Question

A block of mass 100.0 g rests on a frictionless, horizontal plane. It is pressed
firmly against a horizontal spring with spring constant 2000.0 N/m (assume that the spring is massless). The object is held in position such that the spring is compressed 1.00 cm shorter than its undisturbed length. If the block is suddenly released, at what speed will it be traveling when it is free of the spring?

Answer 1

Given,

Mass of the block = 0.1 kg

spring constant = 2000 N/m

spring is compressed to 1.00 * 10^-2 m

so initially total energy is only potential energy due to spring

so initial energy = 0.5 * k * x^2

initial energy = 0.5 * 2000 * (1.00 * 10^-2)^2

initial energy = 0.1 J

final energy is totally kinetic energy = 0.5 * mass * valocity^2

by conservation of energy

initial energy = final energy

0.1 = 0.5 * 0.1 * velocity^2

velocity = 1.414 m/s

speed will it be traveling when it is free of the spring = 1.414 m/s