# Translational equillibrium calculation when forces acting not at COG

1. Dec 1, 2011

### bubsy

I have a question about translational equilibrium.

Consider a 3m by 3m sheet on the x-y plane. The center of mass is at the origin.

Force-1 of 10 N acts on the top left corner of the sheet and points left.

Force-2 of 20 N acts on the bottom right corner of the sheet and is directed downwards.

Force-3 of yet to be determined magnitude and direction, acts on the center of mass. I need to find the magnitude and direction of this force that will result in the sheet being in translational equillibrium.

I can do this problem if Force-1 and Force-2 acted on the center of mass, but in this case the first 2 forces act on corners of the sheet.

Does it matter that the first 2 forces are not acting on the center of mass? Is the problem equivalent if I promote the first 2 forces to act on the center-of-mass?

Thanks

2. Dec 2, 2011

### JHamm

In terms of translation it doesn't matter where the forces act, the only thing that will change if you apply your force on a different part of the shape is the amount of rotation so for this problem you can just pretend they are all acting on the COM :)

3. Dec 2, 2011

### anigeo

jhamm is absolutely right.in translational motion you can just always assume that the forces act on the COM.
proceed and you will find that the force F3 must act on the COM at an angle of 26.56° with the vertical and a magnitude of 10√5 N.