HW 3 Problems

HW 3 Problems - 3 in 80 N 15 in B 4.94 Two transmission...

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Unformatted text preview: 3 in. 80 N 15 in. B 4.94 Two transmission belts pass over sheaves welded to an axle supported 4.94 Two transmission belts pass over sheaves welded to an axle supported Fig. P4.65 A 8. ies C by bearings at B and D. The sheave at A has a radius of 2.5 in., and The sheave as a radius of pin fits in a hole at by bearings at B and D.as a radius ofat A hKnowing that 2.5 in., androtates the sheave at C h 2 in. the system at C has a radius of 2 in. K th system rotates t the shaft at B. If a the sheave constant rate, determine (a)nowing that T,e(b) the reactions at B at a a the tension at a constant tension w (b b r 60 mm. find the reactions at 4.66 and D.rate, determine (a) theB and D T,oes) not 5eactions axial thrust Determine the that the bearing at D d henthe exert any at B Assume reactions at Fig. P4.61 and P4.62 and D. Assume that the bearing at D does not exert any axial thrust and neglect the weights of the sheaves and axle. and neglect the weights of the at B a and when 4.67 Determine the reactionssheaves nd Daxle. b 5 120 mm. 4.68 P A 250 mm Fig. P4.66 and P4.67 24 lb 2 in. 3 in. 75 mm a B B C A C b B 6C in. B z z 5 60 mm. 5 in. 6 in. 6 in. C 18 lb y y 8 in. 890 mm in. D A 18 lb 6 in. D 3 in. D D 55° D 250 mm 50 lb 5 120 mm. A Fig. P4.66 and P4.67 Fig. P4.68 x 3 in. A C y B ystem shown. Knowin cable CD, (b) the 40 mm 0.4 m y 40 mm W 80 mm 120 mm 80 mm 120 mm 200 mm a 200 mm Fig. P4.69 A D A E 185 E 120 mm 120 mm C C 720 N D T T x 720 N B z z Fig. P4.95 Fig. P4.95 0.4 m B W a 4.95 A 200-mm lever and a 240-mm-diameter pulley are welded to the 4.95 4.70 Solvelever and a 240-mm-diameter5 3 m. are welded to the A 200-mm Prob. 4.69, assuming that a pulley axle BE that is supported by bearings at C and D. If a 720-N vertiaxle BE that is supported by bearings at C and D. If a 720-N vertical load is applied at A when the lever is horizontal, determine cal load is applied at ADwhen the lever is horizontal, determine (a) the tension in the cord, (b) the reactions at C and D. Assume (a) the tension in the cord, (b) the reactions at C and D. Assume that the bearing at D does not exert any axial thrust. 1.4 m that the bearing at D d55° not exert any axial thrust. oes x B 4.96 Solve Prob. 4.95, assuming that the axle has been rotated clockwise 4.96 Solve Prob. 4.95, assuming that the axle has been rotated clockwise in its bearings by 30° and that the 720-N load remains vertical. in its bearings by 30° and that the 720-N load remains vertical. 1.4 m C x T T Fig. 4.69 P4.94 P4.94 is attached to 30 lb trolley-beam system shown. Knowthe 30 lb Fig. A 50-kg crate ing that a 5 1.5 m, determine (a) the tension in cable CD, (b) the reaction at B. 5 1.5 in. B Determine the reactions at B and C when a 5 1.5 in. D 80 N b A A 24 lb 75 mm Fig. P4.69 185 downward (f 5 0 ( ) the tension the tension in cables CD and downward (f 5 0), determine ), adetermine (a) in cables CD and a a CE, (bz the . ) CE, (b) the reaction at Areaction at A. x B C a a z 30 in. 30 in. x y y 30 in. 30 in. Fig. P4.103 1.2 m 4.104 The table1.2 m weighs 30 lb and has a diameter of 4 ft. It is supshown Fig. P4.103 ported by three legs equally spaced around the edge. A vertical 1.2 m 1.2 P loadm of magnitude 100 lb is applied to the top of the table at D. E 4.104 The table shown weighs 30 lb and has a diameter E of ft. iItthesup- is not to tip over. of Determine the maximum value 4 a f is table ported by three legs how, on spaced aroundarea edge. A vertical which P can act S equally a sketch, the the of the table over load P of magnitude 100 lb tipping the table.top of the table at D. without is applied to the D D Determine the maximum value of a if the table is not to tip over. Show, on a sketch, the area of the table P a which P can act over C without tipping the table. P 1.5 m a A 1.5 m BD A x x BB 5 kN 5 kN f B 2m 12 m m Fig. P4.104 Fig. P4.109 and P4.110 Fig. P4.109 and P4.110 A z C C