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

Answer:

The speed of disk is 1.98 $\frac{m}{s}$

Explanation:

Given:

Mass of $m = 0.099$ kg

Spring constant $k = 244 \frac{N}{m}$

Compression of spring $x = 4 \times 10^{-2}$ m

From energy conservation theorem,

Spring potential energy converted into kinetic energy,

   $\frac{1}{2} m v^{2} = \frac{1}{2} k x^{2}$

  $v = \sqrt{\frac{k x^{2} }{m} }$

  $v = \sqrt{\frac{244 \times 16 \times 10^{-4} }{0.099} }$

  $v = 1.98 \frac{m}{s}$

Therefore, the speed of disk is 1.98 $\frac{m}{s}$