In an arcade game a 0.135 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
155 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

To find the speed with which the disk slides across the surface, we can use the principle of conservation of energy.

First, let's determine the potential energy stored in the spring when it is compressed. The potential energy stored in a spring is given by the formula:

Potential Energy = (1/2) * k * x^2

where k is the spring constant and x is the compression distance.

Plugging in the values given:
k = 155 N/m
x = 0.07 m

Potential Energy = (1/2) * 155 N/m * (0.07 m)^2

Next, let's find the kinetic energy of the disk. The kinetic energy is given by the formula:

Kinetic Energy = (1/2) * m * v^2

where m is the mass of the disk and v is its velocity.

Plugging in the values given:
m = 0.135 kg

Now, we can set the potential energy equal to the kinetic energy since energy is conserved:

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

Dividing both sides by (1/2):
k * x^2 = m * v^2

Isolating v:
v^2 = (k * x^2) / m

Taking the square root of both sides:
v = sqrt((k * x^2) / m)

Plugging in the values given:
v = sqrt((155 N/m * (0.07 m)^2) / 0.135 kg)

Calculating this equation will give us the speed with which the disk slides across the surface.