Momentum, enegy and collisions

In summary: You should get 3.6 for m.In summary, using the conservation of momentum and kinetic energy, the mass of the second particle was found to be 3.6 u and the final velocity was found to be 1.2x10^6m/s.
  • #1
hellothere123
31
0
A proton (mass 1 u) moving at 7.80 x10^6m/s collides elastically and head-on with a second particle moving in the opposite direction at 2.40x10^6 m/s. After the collision, the proton is moving opposite to its initial direction at 6.60x10^6m/s. Find the mass and final velocity of the second particle. [Take the proton's initial velocity to be in the positive direction.]


I tried using the conservation of momentum and kinetic energy to do this. I get this big mess that i cannot solve for.. Please show me how i would do this. i would like to learn to do these problems. thanks.
 
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  • #2


You should have 2 equations with 2 unknowns from each of the conservations.

Make it simpler by dropping the powers of 10 and add it back as a factor at the end.

Try writing out your equations here.
 
  • #3


so if we let m1 be the proton. we have..
(7.8)-(m2)(2.4)=(-6.6)+m2v2
(7.8^2)+m2(2.4^2)=(6.6^2)+m2(v2)^2

m2 = [(7.8^2)-(6.6^2)]/[(v2)^2-(2.4^2)]

and then when i plug it back in, i get a quadratic. that gives me a mass considerably larger than the other one.
 
  • #4


What do you mean considerably? If your maths is right then what stops the second particle being very large?

The Bob
 
  • #5


my math is probably bad, that is why i was hoping someone could show me the math so i can see where i went wrong
 
  • #6


hellothere123 said:
so if we let m1 be the proton. we have..
(7.8)-(m2)(2.4)=(-6.6)+m2v2
(7.8^2)+m2(2.4^2)=(6.6^2)+m2(v2)^2

m2 = [(7.8^2)-(6.6^2)]/[(v2)^2-(2.4^2)]

and then when i plug it back in, i get a quadratic. that gives me a mass considerably larger than the other one.

OK. So you can say that

m*(v + 2.4) = 14.4 from the first equation. And ...

m*(V2 - 2.42) = 7.82 - 6.62

Note that this factors easily into

m*(V + 2.4)(V - 2.4) = 7.82 - 6.62

But from the first equation you know m*(v + 2.4) = 14.4 So ...

14.4*(V - 2.4) = 7.82 - 6.62

Much easier than a quadratic to solve.

EDIT: Sorry the 7.82 and 6.62 terms got translated incorrectly. I fixed them now.
 
Last edited:
  • #7


that is much easier and such.. and after working it out.. i did not get the right answer. the answer was 3.6 doing that gave me 1.2
 
  • #8


hellothere123 said:
that is much easier and such.. and after working it out.. i did not get the right answer. the answer was 3.6 doing that gave me 1.2

Sorry. I apparently switched two terms inadvertently in typing it out. I just fixed it.
 

1. What is momentum?

Momentum is a measure of an object's motion, which takes into account both its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction. The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity.

2. How is momentum conserved in a closed system?

In a closed system, the total momentum before a collision or interaction is equal to the total momentum after the collision or interaction. This is known as the law of conservation of momentum. This means that the total momentum of all objects in the system remains constant, even if individual objects may have changes in their momentum.

3. What is the difference between elastic and inelastic collisions?

In an elastic collision, both kinetic energy and momentum are conserved. This means that the objects involved bounce off each other without any loss of energy. In an inelastic collision, kinetic energy is not conserved and some energy is lost in the form of heat or sound. However, momentum is still conserved in both types of collisions.

4. How are energy and momentum related in collisions?

In a collision, energy can be transferred between objects as they interact with each other. This transfer of energy is related to the change in momentum of the objects. The more momentum that is transferred, the more energy will be transferred. This is why objects with larger masses and velocities can cause more damage in collisions.

5. How do you calculate the velocity of an object after a collision?

To calculate the velocity of an object after a collision, you can use the formula v = (m1v1 + m2v2) / (m1 + m2), where m1 and m2 are the masses of the objects and v1 and v2 are their velocities before the collision. This formula is derived from the conservation of momentum principle and assumes an elastic collision. In an inelastic collision, more information is needed to calculate the final velocity.

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