p0524 - 268 CHAPTER 5. IMPULSE AND MOMENTUM 5.24 Chapter 5,...

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268 CHAPTER 5. IMPULSE AND MOMENTUM 5.24 Chapter 5, Problem 24 Problem: Ball B of mass 2 m hangs from an inextensible cord attached to support C. Ball A of mass m strikes B with a velocity V as shown. Assuming the collision is perfectly elastic and that all effects of friction can be ignored, determine the height, h , reached by Ball B. Express your answer as a function of V = | V | , θ and gravitational acceleration, g . Solution: The motion of Ball B is constrained as it can only move horizontally immediately after the impact. Thus, our first step is to establish unit vectors along and normal to the line of impact, n and t ,in terms of θ and the Cartesian system unit normals, i and j . Inspection of the figure below indicates that n =sin θ i +cos θ j and t = cos θ i +sin θ j j t i Line of impact θ n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................ . . . . . . . . . . . . . . . . . . . . . . . . . ..................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................................... ......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... . . . . The given velocity vectors for the balls are v A = V n and v B = 0 Hence, in terms of the nt and xy coordinate systems, the initial velocity components of Ball A are ( v A ) n = v A · n = V ( v A ) t = v A · t =0 ( v A ) x = v A · i =
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p0524 - 268 CHAPTER 5. IMPULSE AND MOMENTUM 5.24 Chapter 5,...

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