15. For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. Which of the following law does it describe? A. Law of Inertia B. Law of Acceleration C. Law of Conservation of Mass D. Law of Conservation of Momentum
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Answer:
mcartvcart0+mballvball0=mballvball0
(Cart is at rest; ball is assumed to not roll.) Due to conservation of momentum -
mballvball0=mcartvcart+mballvball
Our second equation of use is conservation of kinetic energy -
12mcartv2cart0+12mballv2ball0=12mballv2ball0
12mballv2ball0=12mcartv2cart+12mballv2ball
You can work your way to a result from there.
Case 2 - Perfectly Inelastic
mballvball0=(mcart+mball)v
Kinetic energy is not conserved here, but the final velocity can be found quite easily.
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answered Jul 12, 2020 at 0:58
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Naganite
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What exactly you mean by launching a ball "into" a cart is important. If this means that the rubber ball lands on a horizontal surface of the cart and bounces back out, the cart doesn't have to move at all (the momentum exchange can be purely in the vertical direction for a perfectly elastic collision) while it does with the sticky ball.
If what you mean is the balls impact the cart from behind, pushing it forward, then yes, since the rubber ball bounces back, conservation of momentum implies that the car impacted by it moves faster.
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