Torque and static equilibrium beam with weights

In summary, the problem involves a beam of weight w, with various blocks also weighing w, resting on a triangular pivot point. 2 blocks are stacked 2L to the left of the pivot, 1 block sits 1L to the right, and another block sits 3L to the right. The question is whether the beam is in equilibrium or not. The equations of static equilibrium suggest that the beam is not in equilibrium, with a net torque of 1wL in the clockwise direction. However, the answer key shows that the beam is in equilibrium, which may be incorrect according to the poster's EE degree son.
  • #1
matermultorum
7
0

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!
 
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  • #2
Why haven't you written the equations of static equilibrium to determine whether the beam is in equilibrium or not?
 
  • #3
SteamKing said:
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.
 
  • #4
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.
 
  • #5
matermultorum said:
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.
 
  • #6
Thank you!
 

Related to Torque and static equilibrium beam with weights

1. What is torque and how is it related to static equilibrium?

Torque is a measure of the amount of rotational force applied to an object. It is related to static equilibrium because in order for an object to be in equilibrium, the sum of all torques acting on it must be zero.

2. How do you calculate torque in a beam with weights?

To calculate torque in a beam with weights, you will need to multiply the weight of each object by its distance from the fulcrum or pivot point. Then, add up all of these individual torques to find the total torque acting on the beam.

3. What is the formula for finding the center of mass of a beam with weights?

The formula for finding the center of mass of a beam with weights is to take the sum of the product of each weight and its distance from the pivot point, and divide it by the total weight of the beam. This will give you the distance from the pivot point to the center of mass.

4. How does the distribution of weights affect the static equilibrium of a beam?

The distribution of weights on a beam can greatly affect its static equilibrium. As a general rule, the heavier weights should be placed closer to the pivot point to maintain balance and prevent the beam from tipping over.

5. How can I ensure that a beam with weights is in static equilibrium?

To ensure that a beam with weights is in static equilibrium, you can use the formula for calculating torque to check that the sum of all torques acting on the beam is equal to zero. You can also visually check that the beam is not tipping or rotating in any direction.

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