply the law of conservation of energy;

¹/₂mv² = ¹/₂kx²

mv² = kx²