Figure Q2 shows a spool with a mass of 20 kg and a radius of gyration ko = 0.16 m. The 15 kg block A is released from rest position. Apply the conservation of energy method to determine the distance that block A must fall for the spool to rotate at an angular velocity of 8 rad/s. (a) (b) Apply the principle of work and energy to determine the tension in the cord when the block is in motion. (b) What are the assumptions made in the analysis? 0.2 m A Figure Q2

Figure Q2 shows a spool with a mass of 20 kg and a radius of gyration ko = 0.16 m. The 15 kg block A is released from rest position. Apply the conservation of energy method to determine the distance that block A must fall for the spool to rotate at an angular velocity of 8 rad/s. (a) (b) Apply the principle of work and energy to determine the tension in the cord when the block is in motion. (b) What are the assumptions made in the analysis? 0.2 m A Figure Q2

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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1) The figure below shows a system in which mass m2 is added to mass m1 (the spring is not stretched). Answer the following questions about the motion when mass m2 is released freely. However, the mass and moment of inertia of the movable pulley are ignored. M X1 mi m2 X2 1) Show the kinetic energy of the entire system using x1 and x2 (just the answer is enough). 2) Show the relationship between x1 and x2 (just the answer is enough). 3) Find the equivalent mass of the entire system. 4) Show the equation of motion of the system using this equivalent mass. However, assume that the damping is zero. 5) Find the natural frequency
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5. An 80 kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height? High bar 1.8 m 3 m ANS. Moment of inertia at full extension, I = 21.6 kg-m^2 Moment of inertia at the tuck I' = 5.4 kg-m^2 Angular velocity at the tuck = 4 rev/sec Time interval in the tuck = 0.5 sec i.e. In 0.5 s, he will be able to execute two revolutions at 4.0 rev/s.
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1. The rod below with a mass of m and total length of L is attached to the table via a pin connection. It is released from rest when it is horizontal. What is the moment of inertia of the rod about the pin, Io? b. What is the angular acceleration of the rod as a function of 0? What is the angular velocity of the rod as a function of 9? d. What is the reaction force at the pin (in vector form) as a function of 0? a. C. L/3 0 2L/3 Ө
Question 6 a) The 40-kg roll of the paper in Figure Q6(a) rests along the wall where the coefficient of kinetic friction is μ= 0.2. If a vertical force of P = 40 N is applied to the paper, determine the angular velocity of the roll when t = 6 s starting from rest. Neglect the mass of the unraveled paper and take the radius of gyration of the spool about the axle O to be ko = 80 mm. B 12 A 13 120 mm Spool M = 30 N·m Figure Q6(a) b) The pendulum is shown in Figure Q6(b) and consists of a 10-kg uniform disk and a 3-kg uniform slender rod. If it is released from rest in the position shown, determine its angular velocity when it rotates clockwise 90°. (mass moment of inertia of a slender rod about the mass 1 center=__m/², mass moment of inertia of a uniform disk about the mass center=--mr²) 12 2m P = 40 N B Figure Q6(b) 0.8 m
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8. 2) Rods AB and BC are linked at Band have weights of 18 lb and 37 lb, respectively. The 8-lb collar C, which is connected to BC and the spring, slides freely along the smooth vertical guide. The lengths of the rods are 4 = 1.4 ft and 2 = 2.9 ft. If the system is released from rest when 0 = 0°, determine the magnitude of the angular velocity (in rad/s) of rod BC when 0 = 90°. The attached spring has spring constant k = 20 Ib/ft, and is unstretched when 0 = 0°. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g= 32.2 ft/s2. k CO Your Answer: Answer
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