Question

A mass of 0.5 kg moving with a speed of 1.5 ms-1 on a horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 nn-1. The maximum compression of the spring would be

Answer 1

Let the maximum compression of the spring would be x.

kinetic energy of moving object = potential energy stored in spring after colliding object to the spring.

or, 1/2 mv² = 1/2 kx²

or, mv² = kx²

or, x = √{mv²/k}

here, m = mass of moving object = 0.5 kg

v = speed of moving object = 1.5 m/s

k = spring constant = 50 N/m

so, x = √{0.5 × (1.5)²/50}

x = √{0.01 × (1.5)²}

x = √{(0.1)² × (1.5)²}

x = 0.1 × 1.5 = 0.15m or 15cm

hence, maximum compression of the spring would be 15cm