Subatomic particle A with mass m traveling with speed v collides elastically with subatomic particle B of mass 2m that is initially at rest. Particle A is scattered at an angle of 90° to its initial direction of travel. (a) At what angle q to the initial direction of travel of particle A does particle B move after the collision? (answer: 30°) (b) What are the final speeds of the particles? (answer: vfinal = v/ for both particles) (c) What fraction of the initial kinetic energy of particle A is transferred to particle B? (answer: 2/3)
Subatomic particle A with mass m traveling with speed v collides elastically with subatomic particle B of mass 2m that is initially at rest. Particle A is scattered at an angle of 90° to its initial direction of travel.
(a) At what angle q to the initial direction of travel of particle A does particle B move after the collision?
(answer: 30°)
(b) What are the final speeds of the particles? (answer: vfinal = v/ for both particles)
(c) What fraction of the initial kinetic energy of particle A is transferred to particle B? (answer: 2/3)
Hint 1: Draw a Cartesian coordinate system and have particle A move initially in the positive (or negative, it doesn’t make a difference) x-direction.
Hint 2: At some point you should get the relationship cos2q - sin2q = ½. To solve this for q, you can write cos2q - sin2q as 2cos2q - (cos2q - sin2q) = 2cos2q - 1 using the trigonometric identity cos2q + sin2q = 1.
Hint 3: It is helpful to write cos30° as cos30° = rather than use the decimal value of cos30°.
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