Flat plate, circular hole center of mass

[gap0063]

Homework Statement

A uniform flat plate of metal with a circular hole, where it is a rectangle starting from -6 to 7 from the length, and the height is -3 to 3.

The circle has a radius of 2, and it starts at 1 to 5.
Calculate the x-coordinate of the center of
mass xcm of the metal plate.

Homework Equations

well Xcm= m₁x₁+m₂x₂/m₁+m₂

The Attempt at a Solution

is this the right equation?
and if so, how do I take out the circular part?

 

[tiny-tim]

hi gap0063!

well Xcm= m₁x₁+m₂x₂/m₁+m₂
…
is this the right equation?

yes

and if so, how do I take out the circular part?

it has negative mass!

(no, seriously, it really does … try it!)

 

[gap0063]

hi gap0063!


yes


it has negative mass!

(no, seriously, it really does … try it!)

this is probably a dumb question, but how do you find the mass of the rectangle and circle?

and is the x₁ and x₂ the coordinates?

 

[tiny-tim]

hi gap0063!

this is probably a dumb question, but how do you find the mass of the rectangle and circle?

and is the x₁ and x₂ the coordinates?

if you're not given the density, then use area instead of mass in the formula

and yes, x₁ and x₂ are the x coordinates of the centre of mass and of the hole respectively (and similarly for y₁ and y₂)

 

[gap0063]

hi gap0063!


if you're not given the density, then use area instead of mass in the formula

and yes, x₁ and x₂ are the x coordinates of the centre of mass and of the hole respectively (and similarly for y₁ and y₂)

alright, is this right:

13*6(1/2)-(7)(2²$$\Pi$$/ (13*6+ 4$$\Pi$$)

 

[tiny-tim]

hi gap0063!

(have a pi: π )

alright, is this right:

13*6(1/2)-(7)(2²$$\Pi$$/ (13*6+ 4$$\Pi$$)

for the total mass (on the bottom) you need minus 4π, don't you?

apart from that, it looks ok, except i don't understand where the (7) comes from

(and i didn't understand what this meant …)

The circle … starts at 1 to 5.

 

[gap0063]

hi gap0063!

(have a pi: π )



for the total mass (on the bottom) you need minus 4π, don't you?

apart from that, it looks ok, except i don't understand where the (7) comes from

(and i didn't understand what this meant …)

Yes I meant minus on the bottom


the 7 is from how far away the cicle is from the begin on the rectangle

sorry I don't have the picture but the shapes are on a coordinate system and inside the rectangle (that goes from (-6,0) to (7,0) ) the circle lies at (1,0) to (5,0).

 

[tiny-tim]

so the centre of the circle is at (3,0)?

ok, then you must use x₂ = 3 …

your x₁ x₂ and x must all be measured from the same origin

 

[gap0063]

so the centre of the circle is at (3,0)?

ok, then you must use x₂ = 3 …

your x₁ x₂ and x must all be measured from the same origin

yes the center of the circle is (3,0)

so what is x₁...? is it 1/2?

 

[tiny-tim]

yes, your x₁ = 1/2 was correct

 

[gap0063]

yes, your x₁ = 1/2 was correct

thanks so much for all your help!

if you wouldn't mind looking at my other problem:

https://www.physicsforums.com/showthread.php?t=439084