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# STATICS E M 306

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GPA 3.93

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This 23 page Class Notes was uploaded by Dr. Cathrine Labadie on Sunday September 6, 2015. The Class Notes belongs to E M 306 at University of Texas at Austin taught by Gregory Rodin in Fall. Since its upload, it has received 117 views. For similar materials see /class/181416/e-m-306-university-of-texas-at-austin in Engineering Mechanics at University of Texas at Austin.

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Date Created: 09/06/15

uilibrium Chap 3 sion of 1000 lb in the screw determine the W0 in diameter cutting wheels Ans R 602 lb the top of a fence post and to a rigid over non of 80 lb To pull up the post a force of end of the blockandtackle rope Point O ble and attachments Determine the verti the post Ans V 1200 lb MI 100 lb 7 QB 117 h center of gravity at section G is to be ngs at A and one at B are to be used If g in each cable at B to 25 tons determine B 118 Problems 81 119 In designing the bracket to support the 1500 lb load the greatest shear force which either bolt will safely support is 5000 lb Determine the minimum distance no 1500 lb PROB 119 120 A painter weighing 150 lb hoists himself on a bosun s chair as shown Determine the force P which he must apply to the rope in order to support himself Ans P 50 lb Q r milk E r tel l L4V gt 239 lt PROB 120 Face 121 121 A man weighing 160 lb hoists himself and the 200 1b platform by pull ing up on the lever shown Determine the reaction R between his feet and the platform 122 If the wood clamp holds the two pieces together with a force of 1001b what are the vertical forces FA and F B in the two screws Ans FB 125 1b FA 2251b 123 What force P must be applied to the 200 lb lawn roller to prevent it from gathering speed as it is rolled down the 10 deg incline 82 Equilibrium Chap 3 4 0 395 1 u 4 5 J 74 7 AVW PROB 122 PROB 123 39 121 A small postal Hmle nullHlSlZH of the plate suspnnrlcrl m A from 1 link whinh nets us the pointer 39I hn srnh e tilts me39iling tn the weight hung from the l39lOUk nt B 111 the unlomierl position shown AB is hurimmtnl The scale weighs 1 oz exclusive of printer and its center of gravity ismquot in from A The weight of the hook negligible Determine the llllgll 0 through which the smile tilts when in 8 oz weight is tttnel39led to the hook nine 0 a 30quot 3hquot PROB 124 125 The 50 lb force exerts a torque or moment about the axis of the bolt of 60 lb ft Find the forces between the smooth jaws of the wrench and the bolt if contact is at the corners A and B of the hexagon l Ans A 5991b B 649 lb 50 lb PROB 125 126 D94 chain hum cannot slip 127 Thu of a square position sh determine tween the load P 128 Fin is applied I vent slippi reaction tn 129 Q produetio the move 86 Equilibrium Chap 3 139 The 100 ft mast with center of gravity at G weighs 1800 lb and is erected as shown The cable passes over the pulleys at C and A and is secured to the mast at D Determine algebraically the tension T required to support the mast in the 30 deg position Neglect the diameters of the two pulleys and also the weight of the struts 0A and AB Discuss any effect on T caused by securing the cable to point A in place of using a pulley at this point Ans T 45001b l9 If K x 140 Solve Prob 139 graphically and determine the bearing reaction R at the bearing 0 141 Determine the least torque M which must be applied to the axle of the 20 lb wheel to cause it to roll over the obstruction if the wheel does not slip Calculate the corresponding friction force F tangent to the Wheel surface exerted on the wheel at A by the obstruction PROB 141 142 The large overhanging roof A shown in section is constructed of rein forced concrete and supported from the concrete bent B The roof weighs 400000 lb for each 30 ft of length normal to the paper and each 30 ft sec tion is supported by a bent and four equally spaced cableandstrut assemblies like the one shown Determine the tension T in the cable of each assembly The roof slab is uniform and may be considered to be hinged to the bent at 039 Am T 260000 lb Chap 3 er of gravity is at the midpoint rble and the reaction on the ball s T 17601b A 5710 lb PROB 153 large forces with a relatively lied load P is