Question

In an arcade game a 0.135 kg disk is shot across a frictionless horizontal surface by compressing it against a spring and releasing it. If the spring has a spring constant of 162 N/m and is compressed from its equilibrium position by 7 cm, find the speed with which the disk slides across the surface. Answer in units of m/s.

Answer 1

Answer:

v=2.42m/s

Explanation:

We use the energy conservation theorem in order to solve the problem. The energy when the spring is compressed is equal at the energy when the disk leaves the spring:

$E_{initial}=E{final}\\E_{k-initial}+E_{p-initial}=E_{k-final}+E_{p-final}\\0+\frac{1}{2}kx^2=\frac{1}{2}mv^2+0$

At the beginning the initial energy is totally potential, energy linked to the compressed spring. At the end the energy is totally kinetics

We solve the equation in order to find the speed.

k=162 N/m

x=7 cm=0.07m

m=0.135 kg

$v=x*\sqrt{k/m}=0.07*\sqrt{162/0.135}=2.42m/s$