Question

In an arcade game a 0.144 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 164 N/m and is compressed from its equilibrium position by 7 cm, find the speed with which the disk slides across the surface.

Answer 1

The speed with which the disk slides across the surface is 2.36 m/s.

Step-by-step explanation:

Given that,

Mass of the disk, m = 0.144 kg

Spring constant of the spring, k = 164 N/m

The spring is compressed from its equilibrium position by 7 cm or 0.07 m

We need to find the speed with which the disk slides across the surface. It is a case of conservation of energy in which the energy of the spring is gained by its kinetic energy. It is given by :

`(1)/(2)kx^2=(1)/(2)mv^2`

v is speed of the disk.

`kx^2=mv^2\\\\v=\sqrt{(kx^2)/(m)} \\\\v=\sqrt{(164* 0.07^2)/(0.144)} \\\\v=2.36\ m/s`

So, the speed with which the disk slides across the surface is 2.36 m/s.