Inelastic Collisions: Solving m1v1 + m2v2 = m1v1' + m2v2

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The equation m1v1 + m2v2 = m1v1' + m2v2' represents the principle of conservation of momentum, applicable in both elastic and inelastic collisions. Calculus is not required to solve for the velocities; simple algebra suffices. The prime notation (') indicates the final velocities after the collision. The discussion clarifies that the equation can also be adapted for relativistic scenarios, where mass may change during the collision. The corrected equation m1v1 + m2v2 = m3v3 + m4v4 encompasses all types of collisions and is valid in both Newtonian and relativistic mechanics.
marshall4
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If i have the equation

m1v1 + m2v2 = m1v1' + m2v2'

would i have to use any calulus to find either velocity of the second object?

What is that the equation for? Is it inelastic collisions?
 
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Originally posted by marshall4
If i have the equation

m1v1 + m2v2 = m1v1' + m2v2'

would i have to use any calulus to find either velocity of the second object?

What is that the equation for? Is it inelastic collisions?
You don't need calculus. Simple algebra. Just solve for v2.

This is the equation for conservation of momentum. It holds in both elastic and inelastic collisions. It's also valid in relativity if the m's are what some people call 'relativistic mass.' In such cases the m's are conserved. I.e. the sum of the m's before the collision is the sum of the m's after the collision.



Pete
 


Originally posted by pmb
You don't need calculus. Simple algebra. Just solve for v2.

This is the equation for conservation of momentum. It holds in both elastic and inelastic collisions. It's also valid in relativity if the m's are what some people call 'relativistic mass.' In such cases the m's are conserved. I.e. the sum of the m's before the collision is the sum of the m's after the collision.



Pete

Doesn't the ' mean prime?

What is the ' there for?

What is the equation for completely inelastic collisions?
 


Originally posted by marshall4
Doesn't the ' mean prime?

What is the ' there for?

What is the equation for completely inelastic collisions?

Actually I meant to write a quote, i.e. "relativistic mass"

I want to applogize. I made an error in that last post. I made a web page on all of this a few weeks ago. See

www.geocities.com/physics_world/sr/inertial_mass.htm

The equation I posted above should have read

m1v1 + m2v2 = m3v3 + m4v4

This will hold in all collisions both eleastic and inelastic, and in both Newtonian mechanics and relativistic mechanics.

Particle N with mass mN and velocity vN. The mass may change in the collision.

Pete
 
The ' is only there to differeniate the original value from the final value.

Nautica
 

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