Center of Mass in a system of cylinders

[noffya]

Homework Statement

A collar brass 50 mm length is mounted on an aluminum bar 80 mm in length (density of brass 8470 kg / m 3 density of aluminum 2800 kg / m 3 ). Find the height to which is the center of mass of the composite body.

Homework Equations

COM= m₁*x₁+m₂x₂/m₁+m₂

The Attempt at a Solution

I tried to solve the problem using the coordinates x,y,z, however didn't get a right solution.
The solution must be equal 27.6 mm
Please help with the equations.
Thanks

 

[a_potato]

You can treat this as a 1d problem. Work out the centre of mass of the two objects. You can then work out the centre of mass of the two points by using the mass of the two objects to weight them.

 

[SteamKing]

If your picture was a little smaller, you couldn't tell what you were doing.

It looks like you calculated the volume of the collar and the bar correctly. What I don't understand is why you have subtracted a mass of 0.2831 kg from the masses of the collar and the bar.

Also, the x values in the equation for the c.o.m. are not the heights of the collar or the bar; the x-values are the x locations of the c.o.m. for each item from the reference.

Since the collar and the bar are symmetrical w.r.t. the y and z axes, your values for the c.o.m. w.r.t. these axes are incorrect. The c.o.m. for a uniformly distributed mass will lie on any axes of symmetry which the mass may have.

 

[Chestermiller]

Homework Statement

A collar brass 50 mm length is mounted on an aluminum bar 80 mm in length (density of brass 8470 kg / m 3 density of aluminum 2800 kg / m 3 ). Find the height to which is the center of mass of the composite body.

Homework Equations

COM= m₁*x₁+m₂x₂/m₁+m₂

The Attempt at a Solution

I tried to solve the problem using the coordinates x,y,z, however didn't get a right solution.
The solution must be equal 27.6 mm
Please help with the equations.
Thanks

Your handwriting is unreadable. Please type out the relationships and results you got for the volumes of the two objects and the masses of the two objects.
Chet

 

[noffya]

If your picture was a little smaller, you couldn't tell what you were doing.

It looks like you calculated the volume of the collar and the bar correctly. What I don't understand is why you have subtracted a mass of 0.2831 kg from the masses of the collar and the bar.

Also, the x values in the equation for the c.o.m. are not the heights of the collar or the bar; the x-values are the x locations of the c.o.m. for each item from the reference.

Since the collar and the bar are symmetrical w.r.t. the y and z axes, your values for the c.o.m. w.r.t. these axes are incorrect. The c.o.m. for a uniformly distributed mass will lie on any axes of symmetry which the mass may have.

thanks a lot!
I subtracted a mass of 0,2831kg considering it a collar hole.
I will try to make calculation based on all the comments. Hopefully that will lead me to the right solution.

 

[SteamKing]

thanks a lot!
I subtracted a mass of 0,2831kg considering it a collar hole.
I will try to make calculation based on all the comments. Hopefully that will lead me to the right solution.

There is no need to subtract the mass of the collar hole if you calculated the volume of a cylinder with a hole removed in the first place, which it appears you did.