Concept explainers
Solve Prob. 16.137 when
The forces exerted on the connecting rod at points B and D.
Explanation of Solution
Given information:
Connecting rod length,
Crank length
Rod mass,
Position vector,
Points D and A horizontal distance,
Position vector
Crank angular velocity in the form of vector,
Point B velocity,
Point B angular velocity in the form of vector is
Point D velocity is given by,
Compare j terms from equation A,
Compare i terms from equation A,
Crank AB angular acceleration is zero i.e.
Vector form of point B relative angular acceleration is
Vector form of point D acceleration is
Point B acceleration,
Point D acceleration,
Here,
Compare j terms in equation B,
Vector form of angular acceleration of connecting rod BD is
Compare i terms in equation B,
Vector form of acceleration of point D is
Pont G acceleration,
Here,
Point G inertial force,
Here,
Force horizontal component from figure 2,
Here,
Connected rod BD moment of inertia,
Moment at B from figure 2,
Here,
Compare K terms from equation C,
Force vertical component from figure 2,
Point B resultant reaction,
Here,
Resultant angle,
The force exerted at point B is
Forces along connecting rod from figure 3,
Hence, piston exerts force in rod which is
Point D resultant reaction,
Resultant angle,
The force exerted at point D is
Conclusion:
The force exerted at point B is
The force exerted at point D is
Want to see more full solutions like this?
Chapter 16 Solutions
Vector Mechanics For Engineers
- 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 double pulley shown has a mass of 3 kg and a radius of gyration of 100 mm. Knowing that when the pulley is at rest, a force P of magnitude 24 N is applied to cord B, determine (a) the velocity of the center of the pulley after 1.5 s,(b) the tension in cord C.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
- Three shafts and four gears are used to form a gear train which will transmit 7.5 kW from the motor at A to a machine tool at F. (Bearings for the shafts are omitted from the sketch.) Knowing that the frequency of the motor is 30 Hz, determine the magnitude of the couple that is applied to shaft (a) AB(b) CD (c) EF.arrow_forwardKnowing that the maximum allowable couple that can be applied to a shaft is 15.5 kip.in., determine the maximum horsepower that can be transmitted by the shaft at (a ) 180 rpm, (b ) 480 rpm.arrow_forwardA shaft carries four masses, B, C, and D of magnitude 200 kg, 300 kg, 400 kg, and 200 kg respectively and revolving at radii 80 mm, 70 mm, 60 mm, and 80 mm in planes measured from A at 300 mm, 400 mm and 700 mm. The angles between the cranks measured anticlockwise are A to B 45º, B to C 70º, and C to D 120º. the balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 100 mm, between X and Y is 400 mm and between Y and D is 200 mm. If the balancing masses revolve at a radius of 100 mm, find their magnitude and angular positions.arrow_forward
- A 240-lb block is suspended from an inextensible cable which is wrapped around a drum of 1.25-ft radius rigidly attached to a flywheel. The drum and flywheel have a combined centroidal moment of intertia of 10.5 lb-ft-s^2. At the instant shown, the velocity of the block is 6 ft/s directed downward. The bearing at A as a frictional moment of 60 lb-ft. What is the kinetic energy of the system after the block moved after 4ft? (in ft-lb)arrow_forwardThe blade of a portable saw and the rotor of its motor have a total weight of 2.5 lb and a combined radius of gyration of 1.5 in. Knowing that the blade rotates as shown at the rate w1= 1500 rpm, determine the magnitude and direction of the couple M that a worker must exert on the handle of the saw to rotate it with a constant angular velocity w2= -(2.4 rad/s)j.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_forward
- Two uniform rods AB and CE, each of weight 3 lb and length 2 ft, are welded to each other at their midpoints. Knowing that this assembly has an angular velocity of constant magnitude w = 12 rad/s, determine the magnitude and direction of the angular momentum HD of the assembly about D.arrow_forwardDisk A, of weight 5 lb and radius r = 3 in., is at rest when it is placed in contact with a belt that moves at a constant speed v = 50 ft/s. Knowing that μk = 0.20 between the disk and the belt, determine the time required for the disk to reach a constant angular velocity.arrow_forwardDisk A, of weight 10 lb and radius r = 6 in., is at rest when it is placed in contact with belt BC, which moves to the right with a constant speed v = 40 ft/s. Knowing that μk = 0.20 between the disk and the belt, determine the number of revolutions executed by the disk before it attains a constant angular velocity.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