Question

In an arcade game a 0.099 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 244 N/m and is compressed from its equilibrium position by 4 cm, find the speed with which the disk slides across the surface. Answer in units of m/s.

Answer 1

The speed of disk is 1.98
`(m)/(s)`

Step-by-step explanation:

Given:

Mass of
`m = 0.099` kg

Spring constant
`k = 244 (N)/(m)`

Compression of spring
`x = 4 * 10^(-2)` m

From energy conservation theorem,

Spring potential energy converted into kinetic energy,

`(1)/(2) m v^(2) = (1)/(2) k x^(2)`

`v = \sqrt{(k x^(2) )/(m) }`

`v = \sqrt{(244 * 16 * 10^(-4) )/(0.099) }`

`v = 1.98 (m)/(s)`

Therefore, the speed of disk is 1.98
`(m)/(s)`