Elastic Collision: Find Speed of Protons After Collision

[shamockey]

A proton, moving with a velocity of v1i collides elastically with another proton that is initially at rest. One proton has three times the speed of the other after the collision. How would I find the speed of each proton after the collision in terms of vi and their velocity vectors after the collision?

I understand that momentum is conserved, but i see how to apply it.

Any help would greatly be appreciated.

 

[dextercioby]

Well,then yes,u must use both momentum conservation (in vector form !) and conservation of KE (since u don't have the #-s you can assume for simplicity non-relativistic case)...

That would be all.Just choose 2 orthonormal axis and simple algebra to find what u want.

Daniel.

 

[thepatientmental]

To find the speed of each proton after the collision, we can use the conservation of momentum and energy principles. In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and the total kinetic energy before the collision must be equal to the total momentum and the total kinetic energy after the collision.

Let us label the protons as P1 and P2, with P1 initially moving with a velocity of v1i and P2 initially at rest. After the collision, P1 has a velocity of v1f and P2 has a velocity of v2f. We can set up the following equations to solve for the final velocities:

Conservation of momentum: m1v1i + m2v2i = m1v1f + m2v2f

Conservation of kinetic energy: (1/2)m1v1i^2 + (1/2)m2v2i^2 = (1/2)m1v1f^2 + (1/2)m2v2f^2

Since we are given that one proton has three times the speed of the other after the collision, we can write v1f = 3v2f. Substituting this into the two equations above, we get:

m1v1i + m2v2i = m1(3v2f) + m2v2f

(1/2)m1v1i^2 + (1/2)m2v2i^2 = (1/2)m1(9v2f^2) + (1/2)m2v2f^2

We now have two equations with two unknowns (v2f and v2i). We can solve these equations to get the final velocities of the protons after the collision. Once we have v2f, we can substitute it into v1f = 3v2f to get the final velocity of P1.

In terms of the velocity vectors, we can represent the initial velocity of P1 as vi = v1i and the initial velocity of P2 as vj = v2i. After the collision, the final velocity of P1 can be represented as v1f = vi' + vj' and the final velocity of P2 as v2f = vj' - vi'. This takes into account the direction of the velocities after the collision