Engineering Mechanics: Statics
13th Edition
ISBN: 9780132915540
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Textbook Question
Chapter 2.9, Problem 136P
Express the force F in Cartesian
Prob. 2-106
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The gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle.
The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear
5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft?
TS
I
y
18T
32T
This
a
12
x
18T
C
48T
5
Question 1. Draw 3 teeth for the following pinion and gear respectively. The teeth
should be drawn near the pressure line so that the teeth from the pinion should
mesh those of the gear. Drawing scale (1:1). Either a precise hand drawing or
CAD drawing is acceptable. Draw all the trajectories of the involute lines and the
circles.
Specification: 18tooth pinion and 30tooth gear. Diameter pitch=P=6 teeth /inch.
Pressure angle:20°, 1/P for addendum (a) and 1.25/P for dedendum (b). For fillet,
c=b-a.
5. The figure shows a gear train. There is no friction at the bearings except for the gear tooth forces.
The material of the milled gears is steel having a Brinell hardness of 170. The input shaft speed (n2)
is 800 rpm. The face width and the contact angle for all gears are 1 in and 20° respectively. In this
gear set, the endurance limit (Se) is 15 kpsi and nd (design factor) is 2.
(a) Find the revolution speed of gear 5.
(b) Determine whether each gear satisfies the design factor of 2.0 for bending fatigue.
(c) Determine whether each gear satisfies the design factor of 2.0 for surface fatigue (contact stress).
(d) According to the computation results of the questions (b) and (c), explain the possible failure
mechanisms for each gear.
N4=28
800rpm
N₁=43
N5=34
N₂=14
P(diameteral pitch)=8 for all gears
Coupled to 2.5hp motor
Chapter 2 Solutions
Engineering Mechanics: Statics
Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Determine the magnitude of the resultant force....Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - Resolve this force into components acting along...Ch. 2.3 - along the v axis. Prob. F2-6Ch. 2.3 - Determine the magnitude of the resultant force FR...Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...Ch. 2.3 - Determine the magnitude of the resultant force FR...
Ch. 2.3 - Prob. 5PCh. 2.3 - Prob. 6PCh. 2.3 - Determine the magnitudes of the two components of...Ch. 2.3 - Solve with F = 350 lb. Prob. 2-4/5Ch. 2.3 - Prob. 9PCh. 2.3 - Prob. 10PCh. 2.3 - Resolve this force into two components acting...Ch. 2.3 - Determine the magnitude of F and its component...Ch. 2.3 - Determine the magnitude of F and its direction ....Ch. 2.3 - Prob. 14PCh. 2.3 - If = 60, determine the magnitude of the resultant...Ch. 2.3 - Also, what is the magnitude of the resultant...Ch. 2.3 - What is the component of force acting along member...Ch. 2.3 - Take = 30. Probs. 2-19/20Ch. 2.3 - Determine the magnitude and direction of the...Ch. 2.3 - Determine the magnitude and direction of the...Ch. 2.3 - If F1 = 400 N and F2 = 600 N, determine the angle...Ch. 2.3 - If their lines of action are at an angle apart...Ch. 2.3 - Prob. 23PCh. 2.3 - Prob. 24PCh. 2.3 - Prob. 25PCh. 2.3 - Prob. 26PCh. 2.3 - Prob. 27PCh. 2.3 - directed along the positive x axis, determine the...Ch. 2.3 - If FB = 3 kN and = 45, determine the magnitude of...Ch. 2.3 - If the resultant force of the two tugboats is...Ch. 2.3 - Prob. 31PCh. 2.4 - Resolve each force acting on the post into its x...Ch. 2.4 - Determine the magnitude and direction of the...Ch. 2.4 - Determine the magnitude of the resultant force...Ch. 2.4 - determine the magnitude of F and its direction ....Ch. 2.4 - If the magnitude of the resultant force acting on...Ch. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Prob. 32PCh. 2.4 - Prob. 33PCh. 2.4 - Resolve F1 and F2 into their x and y components.Ch. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Resolve each force acting on the gusset plate into...Ch. 2.4 - Determine the magnitude of the resultant force...Ch. 2.4 - Prob. 38PCh. 2.4 - Prob. 39PCh. 2.4 - Prob. 40PCh. 2.4 - Prob. 41PCh. 2.4 - Determine the magnitude and orientation of FB so...Ch. 2.4 - measured counterclockwise from the positive y...Ch. 2.4 - Prob. 44PCh. 2.4 - Prob. 45PCh. 2.4 - Prob. 46PCh. 2.4 - Determine the magnitude and direction of the...Ch. 2.4 - Prob. 48PCh. 2.4 - Prob. 49PCh. 2.4 - Prob. 50PCh. 2.4 - Prob. 51PCh. 2.4 - Prob. 52PCh. 2.4 - What is the magnitude of the resultant force?...Ch. 2.4 - Prob. 54PCh. 2.4 - Prob. 55PCh. 2.4 - Prob. 56PCh. 2.4 - Prob. 57PCh. 2.4 - If the magnitude of the resultant force acting on...Ch. 2.4 - Set = 30. Probs. 