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Solutions Manual Engineering Mechanics: Statics 2nd Edition Michael E. Plesha University of Wisconsin–Madison Gary L. Gray The Pennsylvania State University Francesco Costanzo The Pennsylvania State University With the assistance of: Chris Punshon Andrew J. Miller Justin High Chris O’Brien Chandan […]

Problem 1.14 If the weight of a certain object on the surface of the Earth is 0.254 lb, determine its mass in kilograms. Solution We first determine the mass of the object in slugs using wDmg )mDw=g D.0:254 lb/=.32:2 ft=s2/D7:888103lb […]

Problem 10.16 The strength of long bones, as well as slender structural members in general, is directly related to the area moments of inertia, such that if the moments of inertia increase, then strength increases. From the point of view […]

Problem 10.36 Determine the area moments of inertia Ixand Iy. Solution We use the composite shapes shown with the parallel axis theorem. IxD1 12.30 mm/.30 mm/3C.15 mm/2.30 mm/.30 mm/ C1 36.30 mm/.10 mm/3C30 mm C10 mm 321 2.30 mm/.10 mm/ […]

Statics 2e 1499 Problem 10.55 The tapered solid prism shown has density  and rectangular cross section. Use integration to determine the mass moment of inertia indicated, expressing your answer in terms of the mass m of the prism and […]

Problem 10.70 A plastic part with 1100 kg=m3 density is produced by revolving the area shown 360 ı around an axis of revolution. Determine the mass moment of inertia about the axis of revolution indicated. Express your answer in units […]

Problem 10.86 An object is constructed of a brass rod and aluminum cylinder having densities of 8500 kg=m3 and 2700 kg=m3 , respectively. The brass rod fills the hole in the aluminum cylinder. Determine the mass moment of inertia of […]

Problem 10.105 The cross section of a symmetric W815 wide-flange I beam has area AD4:44 in:2 and area moment of inertia about the x1 axis Ix1D121 in:4 . Determine the moment of inertia of the area about the x2axis Ix2. […]

Statics 2e 213 Problem 2.153 For the triangular-shaped window of Prob. 2.109 on p. 95, use the cross product to determine the outward normal unit vector (i.e., pointing away from the origin) and the area of the window. Solution Our […]

Problem 2.165 The vector from point O to point P has magnitude 40 mm and has equal direction angles with the x , y , and ´ axes. Determine the smallest distance from point Pto the infinite plane containing points […]

Statics 2e 249 The vector component of E Pperpendicular to the the fiber direction is then E P?DE PE PkD.10 O k/ kN .3:482 O{3:482 O|5:868 O k/ kN D.3:48 O{C3:48 O|4:13 O k/ kN:(9) As a partial check of […]

Problem 2.13 Add the three vectors shown to form a resultant vector E R , and report your result using polar vector representation. Solution R 80 lb 60 lb 40 lb P 45◦ α α γ Part (a) The vector […]

Statics 2e 73 Problem 2.29 For the following problems, use an xy Cartesian coordinate system where x is horizontal, positive to the right, and y is vertical, positive upward. For problems where the answers require vector expressions, report the vectors […]

Statics 2e 93 Problem 2.46 A Caterpillar Ultra High Demolition machine is shown. The distances between points A and B is 12:5 m, points B and C is 2:8 m, C and D is 7 m, and D and E […]

Problem 2.63 Repeat Prob. 2.62 if point Bis 39 mm from point C. Solution Begin by determining the vector ErCA (where point Ais the head of the vector and point Cis the tail): ErCA D.185 mm 125 mm/O{C.0 144 mm/O|D.60 […]

Problem 2.82 A theodolite is an instrument that measures horizontal and vertical angular orientations of a line of sight. The line of sight may be established optically, or by laser, and many forms of theodolite are used in surveying, construction, […]

Statics 2e 153 Problem 2.98 A wall-mounted jib crane consists of an I beam that is supported by a pin at point A and a cable at point C , where A and C lie in the xy plane. A […]

Problem 2.117 A cantilever I beam has a cable at end B that supports a force E F , and ErAB is the position vector from end A of the beam to end B . Position vectors Er1 and Er2 […]

Problem 2.135 A sports car at point A drives down a straight stretch of road CD . A police car at point B uses radar to measure the speed of the car, and obtains a reading of 80 km=h . […]

Solutions Manual Engineering Mechanics: Statics 2nd Edition Michael E. Plesha University of Wisconsin–Madison Gary L. Gray The Pennsylvania State University Francesco Costanzo The Pennsylvania State University With the assistance of: Chris Punshon Andrew J. Miller Justin High Chris O’Brien Chandan […]

