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Torque and Equilibrium question

  • #1

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
 

Answers and Replies

  • #2
1,137
0
write the two torque acting on pivot due to two masses
 
  • #3
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:
  • #4
1,137
0
Yes you need to equate them

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

but I thought that if the mass was closer to the center of mass it needed more torque.
I cant understand you.
 
  • #5
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?
 
  • #6
1,137
0
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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