Archives: Solution Manual

PROBLEM 2.69 A load Q is applied to the pulley C, which can roll on the cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over the pulley A and supports a […]

PROBLEM 2.59 For the situation described in Figure P2.48, determine (a) the value of α for which the tension in rope BC is as small as possible, (b) the corresponding value of the tension. SOLUTION Free–Body Diagram Force Triangle To […]

PROBLEM 2.49 Two cables are tied together at C and are loaded as shown. Knowing that P = 300 N, determine the tension in cables AC and BC. SOLUTION Free–Body Diagram 0 sin30 sin30 cos45 200N 0 x CA CB […]

PROBLEM 2.39 For the collar of Problem 2.35, determine (a) the required value of α if the resultant of the three forces shown is to be vertical, (b) the corresponding magnitude of the resultant. SOLUTION (100 N)cos (150 N)cos( 30 […]

PROBLEM 2.29 The hydraulic cylinder BD exerts on member ABC a force P directed along line BD. Knowing that P must have a 750–N component perpendicular to member ABC, determine (a) the magnitude of the force P, (b) its component […]

PROBLEM 2.19 Two forces P and Q are applied to the lid of a storage bin as shown. Knowing that P = 48 N and Q = 60 N, determine by trigonometry the magnitude and direction of the resultant of […]

PROBLEM 2.9 A disabled automobile is pulled by means of two ropes as shown. Knowing that the tension in rope AB is 3 kN, determine by trigonometry the tension in rope AC and the value of α so that the […]

CHAPTER 2 PROBLEM 2.1 Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule. SOLUTION (a) Parallelogram law: (b) Triangle rule: We measure: […]

PROBLEM 19.166 (Continued) Amplitude of vibration. Use Eq. (19.53). () () () 22 2 12 1 m f f cn n P k m c c x ω ω ω ω = ⎡⎤ ⎡ ⎤ + − ⎢⎥ ⎢ ⎥ […]

PROBLEM 19.162 The block shown is depressed 1.2 in. from its equilibrium position and released. Knowing that after 10 cycles the maximum displacement of the block is 0.5 in., determine (a) the damping factor c/c, (b) the value of the […]

(b) R ⎝ e ⎟⎜ ⎟ ⎠⎝ ⎠ L ⎜⎟ ⎝⎠ Copyrig h ht © McGra w w -Hill Educ a a tion. Permis s s ion require d d for reprodu ction or display. Rearrangi n Substitute n g […]

PROBLEM 19.148 A 91-kg machine element supported by four springs, each of constant k = 175 N/m, is subjected to a periodic force of frequency 0.8 Hz and amplitude 89 N. Determine the amplitude of the fluctuating force transmitted to […]

PROBLEM 19.140 In Problem 19.139, determine the required value of the coefficient of damping if the amplitude of the steady-state vibration of the element is to be 0.15 in. PROBLEM 19.139 A machine element weighing 800 lb is supported by […]

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 dashpot bumper system (Figure 1). The recorded displacement-time curve of the loaded railroad car after coupling is […]

SO G d Th u f ω 2 n kr ω kr r 2 () f mr e km m ω =+ = = 2 2 2 2 2 () 1 n f n n kre e ω ω ω […]

PROBLEM 19.116 (Continued) Out of phase motion with | | 0.06 in. m x= 0.00125 0.06 0.06 <− ⎜⎟ ⎜⎟ ( ) () 2 2 22 2 ff nn ωω ωω ⎛⎞ ⎛⎞ ⎝⎠ ⎝⎠ 0.00125 0.06 1 0.06 0.05875 […]

PROBLEM 19.109 (Continued) Then 2 224 22 112 1 0and 2 0and 2 nn ff ωω ωω == ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ ⎛⎞ == ⎜⎟ fff nnn ff nn ωω ⎛⎞ ⎛⎞ ⎝⎠ ωωω ωωω ωω ⎡⎤ ⎛⎞ ⎛⎞⎛⎞ ⎢⎥ […]

PROBLEM 19.102 A 64-lb block is attached to a spring of constant 1kip/ftk= and can move without friction in a vertical slot as shown. It is acted upon by a periodic force of magnitude sin , mf P Pt ω […]

PROBLEM 19.93 The motion of the uniform rod AB is guided by the cord BC and by the small roller at A. Determine the frequency of oscillation when the end B of the rod is given a small horizontal displacement […]

SO Ki n LUTION n ematics: PR O Tw o sho w dete r O BLEM 1 9 o uniform rod s w n. Knowing r mine the per i 2 2 2 A AC AC rr θθ θ θ […]

PROBLEM 19.80 (Continued) Conservation of energy. 222 22 2 11 2 2 0 11 1 1 1 :00 22 3 2 2 2 AB m m AB m l TV T V mr ml kr mg θ θθ ⎛⎞ +=+ […]

PROBLEM 19.74 A connecting rod is supported by a knife edge at Point A; the period of its small oscillations is observed to be 1.03 s. Knowing that the distance ra is 6 in. determine the centroidal radius of gyration […]

S O O LUTION PROB L A perio d suspend e 1.25-in.- d radius o f ( MM Σ=Σ L EM 19.67 d of 6.00 s is e d from a wir e d iameter steel f gyration of t […]

PROBLEM 19.60 (Continued) (b) When the disk is riveted at A, it rotates at an angular acceleration . α Equation of motion. 2 eff 1 (): sin , ,sin 2 BB t MM mgl IlmaImr θ αθθ Σ=Σ − =+ […]