Problem 3.133 Frictionless sliders B and C have frictionless pulleys mounted to them, and are connected by a spring with stiffness kD12 N=mm . Around the pulleys is wrapped a cable that supports a weight WD100 N. Member CE is […]

454 Solutions Manual TBE 18 23 CRBx D0; (15) 13 TBE 23 CRBy D0; (16) TBE 6 23 20 lb D0: (17) Solving Eqs. (15)–(17) provides TBE D76:67 lb, RBx D60 lb, and RBy D 43:33 lb. (18) The equilibrium […]

Problem 3.17 Guy wire AB is used to help support the utility pole AC . If the guy wire AB can support a maximum tensile force of 500 lb , and if the pole AC can support a maximum compressive […]

Statics 2e 303 Problem 3.35 Determine the largest weight W that may be supported if the failure strengths of the cables and bars are Member Strength AC 600 lb AE 250 lb CD 300 lb AB 2000 lb tension & […]

Problem 3.50 Repeat Part (b) of Example 3.4 on p. 140, using optimization methods of calculus. Hint: Solve Eqs. (4) and (5) in Example 3.4 for FBD as a function of ˛ . Then solve for the value of ˛ […]

Statics 2e 343 Part (c) The equation is probably very accurate for loads between 0 and 300 lb , and possibly could be used for loads as high as perhaps 400 lb . For loads less than zero, the hanger […]

Statics 2e 363 November 6, 2019 This solutions manual, in any print or electronic form, remains the property of McGraw-Hill, Inc. It may be used and/or possessed only by permission of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. […]

Statics 2e 383 Part (b) With the values WD300 lb , kD25 lb=in: , and rD20 in: given in the problem statement, Eq. (8) contains one unknown, namely d . Two strategies for determining the value of d that satisfies […]

Statics 2e 403 Vector expressions for the forces appearing in the FBD may be written as E WD2kg 9:81 m=s2.O{/;(6) E FEF DFEF cos 20ıO{sin 20ıO|;(7) EnC 0:7500 O{C0:4330 O|0:4330 O k E RCDRC nC DRC 0:9682 ;(8) E RDDRC […]

Statics 2e 423 Problem 3.116 The structure consists of two bars and a vertical force W . When WD0 , point A has the position shown (i.e., its coordinates are A .10; 0/ in. ). When WD50 lb , point […]

Solutions Manual Engineering Mechanics: Statics 2nd Edition Michael E. Plesha University of Wisconsin–Madison Gary L. Gray The Pennsylvania State University Francesco Costanzo The Pennsylvania State University With the assistance of: Chris Punshon Andrew J. Miller Justin High Chris O’Brien Chandan […]

Problem 4.10 Repeat Prob. 4.9 if the moment at point Bmay not exceed 5000 in.lb. Solution The maximum moment for a given value of force F occurs when the moment arm is at its maximum. Using the Pythagorean theorem in […]

Problem 4.28 Structure OAB is built in at point O and supports two forces of magnitude F parallel to the y and ´ axes. If the magnitude of the moment about point O cannot exceed 1:0 kNm, determine the largest […]

Problem 4.44 The system shown is commonly used for supporting a rural mailbox. It has the feature that the mailbox can swing about line a if it is subjected to a ´ direction force, preventing possible damage to the mailbox […]

Problem 4.62 Beam AB has rectangular cross section where point A is at the origin of the coordinate system and point B has the coordinates B .1:2; 0:3; 2:4/ m . The vector Er1D.1 O{C12 O|C1O k/ m is perpendicular […]

Problem 4.79 Determine the distance between the lines of action of the 85 N forces. See the hint in Prob. 4.78. Solution From the geometry provided in the problem statement, we write the following expressions ErCD D2O|m;E FDD.85 N/1 17.8O{12 […]

Problem 4.95 If FD200 N and PD300 N in Fig. P4.17 on p. 217, determine an equivalent force system consisting of a single force, and specify the x coordinate of the point where the force’s line of action intersects the […]

Problem 4.108 Determine a wrench equivalent force system and specify the x and y coordinates of the point where the wrench’s line of action intersects the xy plane. Express your answers in terms of parameters such as F,a, and b. […]

614 Solutions Manual Part (c) As indicated in Part (b), there are many ways to determine the moment of this couple. In general, it is best to use ErDE or ErED so that only one cross product needs to be […]

Statics 2e 645 DF 12p3 1Cp3!CM L p3 1Cp3(11) p3 Part (c) We use Eq. (5.3) and the FBD to the right to find that XFyD0WAyFD0(13) XFxD0WDxD0(14) XMAD0WMDCMCDxLF .2L/ D0: (15) Solving these equilibrium equations, the reactions are found to […]

