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

In summary, the two cars have a combined mass of 3000 kg and a combined momentum of 50400 kg*m/s. The center of mass of the system is located 16 m ahead of the heavier car and has a speed of 16.8 m/s. The total momentum of the system can be calculated using the speed of the center of mass.
  • #1
Soaring Crane
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0
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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  • #2
Looks good
 
  • #3
Your answers are correct. The center of mass of the system is indeed 16 m from the car with the greater mass. The total momentum of the system is 50400 kg*m/s, which is the same as the momentum calculated using the speed of the center of mass. This is because the center of mass represents the average position and velocity of all the particles in the system. Therefore, the total momentum of the system is equal to the mass of the system multiplied by the velocity of the center of mass. Good job!
 

1. What is the center of mass of a car?

The center of mass of a car is the point at which all of its mass is evenly distributed, and the car will balance perfectly on that point.

2. How does the center of mass affect a car's stability?

The lower the center of mass of a car, the more stable it will be. This is because a lower center of mass makes it harder for the car to tip over.

3. Can the center of mass be changed in a car?

Yes, the center of mass can be changed in a car by altering the distribution of its mass. For example, adding weight to the roof of a car would raise its center of mass, making it less stable.

4. How does the center of mass affect a car's handling and performance?

The location of the center of mass can greatly affect a car's handling and performance. A higher center of mass can make a car feel more top-heavy and less responsive, while a lower center of mass can improve handling and stability.

5. Is there a difference in the center of mass between different types of cars?

Yes, there can be a difference in the center of mass between different types of cars. For example, a sports car will typically have a lower center of mass compared to an SUV, making it more stable and better for handling at high speeds.

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