Center of Mass!

vinny380

Question: Three cubes of sides l, 2l, and 3l are placed next to one another (in contact) with their centers along a straight line and the l=2l cube in the center. What is the position, along the line, of the CM of this system? Assume the cubes are made of the same uniform material.

My reasoning: So the equation for CM= M1XI +M2X2 + M3X3/ TM ... where M= mass, and X= distance ....So M(l +2l +3l)/3m = CM
M(6L)/3m = 2L
So, I got the center of Mass is 2L

I dont think my answer is correct, and even if my approach is correct. It is labeled a pretty easy problem, but I get really confused with problems without numbers. Also, I am not sure if you can conclude the total mass is 3M considering that means all the cubes would have to be the same mass .... and I also do not know what the question maker meant when he wrote the l=2l cube in the center .....

Please help!

radou

The coordinates X1, X2, and X3 are the coordinates of the center of mass of each cube. So, all you have to do is place the origin wherever you want and start to calculate. If you place the origin at the beginning of the first cube, then X1 = 0.5 L, and so on..

vinny380

radou ... thanks for the help but i am still confused.... how would you find the total mass of the cubes??

radou

Well, since the cubes are made of the same uniform material, you may assume the density of the cubes is equal. You know the volume, so, you can calculate the mass.

vinny380

finding the volume is easy , but how would you go about finding the density? is it simply a known value?

radou

Yes, call it [tex]\rho[/tex] or something. It will cancel out in the further calculation.

geoffjb

A diagram might help.

center-of-mass.png

vinny380

is the answer 3.08Lo (thats what i got) ???

radou

According to my calculation, it's 3.83L. But I may be wrong. Nevertheless, it's important you understand the principle.

vinny380

yeaaa... i just did it again and got 3.83L ..... but radou, how does that make sense??

radou

What exactly do you mean?

vinny380

well........if the center of mass is 3.83L .... then wouldnt the center of mass be out of the object given (which is impossible)?

radou

No it wouldn't, because the total length of the object is L + 2L + 3L = 6L.

vinny380

thanks radou!!!!!!!!!!!!