What linear speed must a 0.0508-kg hula hoop have if its total kinetic energy is to be 0.164 J? Assume the hoop rolls on the ground without slipping.

PE = m*V^2 = 0.164 J.

.0508*V^2 = 0.164
V^2 = 3.228
V = 1.80 m/s.

To find the linear speed of the hula hoop, we can use the formula for kinetic energy:

Kinetic energy (KE) = 1/2 * mass * velocity^2

Given:
Total kinetic energy (KE) = 0.164 J
Mass (m) = 0.0508 kg

We need to find the velocity (v). Rearranging the formula:

v = sqrt(2 * KE / m)

Substituting the given values:

v = sqrt(2 * 0.164 J / 0.0508 kg)

Now, we can calculate the linear speed.