(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A firefighter who weighs 712 N slides down a vertical pole with an acceleration 3 m/s^{2}, directed downward. What are the (a) magnitude and (b) direction (up or down) of the vertical force on the firefighter from the pole and the (c) magnitude and (d) direction (up or down) of the vertical force on the pole from the firefighter?

2. Relevant equations

Newton's Second Law: F_{net}= ma

Newton's Third Law: F_{1}+ F_{2}= 0

3. The attempt at a solution

I know that the magnitude of the force on the pole from the firefighter will be the same as the force on the firefighter from the pole, but I'm having trouble implementing this to Newton's Second and Third Laws.

(a)

Let [itex]\textit{F}_{P}[/itex] be the vertical force on the firefighter from the pole.

Let [itex]\textit{W}_{F}[/itex] be the weight of the firefighter.

Let [itex]\textit{m}_{F}[/itex] be the mass of the firefighter.

[itex]\textit{m}_{F} = \frac{W_F}{9.8}\textit{ = 72.6531 kg}[/itex]

[itex]\sum\textit{F}_{y} = \textit{F}_{P}\textit{ - W}_{F}\textit{ = m}_{F}\textit{ a}_{y}\textit{ = }\textit{(72.6531 kg)(-3}\frac{m}{s^2}\textit{) + (712 N) = }[/itex][itex]\textit{494.0408 N}[/itex]

This answer is correct according to the text.

(b) Up, to resist the net downward acceleration.

Also correct according to the text.

(c) Now this is where I don't know how to implement the equations properly and visualize the diagram for forces.

First, I tried identifying all the forces on the body of interest; the pole. Since in part (a) I identified all the forces acting on the firefighter, I chose to identify all the forces acting on the pole.

With this, I reasoned that [itex]\textit{W}{_F}[/itex] acts on the pole in the downward direction, while the frictional force [itex]\textit{F}{_f}[/itex] acts upward on the pole.

Since the net acceleration of the body (the pole) was 0, I put [itex]\sum\textit{F}{_y}\textit{ = F}{_f}\textit{ - W}{_F = 0}[/itex]

This is wrong according to the text, but I also feel that I'm missing a key idea for this problem. I just don't know what :/

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# Newton's 3rd Law - Firefighter slides down a pole

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