always directed tension T in the chain in terms litions stated why does the link 111a2cz 2accos0 a b2 2 2bc cosd Lre wrench as shown the wheel tion force between it and the rium determine the horizontal reel by the xed hearing at 0 PROB 155 Problems 9 1 155 The arm of an idler pulley is attached to one end of a coiled spring which ts over the shaft at 0 and is xed at its other end If a torque of 61b in will wind the spring through 1 deg and if the spring is untwisted with the arm in the dotted position determine the tension T in the belt Neglect the weight of the arm and pulley Ans T 669 lb 156 The girder and brackets weigh 250 lb and have a center of gravity at G Determine the force acting on the pin at 0 while the 300 lb force and 600 lb ft couple are acting The contact force at A may be considered vertical 600 113 ft L a39 239 i 539 Mn PROB 156 157 A pipe bender consists of two grooved pulleys mounted and free to turn on a xed frame as illustrated For a 75 lb force on the bent pipe compute the forces A and B on the bearings of the two pulleys similarly labeled Ans A 290113 B 356 lb Paoe 157 158 A wedge is forced into the opening in the split ring and exerts a vertical force of 600 1b on each end of the ring Specify the internal force F and bend ing moment M couple acting at section 0 by isolating the section AC of the ring with a freebody diagram Assume that the force on the section at 0 acts at the mean radius of 6 in Do the same for section B Ans Fa 600 1b Mo 7200 lb in FB 6001b M3 3600 lb in 92 Equilibrium Chap 3 159 The curved pipe A serves as the bracket for the loaded pulley Draw a freebody diagram of that portion of the pipe above section B and determine all unknown actions on the pipe section PROB 158 PROB 159 160 The bar A C has n negligible weight compared with the homogeneous 100 lb steel cylinder welded to its end Determine the force on the pin con nection at A by considering rst the Freebody diagram 0139 the bar and weight together and second the freebody diagrams of the bar and weight separately rare 30quot gtlt 25quot 7 Aim 7 E i I We f Ci B A quot l 5 Weid 45 PROB 160 161 The mobile crane is hoisting the precast tiltup wall panel for a new building If the uniform concrete slab weighs 24 tons determine graphically the cable tension T when the slab reaches the position indicated Neglect the diameter of the pulleys over which the cables run Ans T 549 tons 96 Equilibrium Chap 3 168 Find the minimum angle 0 so that the pile of three identical smooth rollers will not collapse Ans 6 10 55 PROB 168 PROB 169 169 The 40 lb electric motor with center of gravity at G is pivoted freely at 0 and drives the pulley A with a V belt in a counterclockwise direction and at a constant speed If a constant torque of 1201b in is required to drive the pulley about its axis determine the tensions T1 and T2 in the V belt and nd the total force on the supporting pin at O Ans T1 601b T2 2601b 0 557 lb 170 The 21 speed reducer runs at a constant speed and receives an input torque of 200 lb in on shaft C which turns l lOCan39iStP The output shaft D supplies a steady tm quc tn the mnchinc which it drives The reducer unit weighs 80 lb with center of gravity at 6 Determine the net force exerted on the reducer base at A and B by the combined action 11 the foundation and bolts Am A 729 lb down B 1029 lb up PROB 170 171 The gear teeth action for the speed reducer of Prob 170 is shown in the sketch accompanying the gure Determine the resultant force exerted by each gear on its bearing 172 The magic tube if too short will not stand upright on its base be cause of the overturning moment due to the hidden balls inside Determine the minimum weight W of the tube so that it will not overturn The weight of each ball is w and b lt 2739 Am W 2 1 w 142 Structures Chap 4 262 Determine the force in members JD and HD for the crane truss A 1039 B 10quot c K o 45 4 J V D BOOOIb 1039 H 1039 E 1039 a A F a i PROB 262 263 Prob 250 264 Prob 248 265 Prob 252 266 Find the force in member DE for the loaded truss shown PROB 266 267 Find the force in member X Q for the Baltimore truss where all angles are 30 60 90 or 120 deg Ans XQ 289 kips C U V W V 739 s RQ P o gBCDl39FGHlJKLAI V 10quot in PROB 267 lres Chap 4 one or more of the forces in the wrong consistent with the assumption A versing the direction of the force