Concept explainers
Each of the gears A and B has a mass of 10 kg and a radius of gyration of 190 mm, while gear C has a mass of 2.5 kg and a radius of gyration of 80 mm. If a couple M of constant magnitude 6 N
(a)
Number of revolutions of gear C.
Answer to Problem 17.11P
Number of revolutions of gear C is
Explanation of Solution
Given information:
Mass of the gear A (mA) = 10kg.
Radius of gyration of the gear A (kA) = 190mm.
Mass of the gear B (mB) = 10kg.
Radius of gyration of the gear B (kB) = 190mm.
Mass of the gear C (mC) = 2.5kg.
Radius of gyration of the gear C (kC) = 80mm.
Initial angular velocity of gear C (NC)1 = 450rpm
Final angular velocity of gear C (NC)1 = 1800rpm
A couple at gear C (M) = 6N-m.
Radius of gear A (rA) = 250mm
Radius of gear B (rB) = 250mm
Radius of gear C (rC) = 100mm
Calculation:
Moment of inertia of gear A
Moment of inertia of gear B
Moment of inertia of gear C
For Initial condition;
Angular velocity of the gear C is 450 rpm,
Gear C mess with Gear A. So angular velocity ration is given as
Gear C mess with gear B
Initial kinetic energy
For final condition; Angular velocity of the gear C is 1800rpm
Gear C mess with Gear A. So angular velocity ration is given as
Gear C mess with gear B
Final kinetic energy
Work done by the gear C
Substitute the value of E1, E2 and W in work energy equation
(b)
Tangential force on gear A.
Answer to Problem 17.11P
Tangential force on gear A is F = 0.0447N.
Explanation of Solution
Given information:
Mass of the gear A (mA) = 10kg.
Radius of gyration of the gear A (kA) = 190mm.
Mass of the gear B (mB) = 10kg.
Radius of gyration of the gear B (kB) = 190mm.
Mass of the gear C (mC) = 2.5kg.
Radius of gyration of the gear C (kC) = 80mm.
Initial angular velocity of gear C (Nc)1 = 450rpm
Final angular velocity of gear C (NC)1 = 1800rpm
A couple at gear C (M) = 6N-m.
Radius of gear A (rA) = 250mm
Radius of gear B (rB) = 250mm
Radius of gear C (rC) = 100mm
Calculation:
Angle of rotation for gear A
Substitute the value of E1, E2 and W in work energy equation for gear A
Want to see more full solutions like this?
Chapter 17 Solutions
Vector Mechanics For Engineers
- In the helicopter shown; a vertical tail propeller is used to pre- vent rotation of the cab as the speed of the main blades is changed. Assuming that the tail propeller is not operating determine the final angular velocity of the cab after the speed of the main blades has been changed from I80 to 240 rpm. (The speed of the main blades is measured relative to the cab, and the cab has a centroidal moment of inertia of 650 lb.ft.s2. Each of the four main blades is assumed to be a slender rod 14 ft weighing 55 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 connecting rod of a horizontal reciprocating engine is 400 mm and length of the stroke is 200mm. The mass of the reciprocating parts is 125 kg and that the connecting rod is 100 kg. The radius of gyration of the connecting rod about an axis through the centre of gravity is 120 mm and the distance of centre of gravity of the connecting rod from big end centre is 160 mm. The engine runs at750 r.p.m. Determine graphically the torque exerted on the crankshaft when the crank has turned 30° from the inner dead centre.arrow_forward
- A 5.32-kg disk A of radius 0.445 m initially rotating counter-clockwise at 436 rev/min is engaged with a 6.72-kg disk B of radius 0.275 m initially rotating clockwise at 528 rev/min, where the moment of inertia of a disk is given as I = ½ mi?. Determine their combined angular speed (in rpm) and direction of rotation after the meshing of the two disks. Remember to show clearly the equations that you use!!'arrow_forwardThe flywheel of a small punch rotates at 300 rpm. It is known that 1800 ft.1b of work must be done each time a hole is punched. It is desired that the speed of the flywheel after one punching be not less than 90 percent of the original speed of 300 rpm. (a ) Determine the required moment of inertia of the flywheel. (b) If a constant 25-1b.ft couple is applied to the shaft of the flywheel, determine the number of revolutions that must occur between each punching, knowing that the initial velocity is to be 300 rpm at the start of each punching.arrow_forwardThe flywheel of an automobile engine, which is rigidly attached to the crankshaft, is equivalent to a 400-mm-diameter, 15-mm-thick steel plate. Determine the magnitude of the couple exerted by the flywheel on the horizontal crankshaft as the automobile travels around an unbanked curve of 200-m radius at a speed of 90 km/h, with the flywheel rotating at 2700 rpm. Assume the automobile to have (a) a rear-wheel drive with the engine mounted longitudinally, (b) a front-wheel drive with the engine mounted transversely. (Density of steel = 7860 kg/m3.)arrow_forward
- The flywheel of a small punch rotates at 300 rpm. It is known that 1800 ft-lb of work must be done each time a hole is punched. It is desired that the speed of the flywheel after 1 punching be not less than 90 percent of the original speed of 300 rpm. A. Determine the required moment of inertia of the flywheel. B. Keep a constant 25 lb - ft couple is applied to the shaft of the flywheel, determine the number of revolutions which must occur between each punching, knowing that initial velocity is to be 300 rpm at the start of each punchingarrow_forwardThe flywheel of a small punch rotates at 300 rpm. It is known that 1,800 ft lb of work must be done each time a hole is punched. it is desired that the speed of the flywheel after one punching be not less that 90 percent of the original speed of 300 rpm. A. Determine the required moment of inertia of the flywheel. B. If a constant 25 lb ft couple is applied to the shaft at the flywheel, determine the number of revolutions which must occur between each punching, knowing that the initial velocity is to be 300 rpm at the start of each punching.arrow_forwardThe 10-oz disk shown spins at the rate w1 = 750 rpm, while axle AB rotates as shown with an angular velocity w2. Determine the maximum allowable magnitude of w2 if the dynamic reactions at A and B are not to exceed 0.25 lb each.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_forwardEach of the gears A and B has a mass of 675 g and a radius of gyration of 40 mm, while gear C has a mass of 3.6 kg and a radius of gyration of 100 mm. Assume that kinetic friction in the bearings of gears A, B C produces couples of constant magnitude 0.15 N.m, 0.15 N.m, 0.3 N.m, respectively. Knowing that the initial angular velocity of gear C is 2000 rpm, determine the time required for the system to come to rest.arrow_forwardThe mechanism shown is composed of rod GPV pin-connected to rod DPE at point P. Knowing that the velocity of V is 4 m/s downwards, A. Redraw bar GPV and determine its instantaneous center of rotation (label it as point C). Specify all angles and distances needed. B. Determine the angular velocity of rod GPV. C. Determine the velocity of point P. D. Redraw bar DPE and determine its instantaneous center of rotation (label it as point C). Specify all angles and distances needed. E. Determine the angular velocity of rod DPE. Use IC method. Please don't show me the answer in chegg. I think there is an errorarrow_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