2-56/57Ch. 2.6 - Determine the coordinate direction angles of the...Ch. 2.6 - Express the force as a Cartesian vector. Prob....Ch. 2.6 - Express the force as a Cartesian vector. Prob....Ch. 2.6 - Express the force as a Cartesian vector. Prob....Ch. 2.6 - Express the force as a Cartesian vector. Prob....Ch. 2.6 - Determine the resultant force acting on the hook....Ch. 2.6 - Prob. 60PCh. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.6 - Specify the coordinate direction angles of F1 and...Ch. 2.6 - If the magnitude of F is 80 N, and = 60 and =...Ch. 2.6 - Prob. 64PCh. 2.6 - Prob. 65PCh. 2.6 - Prob. 66PCh. 2.6 - Prob. 67PCh. 2.6 - Prob. 68PCh. 2.6 - Prob. 69PCh. 2.6 - Prob. 70PCh. 2.6 - Prob. 71PCh. 2.6 - Prob. 72PCh. 2.6 - Express each force as a Cartesian vector.Ch. 2.6 - Determine the resultant of the two forces and...Ch. 2.6 - Prob. 75PCh. 2.6 - Prob. 76PCh. 2.6 - Prob. 77PCh. 2.6 - Prob. 78PCh. 2.6 - Prob. 79PCh. 2.6 - If the coordinate direction angles for F1 are 3 =...Ch. 2.6 - If the coordinate direction angles for F1 are 3 =...Ch. 2.6 - If the direction of the resultant force acting on...Ch. 2.6 - Express each force in Cartesian vector form and...Ch. 2.6 - Prob. 84PCh. 2.6 - If = 75, determine the magnitudes of F and Fy....Ch. 2.8 - Express the position vector rAB in Cartesian...Ch. 2.8 - What is the angle ? Prob. F2-20Ch. 2.8 - Prob. 21FPCh. 2.8 - Express the force as a Cartesian vector. Prob....Ch. 2.8 - Determine the magnitude of the resultant force at...Ch. 2.8 - Determine the resultant force at A. Prob. F2-24Ch. 2.8 - Prob. 86PCh. 2.8 - Prob. 87PCh. 2.8 - Prob. 88PCh. 2.8 - If F = {350i 250j 450k} N and cable AB is 9 m...Ch. 2.8 - Prob. 90PCh. 2.8 - Prob. 91PCh. 2.8 - If FB = 560 N and FC = 700 N, determine the...Ch. 2.8 - If FB = 700 N, and FC = 560 N, determine the...Ch. 2.8 - Prob. 94PCh. 2.8 - Prob. 95PCh. 2.8 - Prob. 96PCh. 2.8 - Prob. 97PCh. 2.8 - Express this force as a Cartesian vector acting on...Ch. 2.8 - Prob. 99PCh. 2.8 - Prob. 100PCh. 2.8 - Represent each force as a Cartesian vector and...Ch. 2.8 - Prob. 102PCh. 2.8 - If the force in each cable tied to the bin is 70...Ch. 2.8 - Due to symmetry, the tension in the four cables is...Ch. 2.8 - Prob. 105PCh. 2.8 - If the force in each chain has a magnitude of 60...Ch. 2.8 - If the resultant force at O has a magnitude of 130...Ch. 2.8 - Prob. 108PCh. 2.8 - Prob. 109PCh. 2.8 - Prob. 110PCh. 2.8 - Determine the length of the chain, and express the...Ch. 2.9 - Determine the angle between the force and the...Ch. 2.9 - Determine the angle between the force and the...Ch. 2.9 - Determine the angle between the force and the...Ch. 2.9 - Determine the projected component of the force...Ch. 2.9 - Find the magnitude of the projected component of...Ch. 2.9 - Determine the components of the force acting...Ch. 2.9 - Determine the magnitudes of the components of the...Ch. 2.9 - Prob. 112PCh. 2.9 - Determine the angle between the edges of the...Ch. 2.9 - Prob. 114PCh. 2.9 - Prob. 115PCh. 2.9 - Prob. 116PCh. 2.9 - Prob. 117PCh. 2.9 - Determine the projection of the force F along the...Ch. 2.9 - Determine the angle between the y axis of the...Ch. 2.9 - Determine the magnitudes of the components of F =...Ch. 2.9 - Determine the magnitude of the projection of force...Ch. 2.9 - Prob. 122PCh. 2.9 - Prob. 123PCh. 2.9 - Prob. 124PCh. 2.9 - Prob. 125PCh. 2.9 - Determine the magnitude of the projected component...Ch. 2.9 - Determine the angle between the two cables...Ch. 2.9 - Prob. 128PCh. 2.9 - Express this component as a Cartesian vector....Ch. 2.9 - Prob. 130PCh. 2.9 - Determine the angles and made between the axes...Ch. 2.9 - Prob. 132PCh. 2.9 - Prob. 133PCh. 2.9 - Determine the magnitudes of the components of the...Ch. 2.9 - Prob. 135PCh. 2.9 - Express the force F in Cartesian vector form if it...Ch. 2.9 - Express force F in Cartesian vector form if point...Ch. 2.9 - Determine the magnitudes of the projected...Ch. 2.9 - Prob. 139PCh. 2.9 - Prob. 140RPCh. 2.9 - Determine the x and y components of F1 and F2....Ch. 2.9 - Determine the magnitude of the resultant force and...Ch. 2.9 - Determine the magnitude of the resultant force...Ch. 2.9 - Express F1 and F2 as Cartesian vectors.Ch. 2.9 - Determine the magnitude of the resultant force and...Ch. 2.9 - The cable attach to the tractor at B exerts a...Ch. 2.9 - Prob. 147RPCh. 2.9 - Prob. 148RPCh. 2.9 - Prob. 149RP
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