Impulse and Momentum: Substitution Trouble

AI Thread Summary
In this discussion, participants focus on solving a physics problem involving an elastic collision between a van and a car. The initial conditions include a 1055-kg van at rest and a 715-kg car moving at +2.26 m/s. Key points emphasize the importance of using momentum conservation principles to find the final velocities of both vehicles. Participants suggest forming two equations based on initial and final momentum, considering velocities as vectors. The conversation concludes with a clarification that this approach simplifies understanding the problem.
Sakura
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Ok, in this problem I am getting bogged down in the basic algebra part of it. I had one person explain it once but I still missed something.:frown:

a 1055-kg van, stopped at a traffic light, is hit directly in the rear by a 715-kg car traveling with a velocity of +2.26 m/s. Assume that the transmission of the van is in neutral, the brakes are not being applied, and the collision is elastic. What is the final velocity of (a) the car and (b) the van?
m1 = 715 kg
m2 = 1055 kg
vo1 = +2.25 m/s
vo2 = 0 m/s
vf1 = ?
vf2 = ?
http://www35.websamba.com/aerowenkitten/images/untitled.jpg
 
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You know the initial masses and velocities and hence the initial momentum...from this you know the *relative* approach velocity before impact...and as the collision is elastic you also know the relative exit velocity...If you can form 2 equations using this info you should be able to spot a substitution easily...I don't think trying to solve in terms of KE is the best method
 
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Think of it this way.

The initial momentum of the system (the car + the van) must equal the final momentum of the system (the car + the van).

Treat velocities as vectors such that -> would be (+) and <- would be (-).

That should help.
 
AHHH... thank you! lol makes more sense that way!
 
No problem.
 
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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