Question

Responding to an alarm, a 784-N firefighter slides down a pole to the ground floor, 3.0 m below. The firefighter starts at rest and lands with a speed of 4.5 m/s .

Find the average force exerted on the firefighter by the pole.

Answer 1

In Physics, the average force exerted on a sliding firefighter by the pole is found using the work-energy principle and is calculated to be 514.8 N in the opposite direction of motion.

Step-by-step explanation:

The subject of this question is Physics, specifically related to the concepts of mechanics and forces. To calculate the average force exerted on the firefighter by the pole, we must employ the work-energy principle which connects the work done by forces to the change in kinetic energy.

Step-by-Step Solution:

Calculate the work done by gravity as the firefighter slides down: Work by gravity (W_g) = m*g*h, where m is the mass, g is the acceleration due to gravity (9.81 m/s2), and h is the height.

1. Calculate the change in kinetic energy: Change in kinetic energy (ΔKE) = 0.5 * m * v2 - 0, as the firefighter starts at rest.
2. The work done by the pole and gravity must equal the change in kinetic energy: W_g + Work by pole (ΔKE) = ΔKE. We can solve for the work done by the pole.
3. Divide the work done by the pole by the distance to find the average force exerted by the pole (since Work = Force * Distance).

To find the mass (m) of the firefighter, we divide the weight by gravity: m = 784 N / 9.81 m/s2 = 80 kg approximately. Now we can start plugging in the numbers.

W_g = 80 kg * 9.81 m/s2 * 3.0 m = 2354.4 J

ΔKE = 0.5 * 80 kg * (4.5 m/s)2 = 810 J

Subtracting change in kinetic energy from the work by gravity gives us the work by the pole: 2354.4 J - 810 J = 1544.4 J. The average force exerted by the pole is then 1544.4 J / 3.0 m = 514.8 N. The direction of this force is upwards, opposing gravity and the motion of the firefighter.