Three beads are placed on the vertices of an equilateral triangle of side d = 1.8 cm. The first bead of mass m1 = 150 g is placed on the top vertex. The second bead of mass m2 = 55 g is placed on the left vertex. The third bead of mass m3 = 85 g is placed on the right vertex.

Write a symbolic equation for the horizontal position of the center of mass relative to the left vertex of the triangle.

[IMG]http://i62.tinypic.com/wjhroi.png[/IMG]

Question

Three beads are placed on the vertices of an equilateral triangle of side d = 1.8 cm. The first bead of mass m1 = 150 g is placed on the top vertex. The second bead of mass m2 = 55 g is placed on the left vertex. The third bead of mass m3 = 85 g is placed on the right vertex. 

Write a symbolic equation for the horizontal position of the center of mass relative to the left vertex of the triangle.

[IMG]http://i62.tinypic.com/wjhroi.png[/IMG]

anonymous · Answer

attachment

anonymous · Answer

wait so they want you to derive the formula? or simply just use it?

anonymous · Answer

wait I'm being dumb they want you to use it lol. Anyways ever seen this formula: $$x_{cm} = \frac{m_{1}x_{1}+m_{2}x_{2}+...+m_{n}x_{n}}{m_{1}+m_{2}+...+m_{n}}$$?

anonymous · Answer

They want it written it terms of m1, m2, m3, and d. so I tried: 
(m1d + m2d+ m3d)/(m1 + m2 + m3) which is wrong.

anonymous · Answer

ah yes so firstly. The thing that you did (and is correct) is that we can actually simplify this problem to a 1 dimension problem right after all since the x and y components are 90 degrees from one another they don't effect one another.
So the problem actually looks like this right (since this an equilateral triangle)
|dw:1414450129697:dw| Does this make sense?