Two 1 kg balls move away from each other, one traveling 2 m/s to the right, the other 8 m/s to the left. What is the magnitude of the total momentum of the system?

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The definition for the momentum of a single object is given by the following formula:

P = m*v

Note that this is a vector, since velocity is a vector and it is being multiplied by a scalar (a real number), the mass. So, momentum is a vector pointing in the same direction as the velocity.

Now, in our system, we have two objects of mass equal to 1kg each. All we have to do is calculate the momentum of each one and sum them as vectors. The momentum of the ball moving to the left is:

Pl = (1 kg)*(8 m/s) = 8 kg-m/s

and the momentum of the ball moving to the right is:

Pr = (1 kg)*(2 m/s) = 2 kg-m/s

To get the total momentum of the system, we add them. Since they are moving in opposite directions, to sum them as vectors we simply do the following (assuming that the right direction is the positive direction):

Pt = Pr - Pl = (2 kg-m/s) - (8 kg-m/s) = -6 kg-m/s

So the total momentum of the system is -6 kg-m/s, the minus sign indicates that the momentum is pointing to the left. Since this is a 1-dimensional problem—that is, we only talk about moving to the left or to the right—the magnitude will just be the absolute value of this vector, which is 6 kg-m/s!

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