2 dimensional elastic collision

[teleport]

Hey, I'm having problems with this:

A particle m with initial speed V1 collides with a particle at rest with mass 3m. After collision, particle with mass m is seen moving 30 degrees from its initial direction. What is the angle of motion of the 2nd particle after collision?

I can get three equations from momentum and energy for three unknowns but I can't solve it. Help?

 

[KoGs]

Show me your equations.

 

[teleport]

x-component:

V1 = v1cos30 + 3VcosC


y-component:

v1sin30 = 3VsinC


Energy:

V1^2 = v1^2 + 3V^2,

where C is the unknown angle, v1, V are the final velocities of the m and 3m masses.

 

[KoGs]

That's not exactly how I'd go about it. oops nevermind lol.

 

[KoGs]

Well you see your equation 1 gives you what V1 is. So you can plug that into equation 3. Now you are only left with 2 uknowns, V and C. Now equation 2 gives you a way of getting rid of V. So now you only have 1 equation and 1 unknown, C.

btw, conservation of momentun does not use angles.

I should say conservation of momentum does not have to use angles. So if it helps, go ahead and use the total conservation of momentum equation.

 

[teleport]

that's wrong. Ill explain tomorrow why. Anyways thax.

 

[EthanB]

Your equation in the y direction needs a negative sign.

Also, you will use angles.

 

[teleport]

Please can someone actually help?

 

[vanesch]

Please can someone actually help?

Your equations seem correct (C will then be a negative angle). What's your problem in solving them ?

You need to solve for the quantities v1, V and C and you have 3 equations.

Try to eliminate v1 and V using the first two equations to write everything as a function of C in the third one, and you'll have an equation for your angle C.