MOD.MASTER.W/ETEXT ENG.MECHANICS CARD+BK
15th Edition
ISBN: 9780137519170
Author: HIBBELER
Publisher: PEARSON
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Chapter 20, Problem 23P
To determine
The angular velocity of the axle
The angular velocity of the axle
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5
In the image on the right, there is a red gear G1 on the
left with a radius of r1 = 2.81cm. Gear G1 is locked
to the green gear G2 with a radius of r2 = 0.734cm.
Gear G2 then shares the same axle as the blue circular
saw G3, which has a radius of r3
known to make a full rotation every T = 0.836s. Using
at least 6 significant digits in your calculations,
compute the following:
V3!
12.8cm. Gear G1 is
W1
a) The angular speed wi of gear G1. Remember
that angular speed is measured in radians per
T3
r2
unit time.
G2
b) The rim speed vi of gear G1. Since gears G1
and G2 are locked together, the rim speed of G2
is also v1.
G1
G3
c) The angular speed w2 of gear G2. Since gear
G2 and saw G3 share the same axle, the angular
speed of G3 is also w2.
d) The rim speed v3 of saw G3.
2. A shaft is supported on bearings A and B, 800 mm between centres. A 20 degrees straight tooth spur gear having 600 mm pitch diameter, is located 200 mm to the right of the left hand bearing A, and a 700 mm diameter pulley is mounted 250 mm towards the left of bearing B. The gear is driven by a pinion with a downward tangential force while the pulley drives a horizontal belt having 180 degrees angle of wrap. The pulley also serves as a flywheel and weighs 2000 N. The maximum belt tension is 3000 N and the tension ratio is 3: 1. Determine the maximum bending moment and the necessary shaft diameter if the allowable shear stress of the material is 40 MPa.
Chapter 20 Solutions
MOD.MASTER.W/ETEXT ENG.MECHANICS CARD+BK
Ch. 20 - The propeller of an airplane is rotating at a...Ch. 20 - The disk rotates about the z axis at a constant...Ch. 20 - The ladder of the fire truck rotates around the z...Ch. 20 - The ladder of the fire truck rotates around the z...Ch. 20 - At a given instant, the antenna has an angular...Ch. 20 - The disk rotates about the shaft S, while the...Ch. 20 - The electric fan is mounted on a swivel support...Ch. 20 - The electric fan is mounted on a swivel support...Ch. 20 - The truncated double cone rotates about the z axis...Ch. 20 - Prob. 20P
Ch. 20 - Gear B is driven by a motor mounted on turntable...Ch. 20 - Prob. 22PCh. 20 - Prob. 23PCh. 20 - Prob. 26PCh. 20 - Prob. 27PCh. 20 - Prob. 30PCh. 20 - So1ve Example 20.5 such that the x, y, z axes move...Ch. 20 - Prob. 38PCh. 20 - At the instant = 60, the telescopic boom AB of...Ch. 20 - Prob. 40PCh. 20 - Prob. 42PCh. 20 - Prob. 43PCh. 20 - Prob. 44PCh. 20 - Prob. 46PCh. 20 - Prob. 47PCh. 20 - Prob. 48PCh. 20 - Prob. 49PCh. 20 - Prob. 50PCh. 20 - Prob. 51P
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- Two involute gear wheels work with an angle of pressure of 20⁰ and rotate in opposite directions. The smaller wheel has 20 teeth of 5 mm module and rotates at 2000 rev/min. The larger wheel has 80 teeth and is the driven member. If the contact ratio is 1:4, and if the are of recess is 1-2 times as large as the are of approach, determine: (a) the addenda of the teeth on both wheels, (b) the greatest speed of sliding between the teeth, (c) the center distance of the gears, and (d) the working depth.arrow_forwardFor the epicyclic gear train shown, wheels B and C are rigidly attached to the input shaft (p) and they rotate at the same speed as the input shaft. The teeth numbers of the wheels are as given. D=90, B=30, C=20, E=100 Determine the output shaft speed (q) and its direction with respect to the input shaft, when: a. Only wheel D is fixed b. Only wheel E is fixed b. C B The input shaft rotates at 1200 rpm. You are required to forum two tablesarrow_forwardDraw free-body diagrams of the two gears, assuming an input couple M on theOUT X shaft of the larger gear in the direction shown. Include forces at bearings A, B, D and E. M isthe reaction couple at the output shaft - i.e. the resistance to turning of the object being driven.The gears have 48 and 24 teeth respectively. If the input gear (large gear) turns at 100 rpm(= revolutions per minute), the output speed (small gear) is _______rpm.Wil OUT X IN Xl M be larger or smaller than M ?arrow_forward
