Solving for Center of Mass in a Bent Wire: xcm and ycm Values Explained

[squintyeyes]

A wire of uniform density is bent into the shape shown in the figure below.

The value of L is 0.740 cm. Answer the following questions assuming that the origin is at the bottom left corner.

What is the value of xcm?
cm

What is the value of ycm?
cm

Attempt
xcm = 2*.74 = 1.48 cm

ycm = .74 cm

I get the feeling that this is wrong.

 

[cronxeh]

First of all, treat this as 2 separate rods. Find the center of the vertical rod, and find a center of horizontal rod.

Now redraw this problem as a 2 particle problem, where each particle is located at the center of each rod. For the vertical rod, the center is at (0,L/2), and for horizontal rod the center is at (2L/2,0). Now you have 2 particles and you can find a distance between them.

I'll attach the picture but you are going to have to do all the calculations to get actual coordinates. Use it as a visual aid.

Also I'm sure you won't be able to solve this without one more hint: think about the horizontal vs vertical rod. They are not of the same mass, hence the point particles are not of same mass.

 

[squintyeyes]

the answer i put for the first part was 0.493 and it was right. But for the secound part i got 0.493 as well is that right? i am not sure and really need an answer fast.

 

[cronxeh]

the answer i put for the first part was 0.493 and it was right. But for the secound part i got 0.493 as well is that right? i am not sure and really need an answer fast.

Post your work. Refer to my graph I already gave you the center of mass, for y its between 0.1 and 0.15.

 

[squintyeyes]

thanks for all your help! i just forgot to divide by two