Total Momentum of A and B = 2mV0

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In summary, two identical objects A and B with masses M and initial velocities of 3V0 and V0 respectively, collide on a horizontal air track with negligible friction. The total momentum of the system can be expressed as 2m + 4V0. However, this expression is incorrect and cannot be used to determine the total momentum. The correct expression would be 4mV0.
  • #1
kitty9035
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Homework Statement



Two identical objects A and B of mass M move on a one-dimensional, horizontal air track. Object B initially moves to the right with speed V0. Object A initially moves to the right with speed 3V0, so that it collides with object B. Friction is negligble. Determine the total momentum of the system of the two objects. Express answers in terms of M and V0.

Homework Equations



P=mv

The Attempt at a Solution



I got an answer,but i would like verification that it's right.

I did...

Pa=(Ma)(Va) Pb=(Mb)(Vb)
Pa=m(3V0) Pb=m(V0)


Add them together...
m(3V0) + m(V0)

and get...

2m + 4v0
 
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  • #2
kitty9035 said:
Add them together...
m(3V0) + m(V0)

and get...

2m + 4v0

That is so wrong and you know it.
 
  • #3
No, I really don't. What's right?
 
  • #4
Don't you notice that the expression 2m + 4v0 is non-sense? If not, I suggest you go study some algebra.
 
  • #5
You're OK up to that last step. 2m + 4v0 does not make any sense. You cannot separate out the variables like that.

What's the answer to this:

3x + x = ?

If you understand that, you should see what the answer should be.
 

1. What is the meaning of "Total Momentum of A and B = 2mV0"?

The term "Total Momentum" refers to the combined momentum of two objects, A and B. This is calculated by multiplying the mass (m) of each object by its velocity (V) and adding the two resulting values together. The value of "2mV0" indicates that the total momentum of A and B is equal to twice the mass (m) of either object multiplied by its initial velocity (V0).

2. How is the total momentum of A and B calculated?

The total momentum of A and B is calculated by multiplying the mass (m) of each object by its velocity (V) and adding the two resulting values together. The formula for calculating momentum is p = mv, where p is momentum, m is mass, and v is velocity. Therefore, the total momentum of A and B can be expressed as p = mAvA + mBvB.

3. What does the number "2" represent in the equation?

The number "2" represents the fact that the total momentum of A and B is equal to twice the mass (m) of either object multiplied by its initial velocity (V0). This means that both objects have the same initial velocity and are moving in the same direction, resulting in a combined momentum that is twice as large as the momentum of each individual object.

4. Why is the equation for total momentum important in physics?

The equation for total momentum is important in physics because it helps us understand the motion of objects and their interactions with each other. By calculating the total momentum of a system, we can determine how much force is needed to change its motion, or if the system is in equilibrium (when the total momentum is zero). This equation is also important in the study of collisions and explosions, as it allows us to analyze the changes in momentum during these events.

5. Can the total momentum of A and B ever be negative?

No, the total momentum of A and B can never be negative. Momentum is a vector quantity, meaning it has both magnitude and direction. The direction of momentum is always the same as the direction of an object's velocity, and since velocity is always positive, momentum is also always positive. Therefore, the total momentum of A and B, which is the sum of their individual momenta, will always be positive.

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