A 150 g ball rolls at 10 cm/s rightward over a frictionless surface towards a spring 75 cm away, with spring constant 200 N/m. How far does is the spring compressed when the ball is brought to rest

x  =  0.27 cm

Explanation:

given data

mass = 150 g

velocity = 10 cm/s = 0.1 m/s

spring constnat = 200 N/m

solution

as we know that here ball is moving with constant speed

so

0.5 × m × v² = 0.5 × k × x²      1

here x is compression in spring

so put here value and we get

0.5 × 150 × (0.1)² = 0.5 × 200 × x²

solve it we get

x  =  0.27 cm

gets less