A system consists of three balls at different locations near the origin, as show

Question

A system consists of three balls at different locations near the origin, as shown at right. Ball 1 has a mass of 2.0 kg and is located on the x-axis at x1 = –2.0 m; ball 2 has an unknown mass and is located at (x2 = +4.0 m, y2 = +3.0 m); ball 3 is somewhere on the y-axis at an unknown location, and it has a mass of 1.0 kg. The coordinates of the center-of-mass of this system are (xCM = 0, yCM = +2.0 m). The squares on the grid measure 1.0 m × 1.0 m. [4 points] (a) Calculate the mass of ball 2. [4 points] (b) Find the location of ball 3.

Explanation / Answer

m1 =2kg , x1 =-2m , y1 =0

for m2 , x2 =4m , y2 =3 m

m3 = 1kg , x3 =0 , y3 =y3

Xcm = 0

Xcm = (m1x1+m2x2+m3x3)/(m1+m2+m3)

(2*-2)+ (m2*4) +(1*0) = 0

4m = 4

m2 = 1kg

b) Ycm = 2m

Ycm =(m1y1+m2y2+m3y3)/(m1+m2+m3)

2(2+1+1) = (2*0) +(1*3) + (1*y3)

y3 = 5 m

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