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In: Physics

A magnet of mass 0.15 kg is dropped from rest and falls vertically through a 35.0...

A magnet of mass 0.15 kg is dropped from rest and falls vertically through a 35.0 cm copper tube. Eddy currents are induced, causing the copper to warm up. The speed of the magnet as it emerges from the tube is 1.00 m/s. How much heat energy is dissipated to the environment?

Solutions

Expert Solution

Let the lower end of the tube is at height and the upper end of the tube is at height . The gravitational potential energy of the magnet at height h is

The kinetic energy of the magnet when moving at velocity v is

The mechanical energy of the magnet is the sum of its kinetic energy and potential energy.

At the top of the tube, the magnet was at rest, its kinetic energy is zero. The mechanical energy of the magnet at the upper end of the tube is

At the lower end of the tube, the mechanical energy of the magnet is

The change in mechanical energy of the magnet is equal to the energy dissipated to the environment

Substituting we get

genius_generous answered 2 months ago
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