Clockwise or counterclockwise rotation about a fulcrum

[invadertak]

Homework Statement

The diagram shows a uniform plank of length 5m and weight 225N that rests horizontally on two supports, with 1.1 m hanging over the right support. To what distance x can a person who weighs 450 N walk on the overhanging part of the plank before it just begins to tip?

l-x-l

\0/
l
/\
_________________
^ ^
l-1.1m-l

Homework Equations

T=Fl
$$\Sigma$$ T = 0
$$\Sigma$$ F = 0

The Attempt at a Solution

Take upward direction as positive and clockwise direction of motion as positive
Name the leftmost fulcrum L and the right fulcrum R
Fy = F_L + F_R - F_Wplank - F_WPerson
Fy = 0
Thus F_L + F_R - 225N - 450 N = 0
Thus F_L = 675N - + F_R

This is where I get stuck. My equation kept boiling down to rubbish and when I checked the web for a solution, I found out I need to make the torque produced by Force L a negative number with respect to fulcrum R. However, won't the upward force of L produce a clockwise rotation? The rotation at R caused by force L is the only place that I seem to be messing up as other equations are exactly as the memo indicated. But I have taken clockwise to be positive (as the memo also indicated) and yet the memo says that my torque at L is negative.

 

[invadertak]

Sorry-one correction- F_L=675N - F_R

 

[nlightner]

I would like to clarify that the direction of rotation (clockwise or counterclockwise) is not determined by the direction we choose to be positive. It is determined by the direction of the force and the distance from the fulcrum. In this scenario, if we take clockwise direction as positive and consider the force from the left fulcrum L, the torque produced by this force will be negative as it is acting in the opposite direction of the clockwise rotation. This is why it is important to carefully consider the direction of forces and distances when solving for torque and equilibrium in a system. Therefore, in order to solve this problem correctly, we need to assign the direction of forces and distances carefully and consistently throughout the equations.