I'm Stuck on Solving This - R2 Confuses Me

[Bookdigger]

Homework Statement

A 140 lb painter is standing on a uniform plank weighing 15 lbs. and of length 12 feet. It is resting on two supports 1.5 feet from each end, as shown below. How far to the right can he move without tipping the plank (give the distance from the end of the plank)

Relevant Equations

Tccw=Tcw

I tried solving this and realized that I have no idea what r2 is and I can't just insert an equation there

 

[haruspex]

Your diagram is hard to read, and I am not sure what some of your variables mean. Please define them.
I don’t understand how you get a torque equation with a term having a factor (M+m). The weights of those act at different offsets, not some common offset 'a' from somewhere.
Your diagram has the man between the supports. No risk of tipping there.

 

[Bookdigger]

Sorry about that. F1 and F2 are the forces pushing upwards from the supports, I added them together for my counterclockwise direction, which is where i got (M+m)g since F1=mg and F2=Mg. This is the actual diagram without any labelled forces

 

[Bookdigger]

I also just realized that I tried to solve this question using the wrong method. I thought that both supports should have forces but I just realized that if we're talking about the plank tipping then the first support should have no forces.
Sorry if I make no sense, the way I solve equations is weird.

 

[Steve4Physics]

... if we're talking about the plank tipping then the first support should have no forces.

In that case, is there some point about which you can take moments (torques) to make the problem simple?

 

[Bookdigger]

Yup, if the second support (N2) becomes the pivot point then it should make things easier

 

[Bookdigger]

Your diagram is hard to read, and I am not sure what some of your variables mean. Please define them.
I don’t understand how you get a torque equation with a term having a factor (M+m). The weights of those act at different offsets, not some common offset 'a' from somewhere.
Your diagram has the man between the supports. No risk of tipping there.

mg is the force of gravity pushing down on the plank, Mg is the person pushing down on the plank, r1 is the distance between mg and the pivot point, r2 is the distance between the person and the pivot point, a is the distance the person can walk without tipping the plank

 

[Lnewqban]

mg is the force of gravity pushing down on the plank, Mg is the person pushing down on the plank, r1 is the distance between mg and the pivot point, r2 is the distance between the person and the pivot point, a is the distance the person can walk without tipping the plank

That is a little too complicated.
Without that person on the plank, each support is holding half of 15 lbf.
Moments respect to the right support are balanced: CCW moment (15 lbf x 4.5 feet) and CW moment (7.5 lbf (reactive force of left support) x 9 feet).

Then, you place the140 lbf of that person on the right side of the right support.
How far that person can move toward the right before making that left reactive force disappear and breaking the balance of moments?

 

[Bookdigger]

I can understand it now, I also watched a youtube video solving a similar question so I think I'm good now, thank you though