A C f zD 1m Fig. P4.104 4.110 4.110 is supported is supported by a ball-and-socket joint theA and by the A 3-m pole by a ball-and-socket joint at A and by at A 3-m pole c CE. CD and that the line that the of the action of the cables CD andables KnowingCE. Knowingof action line of 5-kN force 5-kN force forms an angle f the vertical the lane, determine forms an angle f 5 30° with 5 30° with xy pvertical xy plane, determine (a the tension a cables (b) and CE, (b the (a) the tension )in cables CDinnd CE, CD the reaction) at A.reaction at A. 4.111 A is held by a is held by a ball-and-socket joint two 4.111 A 48-in. boom 48-in. boom ball-and-socket joint at C and by at C and by two c DAE; F and DAE; cable DAE p a frictionless pulley cables BF andables Bcable DAE passes around asses around a frictionless pulley at A. For theat A. Forshown, determine the tension in each cablein each cable loading the loading shown, determine the tension and the . and the reaction at Creaction at C. y y 20 in. 20 in. 16 in. 16 in. E E C B A A z z 320 lb Fig. P4.111 Fig. P4.111 D D 48 in. 48 in. 20 in. 20 in. C B F 30 in. F x 30 in. 320 lb x bee29400_ch04_156-217.indd Page 208 11/29/08 3:34:07 PM user-s172 that the bearing150 mm at bearing at C is removed and 4.119 Solve Prob. 4.114, assuming that the C can exert couples about axes parallel to the D Problems 205 /Volumes/204/MHDQ076/work% 205 y C c z xes. that the bearing at andan aexert couples about axes parallel to the B y and z axes. 4.120 Solve Prob. 4.117, assuming that the hinge at B is removed and t assuming that A an exert B is removed axes 4.120 Solve Prob. 4.117,hat the hinge atthe chinge at couples about and parallel to the y that the hinge at andan axes. couples about axes parallel to the y A c z exert 400 mm G and z axes. O Equilibrium of Rigid Bodies used to control the .132 Thein a tape that 4 tension T uniform 10-kg rod AB is supported by a ball-and-socket joint 4.121 The assembly shown is 208 passes around a frictionless spool at E. tape that s A and to rods 4.121 The assembly shown is used to control the tension T in a Collar C iatwelded by the cord CG that is attached to the midpoint G of the ABC and spool at E. rotate about shaft F rods od. Knowing that passes around a frictionless CDE. It canCollar C is welded toG but rits motion along the rod leans against a frictionless vertical wall t can rotate prevented by b washer S. For the loading shown, ABC and CDE. It he shaft zis about shaft FG a ut its motion along at B, determine (a) the tension in the cord, (b) the reactions at A A 600 mm determine washer S. For in loading (b) the reaction the shaft is prevented by a(a) the tension T thethe tape, shown, and B. at C. determine (a) the tension T in the tape, (b) the reaction at C. x Fig. P4.132 y y 6 lb 1.6 in. 2 in. B 4.133 The bent rod ABDE is supported by ball-and-socket joints at A and 6 lb 1.6 in. 2a E in.nd B the A by cable DF. If a 60-lb load is applied at C as shown, determine the tension in the cable. 150 mm A C S C z z m D 11 in. E 240 mm z T E Fig. P4.121 150 mm C B F 8 in. F y y S F 4.2 in. 4.2 in. 7 in. D G G E x 2.4 in. 60 lb A 2.4 in. C G O B x 10 in. T E T Fig. P4.121 16 in. 400 mm 9 in. z x A 600 mm x 14 in. T Fig. P4.132 D 4.122 The assembly shown is welded to collar A that fits on the vertical Fig. The collar A that couples about the pin shown.P4.133 4.122 The assembly shown is welded to pin can exert fits on the vertical x and z axes but does not prevent motion about or along 4.133axis. For the loadthe y The bent rod ABDE is supported by ball-and-socket joints at A and and the reaction 400does not prevent ing shown, determine the tension For the cable E and by the cable DF. If a 60-lb load is applied at C as shown, mm 4.134 motion about or along the y that cable DFloadSolve Prob. 4.133, assuming axis. in each is replaced by a cable pin shown. The pin can exert couples about the x and z axes but determine the tension in the cable. at A ing shown, determine. the tension in each cable and the reaction connecting B and F. at