# D the particle moves left comes to a momentary stop

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comes to a stop. (d) The particle moves left, comes to a momentary stop, then accelerates right until it reaches a final constant velocity, approximately 2.3 m/s. (e) The particle moves left, decelerating until it reaches the absolute minimum, then stops. 6

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The particle is initially right moving but deceleration as the slope of the potential is positive. We can calculate the kinetic energy of the particle after U x has a last plasteau. Since dU x 0 dx 0, if this quantity is negative then we have more interesting behaviour of the particle before that point. E t 0 1 2 . 5kg 4m/s 2 E t 0 1 2 . 5kg v 2 1 . 25J K E t 0 1 . 25J 2 . 75J This quantity is positive! Thus the last plateau is an allowed region of space which the particle reaches with that kinetic energy. Converting to velocity yields v x 3 . 3m/s. Choice A . 7. Two balls hang with 150 cm long strings from a common hook. Initially the 200 g ball B is stationary, freely hanging from the string, as shown in the figure, while the 100 g ball A is held in position with a taut string 90 cm higher than ball B. 90 cm A B Ball A is let free, swings and collides elastically with ball B. What is the maximum height that ball B reaches after the collision? (a) 40 cm 4 (b) 45 cm (c) 50 cm (d) 55 cm (e) 60 cm 7
We solve this problem by conservation of energy and momentum constraints: m A v A m A v A m B v B 1 2 m A v 2 A 1 2 m A v 2 A 1 2 m B v 2 B 1 2 m A v 2 A 1 2 m A m A v A m B v B 2 1 2 m B v 2 B m B v A v B 1 m B m A 1 2 m B v 2 B Equating Potential and Kinetic energies: 2 gm B h A h B 1 m B m A m B gh B h B h B 2 h A 1 m B m A h B 4 h A 1 m B m A 2 4 9 h A 40cm Good luck! 8
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