Question about Momentum and Collisions.

AI Thread Summary
The Impulse-Momentum Theorem relates the change in momentum to the force applied over time. Deriving the time two colliding objects stick together without using the left side of the equation is complex and situation-dependent. Factors influencing this include the nature of the collision, material properties, and initial velocities. Different collision scenarios, such as elastic versus inelastic collisions, will yield varying results. Understanding these dynamics is crucial for accurate calculations in physics.
pghazanfari
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I am sure many of you are familiar with the Impulse-Momentum Theorem:

\Deltap = F * \Deltat

Is there any way to mathematically derive the time that the two objects would stick together during the collision without using the left side of the equation?
 
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Depends on the situation.
 
zhermes said:
Depends on the situation.

What would these situations be?
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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