ENGR.MECH.:STAT.+DYNAMICS
15th Edition
ISBN: 9780134780955
Author: HIBBELER
Publisher: RENT PEARS
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Textbook Question
Chapter 12, Problem 15P
A particle is moving with a velocity of v0 when s = 0 and t = 0. If it is subjected to a deceleration of a = –kv3, where k is a constant, determine its velocity and position as functions of time.
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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 12 Solutions
ENGR.MECH.:STAT.+DYNAMICS
Ch. 12 - Initially, the car travels along a straight road...Ch. 12 - A ball is thrown vertically upward with a speed of...Ch. 12 - A particle travels along a straight line with a...Ch. 12 - A particle travels along a straight line with a...Ch. 12 - The position of the particle is given by s = (2t2 ...Ch. 12 - A particle travels along a straight line with an...Ch. 12 - A particle moves along a straight line such that...Ch. 12 - A particle travels along a straight line with a...Ch. 12 - Starting from rest, a particle moving in a...Ch. 12 - If a particle has an initial velocity of v0 = 12...
Ch. 12 - A particle travels along a straight line with a...Ch. 12 - A particle travels along a straight line with a...Ch. 12 - Prob. 5PCh. 12 - A particle is moving along a straight line such...Ch. 12 - A particle moves along a straight line with an...Ch. 12 - A particle travels along a straight-line path such...Ch. 12 - Tests reveal that a normal driver takes about 0.75...Ch. 12 - A particle is moving with a velocity of v0 when s...Ch. 12 - A particle is moving along a straight line with an...Ch. 12 - Car B is traveling a distanced ahead of car A....Ch. 12 - The velocity of a particle traveling along a...Ch. 12 - A freight train travels at v = 60(1 et) ft/s,...Ch. 12 - A particle is moving along a straight line such...Ch. 12 - If the effects of atmospheric resistance are...Ch. 12 - When a particle falls through the air, its initial...Ch. 12 - A sphere is fired downwards into a medium with an...Ch. 12 - Prob. 33PCh. 12 - Prob. 34PCh. 12 - A freight train starts from rest and travels with...Ch. 12 - Prob. 36PCh. 12 - Prob. 37PCh. 12 - Prob. 38PCh. 12 - Prob. 39PCh. 12 - An airplane starts from rest, travels 5000 ft down...Ch. 12 - The elevator starts from rest at the first floor...Ch. 12 - The motion of a jet plane just after landing on a...Ch. 12 - Prob. 44PCh. 12 - The vt graph for a particle moving through an...Ch. 12 - The a-s graph for a rocket moving along a straight...Ch. 12 - The jet car is originally traveling at a velocity...Ch. 12 - The v-t graph for a train has been experimentally...Ch. 12 - A motorcycle starts from rest at s = 0 and travels...Ch. 12 - A motorcycle starts from rest at s = 0 and travels...Ch. 12 - The v-t graph for the motion of a car as it moves...Ch. 12 - An airplane lands on the straight runway,...Ch. 12 - Starting from rest at s = 0, a boat travels in a...Ch. 12 - Starting from rest at s = 0, a boat travels in a...Ch. 12 - The speed of a train during the first minute has...Ch. 12 - A man riding upward in a freight elevator...Ch. 12 - Two cars start from rest side by side and travel...Ch. 12 - If the position of a particle is defined as s =...Ch. 12 - The jet plane starts from rest at s = 0 and is...Ch. 12 - Prob. 67PCh. 12 - Prob. 15FPCh. 12 - Prob. 16FPCh. 12 - A particle is constrained to travel along the...Ch. 12 - Prob. 18FPCh. 12 - A particle is traveling along the parabolic path y...Ch. 12 - Prob. 20FPCh. 12 - The ball is kicked from point A with the initial...Ch. 12 - The ball is kicked from point A with the initial...Ch. 12 - Prob. 23FPCh. 12 - Prob. 24FPCh. 12 - A ball is thrown from A. If it is required to...Ch. 12 - Prob. 26FPCh. 12 - If the velocity of a particle is defined as v(t) =...Ch. 12 - The velocity of a particle is v= {3i + (6 2t)j}...Ch. 12 - A particle, originally at rest and located at...Ch. 12 - The velocity of a particle is given by v ={16t2 i...Ch. 12 - The water sprinkler, positioned at the base of a...Ch. 12 - Prob. 74PCh. 12 - Prob. 75PCh. 12 - A particle travels along the curve from A to B in...Ch. 12 - The position of a crate sliding down a ramp is...Ch. 12 - A rocket is fired from rest at x = 0 and travels...Ch. 12 - The particle travels along the path defined by the...Ch. 12 - The motorcycle travels with constant speed v0...Ch. 12 - A particle travels along the curve from A to B in...Ch. 12 - The roller coaster car travels down the helical...Ch. 12 - Pegs A and B are restricted to move in the...Ch. 12 - The van travels over the hill described by y =...Ch. 12 - The flight path of the helicopter as it takes off...Ch. 12 - Determine the minimum initial velocity v0 and