- A gear system shown in Figure 1 consists of gear B and C with radii of 80 mmand 200 mm, respectively. Gear B with a mass of 0.9 kg is free to rotate at pointA of the arm AO. The arm is free to rotate on the fixed axis O. Whereas, gear Cis fixed on the axles O in a way that it will never rotate. The arm has a mass of0.8 kg and a radius of gyration about O of 140 mm. Moreover, the arm AO hasa center of gravity located at point G.1.1. If the uniform torque of 4 Nm is applied to the arm OA, initially at rest in thehorizontal position, calculate the velocity of point A as it reaches the top point A’.1.2. Use the table method to calculate the angular speed of gear B, provided that thearm rotates at 5,118 rad/s.arrow_forwardThe pinion (gear 2 on shaft a) rotates at 635 rev/min clockwise and transmits 1305 W through the idler pair (gears 3 and 4 on shaft b) to the output gear (gear 5 on shaft c). Gears 2 and 3 have a module of 2 mm, and gears 4 and 5 have a module of 3 mm. Pressure angles are all 20 degrees. Solve for the magnitude of the force that shaft b must apply to gears 3 and 4 to maintain static equilibrium in the figure shown here. The figure is not to scale. 187 327 487arrow_forward5. The pitch circle diameter of the smaller of the two spur wheels which mesh externally and have involute teeth is 100 mm. The number of teeth are 16 and 32. The pressure angle is 20° and the addendum is 0.32 of the circular pitch. Find the length of the path of contact of the pair of teeth.arrow_forward
- A steel shaft 800 mm long transmitting 15 kW at 400 r.p.m. is supported at two bearings at the twoends. A gear wheel having 80 teeth and 500 mm pitch circle diameter is mounted at 200 mm from theleft hand side bearing and receives power from a pinion meshing with it. The axis of pinion and gearlie in the horizontal plane. A pulley of 300 mm diameter is mounted at 200 mm from right hand sidebearing and is used for transmitting power by a belt. The belt drive is inclined at 30° to the vertical inthe forward direction. The belt lap angle is 180 degrees. The coefficient of friction between belt andpulley is 0.3. Design and sketch the arrangement of the shaft assuming the values of safe stresses as :τ = 55 MPa; σt= 80 MPa. Take torsion and bending factor 1.5 and 2 respectively.arrow_forwardIn the gear system shown, the motor applies a 190 lb-ft torque to the gear at A. A torque of Tc = 392 lb-ft is removed from the shaft at gear C, and the remaining torque is removed at gear D. Assume that DA-4-in.-diameter, Dg=12-in.-diameter, L₁=56 in., and L₂-30 in. Segments (1) and (2) are solid 1.5-in.-diameter steel [G = 12200 ksi] shafts, and the bearings shown allow free rotation of the shaft. Determine: (a) the maximum shear stresses T₁, T₂ in segments (1) and (2) of the shaft. (b) the rotation angle D/B of gear D relative to gear B. Answers: (a) T₁ (b) D/B = = i ᎠᏴ ; A DA i B L₁ Tc amala ksi, T₂ = L2 i Tp D ksi.arrow_forwardThe pinion (gear 2 on shaft a) rotates at 695 rev/min clockwise and transmits 1497 W through the idler pair (gears 3 and 4 on shaft b) to the output gear (gear 5 on shaft c). Gears 2 and 3 have a module of 3 mm, and gears 4 and 5 have a module of 2 mm. Pressure angles are all 20 degrees. Solve for the magnitude of the force that shaft b must apply to gears 3 and 4 to maintain static equilibrium in the figure shown here. Co 18T- 327 X 18T 5 -48Tarrow_forward
- A pair of gears, having 40 and 30 teeth respectively, are of 25° involute form. Theaddendum length is 5 mm and the module is 5.5 mm. If smaller wheel is the driver androtates at 1500 r.p.m. find the velocity of sliding at the point of engagement and at thepoint of disengagement.arrow_forwardQ2/ An epicyclic gear train as shown in figure is composed of a fixed annular wheel A having 150 teeth. The arm revolves clockwise at 100 rpm about the axis of A or D If the wheels B and D are Tehaving 25 teeth and 40 teeth respectively, find the speed and direction of rotation of OD S CE B C D Aarrow_forwardProblem 2: Consider the two gears mounted on the shaft, as shown. Distances are L1 = 100 mm, L2 = 250 mm, and L3 = 175 mm. Diameter of shaft AB is 15 mm, diameter of shaft BC is 20 mm, and diameter of shaft CD is 17.5 mm. Young's modulus for each portion is 200 GPa. Determine the displacement of point D with reference to point A. Also, determine the displacement of point A relative to C. b. Determine the axial strain at any point in shaft segments AB, BC and CD, respectively. If Poisson's ratio for the material of the shafts is v = 0.2, determine the lateral strain in each of the shaft segments. Based on your answers to part (a), do the gears move towards each other, or do they separate from each other? Note that in real gearboxes, movement of gears towards or away from each other is prevented by using thrust bearings. 10 kN 4 kN 5 kN 7 kN 4 kN NY 0I 17.arrow_forward
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