Equilibrium and Torque of a table

In summary: Now substitute for the weights of the table and vase and the distances X and Lx in terms of Wv, Wt, Ly and Lx.
  • #1
wootman23
13
0

Homework Statement


The top view of a table, with weight Wt, is shown in the figure. (Figure 1) The table has lost the leg at (Lx, Ly), in the upper right corner of the diagram, and is in danger of tipping over. Company is about to arrive, so the host tries to stabilize the table by placing a heavy vase (represented by the green circle) of weight Wv at ( X, Y). Denote the magnitudes of the upward forces on the table due to the legs at (0, 0), (Lx, 0), and (0, Ly) as F0, Fx, and Fy, respectively.

Find Fx, the magnitude of the upward force on the table due to the leg at (Lx, 0).
Express the force in terms of Wv, Wt, X, Y, Lx, and/or Ly. Note that not all of these quantities may appear in the answer.http://session.masteringphysics.com/problemAsset/1010953/19/MFS_st_0_a.jpg

Homework Equations


ƩTorque = 0

The Attempt at a Solution


I have no idea where to begin. The hint says to "find the y-component of the torque", but I can't find torque cause I don't know where the pivot point (axis of rotation) is.
Please do not answer the question for me, but rather help me understand what to do.
 
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  • #2
wootman23 said:

Homework Statement


The top view of a table, with weight Wt, is shown in the figure. (Figure 1) The table has lost the leg at (Lx, Ly), in the upper right corner of the diagram, and is in danger of tipping over. Company is about to arrive, so the host tries to stabilize the table by placing a heavy vase (represented by the green circle) of weight Wv at ( X, Y). Denote the magnitudes of the upward forces on the table due to the legs at (0, 0), (Lx, 0), and (0, Ly) as F0, Fx, and Fy, respectively.

Find Fx, the magnitude of the upward force on the table due to the leg at (Lx, 0).
Express the force in terms of Wv, Wt, X, Y, Lx, and/or Ly. Note that not all of these quantities may appear in the answer.


http://session.masteringphysics.com/problemAsset/1010953/19/MFS_st_0_a.jpg


Homework Equations


ƩTorque = 0


The Attempt at a Solution


I have no idea where to begin. The hint says to "find the y-component of the torque", but I can't find torque cause I don't know where the pivot point (axis of rotation) is.
Please do not answer the question for me, but rather help me understand what to do.

If the table is stablized then it's not rotating around any axis. So the torques around any axis must balance. Picking the y-axis as the axis of rotation is handy for your problem. Do you see why?
 
  • #3
Dick said:
If the table is stablized then it's not rotating around any axis. So the torques around any axis must balance. Picking the y-axis as the axis of rotation is handy for your problem. Do you see why?

Still not seeing it. Don't I need to choose a pivot point to find Torque? If I choose this pivot point to be at (0,0) then I don't need to worry about the force of the leg at (0,0)? Is that what you want me to see?
 
  • #4
wootman23 said:
Still not seeing it. Don't I need to choose a pivot point to find Torque? If I choose this pivot point to be at (0,0) then I don't need to worry about the force of the leg at (0,0)? Is that what you want me to see?

Close. But, no, you don't have to pick a pivot point. Pick a rotation axis. If the table is stablized then it's not rotating around the y-axis. In that case the forces at (0,0) AND (0,Ly) exert no torque around the y-axis. Do you see what the hint is getting at now?
 
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  • #5
Dick said:
Close. But, no, you don't have to pick a pivot point. Pick a rotation axis. If the table is stablized then it's not rotating around the y-axis. In that case the forces at (0,0) AND (0,Ly) exert no torque around the y-axis. Do you see what the hint is getting at now?

So then the only forces that exert torque are W
, W[vase], and F[x].

I've always used a pivot point for torque, but what I think you are getting at is that you can use a "pivot axis" in about the same way, so...

(F[x] * Lx) - (W
* Lx/2) - (W[vase] * X) = 0

F[x] = (W
/2) + ((W[vase] * X) / Lx)

Thank you!
 
  • #6
wootman23 said:
So then the only forces that exert torque are W
, W[vase], and F[x].

I've always used a pivot point for torque, but what I think you are getting at is that you can use a "pivot axis" in about the same way, so...

(F[x] * Lx) - (W
* Lx/2) - (W[vase] * X) = 0

F[x] = (W
/2) + ((W[vase] * X) / Lx)

Thank you!


Right! If the table isn't rotating then the sum of torques around any pivot point must be zero. But so must the torques around any pivot axis. The y-axis is just a useful one to chose.
 

1. What is equilibrium?

Equilibrium is a state in which all the forces acting on an object are balanced, resulting in no net force and no acceleration.

2. How does equilibrium apply to a table?

Equilibrium applies to a table when the sum of all the forces acting on the table, including the weight of the table and any objects placed on it, is equal to zero. This results in a stable and stationary table.

3. What is torque?

Torque is a measure of the rotational force applied to an object, calculated by multiplying the force by the distance from the point of rotation.

4. How does torque affect a table?

When objects are placed on a table, the weight of those objects creates a torque that acts on the table. This torque can cause the table to rotate or tip over if it is not balanced by an equal and opposite torque from the table's legs.

5. How can you calculate the torque of a table?

The torque of a table can be calculated by multiplying the weight of the objects on the table by the distance from the point of rotation (usually the table's legs). This can be expressed mathematically as T = F x d, where T is torque, F is force, and d is distance.

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