ME3103(HW1) - ME3103 Dynamics and Control for Product...

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Unformatted text preview: ME3103 Dynamics and Control for Product Design Homework Assi mmth 1 Date: February 10, 2011 Deadline for submission: March 2, 2011 The suggested solution of this assignment wili be posted on ME; web site or emailed to you on March 4, 2011. This assignment has 10 questions. A11 questions carry equai scores. Students are reminded that the academic integrity poiiey is enforced in homework assignments. 1. Cable AB is attached to the top of the vertical 3—:1‘1 post, and its tension is 50 1:N . \What are the tensions in cables AC), AC, and AD? ~. (6, 2, 0) m _ m.~‘~.k If 75332335,“ B: .- . *le m L :23 1| 3 3m 2. Cables AB and AC can sustain a maximum tension of 500 N, and the pole can support a maximum compression of 300 N. Determine the maximum weight of the lamp that can be supported in the position shown. The force in the pole acts along the axis of the pole. 3. The spring constant. is 1(19600 N/m and the unstretched length of the spring is 30mm. Treat the bolt at A as a pin support and assume that the surface at C is smooth. Determine the reactions at A and the normal force at C. 4. An 2.4 mmlong boom is heid by a ha]§.—and~socket joint at. C and by two cables AD and BE. Determine the tension in each cabie and the reaction at C. 5 0.9 n“?! 3x” we é . 890 N 5. The rectangular plate has a mass of 15kg and is held in the position shown by hinges A and B and cable BF. Determine the tension in the cable. 541V} Tiiliis‘ m gait} mm “M. ; . {3’ 5i? mm 6. A collar A slides on the circular bar as shown in the following figure. The shape of the circular bar belongs to a semi—circle. (a) Show that the radial position of A (in metres) can be given as function of (9 by r = 20086? . 2 (b) At the instant shown, 6’ 2 250, £91": 4 rad/S and d 6 m U . Determine the acceleration of di dr2 A in terms of the polar coordinates. ll?“ 74 The spring constant is it : 850 N/rn, tnA I 40kg, and inis 7w 60kg. The collar A slides on the smooth horizontal bar. The system is released. from rest in the position shown with the spring unstretched. Use conservation of energy to determine the velocity of the collar A when it has moved 0.5m to the right. imm- es m———: 8. At the instant shown in the following figure, block C is moving upward at 10 cm/s. (2} Locate the instantaneous centre of zero velocity of link BC. (b) Determine the angular velocity of link BC and hence determine the velocity of B. (c) Determine the angular Velocity of link AB. 9. 'I'Rvo rods AB and DJ") are connected as shown in the following figure. Knowing that point B moves downward with a velocity of 1.2 m/ 3, determine at the instant shown (a) the angular velocity of each rod, (b) the velocity of point J; {Fa 3'3 i +724 vvvvvvvv Jill Ami Hi} In 10‘ The angular velocity and angular acceleration of bat AB are (9,13 m 4tad/s and etc/1. 13 = m6 tad/$2. (3) Determine the angular velocities of bats BC and CD. (b) Determine the angular accelerations of bats BC and CD. February 9, 2011 ...
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