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pixietree

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## Homework Statement

A horizontal pole is made of 8 pieces, 1 meter apart each. Forces that do not act at the ends are shown in the picture.

The pole does not rotate, and weighs 20N.

a. What is the sum of forces applied on the pole?

b. Where is it applied?

c. What are the forces at the ends of the pole?

## Homework Equations

$$ \sum_{k=1}^{n} x_nF_n = 0 $$

Equilibrium point with coordinate k must suffice $$k=\frac {\sum_{k=1}^{n} x_nF_n}{\sum_{k=1}^{n} F_n}$$, where F_i is the i'th force and x_i is its coordinate relative to the leftmost point (taking right to be positive direction), given non-zero sum of forces

## The Attempt at a Solution

Let $$\mathbf N_1, \mathbf N_2$$ be the forces applied on the pole at the left, right ends accordingly. I will take the right as shown in the picture to be the positive direction.

Relative to the leftmost point of the pole, the sum of torques is zero because the pole does not rotate.

Hence $$0*N_1-1*10+2*20-7*30+8N_2=0$$, meaning $$\mathbf N_2\ = 22.5\mathbf y\ N $$.

Relative to the rightmost point, the sum of torques is also zero for the same reason.

Hence $$(-8)*N_1+(-7)*(-10)+(-6)*20+(-1)*(-30)=0$$, meaning $$ \mathbf N_1\ = -2.5\mathbf y\ N$$.

And this is where I got stuck - the answer in the book clearly says there is a unique point where the forces may be regarded as being applied there, but the sum of forces is zero if my attempt is right. Probably it was me, so I do not understand what I got wrong.

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