mined from X 20 0 U 283 kips 0 lculated by considering its horizontal J Equilibrium of moments about J lt30 2X10 2X200 ed here by considering its two com a sign indicates that CD was assigned kips C Ans nanged on the freefbody diagram and calculations or else the work may be roper direction in 2 which now includes the known t G is seen to eliminate DE and JK 367 X 60 283 X 0707 X 30 0 Ans rom its components considered as act so that the assumed tensile direction alone also veri es this conclusion ndoubtedly the shortest for obtaining ssibilities It may be observed that l at I were not present but the other E and JE as well as in HF and IF irough members C D DJ JE and LI 3 and a solution for DJ could be ob out A EMS rethod of sections BE and DE for the truss of Prob 239 BE 3464113 0 DE 5771b J r Problems 149 273 Calculate the force in members JH J D and CD for the Warren bridge truss Ans JH 1296 kips 0 JD 292 kips T CD 1133 kips T 1 J 7 H A oi nova l K 4K 14 panels at 10 7 PROB 273 274 Determine the force in members H G CG and BG for the truss of Prob 238 Ans HG 9 kips 039 0G 12 kips T BG 1273 kips O 275 Determine the force in members DF CE and BE for the truss of Prob 250 Solve for each force from an equation which contains that force as the only unknown 276 Calculate the force in members EH and OH for the truss of Prob 248 Ans EH 16600 lb C39 OH 50001b T 277 The truss shown is composed of 45 deg right triangles The crossed members in the center two panels are slender tie rods incapable of supporting J H G F L39 D 4 f r V BE A PROB 277 compression Retain the two rods which are under tension and compute the magnitude of their tensions Also nd the force in member MN 278 Calculate the force in members JH and JD for the truss of Prob 262 Solve for each force from an equa 400 lb 5 panels at 6 tion which contains that force as A the only unknown i 279 Calculate the force in mem ber OJ with only one freebody diagram and one equation of equi librium 280 Determine the force in member BF for the truss of Prob 247 by using only one freebody diagram and one equation of equilibrium Ans BF 2 25701b T PROB 279 a ures Chap 4 uss in Prob 245 determine the force action of the truss 0 0D and DF for the truss of Prob T CD 850 kips 0 BF 8 kips 0 W of the loaded truss All angles are D the truss of Prob 267 DG EG F0 and MG for the canti ering the statical determinateness of G 1155 kips 0 MG 231 kips U L ex actly balanced with a counter termine the force in JG as the bridge of the members are negligible com dway Treat all intersections of the woforce members and assume each Art 31 Space Trusses 151 C I D rJu al B J V quot35quot 5039 A 1 E F 0 171 l39 lt 6039 5039l50quoti 5039 wt i SO J PROB 286 of the joints A E F G H I carries half the weight of the roadway on each side of the joint Figure ABC D is a parallelogram Ans JG 297 tons 039 287 Prob 268 288 In the traveling bridge crane shown all crossed members are slender tie rods incapable of supporting compression Determine the force in members DF and EF and nd the horizontal reaction on the truss at A Show that if CF 0 DE 0 also Ans DF 768 tons 0 EF 364 tons 0 AE 101 tons to the right 3039 5 panels at 20 i 20 tons 3x D 100 tons 55 t B y PROB 288 31 Space Trusses All members of the trusses described in the preceding four articles have been in a single plane so that the equi librium problem has been two dimensional There are however many types of construction which utilize a system of twoforce members in space joined together at their ends to form a rigid structure Such a con guration of bars is known as a space truss In a plane truss it has already been seen that a triangle of pincon nected bars forms a rigid noncollapsible unit A space truss on the uilibrium Chap 3 sion of 1000 lb in the screw determine the W0 in diameter cutting wheels Ans R 602 lb the top of a fence post and to a rigid over non of 80 lb To pull up the post a force of end of the blockandtackle rope Point O ble and attachments Determine the verti the post Ans V 1200 lb MI 100 lb 7 QB 117 h center of gravity at section G is to be ngs at A and one at B are to be used If g in each cable at B to 25 tons determine B 118 Problems 81 119 In designing the bracket to support the 1500 lb load the greatest shear force which either bolt will safely support is 5000 lb Determine the minimum distance