Total momentum after collision physics

[lemon]

1. A proton, moving to the left at 7.0 x 10⁶m/s collides with a neutron (mass approx. same as that of the proton) moving at 4.0x10⁶m/s to the right to form a deuteron. Find the velocity of the deuteron.



2. Total momentum before collision = Total momentum after collision



3. 7.0 x 10⁶m/s - 4.0x10⁶m/s = v
v= 3.0x10⁶m/s. This is an inelastic collision

Could someone check that please?

 

[Fightfish]

Sure, and your answer is...wrong. The mass of the deuteron is twice that of the proton/neutron. You might want to write out the full COLM expression to avoid careless mistakes like that.

 

[lemon]

(M_n x 4.0 x 10⁶m/s) - (M_p x 7.0 x 10⁶m/s) = (M_n+M_p) + v
4.0 x 10⁶m/s - 7.0 x 10⁶m/s = 2M +v
-3.0 x 10⁶m/s = 2Mv
v = -3.0 x 10⁶/2 x M

That seems wrong

 

[Fightfish]

(M_n x 4.0 x 10⁶m/s) - (M_p x 7.0 x 10⁶m/s) = (M_n+M_p) + v

(M_n+M_p)v, not (M_n+M_p) + v !

 

[lemon]

(Mn x 4.0 x 10⁶m/s) - (Mp x 7.0 x 10⁶m/s) = (Mn+Mp)v
4M-7M = (Mn+Mp)v
-3M = 2Mv
v = -3/2 = -1.5

 

[Fightfish]

Yup, that's it, 1.5 X 10^6 m/s to the left.
(always try to give an interpretation to a negative sign)

 

[lemon]

great!
Thank you Fightfish