Question

A mass of 0.5 kg moving with a speed of 1.5m/s on a horizontal smooth surface , collides with a nearly massless spring of force constant k=50N/m. The maximum compression of string would be

Answer 1

Mass of the body = m = 0.5kg

Initial speed of the body = v = 1.5m/s

... now according to the question the body collides with a spring of constant = 50N/m... In an ideal world, we assume that the kinetic energy of the body of 0.5kg was completely transferred to the spring, and that was stored in it as elastic potential energy and it had compressed.

so,

$\frac{1}{2} mv^{2}  = \frac{1}{2} kx^{2}$

where x is the compression of the spring.

1/2 * 0.5 * 1.5 * 1.5 = 1/2 * 50 * x * x

x = 0.15m