no 1500 lb PROB 119 120 A painter weighing 150 lb hoists himself on a bosun s chair as shown Determine the force P which he must apply to the rope in order to support himself Ans P 50 lb Q r milk E r tel l L4V gt 239 lt PROB 120 Face 121 121 A man weighing 160 lb hoists himself and the 200 1b platform by pull ing up on the lever shown Determine the reaction R between his feet and the platform 122 If the wood clamp holds the two pieces together with a force of 1001b what are the vertical forces FA and F B in the two screws Ans FB 125 1b FA 2251b 123 What force P must be applied to the 200 lb lawn roller to prevent it from gathering speed as it is rolled down the 10 deg incline 82 Equilibrium Chap 3 4 0 395 1 u 4 5 J 74 7 AVW PROB 122 PROB 123 39 121 A small postal Hmle nullHlSlZH of the plate suspnnrlcrl m A from 1 link whinh nets us the pointer 39I hn srnh e tilts me39iling tn the weight hung from the l39lOUk nt B 111 the unlomierl position shown AB is hurimmtnl The scale weighs 1 oz exclusive of printer and its center of gravity ismquot in from A The weight of the hook negligible Determine the llllgll 0 through which the smile tilts when in 8 oz weight is tttnel39led to the hook nine 0 a 30quot 3hquot PROB 124 125 The 50 lb force exerts a torque or moment about the axis of the bolt of 60 lb ft Find the forces between the smooth jaws of the wrench and the bolt if contact is at the corners A and B of the hexagon l Ans A 5991b B 649 lb 50 lb PROB 125 126 D94 chain hum cannot slip 127 Thu of a square position sh determine tween the load P 128 Fin is applied I vent slippi reaction tn 129 Q produetio the move 86 Equilibrium Chap 3 139 The 100 ft mast with center of gravity at G weighs 1800 lb and is erected as shown The cable passes over the pulleys at C and A and is secured to the mast at D Determine algebraically the tension T required to support the mast in the 30 deg position Neglect the diameters of the two pulleys and also the weight of the struts 0A and AB Discuss any effect on T caused by securing the cable to point A in place of using a pulley at this point Ans T 45001b l9 If K x 140 Solve Prob 139 graphically and determine the bearing reaction R at the bearing 0 141 Determine the least torque M which must be applied to the axle of the 20 lb wheel to cause it to roll over the obstruction if the wheel does not slip Calculate the corresponding friction force F tangent to the Wheel surface exerted on the wheel at A by the obstruction PROB 141 142 The large overhanging roof A shown in section is constructed of rein forced concrete and supported from the concrete bent B The roof weighs 400000 lb for each 30 ft of length normal to the paper and each 30 ft sec tion is supported by a bent and four equally spaced cableandstrut assemblies like the one shown Determine the tension T in the cable of each assembly The roof slab is uniform and may be considered to be hinged to the bent at 039 Am T 260000 lb Chap 3 er of gravity is at the midpoint rble and the reaction on the ball s T 17601b A 5710 lb PROB 153 large forces with a relatively lied load P is always directed tension T in the chain in terms litions stated why does the link 111a2cz 2accos0 a b2 2 2bc cosd Lre wrench as shown the wheel tion force between it and the rium determine the horizontal reel by the xed hearing at 0 PROB 155 Problems 9 1 155 The arm of an idler pulley is attached to one end of a coiled spring which ts over the shaft at 0 and is xed at its other end If a torque of 61b in will wind the spring through 1 deg and if the spring is untwisted with the arm in the dotted position determine the tension T in the belt Neglect the weight of the arm and pulley Ans T 669 lb 156 The girder and brackets weigh 250 lb and have a center of gravity at G Determine the force acting on the pin at 0 while the 300 lb force and 600 lb ft couple are acting The contact force at A may be considered vertical 600 113 ft L a39 239 i 539 Mn PROB 156 157 A pipe bender consists of two grooved pulleys mounted and free to turn on a xed frame as illustrated For a 75 lb force on the bent pipe compute the forces A and B on the bearings of the two pulleys similarly labeled Ans A 290113 B 356 lb Paoe 157 158 A wedge is forced into the opening in the split ring and exerts a vertical force of 600 1b on each end of the ring Specify the internal force F and bend ing moment M couple acting at section 0 by isolating the section AC of the ring with a freebody diagram Assume that the force on the section at 0 acts at the mean radius of 6 in Do the same for section B Ans Fa 600 1b Mo 7200 lb in FB 6001b M3 3600 lb in 92 Equilibrium Chap 3 159 The curved pipe A serves as the bracket for the loaded pulley Draw a freebody diagram of that portion of the pipe above section B and determine all unknown actions on the pipe section PROB 158 PROB 159 160 The bar A C has n negligible weight compared with the homogeneous 100 lb steel cylinder welded to its end Determine the force on the pin con nection at A by considering rst the Freebody diagram 0139 the bar and weight together and second the freebody diagrams of the bar and weight separately rare 30quot gtlt 25quot 7 Aim 7 E i I We f Ci B A quot l 5 Weid 45 PROB 160 161 The mobile crane is hoisting the precast tiltup wall panel for a new building If the uniform concrete slab weighs 24 tons determine graphically the cable tension T when the slab reaches the position indicated Neglect the diameter of the pulleys over which the cables run Ans T 549 tons 96 Equilibrium Chap 3 168 Find the minimum angle 0 so that the pile of three identical smooth rollers will not collapse Ans 6 10 55 PROB 168 PROB 169 169 The 40 lb electric motor with center of gravity at G is pivoted freely at 0 and drives the pulley A with a V belt in a counterclockwise direction and at a constant speed If a constant torque of 1201b in is required to drive the pulley about its axis determine the tensions T1 and T2 in the V belt and nd the total force on the supporting pin at O Ans T1 601b T2 2601b 0 557 lb 170 The 21 speed reducer runs at a constant speed and receives an input torque of 200 lb in on shaft C which turns l lOCan39iStP The output shaft D supplies a steady tm quc tn the mnchinc which it drives The reducer unit weighs 80 lb with center of gravity at 6 Determine the net force exerted on the reducer base at A and B by the combined action 11 the foundation and bolts Am A 729 lb down B 1029 lb up PROB 170 171 The gear teeth action for the speed reducer of Prob 170 is shown in the sketch accompanying the gure Determine the resultant force exerted by each gear on its bearing 172 The magic tube if too short will not stand upright on its base be cause of the overturning moment due to the hidden balls inside Determine the minimum weight W of the tube so that it will not overturn The weight of each ball is w and b lt 2739 Am W 2 1 w 142 Structures Chap 4 262 Determine the force in members JD and HD for the crane truss A 1039 B 10quot c K o 45 4 J V D BOOOIb 1039 H 1039 E 1039 a A F a i PROB 262 263 Prob 250 264 Prob 248 265 Prob 252 266 Find the force in member DE for the loaded truss shown PROB 266 267 Find the force in member X Q for the Baltimore truss where all angles are 30 60 90 or 120 deg Ans XQ 289 kips C U V W V 739 s RQ P o gBCDl39FGHlJKLAI V 10quot in PROB 267 lres Chap 4 one or more of the forces in the wrong consistent with the assumption A versing the direction of the force mined from X 20 0 U 283 kips 0 lculated by considering its horizontal J Equilibrium of moments about J lt30 2X10 2X200 ed here by considering its two com a sign indicates that CD was assigned kips C Ans nanged on the freefbody diagram and calculations or else the work may be roper direction in 2 which now includes the known t G is seen to eliminate DE and JK 367 X 60 283 X 0707 X 30 0 Ans rom its components considered as act so that the assumed tensile direction alone also veri es this conclusion ndoubtedly the shortest for obtaining ssibilities It may be observed that l at I were not present but the other E and JE as well as in HF and IF irough members C D DJ JE and LI 3 and a solution for DJ could be ob out A EMS rethod of sections BE and DE for the truss of Prob 239 BE 3464113 0 DE 5771b J r Problems 149 273 Calculate the force in members JH J D and CD for the Warren bridge truss Ans JH 1296 kips 0 JD 292 kips T CD 1133 kips T 1 J 7 H A oi nova l K 4K 14 panels at 10 7 PROB 273 274 Determine the force in members H G CG and BG for the truss of Prob 238 Ans HG 9 kips 039 0G 12 kips T BG 1273 kips O 275 Determine the force in members DF CE and BE for the truss of Prob 250 Solve for each force from an equation which contains that force as the only unknown 276 Calculate the force in members EH and OH for the truss of Prob 248 Ans EH 16600 lb C39 OH 50001b T 277 The truss shown is composed of 45 deg right triangles The crossed members in the center two panels are slender tie rods incapable of supporting J H G F L39 D 4 f r V BE A PROB 277 compression Retain the two rods which are under tension and compute the magnitude of their tensions Also nd the force in member MN 278 Calculate the force in members JH and JD for the truss of Prob 262 Solve for each force from an equa 400 lb 5 panels at 6 tion which contains that force as A the only unknown i 279 Calculate the force in mem ber OJ with only one freebody diagram and one equation of equi librium 280 Determine the force in member BF for the truss of Prob 247 by using only one freebody diagram and one equation of equilibrium Ans BF 2 25701b T PROB 279 a ures Chap 4 uss in Prob 245 determine the force action of the truss 0 0D and DF for the truss of Prob T CD 850 kips 0 BF 8 kips 0 W of the loaded truss All angles are D the truss of Prob 267 DG EG F0 and MG for the canti ering the statical determinateness of G 1155 kips 0 MG 231 kips U L ex actly balanced with a counter termine the force in JG as the bridge of the members are negligible com dway Treat all intersections of the woforce members and assume each Art 31 Space Trusses 151 C I D rJu al B J V quot35quot 5039 A 1 E F 0 171 l39 lt 6039 5039l50quoti 5039 wt i SO J PROB 286 of the joints A E F G H I carries half the weight of the roadway on each side of the joint Figure ABC D is a parallelogram Ans JG 297 tons 039 287 Prob 268 288 In the traveling bridge crane shown all crossed members are slender tie rods incapable of supporting compression Determine the force in members DF and EF and nd the horizontal reaction on the truss at A Show that if CF 0 DE 0 also Ans DF 768 tons 0 EF 364 tons 0 AE 101 tons to the right 3039 5 panels at 20 i 20 tons 3x D 100 tons 55 t B y PROB 288 31 Space Trusses All members of the trusses described in the preceding four articles have been in a single plane so that the equi librium problem has been two dimensional There are however many types of construction which utilize a system of twoforce members in space joined together at their ends to form a rigid structure Such a con guration of bars is known as a space truss In a plane truss it has already been seen that a triangle of pincon nected bars forms a rigid noncollapsible unit A space truss on the 4 Problem 11 The value of IT is 314159265 If C is the circumference of a circle and r is its radius deter mine the value of r C to four signi cant digits 1 Solution C 2m gt 1 0159154943 C 271 r To four signi cant digits we have 5 01592 Problem 12 The base of natural logarithms is e 2718281828 a Express 6 to ve signi cant digits b Determine the value of 62 to ve signi cant digits c Use the value of 6 you obtained in part a to deter mine the value of 62 to ve signi cant digits Part c demonstrates the hazard of using roundedoff values in calculations Solution The value of e is e 2718281828 a To ve signi cant gures e 27183 b e2 to ve signi cant gures is 62 73891 c Using the value from part a we nd 62 73892 which is not correct in the fth digit Problem 13 A machinist drills a circular hole in a panel with a nominal radius r 5 mm The actual radius of the hole is in the range r 5 I 001 mm a To what number of signi cant digits can you express the radius b To what number of signi cant digits can you express the area of the hole Solution a The radius is in the range r1 499 mm to r2 501 mm These numbers are not equal at the level of three signi cant digits but they are equal if they are rounded off to two signi cant digits The area of the hole is in the range from A1 nrlz 78226 m2 to A2 Inf 2 78854 m2 These numbers are equal only if rounded to one signi cant digit One A 80 mm2 b Problem 14 The opening in the soccer goal is 24 ft wide and 8 ft high so its area is 24 ft x 8 ft 192 ftz What is its area in m2 to three signi cant digits Solution 1m 2 2 178 m 3281 ft A 178 m2 A192ft2lt Problem 15 The Burj Dubai scheduled for comple tion in 2008 will be the world s tallest building with a height of 705 m The area of its ground footprint will be 8000 m2 Convert its height and footprint area to US customary units to three signi cant digits Solution 3281 ft 3 h705m 231gtlt10 ft 1m 2 3218 ft 2 4 2 A8000m 17 861gtlt10 ft m lh 231 X 103 ft A 861 X 104 ft2 2008 Pearson Education Inc Upper Saddle River NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced in any form or by any means without permission in writing from the publisher 4 4 Problem 16 Suppose that you have just purchased a Ferrari F355 coupe and you want to know whether you can use your set of SAE US Customary Units wrenches to work on it You have wrenches with widths w 14 in 12 in 34 in and 1 in and the car has nuts with dimensions n 5 mm 10 mm 15 mm 20 mm and 25 mm De ning a wrench to t if w is no more than 2 larger than n which of your wrenches can you use T L 7H Solution Convert the metric size n to inches and compute the percentage difference between the metric sized nut and the SAE wrench The results are 1 inch 019685 7 05 5 mm 7 019685 in 100 54 mm 019685 7270 10 mm Mb 7 0 3937 703937 7 0395 100 7 27 0397 254mm quot111 03937 7 39 quot 1 inch 05905 7 05 15 05905 7 100 1537 mm 254 mm m lt 05905 gt quot 1 inch 07874 7 075 20mm 078741n 100 47 54 mm 07874 5mm 09843 in w 100716 54 mm 09843 A negative percentage implies that the metric nut is smaller than the SAE wrench a positive percentage means that the nut is larger then the wrench us 39 39 the de nition of the 2 t the 1 in wrench will t the 5 mm nut The other wrenches cannot be used Problem 17 Suppose that the height of Mt Everest is known to be between 29032 ft and 29034 ft Based on this information to how many signi cant digits can you express the height a in feet b in meters Solution 8 hi 29032 ft hz 29034 ft The two heights are equal if rounded off to four signi cant digits The fth digit is not meaningful 29030 ft Four b In meters we have h1 29032 ft 1 884852 m 3281 ft 1m h2 29034 ft 884913 m 3281 ft These two heights are equal if rounded off to three signi cant digits The fourth digit is not meaningful Three h 7 8850 m Problem 18 The maglev magnetic levitation train from Shanghai t0 the airport at Pudong reaches a speed of 430 kmh Determine its speed a in mih b st Solution km 06214mi i wrmm mm a W h lt 1km gt 267 b 743014111 1000m 1ft 1h 7392f v T 1km 03048m 3600s 5 Problem 19 In the 2006 Winter Olympics the men s 15km crosscountry skiing race was won b Andrus Veerpalu of Estonia in a time of 38 minutes 13 seconds Determine his average speed the distance traveled divided by the time required to three signi cant digits a in kmh b in mih Solution 15 km 60min w 237kmh 17237kmh a 7 13 lt38 min 1m1 b 237kmh 7 147 3901 mih v 1609 gt rm 7 147 2008 Pearson Education lnc Upper Saddle River NJ All rights reserved This material is protected under all copyright laws 5 they currently exist No portion of this material may be reproduced in any form or by any means without permissron in writing from the publisher 47 4 Problem 110 The Porsche s engine exerts 229 ftlb footpounds of torque at 4600 rpm Determine the value of the torque in Nm Newtonmeters Solution T7229ft1b 1N 1m 7310N T 310N 39 022A81b 3281ft 39m 39m Problem 111 The kinetic energy of the man in Active Example 11 is de ned by lmvz where m is his mass and v is his velocity The man s mass is 68 kg and he is moving at 6 ms so his kinetic energy is 68 kg6 ms2 1224 kgm2s2 What is his kinetic energy in US Customary units Solution 1 slug 1ft 1459 kg 03048 In T 122A kgm252 lt T 903 slugftZs 2 gt 903 slugftZs Problem 112 The acceleration due to gravity at sea level in SI units is g 9 ms By converting units use this value to determine the acceleration due to gravity at sea level in US Customary units Solution Use Table 12 The result is 7981Cquot W 732185 R 7322 R gi s2 03048m 7 39 s2 7 39 s2 Problem 113 A fwrlong per fortnight is a facetious unit of velocity perhaps made up by a student as a satirical comment on the bewildering variety of units engineers must deal with A furlong is 660 ft 18 mile A f011night is 2 weeks 14 nights If you walk to class at 2 ms what is your speed in furlongs per fortnight to three signi cant digits Solution 1 ft 1 furlong 3600 s 2A hr 14 day 11 2 ms 7 7 4 03048 m 660 ft hr 1 day 1 fortrnght 000furlongs gt Problem 114 Determine the cross secti0nal area of the beam a in m2 b in i112 Solution A 200 mm2 7 280 mm120 mm 20800 m2 2 gt 00208 m2 A 00208 m2 a A 20800 m2 m 1000 mm 1 2 III b A 20800 m2 lt54 m 322 m2 A 22 m2 zoglnmlm Problem 115 The crosssectional area of the C12gtlt30 y American Standard Channel steel beam is A 881 i112 A What is its crosssectional area in mm 39 Solution 2008 Pearson Education Inc Upper Saddle River NJ All rigth reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced in any form or by any means without permission in writing from the publisher 76197 4 Problem 116 A pressure transducer measures a value of 3001bi112 Determine the value of the pressure in pascals A pascal Pa is one newton per meter squared Solution Convert the units using Table 12 and the de nition of the Pascal unit The result 300 1b 4448N 12111 2 1ft 2 in2 11b 1ft 03048m 20683 105 lt3 207106 Pa m2 Problem 117 A horsepower is 550 ftlbs A watt is Solution 1 Nms Determine how many watts are generated by 550 ftlbs 1 m 1 N the engines of the passenger Jet 1f they are producing P 7000 hp 7 7 522 x 106 W 1 hp 3281 ft 02248 lb 7000 horsepower P 522 x105W Problem 118 Chapter 7 discusses distributed loads Solution that are expressed in units of force per unit length If 02248 lb 1m 3511213133 d1str1buted load 1s 400 Nm what 1s 1ts w 400 Nm 3281 gt 2741bft Problem 119 The moment of inertia of the rectan Solution gular area about the x axis is given by the equation I bha a 1 200 mm100 mm3 667 x 106 run The dimensions of the area are I 200 mm and h 100 mm Determine the value of I to four signi cant b digits in terms of a mm b m c in 4 I 667 x 106 mm4lt gt 667 x10 6 m4 1 m 1000 mm y 1in 254mm 4 c 1667x106mm4lt gt 160139n4 b Problem 120 In Example 13 instead of Einstein s Solution equation consider the equation L me where the mass 3 L m gt m is in kilograms and the velocity of light 6 is in meters per second a What are the SI units of L b If the 7 00685 slug 3281 ft 7 value of L in SI units is 12 what is its value in US b L 7 12 kg39mSlt 1k gt lt 1m gt 7 23970 SIUg39 S 39 9 Customary base un1ts L 27o slugst 2008 Pearson Education Inc Upper Saddle River NJ All rigth reserved This material is protected under all copyright laws 5 they currently exist No portion of this material may be reproduced in any form or by any means without permission in writing from the publisher 76197 4 Problem 121 The equation Solution My 0 1 is used in the mechanics of materials to determine normal stresses in beams a 2000 Nm01 m lt 1 1b 03048 my 1 7 X 105 m4 4448 N ft a When this equation is expressed in terms of SI base b 1b units M is in newtonmeters Nm y is in meters 59700sz m and I is in meters to the fourth power m4 What are the SI units of a b If M2000Nm y01m and I7gtlt 10 5 m4 what is the value of a in US Customary base units Problem 122 The acceleration due to gravity on the Solution surface Of the moon is 162 msz a What would the a The mass does not depend on location The mass in kg is mass of the Cclamp in Active Example 14 be on the surface 00272 Slug 1459 kg 0397 kg of the moon b What would the weight of the C clamp 1 Slug in newtons be on the surface of the moon b The weight on the surface of the moon is W mg 2 0397 kg162 msz 0643 N W 0643N weighs 490 lb at sea level Determine the weight in newtons of a 1m x 1m x 1m cube of the same material at sea level Problem 123 The 1ft x 1ft x 1ft cube of iron 77 T ZIP 490 1b 1 ft3 Solution The weight density is y The weight of the 1 m3 cube is W V 4901b 1 3 1 ft 3 1 N 77 0 W m y 1 13 03048 m 02248 1b k 1 ft 41 ft Problem 124 The area Of the Paci c Ocean is Solution The volume of the ocean is 64186000 square miles and its average depth is 12925 ft Assume that the weight per unit volume of ocean water V 2 64186000 11115023925 ft is 64 lbft3 Determine the mass of the Paci c Ocean a in slugs b in kilograms 5280 ft 2 2312 gtlt1019 113 1 mi 64 lbft3 a m V 2312 gtlt1019 113 460 gtlt1019 slu s p 322 1152 g 1459 kg b 1 slug m 460 gtlt1019 slugs 671 X 1020 kg Problem 125 The acceleration due to gravity at Solution Use Eq 13 a Solve for the mass sea level is g981ms2 The radius of the earth is 6370 km The universal gravitational constant is 2 2 3 m 2 G 667 x 10 11 NmZkgz Use this information to W 37132 93981mS X63701 10 E determine the mass of the earth G Nmz kg2 66710 11 59679 1024 kg 5971024 kg 2008 Pearson Education Inc Upper Saddle River NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced in any form or by any means without permission in writing from the publisher 4

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