SO For a simple pen d d ulum of leng t t h ,OA l= g  22 rk + Co m Copyrig h m paring Equa t ht © McGra w t ions (1) and ( w -Hill Educ […]

PROBLEM 19.46 A three-bladed wind turbine used for research is supported on a shaft so that it is free to rotate about O. One technique to determine the centroidal mass moment of inertia of an object is to place a […]

S O Copyrig h ht © McGra w w -Hill Educ a a tion. Permis s s ion require d d for reprodu ction or disp lay. O LUTION PROB A 6-kg u and is a t is attac h […]

PROBLEM 19.31 (Continued) (a) For 0.5 s: τ = 22 ;0.5 4 τ ωπ === n nn ωω π π Eq. (1): 2 22(600) 0.5 9.81 (4 ) 0.7 0.7m π ⎛⎞ =− ⎜⎟ ⎝⎠ 3.561 kgm = 3.56 kgm […]

PROBLEM 19.23 Two springs of constants 1 k and 2 kare connected in series to a block A that vibrates in simple harmonic motion with a period of 5 s. When the same two springs are connected in parallel to […]

Copyright © McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 19.15 (Continued) Solving for and m x φ 0.26975 m m x=− 0.25531 rad φ = − So, from time of impact, the ‘time of flight’ is the time […]

PROBLEM 19.9 A 10-lb block A rests on a 40-lb plate B which is attached to an unstretched spring of constant k = 60 lb/ft. Plate B is slowly moved 2.4 in. to the left and released from rest. Assuming […]

CHAPTER 19 PROBLEM 19.1 A particle moves in simple harmonic motion. Knowing that the maximum velocity is 200 mm/s and the maximum acceleration is 4 m/s2, determine the amplitude and frequency of the motion. SOLUTION Eq. 19.15: 2 mmn mmn […]

PROBLEM 18.158 The essential features of the gyrocompass are shown. The rotor spins at the rate   about an axis mounted in a single gimbal, which may rotate freely about the vertical axis AB. The angle formed by the […]

PROBLEM 18.153 A homogeneous disk of weight 6 lb W rotates at the constant rate 1 16 rad/s   with respect to arm ABC, which is welded to a shaft DCE rotating at the constant rate 2 8 rad/s. […]

PROBLEM 18.147 Three 25-lb rotor disks are attached to a shaft which rotates at 720 rpm. Disk A is attached eccentrically so that its mass center is 1 4in. from the axis of rotation, while disks B and C are […]

PROBLEM 18.141* (Continued) Given data: 217 011 g a    Substituting into Eq. (6), 22 11 11 sin aa     Letting 22 cos 1 sin ,    we have 2 sin 1.7sin 1 […]

PROBLEM 18.137* The top shown is supported at the fixed Point O. Denoting by ,,   and  the Eulerian angles defining the position of the top with respect to a fixed frame of reference, consider the general motion […]

PROBLEM 18.132 A homogeneous rectangular plate of mass m and sides c and 2c is held at A and B by a fork-ended shaft of negligible mass which is supported by a bearing at C. The plate is free to […]

PROBLEM 18.128 Solve Sample Problem 18.6, assuming that the meteorite strikes the satellite at C with a velocity 0(2000 m/s) .vi PROBLEM 18.6 A space satellite of mass m is known to be dynamically equivalent to two thin disks of […]

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  is the rectangular component of ω along the […]

PROBLEM 18.114 A homogeneous cone of height h = 12 in. and with a base diameter d = 6 in. is attached as shown to a cord AB. Knowing that the angles that cord AB and the axis BC of […]

PROBLEM 18.109 The 85-g top shown is supported at the fixed Point O. The radii of gyration of the top with respect to its axis of symmetry and with respect to a transverse axis through O are 21 mm and […]

PROBLEM 18.104 (Continued) Resolve into components. 2 22 2 22 / 2222 02222 2 2( ) ( ) ( ) ( ) EEAAE AA A xy A l D D M mbl cl mcl bl mb c    […]

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 is supported at A and B by a steel framework, which can rotate about the vertical y axis. […]

PROBLEM 18.95 Two disks, each of mass 5 kg and radius 300 mm, spin as shown at the rate 11200 rpm   about a rod AB of negligible mass which rotates about the horizontal z axis at the rate […]

PROBLEM 18.89 (Continued) Let the reference frame Dxyz be rotating with angular velocity 1.         11 0sin cos GG G xxyy Gxyz II     HH Ηi j i j  […]

PROBLEM 18.84 The essential structure of a certain type of aircraft turn indicator is shown. Each spring has a constant of 500 N/m, and the 200-g uniform disk of 40-mm radius spins at the rate of 10,000 rpm. The springs […]

PROBLEM 18.77 (Continued) (b) Reactions at and for the case 0.AB   2 x yxzyz xz M cA I I I      63 (187.5 10 )(12) 15 10 N 0.150 xz y I Ac  […]

PROBLEM 18.73 (Continued) For calculation of , x z I use pairs of elements 1 dA and 2 :dA 21 dA dA 2 121 0 (4 ) (2 ) (2 ) 22         […]

PROBLEM 18.68 (Continued) Then 2 22 2 2 () () () () 2 22 2 2 2 (2)(1)(0.2) (12) 14.4 N 4(4)(0.2) 0, 14.4 N xz z yzz aa a a I ma m a m a ma ma ma […]