Solve Elastic Collision Homework: Neutron Mass m0

[lydiazmi]

Homework Statement

A neutron of mass m₀ collides with an immobile atomic nucleus of carbon of mass m=12m₀. Collision is considered central and elastic. how many times does the kinetic energy of neutron decreases during the collision.

Homework Equations

m=12m₀

m₀v₀=mu-m₀u

(m₀v₀²)/2=(mu²)/2-(m₀u₀²)/2

The Attempt at a Solution

v₀= (mu-m₀u₀)/m₀=
=(12m₀u-m₀u₀)/m₀=
=12u-u₀

u=(v₀+u₀)/12
u²=(v₀²+2u₀v₀+u₀²)/144


v₀²=12u²-u₀²

u²=(v₀²+u₀²)/12

(v₀²+2u₀v₀+u₀²)/144=(v₀²+u₀²)/12

0=11u₀²-2u₀v₀+11v₀²)

I'm stuck here. I know tht I hv to find x=(u₀²)/(1v₀²) because (m₀u₀²)/2=x(m₀v₀²)/2
u₀²=xv₀²

(the answer is 1.4 times)

 

[Mr.A.Gibson]

Take this equation
v0 =12u+u0 and square it to get
v0^2 = 144u^2 + 24u0u + u0^2
You also have this equation
v0^2=12u^2 + u0^2
So equate those and that leads to
132 u = - 24u0

Substitute this into the first equation I wrote, to see the relative change in velocity, then square it for change in kinetic energy.

 

[lydiazmi]

but m>m0. Shouldnt u0 be negative in both equ?

 

[Mr.A.Gibson]

But it can be negative, you could solve these equations and get u0<0 which would indicate that it is traveling in the other direction.

 

[Mr.A.Gibson]

In this equation tho you stated incorrectly.
(m0v02)/2=(mu2)/2-(m0u02)/2

Since velocity is squared kinetic energy is allows positive. So Kinetic energy before must equal sum of kinetic energies after the collision.
(m0v02)/2=(mu2)/2+(m0u02)/2

 

[ashishsinghal]

I agree with Mr.A.Gibson in all the above posts.

 

[lydiazmi]

yea2, ur right! got it, thank u very much!