Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 13.4, Problem 12P
Cylinder B has a mass m and is hoisted using the cord and pulley system shown. Determine the magnitude of force F as a function of the block’s vertical posit on y so that when F is applied the block rises with a constant acceleration aB. Neglect the mass of the cord and pulleys.
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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
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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 13 Solutions
Engineering Mechanics: Dynamics (14th Edition)
Ch. 13.4 - In each case, determine its velocity when t = 2 s...Ch. 13.4 - In each case, determine its velocity at s = 8 m if...Ch. 13.4 - Determine the initial acceleration of the 10-kg...Ch. 13.4 - Write the equations of motion in the x and y...Ch. 13.4 - The motor winds n the cable with a constant...Ch. 13.4 - If motor M exerts a force of F = (10t2 + 100) N on...Ch. 13.4 - A spring of stiffness k = 500 N/m is mounted...Ch. 13.4 - The spring has a stiffness k = 200 N/m and is...Ch. 13.4 - Block B rests upon a smooth surface. If the...Ch. 13.4 - The 6-lb particle is subjected to the action of...
Ch. 13.4 - The two boxcars A and B have a weight of 20 000 lb...Ch. 13.4 - If the coefficient of kinetic friction between the...Ch. 13.4 - If the 50-kg crate starts from rest and achieves a...Ch. 13.4 - If blocks A and B of mass 10 kg and 6 kg...Ch. 13.4 - The 10-lb block has a speed of 4 ft/s when the...Ch. 13.4 - The 10-lb block has a speed of 4 ft/s when the...Ch. 13.4 - The speed of the 3500-lb sports car is plotted...Ch. 13.4 - The conveyor belt is moving at 4 m/s. If the...Ch. 13.4 - The conveyor belt is designed to transport...Ch. 13.4 - Determine the time needed to pull the cord at B...Ch. 13.4 - Cylinder B has a mass m and is hoisted using the...Ch. 13.4 - Block A has a weight of 8 lb and block B has a...Ch. 13.4 - The 2-Mg truck is traveling at 15 m/s when the...Ch. 13.4 - The motor lifts the 50-kg crate with an...Ch. 13.4 - The 75-kg man pushes on the 150-kg crate with a...Ch. 13.4 - The coefficient of kinetic friction is k, and the...Ch. 13.4 - A 40-lb suitcase slides from rest 20 ft down the...Ch. 13.4 - Solve Prob. 13-18 if the suitcase has an initial...Ch. 13.4 - If the coefficient of kinetic friction between...Ch. 13.4 - The conveyor belt delivers each 12-kg crate to the...Ch. 13.4 - The 50-kg block A is released from rest. Determine...Ch. 13.4 - If the supplied force F = 150 N, determine the...Ch. 13.4 - A 60-kg suitcase slides from rest 5 m down the...Ch. 13.4 - Solve Prob. 13-24 if the suitcase has an initial...Ch. 13.4 - The 1.5 Mg sports car has a tractive force of F =...Ch. 13.4 - The conveyor belt is moving downward at 4 m/s. If...Ch. 13.4 - At the instant shown the 100-lb block A is moving...Ch. 13.4 - Determine the velocity of the 200-lb crate when t...Ch. 13.4 - Determine the velocity of the 400-kg crate A when...Ch. 13.4 - The tractor is used to lift the 150-kg load B with...Ch. 13.4 - If the tractor travels to the right with an...Ch. 13.4 - Block A and B each have a mass m. Determine the...Ch. 13.4 - The 4-kg smooth cylinder is supported by the...Ch. 13.4 - The coefficient of static friction between the...Ch. 13.4 - If the spring is unstretched when s = 0 and the...Ch. 13.4 - Neglecting the mass of the rope and pulley, and...Ch. 13.4 - Determine the force in the cable when t = 5 s, if...Ch. 13.4 - An electron of mass m is discharged with an...Ch. 13.4 - The 400-lb cylinder at A is hoisted using the...Ch. 13.4 - What is their velocity at this instant?Ch. 13.4 - Block A has a mass mA and is attached to a spring...Ch. 13.4 - A parachutist having a mass m opens his parachute...Ch. 13.4 - Neglect the mass of the motor and pulleys.Ch. 13.4 - If the force exerted on cable AB by the motor is F...Ch. 13.4 - Blocks A and B each have a mass m. Determine the...Ch. 13.4 - Blocks A and Beach have a mass m. Determine the...Ch. 13.4 - If the board AC pushes on the block at an angle ...Ch. 13.4 - If a horizontal force P = 12lb is applied to block...Ch. 13.4 - A freight elevator, including its load, has a mass...Ch. 13.4 - The block A has a mass mA and rests on the pan B,...Ch. 13.5 - P13-5.Set up the n, t axes and write the equations...Ch. 13.5 - P13-6.Set up the n, b, t axes and write the...Ch. 13.5 - The block rests at a distance of 2 m from the...Ch. 13.5 - Prob. 8FPCh. 13.5 - A pilot weighs 150 lb and is traveling at a...Ch. 13.5 - The sports car is traveling along a 30 banked road...Ch. 13.5 - If the 10-kg ball has a velocity of 3m/ s when it...Ch. 13.5 - The motorcycle has a mass of 0.5 Mg and a...Ch. 13.5 - Prob. 52PCh. 13.5 - Prob. 53PCh. 13.5 - The 2-kg block B and 15-kg cylinder A are...Ch. 13.5 - Determine the maximum constant speed at which the...Ch. 13.5 - Cartons having a mass of 5 kg are required to move...Ch. 13.5 - Prob. 57PCh. 13.5 - Prob. 58PCh. 13.5 - Prob. 59PCh. 13.5 - Prob. 60PCh. 13.5 - At the instant B = 60, the boys center of mass G...Ch. 13.5 - A girl having a mass of 25 kg sits at the edge of...Ch. 13.5 - The pendulum bob B has a weight of 5 lb and is...Ch. 13.5 - The pendulum bob B has a mass m and is released...Ch. 13.5 - Determine the constant speed of the passengers on...Ch. 13.5 - A motorcyclist in a circus rides his motorcycle...Ch. 13.5 - The vehicle is designed to combine the feel of a...Ch. 13.5 - The 0.8-Mg car travels over the hill having the...Ch. 13.5 - The 0.8-Mg car travels over the hill having the...Ch. 13.5 - When it reaches the curved portion AB, it is...Ch. 13.5 - Determine the resultant normal and frictional...Ch. 13.5 - If he rotates about the z axis with a constant...Ch. 13.5 - Determine the maximum speed at which the car with...Ch. 13.5 - Determine the maximum constant speed at which the...Ch. 13.5 - The box has a mass m and slides down the smooth...Ch. 13.5 - Prove that if the block is released from rest at...Ch. 13.5 - The cylindrical plug has a weight of 2 lb and it...Ch. 13.5 - When crossing an intersection, a motorcyclist...Ch. 13.5 - The airplane, traveling at a constant speed of 50...Ch. 13.5 - The 2-kg pendulum bob moves in the vertical plane...Ch. 13.5 - The 2-kg pendulum bob moves in the vertical plane...Ch. 13.5 - If it has a speed of 1.5 m/s when y = 0.2 m,...Ch. 13.5 - The ball has a mass m and is attached to the cord...Ch. 13.6 - If the attached spring has a stiffness k = 2...Ch. 13.6 - Determine the constant angular velocity of the...Ch. 13.6 - If = ( t2) rad, where t is in seconds, determine...Ch. 13.6 - The 2-Mg car is traveling along the curved road...Ch. 13.6 - The 0.2-kg pin P is constrained to move in the...Ch. 13.6 - If the cam is rotating at a constant rate of 6...Ch. 13.6 - Determine the magnitude of the resultant force...Ch. 13.6 - Determine the magnitude of the unbalanced force...Ch. 13.6 - Rod OA rotates counterclockwise with a constant...Ch. 13.6 - The boy of mass 40 kg is sliding down the spiral...Ch. 13.6 - Using a forked rod, a 0.5-kg smooth peg P is...Ch. 13.6 - The arm is rotating at a rate of = 4 rad/s when ...Ch. 13.6 - If arm OA rotates with a constant clockwise...Ch. 13.6 - Determine the normal and frictional driving forces...Ch. 13.6 - A smooth can C, having a mass of 3 kg, is lifted...Ch. 13.6 - Prob. 96PCh. 13.6 - Prob. 97PCh. 13.6 - The particle has a mass of 0.5 kg and is confined...Ch. 13.6 - A car of a roller coaster travels along a track...Ch. 13.6 - The 0.5-lb ball is guided along the vertical...Ch. 13.6 - The ball of mass misguided along the vertical...Ch. 13.6 - Using a forked rod, a smooth cylinder P, having a...Ch. 13.6 - The pilot of the airplane executes a vertical loop...Ch. 13.6 - The collar has a mass of 2 kg and travels along...Ch. 13.6 - The particle has a mass of 0.5 kg and is confined...Ch. 13.6 - Solve Prob. 13-105 If the arm has an angular...Ch. 13.6 - The forked rod is used to move the smooth 2-lb...Ch. 13.6 - Prob. 108PCh. 13.6 - Rod OA rotates counterclockwise at a constant...Ch. 13.6 - Solve Prob. 13-109 if motion is in the vertical...Ch. 13.7 - If his speed is a constant vP = 80 ft/s, determine...Ch. 13.7 - The earth has an orbit with eccentricity 0.0167...Ch. 13.7 - Prob. 114PCh. 13.7 - Determine the speed of a satellite launched...Ch. 13.7 - Prob. 116PCh. 13.7 - Prove Keplers third law of motion. Hint: Use Eqs....Ch. 13.7 - Prob. 118PCh. 13.7 - Prob. 119PCh. 13.7 - Determine the constant speed of satellite S so...Ch. 13.7 - Prob. 121PCh. 13.7 - Prob. 122PCh. 13.7 - Prob. 123PCh. 13.7 - Prob. 124PCh. 13.7 - The rocket is traveling around the earth in free...Ch. 13.7 - Prob. 127PCh. 13.7 - Prob. 128PCh. 13.7 - Prob. 129PCh. 13.7 - Prob. 130PCh. 13.7 - The rocket is traveling around the earth in free...Ch. 13.7 - Prob. 132PCh. 13.7 - Prob. 3CPCh. 13.7 - If the trailer has a mass of 250 kg and coasts 45...Ch. 13.7 - The coefficient of kinetic friction between the...Ch. 13.7 - Block B rests on a smooth surface. If the...Ch. 13.7 - If the motor draws in the cable at a rate of v =...Ch. 13.7 - The ball has a mass of 30 kg and a speed v = 4 m/s...Ch. 13.7 - If the coefficient of static friction between the...Ch. 13.7 - If at the instant it reaches point A it has a...
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