Problem 13.3 In an experiment to estimate the acceleration due to gravity, a student drops a ball at a distance of 1 m above the floor. This publication is protected by Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording or likewise. At t = 1 s, we haveĬ 2008 Pearson Education South Asia Pte Ltd.
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What are the velocity (in in/s) and acceleration (in in/s2 ) of the head at t = 1 s? Solution: The motion is governed by the equations s = (4 in/s)t − (2 in/s2 )t 2 , Problem 13.2 The milling machine is programmed so that during the interval of time from t = 0 to t = 2 s, the position of its head (in inches) is given as a function of time by s = 4t − 2t 3. We need to first determine the time at which the vehicle hits the ground 2h 2(6 m) = 1.106 s = s = 0 = − 12 gt 2 + h ⇒ t = g 9.81 m/s2 Now we can solve for the velocity v = −gt = −(9.81 m/s2 )(1.106 s) = −10.8 m/s. Solution: The equations that govern the motion are: a = −g = −9.81 m/s2 v = −gt h (a) What is the downward velocity 1 s after it is released? (b) What is its downward velocity just before it reaches the ground?
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Problem 13.1 In Example 13.2, suppose that the vehicle is dropped from a height h = 6m. 13.3 Straight-Line Motion When the Acceleration 26ġ3.4 Curvilinear Motion-Cartesian Coordinates 36ġ3.6 Curvilinear Motion-Normal and Tangential 57ġ3.7 Curvilinear Motion-Polar and Cylindrical 73ġ4.2 Applications-Cartesian Coordinates 101ġ4.3 Applications-Normal and Tangential 138ġ4.4 Applications-Polar and Cylindrical 153ġ5.3 Potential Energy and Conservative Forces 215ġ5.4 Relationships between Force and Potential 233ġ6.1 Principle of Impulse and Momentum 254ġ6.2 Conservation of Linear Momentum and Impacts 275ġ7.1 Rigid Bodies and Types of Motion 333ġ8.1 Momentum Principles for a System 469Ģ0 Three-Dimensional Kinematics and DynamicsĪppendix: Moments and Products of Inertia 690