A firefighter of mass 82 kg slides down a vertical pole with an acceleration of 3.4 m/s2 .
To solve this problem, we can use Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration (F = ma).
In this case, the vertical force acting on the firefighter is the gravitational force, which can be calculated by multiplying the mass of the firefighter (82 kg) by the acceleration due to gravity (9.8 m/s^2). Therefore, the gravitational force is F_gravity = (82 kg) * (9.8 m/s^2).
Since there is an additional vertical force due to acceleration, we need to find the net force. The net force can be calculated using the formula F_net = F_gravity - F_friction, where F_friction is the force opposing the motion.
Since the firefighter is sliding down the pole, we assume that the force of friction is acting in the opposite direction to the motion, so F_friction = -ma.
Now, we can substitute the given values into the equation:
F_net = F_gravity - F_friction
F_net = (82 kg) * (9.8 m/s^2) - (82 kg) * (3.4 m/s^2)
By simplifying this equation, we can find the net force acting on the firefighter as they slide down the pole.