As a fireman of mass 80 kg slides down a pole, he experiences a complex interplay of forces that govern his motion. Gravity propels him downward, while friction between his body and the pole opposes his descent. Air resistance, though negligible, also exerts a small force on his body.
This analysis delves into the forces involved, their magnitudes and directions, and their impact on the fireman’s acceleration, speed, and energy conversion.
The frictional force acting on the fireman plays a crucial role in determining his acceleration and speed. It opposes his motion, dissipating energy and preventing him from accelerating indefinitely. The energy transformations that occur during his descent are also examined, with potential energy being converted into kinetic energy and friction dissipating energy as heat.
A Fireman of Mass 80 kg Slides Down a Pole
When a fireman of mass 80 kg slides down a pole, several forces act upon him. These forces include gravity, friction, and air resistance. Gravity pulls the fireman down the pole, while friction and air resistance oppose his motion.
Forces Involved
Gravityis the force that pulls the fireman down the pole. The magnitude of the gravitational force is given by:
Fg = m
g
where:
- Fg is the gravitational force in newtons
- m is the mass of the fireman in kilograms
- g is the acceleration due to gravity (9.8 m/s^2)
In this case, the gravitational force is:
Fg = 80 kg
9.8 m/s^2 = 784 N
Frictionis the force that opposes the motion of the fireman as he slides down the pole. The magnitude of the frictional force is given by:
Ff = μ
Fn
where:
- Ff is the frictional force in newtons
- μ is the coefficient of friction
- Fn is the normal force in newtons
The normal force is the force that the pole exerts on the fireman in a direction perpendicular to the pole. In this case, the normal force is equal to the weight of the fireman:
Fn = mg = 80 kg
9.8 m/s^2 = 784 N
The coefficient of friction between the fireman and the pole is typically between 0.2 and 0.3. In this case, we will use a coefficient of friction of 0.25.
Therefore, the magnitude of the frictional force is:
Ff = 0.25
784 N = 196 N
Air resistanceis the force that opposes the motion of the fireman as he moves through the air. The magnitude of the air resistance force is given by:
Fa = 0.5
- ρ
- v^2
- A
where:
- Fa is the air resistance force in newtons
- ρ is the density of the air in kilograms per cubic meter
- v is the velocity of the fireman in meters per second
- A is the cross-sectional area of the fireman in square meters
In this case, we will assume that the density of the air is 1.2 kg/m^3, the velocity of the fireman is 2 m/s, and the cross-sectional area of the fireman is 0.5 m^2.
Therefore, the magnitude of the air resistance force is:
Fa = 0.5
- 1.2 kg/m^3
- (2 m/s)^2
- 0.5 m^2 = 1.2 N
The direction of the air resistance force is opposite to the direction of the fireman’s motion.
Friction and Acceleration, A fireman of mass 80 kg slides down a pole
Friction affects the fireman’s acceleration and speed in several ways. First, friction reduces the net force acting on the fireman. The net force is the vector sum of all the forces acting on the fireman. In this case, the net force is:
Fnet = Fg
- Ff
- Fa
The net force is in the direction of the fireman’s motion. The magnitude of the net force is:
Fnet = 784 N
- 196 N
- 1.2 N = 586.8 N
Second, friction increases the time it takes for the fireman to reach the bottom of the pole. This is because friction reduces the fireman’s speed. The acceleration of the fireman is given by:
a = Fnet / m
In this case, the acceleration of the fireman is:
a = 586.8 N / 80 kg = 7.34 m/s^2
If there were no friction, the fireman’s acceleration would be 9.8 m/s^2. Therefore, friction reduces the fireman’s acceleration by 2.46 m/s^2.
Energy Conversion
As the fireman slides down the pole, his potential energy is converted into kinetic energy. Potential energy is the energy stored in an object due to its position or height. Kinetic energy is the energy stored in an object due to its motion.
The potential energy of the fireman at the top of the pole is given by:
PE = mgh
where:
- PE is the potential energy in joules
- m is the mass of the fireman in kilograms
- g is the acceleration due to gravity (9.8 m/s^2)
- h is the height of the pole in meters
In this case, the height of the pole is 10 meters. Therefore, the potential energy of the fireman at the top of the pole is:
PE = 80 kg
- 9.8 m/s^2
- 10 m = 7840 J
As the fireman slides down the pole, his potential energy is converted into kinetic energy. The kinetic energy of the fireman at the bottom of the pole is given by:
KE = 0.5
mv^2
where:
- KE is the kinetic energy in joules
- m is the mass of the fireman in kilograms
- v is the velocity of the fireman in meters per second
In this case, the velocity of the fireman at the bottom of the pole is 4 m/s. Therefore, the kinetic energy of the fireman at the bottom of the pole is:
KE = 0.5
- 80 kg
- (4 m/s)^2 = 640 J
Therefore, the fireman’s potential energy at the top of the pole is converted into kinetic energy at the bottom of the pole. The difference in energy is dissipated by friction.
Safety Considerations
There are several safety considerations that should be taken when sliding down a fire pole. First, the fireman should wear proper safety gear, including a helmet, gloves, and turnout gear. Second, the fireman should inspect the pole before sliding down to ensure that it is in good condition.
Third, the fireman should slide down the pole in a controlled manner, keeping his feet and legs close to the pole.
There are several potential hazards and risks involved in sliding down a fire pole. First, the fireman could fall off the pole if he is not careful. Second, the fireman could burn his hands or feet if the pole is hot.
Third, the fireman could injure his back or neck if he lands incorrectly at the bottom of the pole.
It is important for firemen to receive proper training on how to slide down a fire pole safely. Firemen should also practice sliding down the pole regularly to maintain their skills.
FAQ Corner
What safety precautions should be taken when sliding down a fire pole?
Firefighters should wear appropriate protective gear, including helmets, gloves, and turnout gear. They should ensure the pole is secure and free of obstacles, and they should slide down feet first, maintaining a firm grip on the pole.
What are the potential hazards and risks involved in sliding down a fire pole?
Potential hazards include falls, burns from friction, and injuries to the hands or wrists. Firefighters should be properly trained and should use caution when sliding down poles.
