Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 15.4, Problem 92P
To determine
The coefficient of restitution.
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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
Engineering Mechanics: Dynamics (14th Edition)
Ch. 15.2 - Determine the impulse of the force for t = 2 s.Ch. 15.2 - Determine the magnitude of the impulse the ground...Ch. 15.2 - The crate starts from rest and is towed by the...Ch. 15.2 - Determine the speed of the 25-kg crate when t = 4...Ch. 15.2 - If the car starts from rest, determine its speed...Ch. 15.2 - The traction force developed at the wheels is FD =...Ch. 15.2 - Determine the impulse of his foot on the ball at...Ch. 15.2 - The crate starts from rest and is towed by the...Ch. 15.2 - Determine the average tension in each of the two...Ch. 15.2 - If the uniform beam has a weight of 5000 lb,...
Ch. 15.2 - Determine the magnitude of the net impulse exerted...Ch. 15.2 - If it takes 80 s for the train to increase its...Ch. 15.2 - If they start from rest, determine their speed...Ch. 15.2 - If the impact occurs in 0.06 s, determine the...Ch. 15.2 - The winch delivers a horizontal towing force T to...Ch. 15.2 - If the crate starts from rest and achieves a speed...Ch. 15.2 - To achieve this the 2-kg spike S is fired into the...Ch. 15.2 - If the van has a speed of 20 km/h when t = 0,...Ch. 15.2 - If the speed decreases to 40 km/h in 5 s,...Ch. 15.2 - If it strikes the barrier, determine the...Ch. 15.2 - If the 100 kg crate is originally at rest at t = 0...Ch. 15.2 - From the data shown in the graphs, determine the...Ch. 15.2 - Determine its speed, starting from rest, when t =...Ch. 15.2 - Determine the speed of the crate when t = 3 s and...Ch. 15.2 - If these loadings vary in the manner shown on the...Ch. 15.2 - If the cabinet is initially moving to the left...Ch. 15.2 - The propeller provides the propulsion force F...Ch. 15.2 - Determine the sleds maximum velocity and the...Ch. 15.2 - If the 34-lb crate is originally on the ground at...Ch. 15.2 - If the 34-lb crate is originally at rest on the...Ch. 15.2 - The balloon is rising at a constant velocity of 18...Ch. 15.2 - Prob. 26PCh. 15.2 - Determine the speed of the crate when t = 3 s,...Ch. 15.2 - Determine how high the crate has moved upward when...Ch. 15.2 - As a result of the explosion, the cylinder...Ch. 15.2 - If the carrier is traveling forward with a speed...Ch. 15.2 - If B is moving downward with a velocity (vB)1 = 3...Ch. 15.2 - Prob. 32PCh. 15.2 - The winch delivers a horizontal towing force T to...Ch. 15.2 - It then travels along the trajectory shown before...Ch. 15.2 - Determine the velocity of A after collision if the...Ch. 15.2 - If the cart has a smooth surface and it is...Ch. 15.3 - If the two blocks couple together after collision,...Ch. 15.3 - If the spring is compressed s = 200 mm and then...Ch. 15.3 - If A is stationary and B has a velocity of 15 m/s...Ch. 15.3 - If a 20-kg projectile is fired from the cannon...Ch. 15.3 - Meanwhile a 2-Mg car A is traveling at 15 m/s to...Ch. 15.3 - Determine the distance s the boy reaches up the...Ch. 15.3 - At the same time another car having a mass of 12...Ch. 15.3 - When a 2-g bullet strikes and becomes embedded in...Ch. 15.3 - If he lands on the second fiat car B, determine...Ch. 15.3 - Determine the speed of the block just after the...Ch. 15.3 - Determine the speed of the block just after