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## Homework Statement

Where it says ''from the bottom'' I assumed it's referring to a distance along the ladder. So:

Data:

##w_{ladder} = 98.0\ N##

##w_{person} = 686\ N##

##d_1 = 4\sqrt(2)\ m##

##d_2 = 1\ m##

##d_3 = 2/3\ m##

## Homework Equations

##\sum \tau = 0##

##\sum F = 0##

## The Attempt at a Solution

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Diagram:

I chose my pivot point to be the bottom of the ladder. Hence, torques due to normal force ##N## and friction ##f## are zero. ##ccw## is positive and ##cw## is negative.

##0 = w_pd_2 + w_ld_3 - F_wd_1##

##F_wd_1 = w_pd_2 + w_ld_3##

##F_w = \frac{w_pd_2 + w_ld_3}{d_1} = \frac{686\ N \cdot 1.00\ m + 98.0\ N \cdot 2/3\ m}{4\sqrt{2}\ m} = 133\ N##

##F_w = f = 133\ N##

Then:

##N = w_p + w_l = 686\ N + 98.0\ N = 784\ N##

The force at the top of the ladder is just ##133\ N##.

The force at the bottom is ##\small{\sqrt{N^2+ f^2} = \sqrt{ (784\ N)^2+ (133\ N)^2} = 795\ N}##.

**Doubt:**this magnitude, whether it's correct or not, acts along the ladder, right? (as a tension would?).

The textbook's solutions are ##126\ N## and ##751\ N##, respectively. It seems I haven't missed anything, so I don't know where the mistake is.

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