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

Answer:

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

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 :

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

v is speed of the disk.

$kx^2=mv^2\\\\v=\sqrt{\dfrac{kx^2}{m}} \\\\v=\sqrt{\dfrac{164\times 0.07^2}{0.144}} \\\\v=2.36\ m/s$

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