Find Center of Mass: 3kg at (0,8), 1kg at (12,0), 4kg at (?)

[Sucks@Physics]

A 3kg mass is positioned at (0,8) and 1 kg mass is positioned at (12,0). What are the coordinates of a 4 kg mass, which will result int he center of mass of the system of three masses being located at the origin (0,0)?

I know that m1x1+m2x2...etc but I don't understand how you can do it with actual coordinates, can someone explain?

 

[Ginerva123]

Have you tried finding the distance between the points and the origin?

 

[Sucks@Physics]

This will sound dumb, but I do not remember the distance formula...

 

[Ginerva123]

distance= square root of [(x2-x1)^2 + (y2-y1)^2]

 

[Sucks@Physics]

so the 3 kg is 8 units away and the 1 kg is 12 units away. would that mean that the 4kg had to be 9 units away? and how do you know which way/what coordinates?

 

[Ginerva123]

You know that the 3kg is due north and the 12kg is to the east of the origin. Therefore, you know that the third mass must be placed south-west of the origin to mantain equilibrium. Bear in mind that this is the y=x line.

 

[Sucks@Physics]

i know to use the m1x1+m2x2+m3x3/(m1+m2+m3) but i still don't understand how you get 2 points from this equation

 

[Sucks@Physics]

so the coordinates are oging to (-n,-n) but i still don't see how the formula works

 

[fliinghier]

you will need to think of the vectors in terms of their components, and realize that the third mass will have a vector with components to cancel out the other two masses' vectors.

edit: also, the post saying it's on the x=y line is misinformed. the answer is not in the form (-n,-n).

 

[Sucks@Physics]

so 3 kg directly up 8 units, 1 kg directly right 12 units and 4 kg in quardrant III. the sum equals 36 so the 4 kg would have to be 9 units away from the origin? I don't think I'm doing this right

 

[fliinghier]

not the sum. the vectors are at right angles. the y component of the 4kg mass equals the 3kg mass's vector, and the x component is the 1kg mass's vector

 

[Sucks@Physics]

that would give me (-8,-12) right?

 

[simon1987]

i know to use the m1x1+m2x2+m3x3/(m1+m2+m3) but i still don't understand how you get 2 points from this equation

Then use (m1y1+m2y2+m3y3)/(m1+m2+m3) to find the y-coordinate of the CM.

 

[Sucks@Physics]

i don't know m3y3 so is it (m1y1+m2y2)/(m1+m2+m3) = m3y3?

 

[aq1q]

no, its 0, remember its stated on the problem.. (0,0) is the CM

 

[simon1987]

List everything you know:

m1, x1, y1
m2, x2, y2
CM(x), CM(y)
m3

You need to find x3 and y3.

So set up the equation to find the center of mass,

$$CM{}_x{} = (m{}_1{}x{}_1{} + m{}_2{}x{}_2{} + m{}_3{}x{}_3{}) / (M)$$

Solve it for what you're looking for.

EDIT: To be clearer, a value x1, x2, x3, etc. is the x-coordinate of the position of that mass m1, m2, m3...

 

[aq1q]

maybe this will help you visualize it.. I am not sure if you are familiar of adding vectors using unit vectors--> i(hat) and j(hat). But if you do it like that.. you will have
3(0i+8j) <-- i can multiply by three because mass is a scaler.
1(12i+0j)
-----------
12i + 24j
4(Xi+Yj)
-----------
0i+ 0j <-- center of mass..

Ok, that is more than enough of information.. you should be able to solve it.

 

[Sucks@Physics]

i just don't understand, i give up

 

[simon1987]

i just don't understand, i give up

It's much easier than you are making it. The equation

$$CM_{x} = \frac{m_{1}x_{1} + m_{2}x_{2} + m_{3}x_{3}}{m_{1} + m_{2} + m_{3}}$$

Will give you the x-coordinate for the position of the center of mass: $$CM_{x}$$. You are looking for the position of the 4-kg mass, so solve this equation for x3.

And this second equation

$$CM_{y} = \frac{m_{1}y_{1} + m_{2}y_{2} + m_{3}y_{3}}{m_{1} + m_{2} + m_{3}}$$

will give you the y-coordinate for the center of mass ($$CM_{y}$$). Since you're looking for the position of that m3, solve this second equation for y3.

 

[Sucks@Physics]

(3*0)+(1*12)+(4)/(3+1+4)=2
or
(3*8)+(1*12)+(4)/(3+1+4)=5
or
(3*8)+(1*12)/(3+1+4) =4.5/4 = 1.125

this is what I've done and I'm getting nothing close to the answer. the answer is (-3,-6)

 

[simon1987]

(3*0)+(1*12)+(4)/(3+1+4)=2
or
(3*8)+(1*12)+(4)/(3+1+4)=5
or
(3*8)+(1*12)/(3+1+4) =4.5/4 = 1.125

this is what I've done and I'm getting nothing close to the answer. the answer is (-3,-6)

Solve the equations for x3 and y3 before plugging in numbers.

 

[Sucks@Physics]

i don't know why i can't understand this stupid thing

 

[simon1987]

i don't know why i can't understand this stupid thing

Do you not understand the concept? Or how to solve the equations for x3 and y3, respectively? Or what x3 and y3 represent? Or what CMx and CMy represent?

 

[Sucks@Physics]

CMy and CMx are the origin (0,0). x3 and y3 are the coordinates in which i need to find that have the 4kg mass. I guess I don't know how to solve the equation for x3y3. Would it be...

(m1x1+m2x2)/(m1+m2+m3) or (m1x1+m2x2)/(m1+m2) or (m1x1+m2x2+m3)/(m1+m2+m3)

i feel like I've tried everything

 

[Sucks@Physics]

omg i figured it out. thanks simon for not giving up on me! lol

 

[Sucks@Physics]

i set it up liek this...

(3*0)+(1*12)+(4* ?) = 0
(3*8)+(1*0)+(4* ?) = 0

Will that work?

 

[simon1987]

i set it up liek this...

(3*0)+(1*12)+(4* ?) = 0
(3*8)+(1*0)+(4* ?) = 0

Will that work?

Does it match what you know the answer should be?

 

[Sucks@Physics]

yea its (-3,-6)