Vector Mechanics for Engineers: Dynamics 11th Edition

APPENDIX B Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM B.1 A thin plate of mass m is cut in the shape of an equilateral triangle of

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM B.14 Determine by direct integration the mass moment of inertia and the radius of gyration with respect to the x

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM B.25 A 2-mm thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM B.34 Determine the mass moment of inertia of the steel machine element shown with respect to the yaxis. (The density of

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM B.45 A section of sheet steel 2 mm thick is cut and bent into the machine component shown. Knowing that the

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM B.56 Determine the mass moment of inertia of the steel fixture of Problems 9.145 and 9.149 with respect to the

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM B.68 Given a homogeneous body of mass m and of arbitrary shape and three rectangular axes x , y , and z with origin

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM B.71* (Continued) Now substitute into Eq. (9.57): 22 233 3( ) [ 2.5795( ) ] [0.071276( ) ] 1xx x

CHAPTER 11 Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.1 A snowboarder starts from rest at the top of a double black diamond hill. As he rides

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.131 (Continued) Therefore 520 sin (40 ) sin (130 ) sin (40 ) sin (130 ) sin (40 ) sin (130 )

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.149 A child throws a ball from point A with an initial velocity v0 at an angle of 3 with

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.166 The pin at B is free to slide along the circular slot DE and along the rotating rod OC. Assuming that

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.181* Determine the direction of the binormal of the path described by the particle of Problem 11.96 when (a) 0,t (b) /2

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.192 The end Point B of a boom is originally 5 m from fixed Point A when the driver starts to

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.19 Based on experimental observations, the acceleration of a particle is defined by the relation (0.1a sin x/b), where a and x

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.36 A group of students launches a model rocket in the vertical direction. Based on tracking data, they determine that the

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.52 (Continued) Then, substituting into Eq. (2) 2402 3 mm/s 03Ba or 220 mm/sBa 220.0 mm/sBa (b) From the diagram,

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.64 (Continued) (b) Reading from the xtcurve max 420 mx (c) Between 10 s and 22 s 100 m 420 m

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.77 An accelerometer record for the motion of a given part of a mechanism is approximated by an arc of a

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.91 The motion of a vibrating particle is defined by the position vector (4sin ) (cos2 ) ,tt rij where r is

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.106 At halftime of a football game souvenir balls are thrown to the spectators with a velocity v0. Determine the range

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.116* (Continued) (b) Angle Check the edge. Since the stream clears the edge. .max maxtan 1.87521.466xx61.9361.9 2020tan2cosgxyy xv 2232.2 13.53.6 13.5

CHAPTER 12 Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.1 Astronauts who landed on the moon during the Apollo 15, 16 and 17 missions brought back

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.121 Show that the angular momentum per unit mass h of a satellite describing an elliptic orbit of semimajor axis a and

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.133* (Continued) and and at Note: implies that the slider remains at its initial radial position. With Eq. (2) implies (b)

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.F3 Objects A, B, and C have masses mA, mB, and mC respectively. The coefficient of kinetic friction between A and

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.14 (Continued) Block B 350 1: 350lb 2 32.2 2y BB AF ma T a= = (2) (a) Multiply Eq. (1)

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.24 An airplane has a mass of 25 Mg and its engines develop a total thrust of 40 kN during take-off. If

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.36 A 450-g tetherball A is moving along a horizontal circular path at a constant speed of 4 m/s. Determine (a)

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.50 (Continued) At B: :Bn nBF ma N m= = or 2222,555 m /s54 kg 1200 mBN= or 1014.98 NB=N :

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.62 (Continued) We must determine the values of which maximize the above expression. Thus ( )( )2222sinsin (cos )( cos )cos0sin

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.75 (Continued) Since the particle moves under a central force, 0.=a Magnitude of acceleration. 222020rvraaa r= += Tangential component

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. (b) Acceleration of B relative to the rod. At ( ) 960, ( ) 8 ft/s 96 in./s, 9.6 rad/s10AAAvtv r=

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 12.107 (Continued) (b) From Part (a), we have 2sun112 ()AAABGM r v rr= + Then, for any other elliptic orbit

CHAPTER 13 Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.1 A 400-kg satellite is placed in a circular orbit 6394 km above the surface of the earth.

