Spring Force?

Question

In a arcade game a 0.06 kg disk is shot across a frictionless horizontal surface by compressing it against a spring and releasing it.

If the spring has a constant of 194 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

v = 3.98 m/s

explanation:

Work done by spring is .5kx^2

this is equal to kinetic energy of the mass in motion = .5mv^2

Solving for v yields the answer

Answer 2

Use the conservation of energy in solving this problem.

Energy from spring = Energy absorbed by disk

Energy from spring = (1/2)kx^2

Energy absorbed by disk = (1/2)mV^2

where

k = spring constant = 194 N/m (given)

x = spring's compressed length = 7 cm = 0.07 m (given)

m = mass of disk = 0.06 kg (given)

V = velocity of disk

Substituting appropriate values,

(1/2)(194)(0.07^2) = (1/2)(0.06)V^2

Rearranging,

V^2 = 194 * 0.07^2/0.06

V^2 = 15.84

V = 3.98  m/sec.