The figure below shows an elastic collision between two bodies in which the coll

Question

The figure below shows an elastic collision between two bodies in which the collision is not head-on. Projectile particle m1 is an alpha particle and target m2 is an oxygen nucleus. The oxygen nucleus (m2) is initially at rest. The alpha particle is scattered at angle ?1= 66.0 The figure below shows an elastic collision between two bodies in which the collision is not head-on. Projectile particle m1 is an alpha particle and target m2 is an oxygen nucleus. The oxygen nucleus (m2) is initially at rest. The alpha particle is scattered at angle ?1= 66.0 The figure below shows an elastic collision between two bodies in which the collision is not head-on. Projectile particle m1 is an alpha particle and target m2 is an oxygen nucleus. The oxygen nucleus (m2) is initially at rest. The alpha particle is scattered at angle ?1= 66.0 The figure below shows an elastic collision between two bodies in which the collision is not head-on. Projectile particle m1 is an alpha particle and target m2 is an oxygen nucleus. The oxygen nucleus (m2) is initially at rest. The alpha particle is scattered at angle ?1= 66.0 degree and the oxygen. nucleus recoils with speed 1.10 times 105 m/s at angle ?2 = 55.0 degree . In atomic mass units, the mass of an alpha particle is 4.00 u and the mass of an oxygen nucleus is 16.0 u. Find the final speed of the alpha particle. m/s Find the initial speed of the alpha particle. m/s

Explanation / Answer

Initial x momentum
= malpha vi
= final x momentum
= malpha vf cos (theta1) + mO vrecoil cos(theta2)

Initial y momentum = 0
= final y momentum
= malpha vf sin (theta1) - mO vrecoil sin(theta2)


Solve the second equation for your final speed.
vf = vrecoil (mO / malpha) (sin(theta2) / sin(theta1) )

=1.10x10^5*(16/4) (sin55/sin66)

=3.94x10^5

Solve the first equation for your initial speed:
vi = vf cos (theta1) + mO vrecoil cos(theta2) / malpha

Substitute your final speed into your equation for initial speed:

vi = vrecoil mO sin(theta2) cos(theta1) / (malpha sin(theta1) )
+ mO vrecoil cos(theta2) / malpha

= vrecoil (mO / malpha) ( sin(theta2) cot(theta1) + cos(theta2) )

=1.10 x 10^5 * (16/4) * [sin(55)* cot(66)+cos(55)]

vi=4.128 x 10^5

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