Torque and static equilibrium beam with weights

[matermultorum]

Homework Statement

The answer is to be given in terms of L and w. The picture shows a beam of weight w and various blocks on it also each of weight w. It also shows the gravitational force acting downward on the center of gravity of the beam. The beam rests on a triangular pivot point.

2 blocks of weight w are stacked and sit 2L to the left of the pivot. 1 block sits 1L to the right of the pivot. The center of gravity force is also shown at 1L to the right of the pivot. Another block sits at 3 to the right of the pivot. I am to state why the beam is or is not in equilibrium.

Homework Equations

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The Attempt at a Solution

The answer key shows that it is in equilibrium. I don’t understand why it is. To me it seems that the spot that has the center of gravity will actually have a force of 2w at the center of gravity-one for the block and one for the beam. This gives -3wL + -2wL +4wL or a net torque of 1wL in the clockwise direction. Where am I thinking incorrectly about this? (I have only a small hope that I am right and the answer key is wrong).

Thank you!

 

[SteamKing]

Why haven't you written the equations of static equilibrium to determine whether the beam is in equilibrium or not?

 

[matermultorum]

Why haven't you written the equations of static equilibrium to determine whether the beam is in equilibrium or not?

I thought that is what this is: -3wL + -2wL +4wL=-1wL and since it isn't zero, it isn't in equilibrium.

 

[matermultorum]

My EE degree son is home for the weekend and he thinks that I am right and the key is wrong. If you disagree please post.

 

[Doc Al]

This gives -3wL + -2wL +4wL or a net torque of 1wL in the clockwise direction. Where am I thinking incorrectly about this?

Assuming I understand your description of the problem, you are correct and the answer key is wrong.

 

[matermultorum]

Thank you!