the...Ch. 15.3 - Determine the distance the block will slide before...Ch. 15.3 - When the toboggan reaches the bottom of the slope...Ch. 15.3 - Determine its speed v2 and its direction 2 when it...Ch. 15.3 - A spring, having a stiffness of k = 60 N/m, is...Ch. 15.3 - Determine the maximum compression of the spring...Ch. 15.3 - They are placed on a smooth surface and the spring...Ch. 15.3 - If they exchange positions, A going to B and then...Ch. 15.3 - If A walks to B and stops, and both walk back...Ch. 15.3 - If someone drives the automobile to the other side...Ch. 15.3 - A 10-kg crate is released from rest at A and...Ch. 15.3 - Block A has a mass of 5 kg and is placed on the...Ch. 15.3 - if the coefficient of kinetic friction between A...Ch. 15.3 - When it reaches the bottom, a spring loaded gun...Ch. 15.3 - If the belt starts from rest and begins to run...Ch. 15.3 - If the 10-g bullet is traveling at 300 m/s when it...Ch. 15.3 - The velocities of A and B before and after the...Ch. 15.3 - If the coefficient of restitution between the...Ch. 15.4 - As it slides down the ramp, it strikes the 80-lb...Ch. 15.4 - If the coefficient of restitution between the ball...Ch. 15.4 - Disk B has a mass of 11 kg and is initially at...Ch. 15.4 - Two disks A and B each have a mass of 1 kg and the...Ch. 15.4 - Disk A has a mass of 250 g and is sliding on a...Ch. 15.4 - After the collision, the car moves with a velocity...Ch. 15.4 - If the coefficient of restitution between the...Ch. 15.4 - The block has a velocity v = 10 m/s when it is s =...Ch. 15.4 - If A and B are rolling forward with velocity v and...Ch. 15.4 - If A and B are rolling forward with velocity v and...Ch. 15.4 - If e = 0.7, determine the velocity of each ball...Ch. 15.4 - If the coefficient of restitution between A and B...Ch. 15.4 - If the coefficient of restitution between A and B...Ch. 15.4 - If ball A is released from rest and strikes ball B...Ch. 15.4 - Determine (a) the velocity at which it strikes the...Ch. 15.4 - If the coefficient of restitution between the ball...Ch. 15.4 - If A is given a velocity of 0, while sphere B is...Ch. 15.4 - Determine the initial velocity vA of the ball and...Ch. 15.4 - Determine the initial velocity vA, the final...Ch. 15.4 - If both disks are moving with the velocities shown...Ch. 15.4 - If both disks are moving with the velocities shown...Ch. 15.4 - If the coefficient of restitution between the ball...Ch. 15.4 - If it rebounds to a height of hl, determine the...Ch. 15.4 - If it makes a direct collision with ball B (e =...Ch. 15.4 - If the coefficient of restitution between the...Ch. 15.4 - If they collide with the initial velocities shown,...Ch. 15.4 - If the coefficient of restitution between the ball...Ch. 15.4 - Determine (a) the velocity at which it strikes the...Ch. 15.4 - The box has a velocity v = 15 ft/s when it is 2 ft...Ch. 15.4 - Prob. 83PCh. 15.4 - If it rebounds at an angle and the coefficient of...Ch. 15.4 - If it rebounds at the same angle = 45 , determine...Ch. 15.4 - lf A strikes B with a velocity (vA)1 = 1.5 m/s as...Ch. 15.4 - If each "stone" is smooth and has a weight of 47...Ch. 15.4 - If each "stone" is smooth and has a weight of 47...Ch. 15.4 - If they have masses mA = 4 kg and mB = 2 kg,...Ch. 15.4 - if cranberries having an e 0.8 are to be...Ch. 15.4 - Prob. 91PCh. 15.4 - Prob. 92PCh. 15.4 - If they are sliding on a smooth horizontal plane...Ch. 15.4 - Determine