EBK ENGINEERING MECHANICS
15th Edition
ISBN: 9780137616909
Author: HIBBELER
Publisher: VST
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Chapter 14, Problem 80P
To determine
The speed of the ball and the normal reaction of the circular track on the ball
when
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Students have asked these similar questions
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 14 Solutions
EBK ENGINEERING MECHANICS
Ch. 14 - Prob. 1FPCh. 14 - If the motor exerts a constant force of 300 N on...Ch. 14 - If the motor exerts a force of F = (600 + 2s2) N...Ch. 14 - The 1.8-Mg dragster is traveling at 125 m/s when...Ch. 14 - When s = 0.5 m, the spring is unstretched and the...Ch. 14 - The 5-lb collar is pulled by a cord that passes...Ch. 14 - Prob. 2PCh. 14 - The 100-kg crate is subjected to the forces shown....Ch. 14 - Determine the required height h of the roller...Ch. 14 - When the driver applies the brakes of a light...
Ch. 14 - Prob. 7PCh. 14 - The force F, acting in a constant direction on the...Ch. 14 - The 2-lb brick slides down a smooth roof, such...Ch. 14 - The two blocks A and B have weights WA = 60 lb and...Ch. 14 - A small box of mass m is given a speed of v=14gr...Ch. 14 - Prob. 18PCh. 14 - If the cord is subjected to a constant force of F=...Ch. 14 - The crash cushion for a highway barrier consists...Ch. 14 - The 25-lb block has an initial speed of v0 = 10...Ch. 14 - At a given instant the 10-lb block A is moving...Ch. 14 - Prob. 25PCh. 14 - The catapulting mechanism is used to propel the...Ch. 14 - Prob. 27PCh. 14 - Prob. 31PCh. 14 - When the 150-lb skier is at point A he has a speed...Ch. 14 - Prob. 39PCh. 14 - Prob. 40PCh. 14 - If the contact surface between the 20-kg block and...Ch. 14 - Prob. 8FPCh. 14 - Prob. 9FPCh. 14 - Prob. 10FPCh. 14 - Prob. 11FPCh. 14 - Prob. 12FPCh. 14 - The jeep has a weight of 2500 lb and an engine...Ch. 14 - Determine the power Input for a motor necessary to...Ch. 14 - An automobile having a mass of 2 Mg travels up a 7...Ch. 14 - Prob. 45PCh. 14 - To dramatize the loss of energy in an automobile,...Ch. 14 - Escalator steps move with a constant speed of 0.6...Ch. 14 - Prob. 48PCh. 14 - The 1000-lb elevator is hoisted by the pulley...Ch. 14 - The sports car has a mass of 2.3 Mg, and while it...Ch. 14 - Prob. 54PCh. 14 - Prob. 55PCh. 14 - The 50-lb block rests on the rough surface for...Ch. 14 - The 2-kg pendulum bob is released from rest when...Ch. 14 - Prob. 14FPCh. 14 - Prob. 15FPCh. 14 - Prob. 16FPCh. 14 - The 75-lb block is released from rest 5 ft above...Ch. 14 - Prob. 18FPCh. 14 - The girl has a mass of 40 kg and center of mass at...Ch. 14 - The 30-lb block A is placed on top of two nested...Ch. 14 - The 5-kg collar has a velocity of 5 m/s to the...Ch. 14 - The 5-kg collar has a velocity of 5 m/s to the...Ch. 14 - Prob. 71PCh. 14 - The roller coaster car has a mass of 700 kg,...Ch. 14 - The roller coaster car has a mass of 700 kg,...Ch. 14 - Prob. 76PCh. 14 - The roller coaster car having a mass m is released...Ch. 14 - The spring has a stiffness k = 200 N/m and an...Ch. 14 - Prob. 79PCh. 14 - Prob. 80PCh. 14 - When s = 0, the spring on the firing mechanism is...Ch. 14 - If the mass of the earth is Me, show that the...Ch. 14 - A rocket of mass m is fired vertically from the...Ch. 14 - The 4-kg smooth collar has a speed of 3 m/s when...Ch. 14 - Prob. 85PCh. 14 - Prob. 87PCh. 14 - Prob. 90PCh. 14 - The roller coaster car has a speed of 15 ft/s when...Ch. 14 - Prob. 1RPCh. 14 - The small 2-lb collar starting from rest at A...Ch. 14 - Prob. 3RPCh. 14 - Prob. 4RPCh. 14 - Prob. 5RPCh. 14 - Prob. 6RPCh. 14 - Prob. 7RPCh. 14 - 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
- 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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