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# acceleration after collision

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Hi, I'm not very strong about physics and i have a problem : If i have two spheres the first (A) has a mass of 10 and an acceleration vector of (10,0), (velocity vector = (10, 0)) The second one (B) has a mass of 2 an acceleration of (4, 0), the same velocity vector but a mass of two. I multiply mass by acceleration and i add it to the velocity separatly for each sphere, then what will be the final velocity and acceleration for A and B ?

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Quote:
 I multiply mass by acceleration and i add it to the velocity separatly for each sphere [...]

Mass times acceleration equals force, so adding it to the velocity has no meaning...

Generally, upon a collision, objects change velocity immediately. This change in velocity, is not considered to have been caused by some acceleration, but by an impulse that was applied to the object.

This impulse causes the velocities of the involved objects, to change almost instantly. By solving the system of the principle of preservetion of momentum, and preservation of kinetic energy, the final velocities v1f,v2f of two objects colliding with mass m1 and m2 respectively, are:

v1f = v1i -2*m2(v1i-v2i)/(m1+m2)
v2f = v2i +2*m1(v1i-v2i)/(m1+m2)

(v1i, v2i are the initial velocities.)
These are vector equations, which means that you have to solve them once for each axis, in order to find the respective component of the final velocity. This won't be accurate though, if you want to employ angular effects too...

Generally, you don't need to know acceleration, because it can be found easily from the forces acting on the object. (a = (total F)/mass)

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Thanks, but i have questions :
1)Why do you multiply by 2 ?
2)Why do you divide by the sum of both masses

Do you know a link where i can learn more about this subject ?

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TheSeb,

If you want to make a simple model for collisions, you only need to know the masses and velocities of the objects colliding. Then you can use the principle of the "Conservation of Momentum" to see what the velocities will be after the collision. Just google that phrase, and you will get many hits explaining this.

For instance, here's the Wikipedia article on the topic:

Momentum

It explains more or less someusername's formulas.

Vovan

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ok thanks ! i'll take a look

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I'll pick up the proof from where the link left off:

E.g. for V2f,
V2f = 2m1*V1i/(m1+m2) + (m2-m1)*V2i/(m1+m2) ==
(2m1*V1i - m1*V2i + m2*V2i)/(m1+m2) ==
[m1*(V1i-V2i) + m1*V1i + m2*V2i]/(m1+m2) == (add and subtract m1*V2i)
[m1*(V1i-V2i) + m1*V1i - m1*V2i + m1*V2i +m2*V2i]/(m1+m2) ==
[2m1(V1i-V2i) + V2i*(m1+m2)]/(m1+m2) <==>

V2f == V2i + 2m1*(V1i-V2i)/(m1+m2)

I don't think I missed anything...

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