Starting from rest, a 93-kg firefighter slides down a fire pole. The average frictional force everted on him by the pole has a magnitude of 710 N, and his speed at the bottom of the pole is 3.2 m/s. How far did he slide down the pole?
What equation do you use to determine this.
M*g = 93 * 9.8 = 911.4 N. = Wt. of firefighter.
Mg-Fk = M*a.
911.4 - 710 = 98*a, a = ?.
V = Vo^2 + 2a*d.
3.2 = 0 + 2a*d, d = ?.
To determine the distance the firefighter slides down the pole, you can use the work-energy principle. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the frictional force on the firefighter is converted into his kinetic energy at the bottom of the pole.
The equation you can use to solve for the distance is:
Work = Change in Kinetic Energy
The work done by the frictional force is equal to the magnitude of the force multiplied by the distance the firefighter slides down the pole:
Work = Force x Distance
The change in kinetic energy can be expressed as the final kinetic energy minus the initial kinetic energy:
Change in Kinetic Energy = (1/2) * Mass * (Final Velocity^2 - Initial Velocity^2)
Since the firefighter starts from rest, the initial velocity is 0, and the equation simplifies to:
Change in Kinetic Energy = (1/2) * Mass * Final Velocity^2
By equating the work done by the frictional force to the change in kinetic energy, the equation becomes:
Force x Distance = (1/2) * Mass * Final Velocity^2
Rearranging the equation to solve for distance, you get:
Distance = (Force x Distance) / ((1/2) * Mass * Final Velocity^2)
Substituting the given values:
Distance = (710 N * Distance) / ((1/2) * 93 kg * (3.2 m/s)^2)
This is a quadratic equation, and you can solve it to find the distance the firefighter slides down the pole.