How Do You Calculate Theta and Helium's Velocity After a Neutron Collision?

[McKeavey]

Homework Statement

A neutron with velocity 5E5 m/s and a mass of 1.66E-27 collides with a helium nucleus, mass of 4(1.66E-27) with a velocity of 3.7E5 m/s as shown. If the speed of the neutron after collision is 5E5 m/s and it is moving in the direction of motion of the nucleus after collision, find theta, and velocity of Helium (Prime).
Diagram shown in attachment.
*also the angle 39 + theta does not equal 90 degrees

Homework Equations

P = mv

The Attempt at a Solution

None, I know absolutely nothing about this..
My teacher assigned it to us and expects us to solve it somehow..
Please if someone could lead my through the steps of solving it..It'd be greatly appreciated.

Don't expect me to know anything..

 

[whoareyou]

You apply the same basic principles of conservation of momentum, only now, you have to analyze it in components.

 

[McKeavey]

Which I do not know because I never learned it hah :/
I said I don't know anything about momentum :/

 

[whoareyou]

If you've done 2D kinematics, it should be really simple. Just remember the formula for conservation of momentum:

where u1 and u2 are the velocities before collision, and v1 and v2 are the velocities after collision.

Split each velocity vector up into components and solve for what needs to be solved. So you should have the same equation (^) for both components except one will be analyzing the velocity vectors in the x -direction and one in the y-direction.

 

[asteriatic]

I can understand your confusion and frustration with this problem. Let me guide you through the steps to solve it.

First, let's define some variables:
- m1 = mass of the neutron
- v1 = velocity of the neutron before collision
- m2 = mass of the helium nucleus
- v2 = velocity of the helium nucleus before collision
- v1' = velocity of the neutron after collision
- v2' = velocity of the helium nucleus after collision
- θ = angle between the initial velocity of the neutron and the direction of motion of the helium nucleus after collision

Next, let's write down what we know from the problem:
- m1 = 1.66E-27 kg
- v1 = 5E5 m/s
- m2 = 4(1.66E-27) kg = 6.64E-27 kg
- v2 = 3.7E5 m/s
- v1' = 5E5 m/s
- v2' = to be determined
- θ = to be determined

Now, let's apply the conservation of momentum principle:
- Before collision: m1v1 + m2v2 = (m1+m2)v1' + m2v2'
- After collision: m1v1' + m2v2' = (m1+m2)v1' + m2v2'
- Since the speed of the neutron after collision is the same as its initial speed, we can simplify the equations to: m2v2 = m2v2' and m1v1 = (m1+m2)v1'
- Solving for v2' and v1', we get: v2' = v2 and v1' = v1(m1+m2)/m2
- Now, we can plug in the known values and solve for v2': v2' = (6.64E-27 kg)(3.7E5 m/s)/(1.66E-27 kg) = 1.48E5 m/s
- Finally, we can use the law of cosines to find θ: v2'^2 = v1'^2 + v2^2 - 2v1'v2'cosθ
- Plugging in the known values, we get: (1.48E5 m/s)^2