Particle Collision: Mass and Velocity Ratios Question

[Matt1234]

Hello, I have a new question that i have no idea how to go about.
please advise.

Homework Statement

Two subatomic particles collide. Initially, the more massive particle (A) is at rest and the less massive particle (B) is moving. After the collision, the velocities of A and B make angles of 67.8 and 30 degrees, respectively, to the original direction of B's motion. The ratio of the final speeds of the particles Vb / Va is 3.30. What is the ratio of the masses of the particles Mb / Ma ?

Homework Equations

p =mV
Ma Va = Mb Vb

The Attempt at a Solution

No idea how to attack tha angles.
please advise.

 

[LowlyPion]

You can use momentum in 2 dimensions. You know that it must be conserved in both x and y. That should allow you to write a couple of equations in sine and cosine, and given the initial statement about the final ratio of the velocities ...

 

[Matt1234]

my variables keep canceling each other out, i tried 3 different methods i need some more info please.

 

[Matt1234]

Here is my attempt:

http://img188.imageshack.us/i/attempt.jpg/

 

[LowlyPion]

Here is my attempt:

http://img188.imageshack.us/i/attempt.jpg/

Let M1 be the moving particle.

M1v1 = M1V1(Cos67.8) + M2V2(Cos30)

With no initial velocity in the direction perpendicular to the initial motion then the second equation yields:

M1V1(Sin67.8) = M2V2(Sin30)

The second equation yields your desired result almost by inspection.

 

[Matt1234]

Yes that works very well, however i don't understand how you came up with it.

I don't understand this part " With no initial velocity in the direction perpendicular to the initial motion"

Why the switch from cos to sin?

I do understand the first equation but don't see the initial velocity in the second which i also don't understand. the first equation uses the x component of V1 and V2 yet the second uses the y components of V1 and V2, i thought you would have to incorporate both components into a formula in order to get a valid result.

Thank you sir.

 

[cepheid]

I don't understand this part " With no initial velocity in the direction perpendicular to the initial motion"

Why the switch from cos to sin?

The first equation is conservation of momentum in the x direction. The second is conservation of momentum in the y direction. (Or maybe it's the other way around -- I didn't look at the picture).

It's not that he switched from cos to sin. Those are two entirely different equations.

His statement which you have quoted points out that since the particle is initially moving in a straight line, ONE of those two components of the initial momenta (x or y) is zero, meaning that the final momenta in that direction must also add to zero. Therefore, the components of the momenta of the two particles in that direction are merely negatives of each other.

 

[Matt1234]

ahh ok that makes sense. i understand it now. for the convervation of momentum to hold true initial p must = final p. since the initial py = 0 the final py = 0 So he set the 2 components of final py = to each other. Thats brilliant, unfortunately i will never think of that on a test.

 

[Matt1234]

Thank you for your continued help guys.