Statics 2e 665 Problem 5.32 A motor and mounting hardware with weight WD65 lb are supported by rollers A , B , C , and D . Each pair of rollers is loose-fitting so that only one roller of the […]

Problem 5.51 The horizontal bar ABCD is supported by a link BE with the shape shown. All pins are frictionless, and slots (if present) are loose fitting. Determine the reactions that support bar ABCD. Solution The FBD is shown at […]

Statics 2e 705 Problem 5.71 A model for a 110 V electrical wall switch is shown where force Q that operates the switch is perpendicular to line BCD . If the spring has stiffness kD1:5 N=mm , determine the unstretched […]

Statics 2e 725 Problem 5.90 Identify each of the members cited below as a zero-force, two-force, three-force, or multiforce member. Drum and contents in Example 5.5 on p. 287. Solution Referring to the FBD in Fig. 2 of Example 5.5, […]

Statics 2e 745 Problem 5.109 Member AGDB is supported by a cable DE , a self-aligning bearing at A , and a self-aligning thrust bearing at B. (a) Draw the FBD for AGDB, labeling all forces and moments. (b) Rate […]

Problem 5.123 Alternative equilibrium equations: Consider the FBD shown where F1 , F2 , etc., are the forces acting on the body (including reaction forces from supports), and M1 , M2 , etc., are the moments acting on the body […]

Problem 5.138 Beam ABCD is supported by a vertical bar AE , a pin at point B , and a vertical cable C G. The weights of all members are negligible. (a) If the value of P is known, is […]

Statics 2e 819 Problem 6.13 For the truss shown in Fig. P6.10, each member can support a maximum tensile force of 20 kN and a maximum compressive force of 12 kN. If PD4kN and QD1kN, determine the factor of safety […]

Problem 6.29 By inspection, identify the zero-force members in the truss. Solution Examination of joint Fshows that member EF is zero-force. Examination of joint Hshows that both members EH and GH are zero-force. To summarize, the zero-force members that can […]

Statics 2e 859 Problem 6.41 All members of the truss have the same length. Determine the force supported by members BD,CD, and CE. Solution The FBD for the entire truss is shown at the right, where each truss member has […]

Problem 6.57 Determine if each truss is statically determinate, statically indeterminate, or a mechanism. (a) (b) (c) (d) Solution Using the equation mCr .<; >; D/ 2j; (1) each truss is examined to determine if it is statically determinate, statically […]

Statics 2e 899 Problem 6.69 Imagine you have been retained by an attorney to serve as an expert witness for possible litigation regarding an accident that occurred on the playground structure shown. You have been given only preliminary information on […]

Problem 6.86 For the ladder shown, if WD800 N and h can have any value such that 0h0:9 m, determine the largest force supported by each of the spreader bars BG and DG , and the value(s) of h for […]

Statics 2e 939 )FCD D 25;000 lb:(6) Member ABC:XMBD0W FCF sin 45ı.18 in:/FCD sin 45ı.18 in:/CAy.18 in:/D0; (7) )FCF D27;172 lb:(8) May 11, 2012 This solutions manual, in any print or electronic form, remains the property of McGraw-Hill, Inc. It […]

Problem 6.109 Compared to the truss shown in Fig. P6.109(a): The truss in (b) subdivides members AB and BC in half. The truss in (c) subdivides members AB,BC ,AD, and DC in half. The truss in (d) subdivides members AB […]

Problem 7.140 A scoop for handling animal food is shown. The scoop’s shape is one-half of a truncated circular cone. Use the Pappus-Guldinus theorem to determine the volume of food the scoop will hold, assuming the food is “level.” Also, […]

Problem 7.13 For the area shown, use integration to determine the x and y positions of the centroid. (a) Use a vertical area element. (b) Use a horizontal area element. Solution Part (a) For a vertical area element, we take […]

1006 Solutions Manual QyDy: (9) The xlocation of the centroid of the line is given by NxDRQx dL RdL DR2m 0y2p1C4y2dy R2m 0p1C4y2dy :(10) The ylocation of the centroid of the line is given by NyDRQy dL RdL DR2m 0yp4y2C1 […]

1026 Solutions Manual which yields NxD4:98 in:(3) Using the information in the table, the ylocation of the center of gravity is NyDPQyiwi Pwi ; D0C.3:000 lb/ .30 in:/C.60 in:/ .0:75 lb/C.60 lb/ .2lb/ 9:245 lb C3:000 lb C0:75 lb C2lb […]

Problem 7.65 A solid is generated by rotating the shaded area shown 360 ı about the y axis. Determine the volume and surface area of this solid in terms of the dimension h. Solution To determine the volume of the […]

Problem 7.80 (a) Use integration (Eqs. (7.41) and (7.43) on p. 469) with the appropriate expression(s) for the dis- tributed load w to determine the x position of the line of action for the resultant force produced by the distributed […]

Problem 7.93 Determine the support reactions for the loading shown. Solution The distributed loads are replaced by the resultant forces F1D1 2.6m/ .4kN=m/D12 kN;(1) F2D.6m/ .1kN=m/D6kN:(2) Using the FBD, the equilibrium equations are XFxD0WAxD0; (3) XMAD0WBy.12 m/F1.2 m/CF2.9 m/.15 kN/.6 […]

Problem 7.112 A breakwater along an oceanfront is to be constructed of concrete, and the formwork for retaining the concrete while it is poured is shown. For every 6ft of width (into the plane of the figure), the formwork has […]

Problem 7.130 A solid of revolution is produced by revolving the area shown 360 ı about the x axis. Use integration to determine the xcoordinate of the centroid. Solution To determine the x location of the centroid, we will use […]

Problem 8.94 (a) Use the equilibrium approach to determine the shear as a function of position in the region 0x 3m. (b) Use the integration approach with the results of Part (a) to determine the moment in the region 0x3m. […]

Problem 8.10 A hacksaw for cutting metal is shown. Assume contact between the frame ABC and the handle assembly occurs at points B and C only, neglect friction, and neglect the size of the pin and notch at point B […]

Problem 8.24 Determine the internal forces acting on: The cross section at Ain Example 4.3 on p. 212. Solution We take a cut through cross section A and draw the FBD to the left of the cross section to determine […]

1206 Solutions Manual Using these results, the shear and moment diagrams may be drawn as follows May 11, 2012 This solutions manual, in any print or electronic form, remains the property of McGraw-Hill, Inc. It may be used and/or possessed […]

Problem 8.49 In Example 4.11 on p. 252, numerous equivalent force systems for a cantilever beam were developed. For each of the following force systems, determine the shear and moment as functions of position, and draw the shear and moment […]

Problem 8.60 Determine the shear and moment as functions of position, and draw the shear and moment diagrams. Solution For this problem, wDaCbx. @xD0; w D8kN mDaCb.0/ )aD8kN m;(1) @xD6m; w D4kN mDaCb.6 m/)bD  2 3 kN m2;(2) )wD8kN […]

Problem 8.69 Beam ABCD is used to support a machine tool. The beam weighs 60 lb=ft of length, and the machine weighs 1200 lb with center of gravity at point E . Assuming the machine applies only vertical forces to […]

1286 Solutions Manual Using these results, the shear diagram may be drawn as follows. We determine xusing similar triangles: To construct the moment diagram, we use the shear diagram with the expression MQDMPC V dx : (14) xQ Z xP […]

1306 Solutions Manual Using these results, V .x DL=3/DVBDw0L 6;(11) M.x DL=3/DMBDw0L2 18 :(12) For L=3x2L=3, VDVB x Z xB wdx (13) Dw0L 6 x Z L=3 w0dx Dw0L 6w0xL 3(14) Dw0L 2.w0/x; (15) MDMBC x Z xB Vdx (16) […]

Problem 9.15 Repeat Prob. 9.14 if the reservoir is on the left-hand side of the dam. Solution The FBD for the dam is shown at the right. The water pressure at the bottom of the reservoir (i.e., point A) is […]

Problem 9.30 A table saw for cutting wood is shown. The blade rotates counterclockwise, and the operator pushes the wood into the blade using a stick to help keep his or her hand away from the blade. Despite this safety […]

1390 Solutions Manual If block Bslips, then F2DN2(13) 2 7PD.0:3/15 N12 7P)PD5:625 N:(14) Slip will be impending when Preaches the smaller of Eqs. (9) and (14). Thus block Bwill have impending motion to the left when PD5:63 N: November 6, […]

Problem 9.61 A brake for reducing the speed of a rotating drum is shown. The braking moment is defined as the resultant moment the belt produces about the drum’s bearing, point A . Determine the braking moment if the coefficient […]

Statics 2e 1427 Sliding analysis: When sliding occurs, Coulomb’s law FDN , where the coefficient of static friction is used, provides BxD.0:28/By:(17) Using Eq. (17), the equilibrium equations are XMAD0WP .140 cm/.1000 N/.35 cm/CBy.70 cm/D0; (18) Thus, motion is impending […]