PRACTICE IT Use the worked example above to help you solve this problem. Two bil

Question

PRACTICE IT Use the worked example above to help you solve this problem. Two billiard balls of identical mass move toward each other as shown in the figure. Assume that the collision between them is perfectly elastic. If the initial velocities of the balls are v1i = +30.2 cm/s and v2i = ?21.0 cm/s, what are the velocities of the balls after the collision? Assume friction and rotation are unimportant. (Indicate the direction with the sign of your answer.) v1f = Correct: Your answer is correct. cm/s v2f = Correct: Your answer is correct. cm/s The info above is here so you can put it into the second half of problem EXERCISE HINTS: GETTING STARTED | I'M STUCK! Find the final velocity of the two balls if the ball with velocity v2i = ?21.0 cm/s has a mass equal to half that of the ball with initial velocity v1i = +30.2 cm/s. (Indicate the direction with the sign of your answer.) v1f = Incorrect: Your answer is incorrect. Let the mass of the ball traveling at -21.0 cm/s be equal to m/2. The mass of the ball traveling at 30.2 cm/s would then be equal to m. Write conservation of momentum in terms of m, m/2, and the initial and final velocities of the balls. Apply conservation of energy in the form of v1i - v2i = ?(v1f ? v2f). You have two equations and two unknowns, so you should be able to solve for the unknowns. cm/s v2f = Incorrect: Your answer is incorrect. Let the mass of the ball traveling at -21.0 cm/s be equal to m/2. The mass of the ball traveling at 30.2 cm/s would then be equal to m. Write conservation of momentum in terms of m, m/2, and the initial and final velocities of the balls. Apply conservation of energy in the form of v1i ? v2i = ?(v1f ? v2f). You have two equations and two unknowns, so you should be able to solve for the unknowns. cm/s

Explanation / Answer

m1v1 + m2v2 = m1v1' + m2v2' since the masses are equal. v1+ v2= v1'+v2' 30.2 - 21= v1' +v2' 9.2 = v1'+ v2' co efficient of restituition = ub- ua / va- vb= 1 -23 - 30.2 = v1 '- v2' solve for v1' and v2'

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