# HW3 - ME360 Dynamic Systems Prof Gillespie Fall 2010 HW 3...

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ME360 - Dynamic Systems Prof. Gillespie - Fall 2010 HW 3 - Due Sept 23 Problem 1 Problem 2.3, page 70. For convenience, I will repeat the problem statement here: For the mass shown in Figure 2.1.3b (in the body of Chapter 2), m = 10kg, φ =25 , v (0) = 2m/s and μ = 0 . 3. Determine whether the mass comes to rest if (a) f 1 = 100N and (b) f 1 = 50N. If the mass comes to rest, compute the time at which it stops. Problem 2 Problem 2.19, page 74 in the book. (Note extra part below, not included in book) The geared system shown in Figure P2.19 (same in previous edition) is similar to that used in some vehicle transmissions. The speed ratios (which are the ratios of the gear radii) are ω 2 ω 1 = 3 ω 3 ω 2 = 3 5 ω 4 ω 3 = 13 11 (1) a) Determine the overall speed ratio ω 4 1 b) Derive the equation of motion in terms of the velocity ω 4 , with the torque T 1 as the input. Neglect the inertias of the gears and the shafts. c) In addition, derive the equation of motion in terms of the velocity ω 4 when there is a viscous friction force acting on inertia I with torque

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