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.126 The 18000-kg F-35B uses thrust vectoring to allow it to take off vertically. In one maneuver, the pilot reaches the

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.142 The last segment of the triple jump track-and-field event is the jump, in which the athlete makes a final leap,

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.156 Collars A and B, of the same mass m, are moving toward each other with identical speeds as shown. Knowing

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.167 Two identical hockey pucks are moving on a hockey rink at the same speed of 3 m/s and in perpendicular

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.178 (Continued) Conservation of momentum as A hits B: 22( ) 14.342 ft/s( ) 2.198 ft/sAAvv== 22() ()14.342 0 2.198

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.188 (Continued) Sphere A: Momentum in t-direction: ( ) sin 6.1994 sin 20 2.1203 m/s( ) 2.1203 m/s 70At AAtvv=

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.199 A 2-kg ball B is traveling horizontally at 10 m/s when it strikes 2-kg ball A. Ball A is initially

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.CQ5 The expected damages associated with two types of perfectly plastic collisions are to be compared. In the first case, two

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.18 The subway train shown is traveling at a speed of 30 mi/h when the brakes are fully applied on the

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.31 A 5-kg collar A is at rest on top of, but not attached to, a spring with stiffness k1 =

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.46 A chair-lift is designed to transport 1000 skiers per hour from the base A to the summit B. The average

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.62 An elastic cable is to be designed for bungee jumping from a tower 130 ft high. The specifications call for

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.72 (Continued) Forces at B. 022( ) (10) 6.6667 lb.35sin 1355 in. ft12(0.031056)(205.72)5/1215.3332 lbsBBnFkmvma= = === ==== : siny ys nF

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.86 A satellite describes an elliptic orbit of minimum altitude 606 km above the surface of the earth. The semimajor

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.99 (Continued) Substitute (1) into (2) 228.66 8040 (0.3)2 0.5625 00.339 m and 1.661 mmmmmmmrrrrrr= + == = max1.661 mr= min0.339

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.111* (Continued) Thus, additional kinetic energy at A is 621101 (254.46 10 )( ) ft lb22Ammv E == (1) Conservation of

CHAPTER 14 Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 14.1 A 30-g bullet is fired with a horizontal velocity of 450 m/s and becomes embedded in block

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 14.13 A system consists of three particles A, B, and C. We know that 3 A m kg, 2 B m kg, and 4 C m kg

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 14.27 Derive the relation OG m HrvH between the angular momenta O H and G H defined in Eqs. (14.7) and (14.24), respectively. The vectors

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 14.44 In a game of pool, ball A is moving with the velocity 00 vvi when it strikes balls B and C, which

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 14.55 (Continued) Conservation of energy. Before break: 22022 2 2011(3 ) 32233[(1.3) (2.6) ] 12.67522Tmv mvmv v m m After break:

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 14.73 Prior to take-off the pilot of a 3000-kg twin-engine airplane tests the reversible-pitch propellers by increasing the reverse thrust with

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 14.89 A toy car is propelled by water that squirts from an internal tank at a constant 6 ft/s relative to

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 14.104 In a rocket, the kinetic energy imparted to the consumed and ejected fuel is wasted as far as propelling the rocket

CHAPTER 15 PROBLEM 15.1 The brake drum is attached to a larger flywheel that is not shown. The motion of the brake drum is defined by the relation 2 36 1.6 ,tt = where is expressed in radians and t in seconds. Determine (a) the angular

PROBLEM 15.133 Knowing that at the instant shown bar AB has an angular velocity of 4 rad/s and an angular acceleration of 2 rad/s2, both clockwise, determine the angular acceleration (a) of bar BD, (b) of bar DE by using the vector approach as is done in Sample Problem

PROBLEM 15.148* A wheel of radius r rolls without slipping along the inside of a fixed cylinder of radius R with a constant angular velocity . Denoting by P the point of the wheel in contact with the cylinder at 0,t= derive expressions for the horizontal and vertical components

PROBLEM 15.164 At the instant shown the length of the boom AB is being decreased at the PROBLEM 15.164 At the instant shown the length of the boom AB is being decreased at the PROBLEM 15.164 At the instant shown the length of the boom AB is being decreased

PROBLEM 15.176 Knowing that at the instant shown the rod attached at A has an angular velocity of 5 rad/s counterclockwise and an angular acceleration of 2 rad/s2 clockwise, determine the angular velocity and the angular acceleration of the rod attached at B. SOLUTION Geometry: Apply the law

PROBLEM 15.187 At the instant considered the radar antenna shown rotates about the origin of coordinates with an angular velocity xyz =++i jk . Knowing that ( ) 15 Ay v= in./s, ( ) 9 By v= in./s, and ( ) 18 Bz v= in./s, determine (a) the angular velocity of the antenna, (b) the velocity of point A.

