PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 15, Problem 3FP
To determine
The speed of the crate when
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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 15 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
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Ch. 15 - Prob. 9PCh. 15 - During operation the jack hammer strikes the...Ch. 15 - For a short period of time, the frictional driving...Ch. 15 - The 2.5-Mg van is traveling with a speed of 100...Ch. 15 - Prob. 14PCh. 15 - The towing force acting on the 400-kg safe varies...Ch. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - If it takes 35 s for the 50-Mg tugboat to increase...Ch. 15 - Prob. 23PCh. 15 - The balloon has a total mass of 400 kg including...Ch. 15 - Prob. 26PCh. 15 - Prob. 30PCh. 15 - Prob. 7FPCh. 15 - The cart and package have a mass of 20 kg and 5...Ch. 15 - The 5-kg block A has an initial speed of 5 m/s as...Ch. 15 - Prob. 10FPCh. 15 - Prob. 11FPCh. 15 - The cannon and support without a projectile have a...Ch. 15 - The 5-Mg bus B is traveling to the right at 20...Ch. 15 - Prob. 36PCh. 15 - A railroad car having a mass of 15 Mg is coasting...Ch. 15 - A ballistic pendulum consists of a 4-kg wooden...Ch. 15 - Prob. 39PCh. 15 - Prob. 43PCh. 15 - Prob. 44PCh. 15 - Prob. 45PCh. 15 - The 30-Mg freight car A and 15-Mg freight car B...Ch. 15 - Blocks A and B have masses of 40 kg and 60 kg,...Ch. 15 - Block A has a mass of 5 kg and is placed on the...Ch. 15 - Solve Prob. 15-53 if the coefficient of kinetic...Ch. 15 - Prob. 56PCh. 15 - Prob. 13FPCh. 15 - Prob. 14FPCh. 15 - The 30-lb package A has a speed of 5 ft/s when it...Ch. 15 - The ball strikes the smooth wall with a velocity...Ch. 15 - Prob. 17FPCh. 15 - Prob. 18FPCh. 15 - Prob. 58PCh. 15 - Prob. 59PCh. 15 - Prob. 61PCh. 15 - Prob. 62PCh. 15 - Prob. 63PCh. 15 - Prob. 64PCh. 15 - A 1-lb ball A is traveling horizontally at 20 ft/s...Ch. 15 - Prob. 69PCh. 15 - Prob. 73PCh. 15 - Two smooth disks A and B each have a mass of 0.5...Ch. 15 - Prob. 75PCh. 15 - The cue ball A is given an initial velocity (vA)1...Ch. 15 - Prob. 78PCh. 15 - Prob. 79PCh. 15 - A ball of negligible size and mass m is given a...Ch. 15 - Prob. 81PCh. 15 - The 20-lb box slides on the surface for which k =...Ch. 15 - Prob. 84PCh. 15 - Prob. 85PCh. 15 - Prob. 90PCh. 15 - Prob. 92PCh. 15 - Disks A and B have a mass of 15 kg and 10 kg,...Ch. 15 - Prob. 19FPCh. 15 - Prob. 20FPCh. 15 - Initially the 5-kg block is moving with a constant...Ch. 15 - Prob. 22FPCh. 15 - Prob. 23FPCh. 15 - Prob. 24FPCh. 15 - Determine the angular momentum HO of the 6-lb...Ch. 15 - Determine the angular momentum HP of the 6-lb...Ch. 15 - Prob. 96PCh. 15 - Determine the angular momentum Hp, of each of the...Ch. 15 - Prob. 98PCh. 15 - Determine the angular momentum Hp of the 3-kg...Ch. 15 - The 800-lb roller-coaster car starts from rest on...Ch. 15 - The 800-lb roller-coaster car starts from rest on...Ch. 15 - If the rod of negligible mass is subjected to a...Ch. 15 - The amusement park ride consists of a 200-kg car...Ch. 15 - An earth satellite of mass 700 kg is launched into...Ch. 15 - Prob. 115PCh. 15 - Prob. 116PCh. 15 - Prob. 119PCh. 15 - The gauge pressure of water at A is 150.5 kPa....Ch. 15 - Prob. 121PCh. 15 - The fountain shoots water in the direction shown....Ch. 15 - A plow located on the front of a locomotive scoops...Ch. 15 - Prob. 124PCh. 15 - Water is discharged from a nozzle with a velocity...Ch. 15 - Prob. 127PCh. 15 - Prob. 128PCh. 15 - Sand drops onto the 2-Mg empty rail car at 50 kg/s...Ch. 15 - Prob. 133PCh. 15 - A rocket has an empty weight of 500 lb and carries...Ch. 15 - Prob. 135PCh. 15 - Prob. 138PCh. 15 - The missile weighs 40 000 lb. The constant thrust...Ch. 15 - Prob. 140PCh. 15 - Prob. 1RPCh. 15 - Prob. 2RPCh. 15 - Prob. 3RPCh. 15 - Prob. 4RPCh. 15 - The 200-g projectile is fired with a velocity of...Ch. 15 - Block A has a mass of 3 kg and is sliding on a...Ch. 15 - Two smooth billiard balls A and B have an equal...Ch. 15 - Prob. 8RP
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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 Darrow_forward3 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?arrow_forward2. 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…arrow_forward
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