To determine Determine the angular velocity of the bar when θ = 60 ° . Explanation Show the displacement diagram of rod as in Figure (1). Express the position G when θ = 90 ° . O G 1 = b + 2 b 2 = 1.5 b (I) Express the position G when θ = 60 ° . O G 2 = b + 2 b 2 sin 60 ° = 1.5 b sin 60 ° (II) Apply the work and energy principal between the initial and final states. T 1 + U 1 − 2 = T 2 T 1 + U b l o c k − U a r m = T 2 T 1 + m 2 g ( A 1 C − A 2 C ) − m 1 g ( O G 1 − O G 2 ) = 1 2 m 2 v 2 + 1 2 I ω 2 (III) Here, the initial and final kinetic energy of the slender rod is T 1 and T 2 respectively, the sum of the work done between initial and final positions is U 1 − 2 , the potential energy of the block is U b l o c k , the potential energy of the arm is U a r m , mass of the slender rod and load is m 1 and m 2 respectively, moment of inertia of bar is I and acceleration due to gravity is g . Conclusion: Substitute 0.4 m for b in Equation (I). O G 1 = 1.5 ( 0.4 ) = 0.6 m Substitute 0.4 m for b in Equation (II). O G 2 = 1.5 ( 0.4 ) sin 60 ° = 0.5196 m Refer Figure (1) and express the initial length of the link A C . A 1 C = ( O A 1 ) 2 + ( O C ) 2 = b 2 + ( 2 b ) 2 = 5 b Refer Figure (1) and express the final length of the link A C . A 2 C = ( O A 2 ) 2 + ( O C ) 2 − 2 ( O A 2 ) ( O C ) cos 60 ° = b 2 + ( 2 b ) 2 − 2 ( b ) ( 2 b ) ( cos 60 ° ) = 3 b Substitute b ω for v , 1 3 m 1 l 2 for l and ( b + 2 b ) for l in Equation (III)

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

See similar textbooks

Videos

Question

Chapter 6.6, Problem 134P

To determine

Determine the angular velocity of the bar when θ=60°.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.6, Problem 133P

Chapter 6.6, Problem 136P

Students have asked these similar questions

A 10-kg box is pulled along P,Na rough surface by a force P, as shown in thefigure. The pulling force linearly increaseswith time, while the particle is motionless att = 0s untilit reaches a maximum force of100 Nattimet = 4s. If the ground has staticand kinetic friction coefficients of u, = 0.6 andHU, = 0.4 respectively, determine the velocityof the A 1 0 - kg box is pulled along P , N a rough surface by a force P , as shown in the figure. The pulling force linearly increases with time, while the particle is motionless at t = 0 s untilit reaches a maximum force of 1 0 0 Nattimet = 4 s . If the ground has static and kinetic friction coefficients of u , = 0 . 6 and HU , = 0 . 4 respectively, determine the velocity of the particle att = 4 s .

Calculate the speed of the driven member with the following conditions: Diameter of the motor pulley: 4 in Diameter of the driven pulley: 12 in Speed of the motor pulley: 1800 rpm

4. In the figure, shaft A made of AISI 1010 hot-rolled steel, is welded to a fixed support and is subjected to loading by equal and opposite Forces F via shaft B. Stress concentration factors K₁ (1.7) and Kts (1.6) are induced by the 3mm fillet. Notch sensitivities are q₁=0.9 and qts=1. The length of shaft A from the fixed support to the connection at shaft B is 1m. The load F cycles from 0.5 to 2kN and a static load P is 100N. For shaft A, find the factor of safety (for infinite life) using the modified Goodman fatigue failure criterion. 3 mm fillet Shaft A 20 mm 25 mm Shaft B 25 mm

Chapter 6 Solutions

Engineering Mechanics: Dynamics

Ch. 6.4 - Prob. 1P Ch. 6.4 - In Prob. 6/1, if the plate is given a horizontal...Ch. 6.4 - The driver of a pickup truck accelerates from rest...Ch. 6.4 - A passenger car of an overhead monorail system is...Ch. 6.4 - The uniform box of mass m slides down the rough...Ch. 6.4 - The uniform slender bar of mass m and length L is...Ch. 6.4 - Prob. 7P Ch. 6.4 - The frame is made from uniform rod which has a...Ch. 6.4 - Prob. 9P Ch. 6.4 - Determine the value of P which will cause the...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.