Concept explainers
Solve Prob. 16.137 when θ = 90°.
16.137 In the engine system shown, l = 250 mm and b = 100 mm. The connecting rod BD is assumed to be a 1.2-kg uniform slender rod and is attached to the 1.8-kg piston P. During a test of the system, crank AB is made to rotate with a constant angular velocity of 600 rpm clockwise with no force applied to the face of the piston. Determine the forces exerted on the connecting rod at B and D when θ = 180°. (Neglect the effect of the weight of the rod.)
Fig. P16.137
The forces exerted on the connecting rod at B and D when
Answer to Problem 16.138P
The forces exerted on the connecting rod at B is
The forces exerted on the connecting rod at D is
Explanation of Solution
Given information:
The length of the rod BD is
The length of the rod AB is
The mass of the rod BD is
The mass of the piston P is
The angular velocity of AB is
Calculation:
Consider the acceleration due to gravity
Calculate the angular velocity in
Sketch the Free body Diagram of the system as shown in Figure 1.
Refer to Figure 1.
Calculate the distance
Substitute
Calculate the position vectors as shown below.
Position of B with respect to A.
Position of D with respect to B.
Position of mass center G with respect to D.
Calculate the velocity at B
Substitute
Calculate the velocity at D
Substitute
Resolving the i and j components as shown below.
For j component.
For i component.
Substitute
Consider that the angular acceleration as
Calculate the acceleration at B
Substitute
Calculate the acceleration
Substitute
Resolving i and j components as shown below.
For j component.
For i component.
Substitute
Calculate the acceleration of mass center G of bar BD
Substitute
Resolving the components as shown below.
Calculate the mass moment of inertia for BD
Substitute
Sketch the Free Body Diagram of the piston with the bar BD as shown in Figure 2.
Refer to Figure 2.
Apply the Equilibrium of forces along x direction as shown below.
Substitute
Apply the Equilibrium of moment about B as shown below.
Substitute
Apply the Equilibrium of forces along y direction as shown below.
Substitute
Calculate the force acting at B as shown below.
Substitute
Hence, the forces exerted on the connecting rod at B is
Sketch the Free Body Diagram of the piston as shown in Figure 3.
Refer to Figure 3.
Calculate the force acting on the rod at D as shown below.
Substitute
Calculate the magnitude of force at D as shown below.
Therefore, the forces exerted on the connecting rod at D is
Want to see more full solutions like this?
Chapter 16 Solutions
<LCPO> VECTOR MECH,STAT+DYNAMICS
Additional Engineering Textbook Solutions
Fundamentals of Aerodynamics
Foundations of Materials Science and Engineering
Applied Fluid Mechanics (7th Edition)
Fluid Mechanics Fundamentals And Applications
Engineering Mechanics: Statics
Mechanics of Materials (10th Edition)
- The 200-mm 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 20 kg.m² and the coefficient of kinetic friction between the drum and the brake shoe at B is 0.35. Knowing that the angular velocity of the flywheel is 360 rpm counterclockwise when a force P of magnitude 350 N is applied to the pedal C, determine the number of revolutions executed by the flywheel before it comes to rest. 150 mm 250 mm 200 mm B 375 mmarrow_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_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 and the coefficient of kinetic friction between the drum and the brake shoe is 0.40. Knowing that the initial angular velocity is 240 rpm clockwise, determine the force that must be exerted by the hydraulic cylinder if the system is to stop in 75 revolutions.arrow_forward
- Question 4: The brake drum of radius 10 cm is attached is a larger flywheel that is not shown. The total mass moment of inertia of the drum and the flywheel is 50 kg.cm? and the coefficient of kinetic friction between the drum and the brake shoe is 0.35. Knowing that the angular velocity of the flywheel is 360 rpm counterclockwise when a force P of magnitude 40 N is applied to the pedal C, determine the number of revolutions executed by the flywheel before it comes to rest. 15 сm |A 25 cm D 10 cm 35 cm-arrow_forwardA 255-lbf block is suspended from an inextensible cable which is wrapped around a drum of 1.75-ft radius rigidly attached to a flywheel. The drum and flywheel have a combined centroidal moment of inertia 12 lb . ft . s 2 . At the instant shown, the velocity of the block is unknown directed downward. Knowing that the bearing at A is poorly lubricated and that the bearing friction is equivalent to a couple M of magnitude 65 lb .ft, determine the velocity of the block before it has moved 3.5 ft downward if at S2 speed is 13.5ft/sarrow_forwardA 197-kg flywheel is at rest when a constant 300 N·m couple is applied. After executing 560 revolutions, the flywheel reaches its rated speed of 2400 rpm. Knowing that the radius of gyration of the flywheel is 400 mm, determine the average magnitude of the couple due to kinetic friction in the bearing. N.m. The average magnitude of the couple due to kinetic friction in the bearing is [arrow_forward
- Each of the gears A and B has a mass of 2.4 kg and a radius of gyration of 60 mm, while gear C has a mass of 12 kg and a radius of gyration of 150 mm. A couple M of constant magnitude 10 N.m is applied to gear C determine a ) the number of revolutions of gear C required for its angular velocity to increase from 100 to 450 rpm, (b) the corresponding tangential force acting on gear A.arrow_forwardThe 8-inch radius brake drum is attached to a flywheel not shown. The total mass moment of inertia of the drum and the flywheel is 20 slug ft2, about an axis perpendicular to the wall through its center D, and the coefficient of kinetic friction between the drum and the brake shoe at B is 0.3. Knowing that the angular velocity of the flywheel is 330 rev/min, clockwise, when a force P of magnitude 115 lb is applied to pedal C, determine the number of revolutions the flywheel makes before coming to a stop... C 10 in. B 15 in.. 6 in. A 8 in. Darrow_forwardThe flywheel of a punching machine has a mass of 300 kg and a radius of gyration of 600 mm. Each punching operation requires 2500 J of work. (a ) Knowing that the speed of the flywheel is 300 rpm just before a punching, determine the speed immediately after the punching. (b) If a constant 25-N.m couple is applied to the shaft of the flywheel, determine the number of revolutions executed before the speed is again 300 rpm.arrow_forward
- 4arrow_forwardThe 200-mm-radius brake drum is attached to a larger Bywheel. The total mass moment of inertia of the flywheel and drum is 19 kg. and the coefficient of kinetic friction between the drum and the brake shoe is 035, Knowing that the initial angular velocity of the flywheel is 180 rpm clockwise, determine the vertical force P that must be applied to the pedal C if the system is to stop in 100 revolutions. 150 mm 250 mm B ne: P= 172.88 N C 375 mm 200 mmarrow_forward16.137 In the engine system shown, I = 250 mm and b = 100 mm. The con- necting rod BD is assumed to be a 1.2-kg uniform slender rod and is attached to the 1.8-kg piston P. During a test of the system, crank AB is made to rotate with a constant angular velocity of 600 rpm clockwise with no force applied to the face of the piston. Determine the forces exerted on the connecting rod at B and D when ở = 180°. (Neglect the effect of the weight of the rod.)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