Concept explainers
Three 25-lb rotor disks are attached to a shaft that rotates at 720 rpm. Disk A is attached eccentrically so that its mass center is
Fig. P18.147
Where should 2 lb weights be bolted to disks B and C to balance the system dynamically.
Answer to Problem 18.147RP
The 2 lb weights be bolted to disks B and C to balance the system dynamically are
Explanation of Solution
Given Information:
The weight (W) of the disk is 25 lb.
The shaft rotates at 720 rpm.
The mass center of the disk A is
Calculation:
Draw the free body diagram of the system as shown in Figure (1).
The angular velocity of the shaft is constant. So, the rate of change of angular momentum is zero.
Express the effective force
Here,
Express the effective force
Express the effective force
The sum of the effective forces of the discs should be equal to zero for the system to be in dynamic balance.
Substitute
Substitute
According to principle of impulse momentum, the total momentum is zero.
Express the moment about O:
Here,
Substitute
Substitute
Multiply Equation (1) by
The 2 lb weight is be placed above the shaft for disk C.
Substitute
The 2 lb weight is be placed below the shaft for disk B.
Thus, the 2 lb weights be bolted to disks B and C to balance the system dynamically are
Want to see more full solutions like this?
Chapter 18 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- A shaft turning at a uniform speed carries two uniform discs A and B of masses 10kg and 8kg respectively. The centres of the mass of the discs are each 2.5mm from the axis of rotation. The radii to the centres of mass are at right angles. The shaft is carried in bearings C and D between A and B such that AC = 0.3m, AD = 0.9m and AB = 1.2m. It is required to make dynamic loading on the bearings equal and a minimum for any given shaft speed by adding a mass at a radius 25mm in a plane E. Determine: (a) The magnitude of the mass in plane E and its angular position relative to the mass in plane A (b) The distance of the plane E from plane A (c) The dynamic loading on each bearing when the mass in plane E has been attached and the shaft rotates at 200 rev/min. For the bearing loads in the opposite direction determine all the unknown values. For the bearing loads in the same direction, show the diagrams and equations only to use for a possible solution.arrow_forwardThree 25-lb rotor disks are attached to a shaft that rotates at 720 rpm. Disk A is attached eccentrically so that its mass center is in. from the axis of rotation, while disks B and C are attached so that their mass centers coincide with the axis of rotation. Where should 2-lb weights be bolted to disks B and C to balance the system dynamically?arrow_forwardProblem No. 5 A rotating shaft carries four masses A, B, C and D rigidly attached to it; the centers of mass are at 30 mm, 36 mm, 39 mm and 33 mm respectively from the axis of rotation. The masses are 7.5 kg, mB, 5 kg and 4 kg respectively. The axial distance between A and B is 0.4 m, that between B and C is 0.5 m and the axial distance between C and D is H meters. The eccentricities of A and C are at 90° to one another. If the shaft is to be balanced completely, find mB, H and the angular positions of the masses B and D.arrow_forward
- machine theoryarrow_forwardA shaft carries four masses A, B, C and D of magnitude 10 kg, 20 kg, 15 kg and 25 kg respectively and revolving at radii 100 mm, 50 mm, 80 mm and 120mm in planes measured from A at 100 mm, 300 mm and 500 mm. The angles between the cranks measured anticlockwise are A to B = 40°, B to C = 50° and C to D = 150°. The balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 50 mm, between X and Y is 350 mm. If the balancing masses revolve at a radius of 50 mm, find the magnitude for mass on plane X (consider plane X as the refernce plane).arrow_forwardA shaft carries four masses A, B, C and D of magnitude 10 kg, 20 kg, 15 kg and 25 kg respectively and revolving at radii 100 mm, 50mm, 80 mm and 120mm in planes measured from A at 100 mm, 300 mm and 500 mm.The angles between the cranks measured anticlockwise are A to B = 40°, B to C = 50° and C to D = 150°.The balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 50 mm, between X and Y is 350mm.If the balancing masses revolve at a radius of 50 mm, find the magnitude for mass on plane X (consider plane X as the refernce plane).Select one:A.78.8 kgB.68.8 kgC.98.8 kgD.48.8 kg For the data given in Question 4, find the magnitude for mass on plane Y (consider plane X as the reference plane).Select one:A.59.1 kgB.69.1 kgC.99.1 kg D.49.1 kgarrow_forward
- A loaded porter governor has four links each of 250mm long.two revolving masses each of 3kg and a central dead weight of mass 20kg .all the links are attached to respective sleeves at a distance of 40mm from the axis of rotation.the masses revolve at a radius of 150 mm at minimum speed and at a radius of 200mm at maximum speed , Determine the range of speedarrow_forwardA uniform disc of diameter 315mm and of mass 14 kg is mounted on one end of an arm of length 600 mm.Then the couple will _________________N-marrow_forwardM Axis 28 Fig. 2 Question 2: Two identical spheres, each of mass M=100g and negligible radius, are fastened to opposite ends of a magnetic rod of negligible mass and length 10m. This system is initially at rest with the rod horizontal, as shown in fig.2, and is free to rotate about a frictionless, horizontal axis through the center of the rod and perpendicular to the plane of the page. A bird, of mass 3M, lands gently on the sphere on the left. Determine the torque about (a) the axis immediately after the bird lands on the sphere. (b) the bird lands. Determine the angular acceleration of the rod-spheres-birds system immediately after (c) iron ball with mass 200g is thrown towards the road from top and when it reaches the rod with velocity 50m/s, sticks to it at midpoint between axis and the sphere on the left. Find the angular speed of the system. Consider the system is initially at rest with the rod horizontal, as shown in fig.2. A smallarrow_forward
- Each arm of a Proell governor is 240 mm long and each 240 h = 190 rotating ball has a mass of 3 kg. The central load acting on the sleeve is 30 kg. The pivots of all the arms are 30 mm from the axis of rotation. The vertical height of the T. Tcos e governor is 190 mm. The extension links of the lower arms are vertical and the governor speed is 180 rpm when the sleeve is in the mid-position. Determine the lengths of the extension links (e) and tension in the upper 3 kg 240 B arms (T). 30 30 kgarrow_forwardA shaft with 3 meters span between two bearings carries two masses of 120 g and 100 g acting at the extremities of the arms 40 mm and 50 mm long respectively. The planes in which these masses rotate are 1.5 m and 2.5 m respectively from the left end bearing supporting the shaft. The angle between the arms is 120°. The speed of rotation of the shaft is 200 r.p.m. If the masses are balanced by two counter-masses rotating with the shaft acting at radii of 0.3 m and placed at 0.5 m from each bearing centers, estimate the magnitude of the two balance masses and their orientation with respect to the X-axis, i.e. mass of 120 g.arrow_forwardProblem 8 Another Gear Two disks are connected to one another with a belt as shown. Both disks have mass m but the larger one has radius 4R and the smaller has radius R. The larger disk is powered by a motor that produces a constant torque, To, in the counter- clockwise direction. (a) By using the rotational equivalent of Newton's laws on the larger disk show that the difference in the tension at the top with the tension at the bottom is: Tto - Thot 1 4R (TO - 2m Ra), where a is the linear accleration of the elt. (b) Do the same (find Ttop - Tbot) with the smaller disk. (c) Use your two expressions to find the gular acceleration of the smaller disk. You answer should have m, R, and To in it only. (Careful, the sr aller disk does not have the same angular acceleration as the larger one).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