the...Ch. 12 - The catapult is used to launch a ball such that it...Ch. 12 - Neglecting the size of the ball, determine the...Ch. 12 - The girl at A can throw a ball at vA = 10 m/s....Ch. 12 - Show that the girl at A can throw the ball to the...Ch. 12 - The ball at A is kicked with a speed vA, = 80ft/s...Ch. 12 - The ball at A is kicked such that A = 30. If it...Ch. 12 - A golf ball is struck with a velocity of 80 ft/s...Ch. 12 - A golf ball is struck with a velocity of 80 ft/s...Ch. 12 - The basketball passed through the hoop even...Ch. 12 - It is observed that the skier leaves the ramp A at...Ch. 12 - It is observed that the skier leaves the ramp A at...Ch. 12 - Determine the horizontal velocity vA of a tennis...Ch. 12 - The missile at A takes off from rest and rises...Ch. 12 - The projectile is launched with a velocity v0....Ch. 12 - Prob. 101PCh. 12 - Prob. 102PCh. 12 - If the dart is thrown with a speed of 10 m/s,...Ch. 12 - Prob. 104PCh. 12 - Prob. 105PCh. 12 - Prob. 106PCh. 12 - Prob. 107PCh. 12 - Prob. 108PCh. 12 - The catapult is used to launch a ball such that it...Ch. 12 - Prob. 27FPCh. 12 - Prob. 28FPCh. 12 - Prob. 29FPCh. 12 - Prob. 30FPCh. 12 - Prob. 31FPCh. 12 - Prob. 32FPCh. 12 - The position of a particle is defined by r = {4(t ...Ch. 12 - The automobile has a speed of 80 ft/s at point A...Ch. 12 - The satellite S travels around the earth in a...Ch. 12 - The car passes point A with a speed of 25 m/s...Ch. 12 - Prob. 122PCh. 12 - Prob. 127PCh. 12 - Prob. 128PCh. 12 - Prob. 129PCh. 12 - Prob. 130PCh. 12 - A boat is traveling along a circular path having a...Ch. 12 - Prob. 132PCh. 12 - Prob. 133PCh. 12 - Prob. 134PCh. 12 - When t = 0, the train has a speed of 8 m/s, which...Ch. 12 - The ball is ejected horizontally from the tube...Ch. 12 - The race car has an initial speed vA = 15 m/s at...Ch. 12 - Particles A and B are traveling counter-clockwise...Ch. 12 - Prob. 146PCh. 12 - Prob. 149PCh. 12 - The train passes point A with a speed of 30 m/s...Ch. 12 - The particle travels with a constant speed of 300...Ch. 12 - Prob. 152PCh. 12 - If the speed of the crate at A is 15 ft/s, which...Ch. 12 - The car has a speed of 55 ft/s. Determine the...Ch. 12 - The platform is rotating about the vertical axis...Ch. 12 - Peg P is driven by the fork link OA along the...Ch. 12 - Prob. 36FPCh. 12 - Prob. 37FPCh. 12 - Prob. 38FPCh. 12 - An airplane is flying in a straight line with a...Ch. 12 - The small washer is sliding down the cord OA. When...Ch. 12 - If a particle moves along a path such that r = (2...Ch. 12 - Prob. 162PCh. 12 - The time rate of change of acceleration is...Ch. 12 - A particle moves in the x y plane such that its...Ch. 12 - At the instant shown, the man is twirling a hose...Ch. 12 - The rod OA rotates clockwise with a constant...Ch. 12 - Determine the magnitude of the acceleration of the...Ch. 12 - The rod OA rotates counterclockwise with a...Ch. 12 - Determine the magnitude of the acceleration of the...Ch. 12 - Prob. 189PCh. 12 - Determine the velocity of block D if end A of the...Ch. 12 - Prob. 40FPCh. 12 - Prob. 41FPCh. 12 - Prob. 42FPCh. 12 - Prob. 43FPCh. 12 - Prob. 44FPCh. 12 - If the end of the cable at A is pulled down with a...Ch. 12 - The motor at C pulls in the cable with an...Ch. 12 - Determine the displacement of the log if the truck...Ch. 12 - Determine the constant speed at which the cable at...Ch. 12 - Starting from rest, the cable can be wound onto...Ch. 12 - If the end A of the cable is moving at vA = 3 m/s,...Ch. 12 - Determine the time needed for the load at B to...Ch. 12 - The cable at A is being drawn toward the motor at...Ch. 12 - Determine the speed of the block at B.Ch. 12 - The roller at A is moving with a velocity of A = 4...Ch. 12 - Prob. 213PCh. 12 - At the instant shown, the car at A is traveling at...Ch. 12 - The motor draws in the cord at B with an...Ch. 12 - If block B is moving down with a velocity vB and...Ch. 12 - Two planes, A and B, are flying at the same...Ch. 12 - Prob. 219PCh. 12 - The boat can travel with a speed of 16 km/h in...Ch. 12 - Two boats leave the pier P at the same time and...Ch. 12 - Prob. 222PCh. 12 - At the instant shown, car A has a speed of 20...Ch. 12 - Cars A and B are traveling around the circular...Ch. 12 - At the instant shown, cars A and B are traveling...Ch. 12 - Prob. 228PCh. 12 - Prob. 230PCh. 12 - Prob. 232PCh. 12 - Prob. 1RPCh. 12 - Prob. 2RPCh. 12 - Prob. 3RPCh. 12 - Prob. 4RPCh. 12 - Prob. 5RPCh. 12 - Prob. 6RPCh. 12 - Prob. 7RPCh. 12 - Prob. 8RPCh. 12 - Prob. 9RPCh. 12 - Prob. 10RPCh. 12 - Prob. 11RP
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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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