Elastic Collision in Deep Space

AI Thread Summary
In an elastic collision in deep space between two equal mass objects, object A initially moves with velocity v while object B is at rest. After the collision, object A's final velocity is suggested to be 0, while object B's final velocity equals A's initial velocity, v. The minimum kinetic energy of the system occurs at the midpoint of the collision, around 1 second, when there is no relative motion. Kinetic energy can convert into internal energy, although sound and thermal energy are not applicable in the vacuum of space. The discussion emphasizes the importance of using equations to validate intuitive answers in physics problems.
Rookie
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Hello! I need help with this physics problem, I've some what attempted it and I need some feedback. ANY help would be awesome!

Homework Statement


Two objects (A and B) of equal mass, undergo an elastic collision in deep space. Initially, B is at rest and A approaches at velocity v. The duration of contact is 2 seconds.

(a) What is the velocity of object A after the collision (final velocity)?
(b) What is the final velocity of B?
(c) At what time is the kinetic energy of the two object system a minimum?
(d) What has the kinetic energy been converted to?

Homework Equations


The Attempt at a Solution


(a) A velocity is 0.
(b) B velocity is equal to A initial velocity, v.
(c) I don't know :|
(d) Momentum (not sure).
 
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Hi Rookie,

a,b) Your answers seem intuitive and while they could be right you need to use equations to validate your claims.

c) What is the sequence of events of the elastic collision? This can help you understand the question.
d) What can Kinetic Energy convert into?
 
c) Would it be at the middle of the collision, 1 second? Where minimum there is no relative motion, I think?
d) Sound energy and thermal energy?
 
c) That is where it should be in ideal conditions.
d) Well those are true but do not happen in space during an assumed ideal elastic collision. What else can store energy in this setup?
 
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Ahh is it internal energy?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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