How to Calculate the Work Done on a Rolling Hoop

How much work must be done on a 140 kg hoop rolling along a horizontal floor with a speed of 0.150 m/s?

The work done on the hoop can be calculated by considering both the translational and rotational kinetic energy. The work done is equal to the change in total kinetic energy of the hoop. The translational kinetic energy of the hoop is given by KE_translational = (1/2) * m * v^2, where m is the mass of the hoop and v is its speed.

Calculating Work Done on a Rolling Hoop

Translational Kinetic Energy:

The translational kinetic energy of the hoop is calculated as KE_translational = (1/2) * 140 kg * (0.150 m/s)^2.

Rotational Kinetic Energy:

For a hoop, the moment of inertia is I = m * R^2, where R is the radius of the hoop. We can express the rotational kinetic energy as KE_rotational = (1/2) * m * v^2.

Total Kinetic Energy:

The total kinetic energy of the hoop is the sum of the translational and rotational kinetic energies, KE_total = (1/2) * m * v^2 + (1/2) * m * v^2 = m * v^2.

Calculating Work Done:

The work done on the hoop is equal to the change in kinetic energy, which is W = ΔKE = KE_final - KE_initial. Assuming the hoop starts from rest, the work done on the hoop is W = 140 kg * (0.150 m/s)^2.