Calculating Maximum Weight on a Tipping Table with a Cat: Torque Analysis

In summary, the image provided shows a problem with a cat sitting on a table and the solution to previous problems. The equation used for this problem is net torque = 0 and the attempt at solving it involved setting the axis of rotation at the bottom of the table and considering the torque due to downward and upward forces. After rearranging the equation, the final answer is Wmax = Wv(1 - X/Lx - Y/Ly). However, after realizing that the distance of the cat from the axis of rotation was not included, the attempt was redone and the final answer was Wmax = 0, taking into account the downward force exerted by the cat on the table.
  • #1
henry3369
194
0

Homework Statement


http://imgur.com/dMw79w1

The image contains the problem as well as the answers to the previous problems.

Homework Equations


Net torque = 0

The Attempt at a Solution


First, I set the axis of rotation to be the bottom of the table (where it goes through Fx and F0)
τdue to downward forces = τdue to upward forces
τvase + τtable + τcat = τdue to Fy (Fy (the solution to Fy is in the image)
WvY + WtLy/2 + WmaxLy = Wt/2 + WvY/Ly

Rearrange for Wmax:
Wmax = Wt/2Ly + WvY/Ly2 - WvY/Ly - Wt/2

The answer to the question is:
Wmax = Wv(1 - X/Lx - Y/Ly)

I don't know how to obtain this answer from my answer above.
 
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  • #2
It seems that I forgot to include the distance the cat is from the axis of rotation (Ly). After including it, I got Wmax = 0.
 
  • #3
So here it the attempt once again:
WvY + WtLy/2 + WmaxLy = (Wt/2 + WvY/Ly)(Ly)

Rearranging for Wmax:
WmaxLy = (Wt/2 + WvY/Ly)(Ly) - WvY - WtLy/2
Wmax = Wt/2 + WvY/Ly - WvY/Ly - Wt/2
Wmax = 0 N
 
  • #4
henry3369 said:
So here it the attempt once again:
WvY + WtLy/2 + WmaxLy = (Wt/2 + WvY/Ly)(Ly)

Rearranging for Wmax:
WmaxLy = (Wt/2 + WvY/Ly)(Ly) - WvY - WtLy/2
Wmax = Wt/2 + WvY/Ly - WvY/Ly - Wt/2
Wmax = 0 N
The upward forces were calculated in the absence of a cat.
 
  • #5
haruspex said:
The upward forces were calculated in the absence of a cat.
The cat exerts a downward force on the table though (the weight), which is shonw by WmaxLy
 
  • #6
henry3369 said:
The cat exerts a downward force on the table though (the weight), which is shonw by WmaxLy
Yes, but you used the expressions obtained for Fx etc. in the first part. There was no cat then. The forces will be different now.
 

FAQ: Calculating Maximum Weight on a Tipping Table with a Cat: Torque Analysis

What is torque and how does it relate to table tipping?

Torque is a measure of the force that causes an object to rotate around an axis. In the context of table tipping, torque is the force applied to the table by the participants, causing it to rotate or move in a certain direction.

How is torque measured in table tipping experiments?

Torque can be measured using a device called a torque sensor, which measures the force and direction of the applied torque. In table tipping experiments, the torque sensor is typically attached to the table to measure the force applied by the participants.

What factors influence the amount of torque in table tipping?

The amount of torque in table tipping can be influenced by various factors, such as the weight and position of the participants around the table, the shape and size of the table, and the surface on which the table is placed. The type and intensity of the force applied by the participants can also affect the torque.

How does torque play a role in determining the outcome of table tipping experiments?

In table tipping experiments, the amount of torque applied to the table determines its movement or tipping. If the participants apply a sufficient amount of torque, the table will tip in the direction of the applied force. However, if the torque is not strong enough, the table may not move or may move in a different direction.

Can torque be controlled in table tipping experiments?

Yes, torque can be controlled to a certain extent in table tipping experiments. The amount and direction of torque can be manipulated by changing the variables mentioned earlier, such as the weight and position of the participants, the shape and size of the table, and the type of force applied. However, there are also factors that cannot be controlled, such as external forces or interferences, which may affect the outcome of the experiment.

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