Torque and Equilibrium question

In summary, the mass labeled "?" can be found by equating the two torque acting on the pivot due to the two masses. By setting the sum of the torques to 0, we can find that the mass is equal to 3M/2.
  • #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
 
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  • #2
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
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.
 
  • #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
You wrote the eqn correct

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

1. What is torque and how is it measured?

Torque is a measure of the twisting force applied to an object. It is calculated by multiplying the force applied by the distance from the point of rotation to the point where the force is applied. The unit of torque is Newton-meters (Nm).

2. What is the difference between clockwise and counterclockwise torque?

Clockwise torque produces a clockwise rotation, while counterclockwise torque produces a counterclockwise rotation. This is determined by the direction in which the force is applied relative to the direction of the rotation.

3. How does torque affect rotational equilibrium?

In order for an object to be in rotational equilibrium, the net torque acting on it must be zero. This means that the clockwise and counterclockwise torques must be balanced. If the torques are not balanced, the object will rotate in the direction of the greater torque.

4. What is the principle of moments?

The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments must equal the sum of the counterclockwise moments. This is another way of saying that the net torque must be zero.

5. How can torque be increased or decreased?

Torque can be increased by increasing the force applied or by increasing the distance from the point of rotation to the point where the force is applied. It can be decreased by decreasing the force or by decreasing the distance. Additionally, changing the direction of the force can also affect the torque.

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