The alarm at a fire station rings and a 83-kg fireman, starting from rest, slides down a pole to the floor below (a distance of 3.9 m). Just before landing, his speed is 1.3 m/s. What is the magnitude of the kinetic frictional force exerted on the fireman as he slides down the pole?

To find the magnitude of the kinetic frictional force exerted on the fireman as he slides down the pole, we can use the work-energy principle.

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done against friction will be equal to the change in the fireman's kinetic energy.

First, let's find the initial kinetic energy of the fireman. The fireman is starting from rest, so his initial kinetic energy is zero.

Next, let's find the final kinetic energy of the fireman just before landing. The formula for kinetic energy is given by:

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

Plugging in the given values, we have:

Final kinetic energy = (1/2) * 83 kg * (1.3 m/s)^2

Now, let's find the work done against friction. Since the fireman is sliding down the pole, the frictional force is opposing his motion and doing negative work. Therefore, the work done against friction is equal to the negative change in the fireman's kinetic energy.

Work = - (final kinetic energy - initial kinetic energy)

Work = - [(1/2) * 83 kg * (1.3 m/s)^2 - 0]

Now, we can use the definition of work to find the frictional force. The formula for work is given by:

Work = force * distance

Since the fireman experiences constant frictional force throughout the sliding distance of 3.9 m, we can write:

Work = frictional force * 3.9 m

Setting the two equations for work equal to each other, we have:

Frictional force * 3.9 m = - [(1/2) * 83 kg * (1.3 m/s)^2 - 0]

Finally, we can solve for the frictional force:

Frictional force = - [(1/2) * 83 kg * (1.3 m/s)^2 - 0] / 3.9 m

Evaluating the expression, we can find the magnitude of the kinetic frictional force exerted on the fireman as he slides down the pole.

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