## Equation of Two Masses Of Center of Gravity

### Tae Yeong Kim (view profile)

on 23 Jun 2013

I am trying to calculate the limits (range) of the center of gravity of two masses (boxes) when there is a force that hit the masses.

Above is the free body diagram of the two masses, and the equation; however, how would I convert this to Matlab compatible equation or code?

I will appreciate all the answers

Roger Stafford

### Roger Stafford (view profile)

on 23 Jun 2013

Calculating the center of gravity for the two boxes in your diagram should be a matter of simple geometry if their densities are uniform, given their dimensions, relative positions, and the angle phi. In what way do you see a "range" of possible values for this?

As to the effect on the boxes of the impulse force you depict, you need more than their center of gravity to determine that. You also need their moment of inertia, since there is a torque involved.

Tae Yeong Kim

### Tae Yeong Kim (view profile)

on 23 Jun 2013

Thank you for your effort, and what kind of equation would you use to calculate the c.g. with the moment of inertia given?

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### Roger Stafford (view profile)

on 23 Jun 2013
Edited by Roger Stafford

### Roger Stafford (view profile)

on 23 Jun 2013

Let the lower box have width a and height b, and for the upper box width c and height d. Let e be the amount the upper box is offset from the right edge of the lower box. Assuming the lower left corner of the lower box is the coordinate origin and assuming uniform densities, the centers would be:

``` c1 = [a/2;b/2]; % c.g. before rotation by phi
c2 = [e+c/2;b+d/2];
R = [cos(phi),-sin(phi);sin(phi),cos(phi)]; % rotation matrix
c1 = R*c1; % c.g. after rotation by phi
c2 = R*c2;```

You still haven't said where there is any "range" involved.

The centers of gravity don't depend on the moment of inertia. The effect of the impulse force on the boxes does.

The moment of inertia computation will also have to involve a, b, c, d, and e. I'll leave that one to you.

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