Calculating the Work Done on a Hoop to Stop It

Explanation:

Given Data:
Mass of the hoop, m = 130 kg
Initial speed of the hoop, u = 0.18 m/s
Finally it stops, v = 0

We know that the work done by an object is equal to the change in its kinetic energy. Final kinetic energy of the hoop is equal to 0 as the hoop stops. So, W=-(K_t+K_r), where K_t and K_r are translational and rotational kinetic energy of the hoop.
Therefore, W=-(1/2 * m * v^2 + 1/2 * I * ω^2), where I = m * r^2 and ω = v/r.

Substitute the given values:
W = -m * v^2
W = -130 kg * (0.18 m/s)^2
W = -4.21 Joules
So, the work done on the hoop to stop it is 4.21 Joules.

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