(a) Explanation Given information: The mass of slender rod is m . The length of slender rod is L . The impact at D is perfectly plastic. The length b is 0.6 L . Calculation: The motion is falling motion before impact. Consider the position 1 is before impact. Sketch the position 1 of the rod as shown in Figure (1). Consider the position 2 is just before impact. (The rod is in horizontal position). Sketch the position 2 of the rod as shown in Figure (2). Refer Figure (2), Before the impact the rotation is about point A . Write the equation of velocity ( v ¯ 2 ) of rod before impact. v ¯ 2 = L 2 ω 2 Here, ω 2 is the angular velocity of rod at position 2. At position 1, the rod is at rest. Therefore, the kinetic energy of rod ( T 1 ) at position 1 is zero. Write the equation of potential energy ( V 1 ) of rod at position 1. V 1 = m g L 4 At position 2, the rod is in horizontal position. Therefore, the potential energy of rod ( V 2 ) at position 2 is zero. Write the equation of kinetic energy ( T 2 ) of rod at position 2. T 2 = 1 2 m ( L 2 ω 2 ) 2 + 1 2 ( 1 12 m L 2 ) ω 2 2 = 1 6 m L 2 ω 2 2 Apply conservation of energy for position 1 and 2. T 1 + V 1 = T 2 + V 2 Substitute 0 for T 1 , m g L 4 for V 1 , 1 6 m L 2 ω 2 2 for T 2 , and 0 for V 2 . T 1 + V 1 = T 2 + V 2 0 + m g L 4 = 1 6 m L 2 ω 2 2 + 0 ω 2 2 = m g L 4 × 6 m L 2 ω 2 2 = 3 g 2 L ω 2 = 3 g 2 L Consider the impulse and momentum principle. Syst Momenta 1 + Syst Ext Imp 1y2 = Syst Momenta 2 Sketch the impulse and momentum diagram of the system as shown in Figure (3). Refer Figure (3). Take moments about D (anticlockwise moment as positive). I ¯ ω 2 − m v ¯ 2 ( L 10 ) = I ¯ ω 3 + m v ¯ 3 ( L 10 ) (1) Here, v ¯ 3 is the angular velocity of rod just after the impact. Consider the position 3 is just after impact. Sketch the position 3 of the rod as shown in Figure (4) (b) To determine The maximum angle through which the rod will rotate after the impact.

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 17.3, Problem 17.117P

(a)

To determine

The angular velocity of the rod immediately after the impact.

(b)

To determine

The maximum angle through which the rod will rotate after the impact.

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Chapter 17.3, Problem 17.116P

Chapter 17.3, Problem 17.118P

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