Calculating Center of Mass Velocity for Two 30 kg Masses | Find v in m/s

In summary, center mass velocity, also known as center of mass velocity, is the average velocity of an object's mass. It is calculated by dividing the total momentum of the object by its total mass or by integrating the mass times the velocity over the entire mass distribution of the object. This concept is important in physics because it helps us analyze the overall motion of an object and understand how different forces are acting on it. Center mass velocity differs from average velocity in that it takes into account both the mass and velocity of the object. It can change if there are external forces acting on the object, but will remain constant if there are no external forces.
  • #1
cgward
5
0
1. Two 30 kg masses have velocities (in m/s) of v 1 = 14 i - 18 j and v 2 = - 28 i + 14 j. Determine the velocity of the center of mass of the system.



I am having a problem on how to set the problem up to find the velocity in terms of v= i and j
 
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  • #2
Start with conservation of momentum
 
  • #3
.

To calculate the center of mass velocity for the two 30 kg masses, we can use the formula v = (m1v1 + m2v2) / (m1 + m2), where m1 and m2 are the masses of the two objects and v1 and v2 are their respective velocities.

In this case, m1 = m2 = 30 kg, v1 = 14i - 18j, and v2 = -28i + 14j. Plugging these values into the formula, we get:

v = (30 kg)(14i - 18j) + (30 kg)(-28i + 14j) / (30 kg + 30 kg)

= (420i - 540j - 840i + 420j) / 60 kg

= (-420i - 120j) / 60 kg

= (-7i - 2j) m/s

Therefore, the velocity of the center of mass of the system is -7i - 2j m/s. This means that the center of mass is moving in the negative x-direction with a velocity of 7 m/s and in the negative y-direction with a velocity of 2 m/s.
 

Related to Calculating Center of Mass Velocity for Two 30 kg Masses | Find v in m/s

1. What is center mass velocity?

Center mass velocity, also known as center of mass velocity, is the average velocity of an object's mass. It takes into account the different velocities of individual particles that make up the object and calculates the overall velocity of the center of mass of the object.

2. How is center mass velocity calculated?

The center mass velocity can be calculated by dividing the total momentum of the object by its total mass. This can also be expressed as the integral of the mass times the velocity over the entire mass distribution of the object.

3. Why is center mass velocity important in physics?

Center mass velocity is important because it allows us to analyze the overall motion of an object, particularly in cases where the object is not moving with a constant velocity. It helps us understand how different forces are acting on an object and how it will move as a result.

4. How does center mass velocity differ from average velocity?

Average velocity is the total displacement of an object over a period of time, while center mass velocity is the average velocity of the center of mass of an object. Average velocity only takes into account the distance traveled, while center mass velocity takes into account the mass and velocity of the object.

5. Can the center mass velocity of an object change?

Yes, the center mass velocity of an object can change if there is an external force acting on the object. This can cause the object's mass or velocity to change, which in turn will affect the center mass velocity. However, if there are no external forces acting on the object, the center mass velocity will remain constant.

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