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ShawnBradley · 2006-03-28 02:22:21

A 33 kg round table is supported by three legs placed equal distances apart on the edge. What minimum mass, placed on the table's edge, will cause the table to overturn?

Last edited by ShawnBradley (2006-04-01 02:52:45)

Chris · 2006-04-07 23:05:36

I've added an upload feature, so now you should be able to provide us with a free-body diagram.

This is also a rotational dynamics problem with torques.

ShawnBradley · 2006-04-10 01:10:02

No diagram came with the problem, so should I just make one looking down on a circular table?

Chris · 2006-04-12 03:56:40

You have to draw your own diagram! That should be the first thing you are taught -- DRAW A PICTURE.

Hmmmm. This is a non-trivial problem.

Here is the picture I have in mind:

Uploaded Images

Chris · 2006-04-12 16:53:15

I don't know why the thumbnail looks like a black box!

Click on the black box and the figure I'm talking about will show full size.

ShawnBradley · 2006-04-13 01:50:19

So what should you calculate the torque about? The center of the circle?

Chris · 2006-04-13 02:15:19

Nope. You have to calculate the torque about the fulcrum, which is the intersection of r and the line that connects the two legs.

The only way I can see to do this properly is with calculus, though. You can't quite consider the mass of the table to be concentrated at the center of mass, since some of the table will hang over its support base.

If you do consider the table's mass to be concentrated at center of mass, then the problem is easier. Sum the torques and set equal to zero. Solve for object mass.

ShawnBradley · 2006-04-14 03:48:01

Chris wrote:
Nope. You have to calculate the torque about the fulcrum, which is the intersection of r and the line that connects the two legs.

It looks like r is a line that connects the two legs. There are two r's in your drawing, so I am not really sure which you are referring to.

Chris · 2006-04-14 17:27:17

Opps. There is an extra r in there! I'm refering to the vector r that bisects the line between the two legs. A little geometry will tell you the distance between the legs with respect to r.

I'm also making the assumption that the legs are placed at the exact edge of the table. (I have to if the problem is to be solvable with the info given.)

ShawnBradley · 2006-04-16 00:53:28

Chris wrote:
Nope. You have to calculate the torque about the fulcrum, which is the intersection of r and the line that connects the two legs.

How do you know that this is the fulcrom?

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#1 2006-03-28 02:22:21

Equilibrium Problem

#2 2006-04-07 23:05:36

Re: Equilibrium Problem

#3 2006-04-10 01:10:02

Re: Equilibrium Problem

#4 2006-04-12 03:56:40

Re: Equilibrium Problem

#5 2006-04-12 16:53:15

Re: Equilibrium Problem

#6 2006-04-13 01:50:19

Re: Equilibrium Problem

#7 2006-04-13 02:15:19

Re: Equilibrium Problem

#8 2006-04-14 03:48:01

Re: Equilibrium Problem

Chris wrote:

#9 2006-04-14 17:27:17

Re: Equilibrium Problem

#10 2006-04-16 00:53:28

Re: Equilibrium Problem

Chris wrote:

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