In an arcade game a 0.144 kg disk is shot

across a frictionless horizontal surface by com-
pressing it against a spring and releasing it.
If the spring has a spring constant of
164 N/m and is compressed from its equi-
librium position by 7 cm, find the speed with
which the disk slides across the surface.
Answer in units of m/s

Compressed spring potential energy = Released disk kinetic energy.

(1/2) k X^2 = (1/2) m V^2

k = 163 N/m

V = X* sqrt(k/m)
= (0.07 m)*sqrt(167/0.144)

You do the numbers.

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

When the spring is compressed, it contains potential energy, which is converted into kinetic energy as the disk is released. Assuming no energy is lost to friction or other dissipative forces, we can equate the potential energy stored in the spring to the kinetic energy of the disk:

Potential energy stored in the spring = Kinetic energy of the disk

The potential energy stored in the spring is given by the formula:

Potential energy = (1/2)kx^2

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

The kinetic energy of the disk is given by the formula:

Kinetic energy = (1/2)mv^2

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

Setting these two equations equal to each other:

(1/2)kx^2 = (1/2)mv^2

Now, let's plug in the given values:

k = 164 N/m (spring constant)
x = 7 cm = 0.07 m (compression distance)
m = 0.144 kg (mass of the disk)

Substituting these values into the equation:

(1/2)(164 N/m)(0.07 m)^2 = (1/2)(0.144 kg)v^2

Simplifying the equation:

(1/2)(164 N/m)(0.0049 m^2) = (1/2)(0.144 kg)v^2

Simplifying further:

0.03998 N·m = 0.072 kg·v^2

Now, divide both sides of the equation by 0.072 kg to isolate v^2:

v^2 = 0.03998 N·m / 0.072 kg

v^2 = 0.5553 N·m/kg

Finally, take the square root of both sides of the equation to find the velocity:

v = √(0.5553 N·m/kg)

v ≈ 0.745 m/s

Therefore, the speed with which the disk slides across the surface is approximately 0.745 m/s.