An 83-kg fireman slides down a fire pole. He holds the pole, which exerts 500-N steady resistive force on the fireman. At the bottom he slows to a stop in 0.49 m by bending his knees. Determine the acceleration of the fireman while sliding down the pole.
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To determine the acceleration of the fireman while sliding down the pole, we can use Newton's second law of motion. Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Step 1: Identify the given values:
- Mass of the fireman (m) = 83 kg
- Resistive force (Fres) = 500 N
- Stopping distance (d) = 0.49 m
Step 2: Calculate the net force acting on the fireman:
The net force acting on the fireman is equal to the difference between the resistive force and the force exerted by the fireman. Since the fireman is sliding down the pole, the force exerted by the fireman can be considered negligible. Thus, the net force can be calculated as:
Net force (Fnet) = Resistive force (Fres)
Step 3: Calculate the acceleration of the fireman:
Using Newton's second law, we can rearrange the formula to solve for acceleration (a):
Fnet = m * a
Substituting the values we know:
Fres = m * a
500 N = 83 kg * a
Step 4: Solve for acceleration:
Divide both sides of the equation by the mass of the fireman:
a = fres / m
a = 500 N / 83 kg
a ≈ 6.02 m/s^2
Therefore, the acceleration of the fireman while sliding down the pole is approximately 6.02 m/s^2.