Center of Mass: Finding the Third Particle's Position

[shell4987]

Homework Statement

A 2.80 kg particle has the xy coordinates (-2.00 m, 0.950 m), and a 3.30 kg particle has the xy coordinates (0.672 m, -0.0440 m). Both lie on a horizontal plane. At what (a)x and (b)y coordinates must you place a 3.39 kg particle such that the center of mass of the three-particle system has the coordinates (-0.663 m, -0.527 m)?

Homework Equations

The Attempt at a Solution

I don't even know what equation I have to use to find this, I looked in the book and I can't find anything about it. Can anyone help me with this?

 

[Doc Al]

You need to understand the basic definition of center of mass: Center of Mass

 

[shell4987]

You need to understand the basic definition of center of mass: Center of Mass

How do I find the coordinates of the center of mass if they already gave them to me though? I now know what equation to use but I don't know how to apply it to this problem.

 

[arildno]

How do I find the coordinates of the center of mass if they already gave them to me though? I now know what equation to use but I don't know how to apply it to this problem.

You must solve two equations for the coordinates of the final particle.

 

[shell4987]

You must solve two equations for the coordinates of the final particle.

Now I'm confused which two equations do I use?

xcom=(m1x1+m2x2)/M and...?

 

[Doc Al]

You'll need one equation for the x-component and another for the y-component.

 

[arildno]

You have THREE particles here, not two!

YOu have, for the x's:
$$x_{c.m}=\frac{m_{1}x_{1}+m_{2}x_{2}+m_{3}x_{3}}{m_{1}+m_{2}+m_{3}}$$

Now, in this expression, what quantities are KNOWN, which quantity (or quantities) is unknown?

 

[shell4987]

You have THREE particles here, not two!

YOu have, for the x's:
$$x_{c.m}=\frac{m_{1}x_{1}+m_{2}x_{2}+m_{3}x_{3}}{m_{1}+m_{2}+m_{3}}$$

Now, in this expression, what quantities are KNOWN, which quantity (or quantities) is unknown?

what's unknown is the ycom and the xcom... so i put my information in that equation and solved it and got xcom= -0.593 and ycom=0.0767 and they are wrong. i have no idea what I'm doing wrong here.

 

[Doc Al]

What's unknown are the coordinates of the third particle: x_3 and y_3. The coordinates of the center of mass are known.

 

[arildno]

Remember that your exercise can be equivalently rephrased into:
(First some blah&info about the two first particles)
..The common centre of mass of the three-particle system IS (-0.663,-0.527), and the mass of the third particle IS 3.39kg.
Question:
What is the position of the third particle?