
Engineering Mechanics: Dynamics
8th Edition
ISBN: 9781118885840
Author: James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher: WILEY
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Chapter 7.5, Problem 22P
To determine
The angular velocity and the angular acceleration of OA when
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1. The rotating steel shaft is simply supported by bearings at points of B and C, and is driven by a spur
gear at D, which has a 6-in pitch diameter. The force F from the drive gear acts at a pressure angle of
20°. The shaft transmits a torque to point A of TA =3000 lbĘ in. The shaft is machined from steel with
Sy=60kpsi and Sut=80 kpsi.
(1) Draw a shear force diagram and a bending moment diagram by F. According to your analysis, where is
the point of interest to evaluate the safety factor among A, B, C, and D? Describe the reason. (Hint: To find
F, the torque Tд is generated by the tangential force of F (i.e. Ftangential-Fcos20°)
When n=2.5, K=1.8, and K₁ =1.3, determine the diameter of the shaft based on
(2) static analysis using DE theory (note that fatigue stress concentration factors need to be used for this
question because the loading condition is fatigue) and
(3) a fatigue analysis using modified Goodman.
Note) A standard diameter is not required for the questions.
10 in
D
3
N2=28
P(diametral pitch)=8 for all gears
Coupled to 25 hp motor
N3=34
Full depth spur gears with pressure angle=20°
N₂=2000 rpm
(1) Compute the circular pitch, the center-to-center distance, and base circle radii.
(2) Draw the free body diagram of gear 3 and show all the forces and the torque.
(3) In mounting gears, the center-to-center distance was reduced by 0.1 inch.
Calculate the new values of center-to-center distance, pressure angle, base circle radii,
and pitch circle diameters.
(4)What is the new tangential and radial forces for gear 3?
(5) Under the new center to center distance, is the contact ratio (mc) increasing or
decreasing?
2. A flat belt drive consists of two 4-ft diameter cast-iron pulleys spaced 16 ft apart.
A power of 60 hp is transmitted by a pulley whose speed is 380 rev/min. Use a
service factor (Ks) pf 1.1 and a design factor 1.0. The width of the polyamide A-3
belt is 6 in. Use CD=1. Answer the following questions.
(1) What is the total length of the belt according to the given geometry?
(2) Find the centrifugal force (Fc) applied to the belt.
(3) What is the transmitted torque through the pulley system given 60hp?
(4) Using the allowable tension, find the force (F₁) on the tight side. What is the
tension at the loose side (F2) and the initial tension (F.)?
(5) Using the forces, estimate the developed friction coefficient (f)
(6) Based on the forces and the given rotational speed, rate the pulley set. In other
words, what is the horse power that can be transmitted by the pulley system?
(7) To reduce the applied tension on the tight side, the friction coefficient is
increased to 0.75. Find out the…
Chapter 7 Solutions
Engineering Mechanics: Dynamics
Ch. 7.5 - Place your textbook on your desk, with fixed axes...Ch. 7.5 - Repeat the experiment of Prob. 7/1 but use a small...Ch. 7.5 - Prob. 3PCh. 7.5 - A timing mechanism consists of the rotating...Ch. 7.5 - Prob. 5PCh. 7.5 - Prob. 6PCh. 7.5 - Prob. 7PCh. 7.5 - Prob. 8PCh. 7.5 - Prob. 9PCh. 7.5 - Prob. 10P
