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5c. Milly (mass 60.9 kg) runs at 4.11 m/s along the positive x-axis and then jumps...

5c.

Milly (mass 60.9 kg) runs at 4.11 m/s along the positive x-axis and then jumps onto a stationary 112 kg box. Milly and the box slide across the floor for distance 0.244 m, and then they come to a stop. Find the coefficient of kinetic friction between the box and the floor.

Solutions

Expert Solution

This problem combines concepts of conservation of momentum, energy conservation and friction.

Finding the velocity and kinetic energy of Milly and the box

When Milly jumps onto the box, it is technically an inelastic collision, where momentum is conserved.

Since momentum is conserved, we can equate these two to find the velocity of Milly and the box.

The kinetic energy of the box and Milly together is

Finding out the frictional force and the work done by it

The work done by the frictional force is equal to it times the distance over which it acts.

The frictional force is

where is the coefficient of kinetic friction we have to find out.

Equating the two quantities and solving for the coefficient of kinetic friction

Once the frictional force does negative work with the same magnnitude as the kinetic energy, the box and Milly will come to a stop.

Solving for , we get

genius_generous answered 8 months ago

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