What Happens to Atom Speeds and Directions in an Elastic Collision?

[John O' Meara]

An atom of mass m moving in the x direction with speed v collides elastically with an atom of mass 3m at rest. After the collision the first atom moves in the y direction. Find the direction of motion of the second atom and speed of both atoms (in terms of v) after the collision?
Ans: mass m moves at v/sqrt(2), mass 3m moves at v/sqrt(6) in the direction theta=-35.3 degrees.

Momentum before = momentum after

MV1i + MV2i = MV1f + MV2f

x-direction MV1i = MV1fx + MV2fx

y-direction 0 = MV1fy + MV2fy

this translates into

mv = mV1fx + 3mV2fx ......(i)

0 = mV1fy + 3mV2fy ......(ii)

mv^2 = m(0 + V1fy^2) + 3m(V2fx^2 + V2fy^2) ...(iii)

where :
M, V1i, V2i, V1f, V2f, V1fx, V2fx, V1fy, V2fy , etc are variables

m,v are values

x = x-component , y = y-component, f = final , i = initial

The question is are these equations right, as I cannot get the above answers
Thanks and regards.

 

[Doc Al]

this translates into

mv = mV1fx + 3mV2fx ......(i)

0 = mV1fy + 3mV2fy ......(ii)

mv^2 = m(0 + V1fy^2) + 3m(V2fx^2 + V2fy^2) ...(iii)

OK, but realize that V1fx = 0, V1fy = v1f. That will simplify things, giving you three equations and three unknowns.

 

[thepatientmental]

Yes, these equations are correct. To solve for the direction and speed of the atoms after the collision, we can use the conservation of momentum and kinetic energy equations. Solving these equations simultaneously, we get the values for V1fy and V2fx, which can then be used to find the direction and speed of the atoms. The values you have obtained for the direction and speed of the atoms after the collision seem to be correct. However, it is always a good idea to double check your calculations and equations to ensure accuracy.