3. A neutron with a mass of 1.0 amu (atomic mass unit) moving along the +x axis

Question

3. A neutron with a mass of 1.0 amu (atomic mass unit) moving along the +x axis at +5.00 x 105 m/s, collides with a helium nucleus with a mass of 4.0 amu, traveling perpendicular to it, in the -y direction at - 3.75 x 105 m/s as shown in Figure3. If the resultant speed of the neutron after the collision is 5.00 x 105 m/s in the direction shown, find the resultant speed and direction of the helium nucleus after the collision. The masses of the 2 objects remain un-changed before and after the collision. From your answers, show that the momentum of the x and y components of the 2 objects before and after the collision is conserved, assuming there are no other forms of energy losses resulting from the collision. Figure 3 helium (m2 4amu) : v20,--3.75 x 105 m/s neutron ( m1 = 1 amu ) V10x5.00 x 105 V1f V2f V1f-5.00 x 105 m/s +V2fx

Explanation / Answer

Applying momentum conservation,

(1 x 5 x 10^5 i) + (4 x -3.75 x 10^5) = (1 x 5 x 10^5)(-sin37i - cos37 j) + 4 v

v = 2 x 10^5 i - 2.75 x10^5 j m/s

Speed = sqrt(2^2 + 2.75^2) x 10^5 = 3.40 x 10^5 m/s .......Ans

direction angle = tan^-1(2 / 2.75) = 36 deg .......Ans

Pix = 5 x 10^5 kg m/s

Pfx = (5 x 1 x 10^5 x - sin37) + (3.40 x 4 x 10^5 sin36) = 5 x 10^5 kg m/s

Piy = -3.75 x 4 x 10^5 = - 15 x 10^5 kg m/s  

Pfy = (1 x 5 x 10^5 x - cos37) + (4 x -3.40 x 10^5 x cos36)

= - 15 x 10^5 kg m/s

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