Center of Mass?

Question

At one instant the center of mass of a system of a two particles is located on the x-axis at x=2 m and has a velocity of (5.0m/s)i. One of the particles is at the origin. The other particle has a mass of 0.10 kg and is at rest on the x-axis at x=8.0. What is the mass of the particle at the origin? Total momentum? Velocity of particle at origin?

I have no clue how to solve this. I tried to use xcm = m1+v1+v2*m2..../m1+m2....
and got
m1=(0,0)
m2=(2,0)
m3=(8,0)

xcm= m1*(0)+(2)m2+.10(80)/m1+m2+.10

but then i have to many unknown values to solve for m

Answer 1

m1=0,0
m2=8,0 ; .1kg
cg=2,0

m2*d2+m1*d1=cg*(m2+m1)
8*.1+0*m1=2*(.1+m1)
.8=.2+2*m1

m1=.3 [kg]

Total Momentum:
(m1+m2)*v
(.1+.3)*5=2 [kgm/s]

Velocity:
m1v1+m2v2=2 [kgm/s]
.3*v1+0=2

v1=20/3 [m/s]

Answer 2

Let's start with the mass of the particle at the origin. We don't need to do anything with the velocity or momentum to get that. We know that there's a 0.1 kg mass at x = 8, a mass of unknown value Z at the origin, and that the center of mass is at x=2. So think of it like a balanced seesaw with the fulcrum at x=2. Mass x distance from fulcrum must be the same on each side. So:

2Z = 0.1(8-2)
2Z = 0.6
Z = 0.3

So the unknown mass at the origin has a value of 0.3 kg.

That in turn means that the total mass of the system is 0.4 kg. Since the center of mass has a velocity of 5 m/s, the total momentum is simply that velocity times total mass, i.e. 0.4 x 5 = 2 kg m/s.

That total momentum must equal the sum of the momenta of the two particles. The 0.1 kg particle at x=8 is not moving, so *all* of that momentum must be coming from the 0.3 kg particle at the origin. If it is moving at velocity V, we therefore have --

2 kg m/s = 0.3 kg x V

So V = 6.67 m/s

Ta-da!

Answer 3

If the mass of the particle at the origin is m, the position of the centre of mass will be
(m(0.0) + 0.10(8.0)) / (m + 0.10) = 0.80 / (m + 0.10)
and we know this is 2, so we have
m + 0.10 = 0.80/2= 0.40
so m = 0.30 kg.

The total mass of the system is 0.40 kg, so the total momentum is 0.40 (5.0) = 2.0 kg m / s in the positive x direction.

The momentum of the particle at x = 8.0 is 0, since it is at rest, so the momentum of the system is coming wholly from the particle at the origin. So we have
p = mv => 2.0 = 0.30 v => v = 6.7 m/s.

Answer 4

Draw a Cartesian Coordinate system with Zero at the center, negative integers to the left of the zero on the X axis--horizontal(abcissa) and positive intergers to the right.
Y axis--vertical(Ordinate) negative integers below the zero in the center and positive intergers above the zero.

Plot your coordinates m1=(0,0), m2=(2,0), etc. and connect the dots.

Answer 5

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