Ch. 7.5 - Prob. 11PCh. 7.5 - Prob. 12PCh. 7.5 - Prob. 13PCh. 7.5 - In manipulating the dumbbell, the jaws of the...Ch. 7.5 - Prob. 15PCh. 7.5 - Prob. 16PCh. 7.5 - For the robot of Prob. 7/16, determine the angular...Ch. 7.5 - Prob. 18PCh. 7.5 - Prob. 19PCh. 7.5 - The circular disk of 120-mm radius rotates about...Ch. 7.5 - Prob. 21PCh. 7.5 - Prob. 22PCh. 7.5 - Prob. 23PCh. 7.5 - Prob. 24PCh. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.5 - The pendulum oscillates about the x-axis according...Ch. 7.5 - Prob. 28PCh. 7.6 - Prob. 29PCh. 7.6 - Prob. 30PCh. 7.6 - Prob. 31PCh. 7.6 - Prob. 32PCh. 7.6 - Prob. 33PCh. 7.6 - Prob. 34PCh. 7.6 - Prob. 35PCh. 7.6 - Prob. 36PCh. 7.6 - Prob. 37PCh. 7.6 - Prob. 38PCh. 7.6 - Prob. 39PCh. 7.6 - Prob. 40PCh. 7.6 - Prob. 41PCh. 7.6 - Prob. 42PCh. 7.6 - Prob. 43PCh. 7.6 - Prob. 44PCh. 7.6 - Prob. 45PCh. 7.6 - Prob. 46PCh. 7.6 - The center O of the spacecraft is moving through...Ch. 7.6 - Prob. 48PCh. 7.6 - Prob. 49PCh. 7.6 - Prob. 50PCh. 7.6 - Prob. 51PCh. 7.6 - Prob. 52PCh. 7.8 - Prob. 53PCh. 7.8 - Prob. 54PCh. 7.8 - The aircraft landing gear viewed from the front is...Ch. 7.8 - Prob. 56PCh. 7.8 - Prob. 57PCh. 7.8 - Prob. 58PCh. 7.8 - Prob. 59PCh. 7.8 - Prob. 60PCh. 7.8 - Prob. 61PCh. 7.8 - Prob. 62PCh. 7.8 - Prob. 63PCh. 7.8 - Prob. 64PCh. 7.8 - Prob. 65PCh. 7.8 - Prob. 66PCh. 7.8 - Prob. 67PCh. 7.8 - Prob. 68PCh. 7.8 - Prob. 69PCh. 7.8 - Prob. 70PCh. 7.8 - The assembly, consisting of the solid sphere of...Ch. 7.8 - Prob. 72PCh. 7.10 - Prob. 73PCh. 7.10 - The slender shaft carries two offset particles,...Ch. 7.10 - Prob. 75PCh. 7.10 - Prob. 76PCh. 7.10 - Prob. 77PCh. 7.10 - Prob. 78PCh. 7.10 - Prob. 79PCh. 7.10 - Prob. 80PCh. 7.10 - Prob. 81PCh. 7.10 - Prob. 82PCh. 7.10 - Prob. 83PCh. 7.10 - Prob. 84PCh. 7.10 - Prob. 85PCh. 7.10 - Prob. 86PCh. 7.10 - The thin circular disk of mass m and radius R is...Ch. 7.10 - Prob. 88PCh. 7.10 - Prob. 89PCh. 7.10 - Prob. 90PCh. 7.10 - Prob. 91PCh. 7.10 - Prob. 92PCh. 7.10 - Prob. 93PCh. 7.10 - Prob. 94PCh. 7.11 - Prob. 95PCh. 7.11 - Prob. 96PCh. 7.11 - Prob. 97PCh. 7.11 - The 50-kg wheel is a solid circular disk which...Ch. 7.11 - The special-purpose fan is mounted as shown. The...Ch. 7.11 - Prob. 100PCh. 7.11 - Prob. 101PCh. 7.11 - Prob. 102PCh. 7.11 - Prob. 103PCh. 7.11 - Prob. 104PCh. 7.11 - Prob. 105PCh. 7.11 - Prob. 106PCh. 7.11 - Prob. 107PCh. 7.11 - Prob. 108PCh. 7.11 - Prob. 109PCh. 7.11 - Prob. 110PCh. 7.11 - Prob. 111PCh. 7.11 - Prob. 112PCh. 7.11 - Prob. 113PCh. 7.11 - Prob. 114PCh. 7.11 - Prob. 115PCh. 7.11 - Prob. 116PCh. 7.11 - Prob. 117PCh. 7.11 - Prob. 118PCh. 7.11 - Prob. 119PCh. 7.11 - Prob. 120PCh. 7.11 - Prob. 121PCh. 7.11 - The uniform slender bar of mass m and length l is...Ch. 7.11 - Prob. 123PCh. 7.11 - Prob. 124PCh. 7.11 - Prob. 125PCh. 7.11 - Prob. 126PCh. 7.12 - Prob. 127RPCh. 7.12 - The solid cube of mass m and side a revolves about...Ch. 7.12 - Prob. 129RPCh. 7.12 - Prob. 130RPCh. 7.12 - Prob. 132RPCh. 7.12 - The solid cone of mass m, base radius r, and...Ch. 7.12 - Prob. 135RPCh. 7.12 - Prob. 136RPCh. 7.12 - Prob. 137RPCh. 7.12 - Prob. 138RPCh. 7.12 - Prob. 139RPCh. 7.12 - Prob. 140RPCh. 7.12 - Prob. 141RPCh. 7.12 - Prob. 142RPCh. 7.12 - Prob. 143RPCh. 7.12 - Prob. 144RPCh. 7.12 - Prob. 145RPCh. 7.12 - Prob. 146RP
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- The tooth numbers for the gear train illustrated are N₂ = 24, N3 = 18, №4 = 30, №6 = 36, and N₁ = 54. Gear 7 is fixed. If shaft b is turned through 5 revolutions, how many turns will shaft a make? a 5 [6] barrow_forwardCE-112 please solve this problem step by step and give me the correct answerarrow_forwardCE-112 please solve this problem step by step and give me the correct answerarrow_forward
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Dynamics - Lesson 1: Introduction and Constant Acceleration Equations; Author: Jeff Hanson;https://www.youtube.com/watch?v=7aMiZ3b0Ieg;License: Standard YouTube License, CC-BY