Concept explainers
The 6-kg rod BC connects a 10-kg disk centered at A to a 5-kg rod CD. The motion of the system is controlled by the couple M applied to disk A. Knowing that at the instant shown disk A has an angular velocity of 36 rad/s clockwise and no angular acceleration, determine (a) the couple M, (b) the components of the force exerted at C on rod BC.
Fig. P16.135 and P16.136
(a)
Find the couple M.
Answer to Problem 16.135P
The couple M is
Explanation of Solution
Given information:
The mass of the rod BC is
The mass of the disk is
The mass of the rod CD is
The angular velocity is
The angular acceleration is
Calculation:
Consider the acceleration due to gravity as
Calculate the velocity of disk AB
Substitute
Calculate the velocity of rod BC
The velocity of disk AB is equal to the velocity of rod BC.
Substitute
Calculate the angular velocity of rod CD
Substitute
Apply the acceleration analysis as shown below.
Calculate the acceleration for disk AB
Substitute
Calculate the acceleration for rod BC
Substitute
Calculate the acceleration for rod CD
Substitute
Equating the components of Equations (1) and (2) as shown below.
Along x component.
Along y component.
Substitute
Calculate the acceleration of the mass centers as shown below.
Calculate the acceleration of mass center for disk AB
Calculate the acceleration of the mass center at P for rod BC
Substitute
Substitute
Calculate the acceleration of the mass center at Q for rod CD
Substitute
Calculate the inertial terms at mass centers as shown below.
The inertia terms at centers are
For disk AB.
For rod BC.
Substitute
For rod CD.
Substitute
Calculate the mass moment of inertia
For disk AB.
Substitute
For rod BC.
Substitute
For rod CD.
Substitute
Calculate the effective couples at mass centers as shown below.
The inertia terms at centers are
For disk AB.
For rod BC.
Substitute
For rod CD.
Substitute
Sketch the effective force and couples on the system as shown in Figure 1.
Sketch the Free Body Diagram of the rod BC as shown in Figure 2.
Refer to Figure 2.
Apply the Equilibrium of moment about B as shown below.
Substitute
Sketch the Free Body Diagram of the rod CD as shown in Figure 3.
Refer to Figure 3.
Apply the Equilibrium of moment about D as shown below.
Substitute
Sketch the Free Body Diagram of the rod AB and BC as shown in Figure 4.
Refer to Figure 4.
Apply the Equilibrium of moment about A as shown below.
Substitute
Therefore, the couple M is
(b)
The components of force exerted at C on rod BC.
Answer to Problem 16.135P
The components of force exerted at C on rod BC is
Explanation of Solution
Given information:
The mass of the rod BC is
The mass of the disk is
The mass of the rod CD is
The angular velocity is
The angular acceleration is
Calculation:
Refer to part (a).
The components of force exerted at C on rod BC along x direction is
The components of force exerted at C on rod BC along y direction is
Therefore, the components of force exerted at C on rod BC is
Want to see more full solutions like this?
