General Question- Compuing velocity of a center of mass

In summary, center of mass is the point of equilibrium where the total momentum of an object is equal to the change in momentum of that object. However, because center of mass applies to an object as a whole, not a system, it is difficult to find the velocity of the center of mass without doing a calculation.
  • #1
integra2k20
35
0
General Question-- Compuing velocity of a center of mass

Homework Statement



A ball of mass 0.198 kg has a velocity of 1.47 i m/s; a ball of mass 0.309 kg has a velocity of -0.401 i m/s.They meet in a head-on elastic collision.

(a) Find their velocities after the collision.

(b) Find the velocity of their center of mass before and after the collision.


Homework Equations



v1f = ((m1-m2)/(m1+m2))(v1i)+(2(m2)/(m1+m2))(v2i)

(m1)(v1i)+(m2)(v2i)=(m1)(v1f)+(m2)(v2f)

The Attempt at a Solution



a.) Calculated velocities correctly: v1f = -.8106m/s, v2f = 1.0604m/s

b.) This is my problem

As i understand center of mass, it applies to an object as a whole, not a system. I have only been taught how to compute center of mass for an object with specific x and y dimensions, i have no idea how to find the center of mass of a system let alone the VELOCITY of the center of mass as is asked in this question.

my only guess is that since p = m(delta v) and p = m(v center of mass), that maybe the velocity of the center of mass is equal to the change in velocity?
 
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  • #2
Think about it this way..
Center of mass means you're treating the TOTAL momentum of the system as if it's the momentum of ONE object which composes of both the objects' masses! (Since the total mass of the objects would be concentrated at the center of mass)
I think I said too much..
 
  • #3
Pseudo Statistic said:
Think about it this way..
Center of mass means you're treating the TOTAL momentum of the system as if it's the momentum of ONE object which composes of both the objects' masses! (Since the total mass of the objects would be concentrated at the center of mass)
I think I said too much..

im still not quite sure how you would obtain the velocity of the center of mass from this. apparently its not as simple as i'd thought...
 
  • #4
integra2k20 said:
im still not quite sure how you would obtain the velocity of the center of mass from this. apparently its not as simple as i'd thought...

What is the definition of center of mass? If you know how to find it in some cases, you must know its definition.

integra2k20 said:
As i understand center of mass, it applies to an object as a whole, not a system. I have only been taught how to compute center of mass for an object with specific x and y dimensions, i have no idea how to find the center of mass of a system let alone the VELOCITY of the center of mass as is asked in this question.
 
  • #5
integra2k20 said:
im still not quite sure how you would obtain the velocity of the center of mass from this. apparently its not as simple as i'd thought...

What's the momentum of a single particle whose mass = (m1 + m2), and which moves with speed Vcm? Does this have any relationship to your system, in other words?

Dorothy
 
  • #6
Dorothy Weglend said:
What's the momentum of a single particle whose mass = (m1 + m2), and which moves with speed Vcm? Does this have any relationship to your system, in other words?

Dorothy

While this is certainly a valid observation, it is sort of using the answer to find the answer. At least once in a lifetime every physics student should have to actually compute the velocity of the CM from the individual velocities of the particles in the system to verify the conclusion to be reached in this exercise.
 
  • #7
Oh. Sorry :-(

I'm not sure I have ever done that... When I solved this problem, I just took the derivative of the position vector of the CM, and that's what I ended up with, which I thought was interesting... Maybe I should have just suggested that..

Sorry again.
Dorothy
 
  • #8
Dorothy Weglend said:
Oh. Sorry :-(

I'm not sure I have ever done that... When I solved this problem, I just took the derivative of the position vector of the CM, and that's what I ended up with, which I thought was interesting... Maybe I should have just suggested that..

Sorry again.
Dorothy
No need to be sorry. Your observations are valid.

The derivative is the approach to doing the direct calculation, and it is what I think he problem intended. I thought you were suggesting that since the total mometum has been calculated one only need to divide by the total mass, which is the conclusion the problem is trying to reach. It is a subtle difference.
 
  • #9
Well, sometimes when I work through these calculations, I end up with a result that I say, "Oh, of course. I should have seen that..." a sort of an "Ah hah" moment, and I think I should have been able to see it without doing the calculation, just from the concepts.

I was trying to create an "Ah Hah!" moment for someone else, having missed it myself :-)

Thanks for all the help you give all of us, btw.

Dorothy
 
  • #10
Dorothy Weglend said:
Well, sometimes when I work through these calculations, I end up with a result that I say, "Oh, of course. I should have seen that..." a sort of an "Ah hah" moment, and I think I should have been able to see it without doing the calculation, just from the concepts.

I was trying to create an "Ah Hah!" moment for someone else, having missed it myself :-)

Thanks for all the help you give all of us, btw.

Dorothy

And that is exactly the point of doing the exercise! :smile: Those moments are memorable and help to drive home the concepts.
 

What is the center of mass?

The center of mass is a point in a system where the total mass can be considered to be concentrated. It is the point at which the system can be balanced and behaves as if all the mass is located at that single point.

Why is it important to compute the velocity of a center of mass?

Computing the velocity of a center of mass can help us understand the motion of a system as a whole. It allows us to analyze the overall movement of the system and make predictions about its future motion.

What is the formula for computing the velocity of a center of mass?

The formula for computing the velocity of the center of mass is v = (m1v1 + m2v2 + ... + mnvn) / (m1 + m2 + ... + mn), where m is the mass and v is the velocity of each individual object in the system.

What is the difference between center of mass and center of gravity?

The center of mass is a point where the mass of a system is evenly distributed, while the center of gravity is a point where the gravitational force acting on the system is evenly distributed. In most cases, the center of mass and center of gravity are at the same location, but they can be different if the system is affected by external forces.

Can the velocity of the center of mass change?

Yes, the velocity of the center of mass can change if there is an unbalanced external force acting on the system. This can cause the center of mass to accelerate or decelerate, depending on the direction of the external force.

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