Torque and Equilibrium question

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    Equilibrium Torque
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A uniform wooden board of mass 10M is in static equilibrium with two blocks, one of mass M positioned L/2 from the pivot and another block of unknown mass hung at L/3. The discussion revolves around finding the unknown mass, denoted as "?". Participants clarify that the torques created by each mass must be equal for the system to maintain equilibrium. The correct equation for torque is established as (Mg)(L/2) = x(L/3), leading to the conclusion that the unknown mass is 3M/2. The conversation emphasizes the importance of equating torques to solve for the unknown mass in static equilibrium scenarios.
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Homework Statement


A uniform wooden board of mass 10 M is held up by a nail hammered into a wall. A block of mass M rests L/2 away from the pivot. Another block of a certain mass (?) is hung a distance L/3. The system is in static equilibrium.

What is the measure of the mass labeled "?"


Homework Equations


T=(D)(F)



The Attempt at a Solution


I know that the answer is 3M/2, but I just cannot find the thought process behind the answer. I tried to set up an equation so that T=(M)(L/2)= (M)(L/3), to try and find the answer, but obviously it isn't correct. Could I use imaginary numbers for the Mass and the length to find a fake torque then find the mass when it's at equilibrium?

Please, someone help me at least get started, I really need the help
 
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write the two torque acting on pivot due to two masses
 
Sorry, but I don't really understand what you mean. Do I need to set them equal to each other?


So I tried to substitute in fake values and when I found both the torques, they equalled each other. I think I have the right work, but I thought that if the mass was closer to the center of mass it needed more torque.
 
Last edited:
Yes you need to equate them

If Στ=0 then α=0
which means that body is in rotational equilibrium

SPCPhysicss said:
but I thought that if the mass was closer to the center of mass it needed more torque.

I can't understand you.
 
Hmm I see, so the equation I should write would look like,

(Mg)(L/2)=x(L/3)?

I don't quite know what to do from there I assume you need to divide by a 2? and then somehow multiply the Mass by 3?
 
You wrote the eqn correct

Now just cancel L and take 3 to other side and you'll get ? = 3M/2
 
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