PROBLEM 15.202 In Problem 15.201 the speed of Point B is known to be constant. For the position shown, determine (a) the angular acceleration of the guide arm, (b) the acceleration of Point C. PROBLEM 15.201 Several rods are brazed together to form the robotic guide arm shown, which

PROBLEM 15.215 In Problem 15.205, determine the acceleration of collar C. PROBLEM 15.205 Rod BC and BD are each 840 mm long and are connected by ball-and-socket joints to collars which may slide on the fixed rods shown. Knowing that collar B moves toward A at a constant speed

PROBLEM 15.227 (Continued) (a) Velocity of Point D. /(0.75 m/s) (0.75 3 m/s) ( 3 m/s)D D DFD= +=+vvvv i jk (0.750 m/s) (1.299 m/s) (1.732 m/s)D=+v i jk Coriolis acceleration. /2DFv /22 (2)(10 ) (0.75 0.75 3 )(15 m/s )DF= += v j i jk (b) Acceleration of

PROBLEM 15.239 (Continued) Velocity of Point B. /2.5 3 4 3 4 1.5sin 30 1.5cos 30B B BFB= += + + + vvvv i jk j k (4.33 ft/s) (6.18 ft/s) (5.30 ft/s)B=+v i jk Coriolis acceleration. /2BFv /2 222 (2)(0.40 0.25 ) (1.5sin 30 1.5cos30 )(0.64952 ft/s )

PROBLEM 15.249 Two blocks and a pulley are connected by inextensible cords as shown. The relative velocity of block A with respect to block B is 2.5 ft/s to the left at time t = 0 and 1.25 ft/s to the left when t = 0.25 s. Knowing that

PROBLEM 15.17 The earth makes one complete revolution on its axis in 23 h 56 min. Knowing that the mean radius of the earth is 3960 mi, determine the linear velocity and acceleration of a point on the surface of the earth (a) at the equator, (b) at Philadelphia, latitude

PROBLEM 15.257 (Continued) The corresponding Coriolis acceleration is 11[2 u=a1] [(2)( 20)u= 1] 40u= 1HHu= +vv[1154.7 mm= 1]+[u] (1) 1[HHau= +a1] [40u+] [230.9 mm/s=2] [23094 mm/s+1][u+1] [40u+] (2) Now consider the double slider H as a particle sliding along the rotating rod BD with relative velocity u2 60 and

PROBLEM 15.33 Two friction wheels A and B are both rotating freely at 300 rpm counterclockwise when they are brought into contact. After 12 s of slippage, during which time each wheel has a constant angular acceleration, wheel B reaches a final angular velocity of 75 rpm counterclockwise. Determine

PROBLEM 15.51 In the simplified sketch of a ball bearing shown, the diameter of the inner race A is 60 mm and the diameter of each ball is 12 mm. The outer race B is stationary while the inner race has an angular velocity of 3600 rpm. Determine (a)

PROBLEM 15.67 Roberts linkage is named after Richard Robert (17891864) and can be used to draw a close approximation to a straight line by locating a pen at Point F. The distance AB is the same as BF, DF and DE. Knowing that the angular velocity of plate BDF

PROBLEM 15.82 An overhead door is guided by wheels at A and B that roll in horizontal and vertical tracks. Knowing that when 40 = the velocity of wheel B is 1.5 ft/s upward, determine (a) the angular velocity of the door, (b) the velocity of end D of

PROBLEM 15.97 At the instant shown, the velocity of collar A is 0.4 m/s to the right and the velocity of collar B is 1 m/s to the left. Determine (a) the angular velocity of bar AD, (b) the angular velocity of bar BD, (c) the velocity of point