its angular momentum HO about point O.Ch. 15.4 - Determine its angular momentum Hp about point P.Ch. 15.7 - If a constant tangential force F = 5 N is applied...Ch. 15.7 - If the block starts from rest, determine its speed...Ch. 15.7 - If the system is subjected to a couple moment M =...Ch. 15.7 - If the spheres are subjected to tangential forces...Ch. 15.7 - Determine the angular momentum HO of the 6-lb...Ch. 15.7 - Determine the angular momentum HP of the 6-lb...Ch. 15.7 - Determine the angular momentum HO, of each of the...Ch. 15.7 - Determine the angular momentum Hp, of each of the...Ch. 15.7 - Determine the angular momentum HO of the 3-kg...Ch. 15.7 - Determine the angular momentum Hp of the 3-kg...Ch. 15.7 - If the rod is subjected to a torque M = (t2 + 2) N...Ch. 15.7 - If the helix descends 8 ft for every one...Ch. 15.7 - If the helix descends 8 ft for every one...Ch. 15.7 - If the attached cord is pulled down through the...Ch. 15.7 - If the attached cord is pulled down through the...Ch. 15.7 - The blocks are fixed to the horizontal rods, and...Ch. 15.7 - The particle is placed at the position shown and...Ch. 15.7 - The car starts from rest. The total mass of the...Ch. 15.7 - If the force F on the cord is increased, the bob...Ch. 15.7 - It is attached to a fixed point at A and a block...Ch. 15.7 - If at t = 0, the cable OA is pulled in toward O at...Ch. 15.7 - If the rope is pulled inward with a constant speed...Ch. 15.7 - If the track is flat and banked at an angle of 60,...Ch. 15.7 - If the launch angle at this position is A = 70,...Ch. 15.7 - Prob. 114PCh. 15.9 - If the water has a cross-sectional area of 0.05...Ch. 15.9 - If the fan ejects air with a speed of 14 m/s,...Ch. 15.9 - Prob. 117PCh. 15.9 - Prob. 118PCh. 15.9 - If one-fourth of the water flows downward while...Ch. 15.9 - Water flows through the pipe at A with a velocity...Ch. 15.9 - Prob. 121PCh. 15.9 - Prob. 122PCh. 15.9 - If the locomotive is traveling at a constant speed...Ch. 15.9 - Prob. 124PCh. 15.9 - Prob. 125PCh. 15.9 - The machine discharges the snow through a tube T...Ch. 15.9 - Prob. 127PCh. 15.9 - Prob. 128PCh. 15.9 - It is then divided equally between the two outlets...Ch. 15.9 - Prob. 130PCh. 15.9 - Prob. 131PCh. 15.9 - Prob. 132PCh. 15.9 - Prob. 133PCh. 15.9 - Prob. 134PCh. 15.9 - Prob. 135PCh. 15.9 - Prob. 136PCh. 15.9 - Prob. 137PCh. 15.9 - Prob. 138PCh. 15.9 - Prob. 139PCh. 15.9 - The jet is traveling at a speed of 720 km/h. If...Ch. 15.9 - Prob. 141PCh. 15.9 - Air enters the intake scoops S at the rate of 50...Ch. 15.9 - Prob. 143PCh. 15.9 - Prob. 144PCh. 15.9 - Prob. 145PCh. 15.9 - Prob. 146PCh. 15.9 - Prob. 147PCh. 15.9 - Prob. 148PCh. 15.9 - Prob. 149PCh. 15.9 - If the ball then moves horizontally to the right,...Ch. 15.9 - Prob. 2CPCh. 15.9 - If the coefficient of kinetic friction between the...Ch. 15.9 - The coefficient of kinetic friction between the...Ch. 15.9 - If a horizontal force F is applied such that it...Ch. 15.9 - They are traveling along the track with the...Ch. 15.9 - If the projectile penetrates and emerges from the...Ch. 15.9 - If the collision is perfectly elastic (e = 1),...Ch. 15.9 - If A strikes B with a velocity of (vA)1 = 2 m/s as...Ch. 15.9 - If the frame is subjected to a couple M = (8t2 +...
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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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