Chapter 16 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Additional Engineering Textbook Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Heat and Mass Transfer: Fundamentals and Applications
Statics and Mechanics of Materials (5th Edition)
Mechanics of Materials
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
Thermodynamics: An Engineering Approach
- The mechanism shown is one of two identical mechanisms attached to the two sides of a 200-lb uniform rectangular door. Edge ABC of the door is guided by wheels of negligible mass that roll in horizontal and vertical tracks. A spring with a constant k is attached to wheel B in such a way that its tension is zero when 0 = 30°, Knowing that the door is released from rest in the position 0 = 45° and reaches the vertical position with an angular velocity of 0.6 rad/s, determine the spring constant k.arrow_forwardThe 10-in.-radius brake drum is attached to a larger flywheel which is not shown. The total mass moment of inertia of the flywheel and drum is 22 lb ⋅ ft ⋅ s 2 and the coefficient of kinetic friction between the drum and the brake shoe is 0.41. Knowing that the initial angular velocity is 255 rpm clockwise, determine the force which must be exerted by the hydraulic cylinder at point B if the system is to stop in 85 revolutions. DO NOT ROUND OFF IN THE SOLUTION. ROUND OFF ONLY THE FINAL ANSWERarrow_forwardThe 8-in. radius brake drum is attached to a larger flywheel that is not shown. The total mass moment of inertia of the drum and the flywheel is 15 lb.ft.s2 and the coefficient of kinetic friction between the drum and the brake shoe is 0.40. Knowing that the angular velocity of the flywheel is 450 rpm clockwise when a force P of magnitude 65 lbf. is applied to the pedal C, determine the number of the revolutions executed by the flywheel before it comes to rest. (The final answer should be in two decimal places with correct units)arrow_forward
- The shutter shown was formed by removing one quarter of a disk of 0.75-in. radius and is used to interrupt a beam of light emanating from a lens at C. Knowing that the shutter weighs 0.125 lb and rotates at the constant rate of 24 cycles per second, determine the magnitude of the force exerted by the shutter on the shaft at Aarrow_forwardThe 10-in.-radius brake drum is attached to a larger flywheel which is not shown. The total mass moment of inertia of the flywheel and drum is 22 lb ⋅ ft ⋅ s 2 and the coefficient of kinetic friction between the drum and the brake shoe is 0.41. Knowing that the initial angular velocity is 255 rpm clockwise, determine the force which must be exerted by the hydraulic cylinder at point B if the system is to stop in 85 revolutions.arrow_forwardA 1200-kg satellite designed to study the sun has an angular velocity of w0 = (0.050 rad/s)i + (0.075 rad/s)k when two small jets are activated at A and B in a direction parallel to the y axis. Knowing that the coordinate axes are principal centroidal axes, that the radii of gyration of the satellite are and that each jet produces a 50-N thrust, determine (a ) the required operating time of each jet if the angular velocity of the satellite is to be reduced to zero, (b ) the resulting change in the velocity of the mass center G.arrow_forward
- In the gear arrangement shown, gears A and C are attached to rod ABC, that is free to rotate about B, while the inner gear B is fixed. Knowing that the system is at rest, determine the magnitude of the couple M that must be applied to rod ABC, if 2.5 s later the angular velocity of the rod is to be 240 rpm clockwise. Gears A and C ABC weighs 4 lb.arrow_forwardA 3-kg bar AB is attached by a pin at D to a 4-kg square plate, which can rotate freely about a vertical axis. Knowing that the angular velocity of the plate is 120 rpm when the bar is vertical, determine (a ) the angular velocity of the plate after the bar has swung into a horizontal position and has come to rest against pin C, (b) the energy lost during the plastic impact at C.arrow_forwardThe rotor of an electric motor has an angular velocity of 3600 rpm when the load and power are cut off. The 110-lb rotor, which has a centroidal radius of gyration of 9 in., then coasts to rest. Knowing that the kinetic friction of the rotor produces a couple with a magnitude of 2.5 1b.ft determine the number of revolutions that the rotor executes before coming to rest.arrow_forward
- A 48-kg advertising panel of length 2a = 2.4 m and width 2b = 1.6 m is kept rotating at a constant rate w1 about its horizontal axis by a small electric motor attached at A to frame ACB. This frame itself is kept rotating at a constant rate w2 about a vertical axis by a second motor attached at C to the column CD. Knowing that the panel and the frame complete a full revolution in 6 s and 12 s, respectively, express, as a function of the angle 0, the dynamic reaction exerted on column CD by its support at D.arrow_forwardTwo uniform cylinders, each of weight W = 14 lb and radius r = 5 in., are connected by a belt as shown. Knowing that at the instant shown the angular velocity of cylinder B is 30 rad/s clockwise, determine (a) the distance through which cylinder A will rise before the angular velocity of cylinder B is reduced to 5 rad/s, (b ) the tension in the portion of belt connecting the two cylinders.arrow_forwardThe rotor of an electric motor has an angular velocity of 3570 rpm when the load and power are cut off. The 65-kg rotor, which has a centroidal radius of gyration of 175mm, until it reaches the maximum speed of 5250 rpm. Knowing that the kinetic friction results in a couple of magnitude 4.5 N.m exerted on the rotor, determine the number of revolutions that the rotor executes, before achieving its maximum speed and the time it took. (The final answer should be in two decimal places with correct units)arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY