The alarm at a fire station rings and a 87-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, we can use the work-energy principle. The work-energy principle states that the work done on an object is equal to its change in kinetic energy.

First, let's find the initial kinetic energy of the fireman.

The fireman starts from rest, so the initial velocity is 0 m/s. Therefore, the initial kinetic energy is:

KE1 = 1/2 * m * v1^2
= 1/2 * 87 kg * (0 m/s)^2
= 0 J

Next, let's find the final kinetic energy of the fireman.

The final velocity of the fireman is 1.3 m/s. Therefore, the final kinetic energy is:

KE2 = 1/2 * m * v2^2
= 1/2 * 87 kg * (1.3 m/s)^2
= 73.18 J

Since the fireman is sliding down the pole, the work done against friction is negative because the force of friction acts in the opposite direction of the motion.

Therefore, the work done against friction is:

W_friction = - (KE2 - KE1)
= - (73.18 J - 0 J)
= - 73.18 J

Now, we can use the definition of work to find the magnitude of the frictional force:

W_friction = F_friction * d

where F_friction is the magnitude of the frictional force and d is the distance over which the force is applied.

We know the distance (d) is 3.9 m. Plugging this value into the equation, we can solve for the magnitude of the frictional force:

- 73.18 J = F_friction * 3.9 m

F_friction = - 73.18 J / 3.9 m
= - 18.77 N

Since the problem asks for the magnitude of the frictional force, the negative sign indicates that the frictional force is acting in the opposite direction of the motion. Therefore, the magnitude of the kinetic frictional force exerted on the fireman as he slides down the pole is approximately 18.77 N.

The frictional heat loss F*X equals the loss of mechanical energy

M g H - (1/2)M*Vfinal^2 = F*X

M cancels out Solve for F

H = 3.9 m
g = 9.8 m/s^2
Vfinal = 1.3 m/s