Zero Torque and Static Equilibrium

[dalitwil]

Question: A 0.110kg remote control 21.0 cm long rests on a table with a length L overhanging its edge. To operate the power button on this remote requires a force of 0.365 N. How far can the remote control extend beyond the edge of the tabel and still not tip over when you press the power button? Assuming the mass of the remote is distributed uniformly, and that the power button is on the end of the remote overhanging the table.

I understand that i need to set both my torque and force equal to zero. My main problem is trying to figure out where else i have force vectors, besides the obvious one pointing down to the power button. Would the force at the other end of the remote be pointing down as well as to keep it balanced?

The answer is 7.85cm, any help to starting this problem would be greatly appreciated!

 

[krusty the clown]

Assuming the mass of the remote is distributed uniformly, and that the power button is on the end of the remote overhanging the table.

You have two forces downwards, pusing the power button and the force due to gravity that you can place at the center of mass which is the center of the remote.

 

[dalitwil]

I still can't figure it out:(

 

[robphy]

Might there be a third force in the problem?
Can you draw the Free-Body Diagram of the remote?

 

[dalitwil]

Thats my problem, I can't figure out what/where the third force comes into play, however, i am pretty sure that there is a third force...

My FBD would consist of F1 pointing downwards at the end of the remote (the end not resting on the table), possibly a force of mg pointing upwards at the center of mass? And then another force of mg pointing downwards at the other end of the remote.

This isn't working out thus far. I suspect that I am on the right path, but may be mixed up?

 

[robphy]

For each force on the remote, what is the object pushing or pulling on the remote?
This might help you identify the forces and roughly determine the direction of each force.

 

[krusty the clown]

There are only the two forces, gravity and the pushing of the button. When you draw the FBD there is the force of 0.356N straight down at one end, then with the force of gravity you draw it at the center of mass (center of the remote) also straight down.

To have the remote hang off the table the maximum distance your net torque must equal zero. Btw, for this problem you don't need to worry about setting the net force equal to zero (the normal force takes care of this).

When you set up the net torque equation it should look something like this

(force on button)(length of overlap "L")-(force of gravity)(0.105m-L)=0

Then, simply solve for L.

I made the FBD with paint, but I can't figure out how to make it small enough to post it here. If you would like to see it I could email it to you.

Hope this helps.

Erik