What Is the Center of Mass of a System of Moving Cars?

AI Thread Summary
The discussion focuses on calculating the center of mass and momentum of a system of two moving cars. The position of the center of mass is determined to be 16 m, using the mass and position of each vehicle. The total momentum of the system is calculated as 50,400 kg*m/s, derived from the individual momenta of both cars. The speed of the center of mass is found to be 16.8 m/s, which is consistent when recalculated using the total momentum. The calculations are confirmed to be correct.
Soaring Crane
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Please check my answers.

A 1200-kg station wagon is moving along a straight highway at 12.0 m/s. Another car, with mass 1800 kg and speed 20.0 m/s, has its center of mass 40.0 m ahead of the center of mass of the station wagon.

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.

a.x_cm = [40 m(1200 kg)]/(1200 kg + 1800 kg) = 16 m ? I set the car with the greater mass at (0,0).

b.Total p = 1200 kg*12 m/s + 1800 kg*20.0 m/s = 50400 kg*m/s

c.V_cm = (50400 kg*m/s)/( 1800 kg + 1200 kg) = 16.8 m/s

d.Using the answer from part c, (16.8 m/s)*(1200 kg + 1800 kg) = 50400 kg*m/s again

Thanks.
 
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