A 1200 - kg station wagon is moving along a straight highway at 12.0 m/s. Anothe

Question

A 1200 - kg station wagon is moving along a straight highway at 12.0 m/s. Another car, with mass 1800 kgand speed 20.0 ,m/s has its center of mass 40.0 mahead of the center of mass of the station wagon (Figure 1) . A.) Find the position of the center of mass of the system consisting of the two automobiles. B.) Find the magnitude of the total momentum of the system from the above data. C.) Find the speed of the center of mass of the system. D.) Find the total momentum of the system, using the speed of the center of mass.

Explanation / Answer

a) look at it as two objects on a balance, what is the balance point.
x and y are distances from CM to each car.
x + y = 40
x = 40-y
1200x = 1800y
2x = 3y
2(40-y) = 3y
80 - 2y = 3y
y = 16
x = 24
center of mass is 24 meters from wagon to second car

b) P = 1200*12 + 1800*20 = 14400 + 36000 = 50400

c) speed of center of mass? I don't think it is as simple as the average.
We have one point. Do another point 10 seconds later.
First car has moved forward 120 m, second has moved 200 m
Since the initial separation was 40 m, the separation is now 120 m

Repeat the above CM calc,
x + y = 120
x = 120-y
1200x = 1800y
2x = 3y
2(120-y) = 3y
240 - 2y = 3y
y = 48
x = 120-48 = 72
So the center of mass is 72 meters from the wagon, which has moved 120 meters, so it has moved 192 meters - 24 meters = 168

So the CM has moved 168 meters in 10 seconds, or 16.8 m/s

d) 16.8 x (1200+1800) = 16.8 x 3000 = 50400
which is the same as in (b) as it should be.

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