PROBLEM 15.112 The 18-in.-radius flywheel is rigidly attached to a 1.5-in. -radius shaft that can roll along parallel rails. Knowing that at the instant shown the center of the shaft has a velocity of 1.2 in./s and an acceleration of 2 0.5 in./s , both directed down to the left, determine

PROBLEM 15.122 (Continued) Components 45 : 221233.7 (0.19)(41.337) 1558.4 m/sDa=+= 21558 m/sD=a 45 Rod BE. 0.05sin , 15.258 , 45 29.7420.19 = = = = EEv=v 45 Since Ev is parallel to ,Bv 0.BE= EEa=a 45 2/( ) 0.19 0B E n BEa= = //( )( )EB t EB

CHAPTER 16 Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.1 A 60-lb uniform thin panel is placed in a truck with end A resting on

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.118 The 10-lb-uniform rod AB has a total length 2L = 2 ft and is attached to collars of negligible mass

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.128 (Continued) Kinematics: Equating i-terms: Relative Acceleration: 2BC= =aa2+rar Equating i-terms: Relative Acceleration: 2BC= =aa2+rar Equating i-terms: Relative Acceleration: 2 BC = =aa 2 +ra r Equating

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.145 (Continued) Rod eff /( ) : 0 ( ) ( cos 25 )22A A RGR RCM M I

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.157 The uniform rod AB of weight W is released from rest when 70 . = Assuming that the friction

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.164 The Geneva mechanism shown is used to provide an intermit- tent rotary motion of disk S. Disk D weighs 2 lb

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.13 (Continued) (b) Tension in link AB. A Taking mg to be half the weight of the machine, 21(20 kg)(9.81 m/s

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.27 The 8-in.-radius brake drum is attached to a larger flywheel that is not shown. The total mass moment of inertia

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.39 (Continued) Check that belt does not slip. From (2): 6AF= = From (4): 3.60 0.720 2.88 lbeAF PF== = But

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.50 A force P of magnitude 3 N is applied to a tape wrapped around the body indicated. Knowing that the

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.66 A thin plate of the shape indicated and of mass m is suspended from two springs as shown. If spring

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.79 In Problem 16.78, determine (a) the distance h for which the horizontal component of the reaction at A is zero,

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.93 Show that in the case of an unbalanced disk, the equation derived in Problem 16.92 is valid only when the mass

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 16.107 A 12-in.-radius cylinder of weight 16 lb rests on a 6-lb carriage. The system is at rest when a force

CHAPTER 17 Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.1 A 200-kg flywheel is at rest when a constant 300 N m couple is applied. After executing

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.112 (Continued) moments about B: 000224 422tmv mv L mv L mL L I 22001222114244412mv L m v L L

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.123 A slender rod AB is released from rest in the position shown. It swings down to a vertical position and strikes

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.132 (Continued) Add Equations (1) and (2) to eliminate .Pdt 11 or AB BA mv mv mv v v v (3) Condition

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.142 (Continued) Panel in down position 22 2 panel 1 4410125tb 4410125tb 4 4 10 12 5 tb 1 ( ) (2 )[ (2 ) ] 126tb 126tb 12 6 tb Itbbb Conservation of angular momentum about the

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.CQ3 Slender bar A is rigidly connected to a massless rod BC in Case 1 and two massless cords in Case 2

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.15 Gear A has a mass of 1 kg and a radius of gyration of 30 mm; gear B has a

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.27 Greek engineers had the unenviable task of moving large columns from the quarries to the city. One engineer, Chersiphron, tried

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.38 A long ladder of length l, mass m, and centroidal mass moment of inertia I is placed against a house

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.48 Knowing that the maximum allowable couple that can be applied to a shaft is 15.5 kip in., determine the maximum horsepower

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.64 (Continued) Moments about A: 0 AAB AA A A rT t rTt I 6 0.9 0.9 0 ( ) (0.75)(0.24) (169.837 10

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.76 (Continued) Moments about B: 2(4 )14( ) (4 )12ABCABCMt Qt r IMt Qt r m r 244( ) 3ABCMtQtrmr

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.89 (Continued) Solving the quadratic equation for ,I 0.04965167 0.126590 0.050804 and 0.0221793.46904I Reject the negative root. From Equation (10), 2(21)(0.050804)

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 17.100 (Continued) Principle of impulse and momentum. 1 Syst. Momenta 12 Syst. Ext. Imp. 2 Syst. Momenta Moments about A:

CHAPTER 18 Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.1 A thin, homogeneous disk of mass m and radius r spins at the constant rate 1 about

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.109 The 85-g top shown is supported at the fixed Point O. The radii of gyration of the top with respect

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.120 (a) Show that for an axisymmetrical body under no force, the rate of precession can be expressed as cos z I I = where z

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.132 A homogeneous rectangular plate of mass m and sides c and 2c is held at A and B by a

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.141* (Continued) Given data: 217 011 g a = Substituting into Eq. (6), 11 11 sinaa= = Letting 22cos 1 sin ,= we

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.151 A four-bladed airplane propeller has a mass of 160 kg and a radius of gyration of 800 mm. Knowing that

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.16 For the assembly of Prob. 18.15, determine (a) the angular momentum B H of the assembly about point B, (b) the

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.29 A circular plate of mass m is falling with a velocity 0 v and no angular velocity when its edge C

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.41 Determine the kinetic energy of the assembly of Problem 18.3. PROBLEM 18.3 Two uniform rods AB and CE, each of

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.56 Determine the rate of change G H of the angular momentum G H of the plate of Problem 18.2. PROBLEM 18.2 A

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.68 (Continued) Then 22 2 2( ) ( ) () () 222 2 22 (2)(1)(0.2) (12) 14.4 N4 (4)(0.2)0, 14.4 Nxzzy

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.77 (Continued) (b) Reactions at and for the case 0.AB = x y xz yz xzM cA I I I ==

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.89 (Continued) Let the reference frame Dxyz be rotating with angular velocity 1 .= ( ) ( ) ( ) 11 0 sin cos G G G

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 18.100 An experimental Fresnel-lens solar-energy concentrator can rotate about the horizontal axis AB, which passes through its mass center G. It

CHAPTER 19 Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 19.1 A particle moves in simple harmonic motion. Knowing that the maximum velocity is 200 mm/s and the maximum

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 19.132 A loaded railroad car weighing 30,000 lb is rolling at a constant velocity v0 when it couples with a spring and

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 19.148 A 91-kg machine element supported by four springs, each of constant k = 175 N/m, is subjected to a periodic

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 19.161 (Continued) P osition 2 2 2 2 0 2 C Cm T Vmgh mg = = = Conservation of energy and simple harmonic motion. 11 2 22222222221002222()25 (32.2 ft/s )(12 30) 65ft21212.39 smnmCBmBABnmCCnBABCnnTV

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 19.15 (Continued) Solving for and mx 0.26975 mmx= 0.25531 rad= So, from time of impact, the time of flight is the

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 19.31 (Continued) (a) For 0.5 s:= 22;0.5 4nnn=== Eq. (1): 222(600) 0.5 9.81(4 ) 0.7 0.7m= 3.561 kgm= 3.56 kgm= (b)

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 19.74 A connecting rod is supported by a knife edge at Point A; the period of its small oscillations is observed

SO KinLet Pos Copyrighnematics: sition1 ht McGraww-Hill Educa222AACACrr===2(2(Ammm===112T=+111121211212120ACABIIITTV======ation. PermissCCC ))mCmCm 21(22122AmCABmIIlm++2222222(4 )(2 )81()() 21 282510 3CDmrmrmml Irmrmr l==++ sion required2212)2122mABCDIlm++22222228112412 3mmrmrmlll=+++d for reprodu221(2222mCDmI+224ll++ ction or disp2)m lay. KinLet Pos Copyrighnematics: sition1 ht McGraww-Hill Educa222AACACrr===2(2(Ammm===112T=+111121211212120ACABIIITTV======ation. PermissCCC ))mCmCm 21(22122AmCABmIIlm++2222222(4 )(2 )81()() 21 282510 3CDmrmrmml Irmrmr l==++ sion required2212)2122mABCDIlm++22222228112412 3mmrmrmlll=+++d for reprodu221(2222mCDmI+224ll++ ction

Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. Copyright McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 19.116 (Continued) Out of phase motion with | | 0.06 in.mx= ()()222220.001250.0610.00125 0.06 0.060.06 0.05875fnfnffnnfn< < < 0.06 1.010580.05875fn>= (1.01058)(34.047) 34.407