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 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 cos2 - sin2 = ½. To solve this for , you can write cos2 - sin2 as 2cos2 - (cos2 - sin2) = 2cos2 - 1 using the trigonometric identity cos2 + sin2 = 1. Hint 3: It is helpful to write cos30 as cos30 = rather than use the decimal value of cos30.
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 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 cos2 - sin2 = ½. To solve this for , you can write cos2 - sin2 as 2cos2 - (cos2 - sin2) = 2cos2 - 1 using the trigonometric identity cos2 + sin2 = 1.
Hint 3: It is helpful to write cos30 as cos30 = rather than use the decimal value of cos30.
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