A. 4.135 The 50-kg plate ABCD is supported by E hinges along edge AB and 200 mm x 8 in. y by wire CE. Knowing that the y plate is uniform, determine the tenE B y sion in the wire. 7 in. F 4.136 A F 60 mm 80 D 90 mm mm E C 45 mm 400 mm A C D x C 45 mm 480ig. P4.122 FN 90 mm z 10 in. x 14 in. 16 in. D 400 mm 4.134 Solve Prob. 4.133, assuming that cable DF is replaced by a cable connecting B and F. z 200 mm 4.135 The 50-kg plate ABCD is supported by hinges along edge AB and 200 mm x B by wire CE. Knowing that the plate is uniform, determine the tension in the wire. 480 mm C Fig. P4.135 E x B Fig. P4.133 480 N D Fig. P4.122 60 lb 11 in. 240 mm z 80 mm A 120 mm 240 mm 60 mm z 9 in. Solve Prob. 4.135, assuming that wire CE is replaced by a wire 120 mm A connecting yE aF D. nd 4.136 Solve Prob. 4.135, assuming that wire CE is replaced by a wire connecting E and D. 5.25 Fig. P5.2. the wire figure thus formed. Fig. P5.3. 5.26 5.24 Fig. P5.1. 5.27 Fig. P5.7. 5.25 Fig. P5.2. r 5.26 5.28 A uniform circular rod of weight 8 lb and radius 10 in. is attached Fig. P5.3. 5.27 Fig. P5.7. a pin at C and to the cable AB. Determine (a) the tension in to r C the cable, (b) the reaction at C. 5.28 A uniform circular rod of weight 8 lb and radius 10 in. is attached to a pin at C.29 Member ABCDE Determine (a) the a mobilein 5 and to the cable AB. is a component of tension and is formed from C the cable, (b) the reaction at C. of aluminum tubing. Knowing thatFig. P5.28 is a single piece the member supported at C and that l 5 2 m, determine the distance d so that 5.29 Member ABCDE iportion BCD ofof a mobile and horizontal.from s a component the member is is formed a single piece of aluminum tubing. Knowing that the member is supported at C and that l 5 2 m, determine 1.50 m the distance d so that portion BCD of the member is horizontal. d C B 1.50 m d 55° C B 55° Fig. P5.28 D 55° 0.75 m D A 55° 0.75 m l A l E Fig. P5.29 and P5.30 E 5.30 Member ABCDE is a component of a mobile and is formed from bee29400_ch05_218-283.indd Page 257 11/29/08 4:55:00 tubing. Knowing a single piece of aluminum PM user-s172 /Volumes/204/MHDQ076/work%0/indd%0 that the member is supported at C and that d is 0.50 m, determine the length l of arm 5.30 Member ABCDE iDa component portion of and is formed from s E so that 4:55:00 PM user-s172 e29400_ch05_218-283.indd Page 257 11/29/08 thisof a mobile the member is horizontal. a single piece of aluminum tubing. Knowing that the member is supported at C and that d is 0.50 m, determine the length l of arm DE so that this portion of the member is horizontal. Fig. P5.29 and P5.30 /Volumes/204/MHDQ076/work%0/indd%0 5.90 A long trough is supported by a continuous hinge along its lower edge and by a series of horizontal cables attached to its upper edge. Determine the tension in each of the cables, its time 5.90 A long trough is supported by a continuous hinge along at alower when the trough is of horizontal cables attached to its upper edge. edge and by a series completely full of water. Determine the tension in each of the cables, at a time when the trough is completely full of water. Problems Problems 257 20 in. 20 in. 20 in. 20 in. 20 in. 20 in. r = 24 in. r = 24 in. A A Fig. P5.90 Fig. A 4 5.91P5.903 2-ft gate is hinged at A and is held in position by rod CD. A d A d End D rests against a spring whose constant is 828 lb/ft. The spring 4 ft undeformed at A the is held in position by rod that 5.91 A 4 3 2-ftisgate is hingedwhen and gate is vertical. Assuming CD. the force 4 ft 3 ft C e against a rod C whose constant is 828 horizontal, determine the End D restsxerted by springD on the gate remainslb/ft. The spring B minimum the gate is vertical. Assuming that the of the is undeformed whendepth of water d for which the bottom B force gate will Fig. P5.91 exerted bymoveCD the the gate remains horizontal, determine the rod to on end of the cylindrical portion of the floor. 2 ft minimum depth of water d for which the bottom B of the gate will 5 to Solve of the cylindrical portion of the floor. move.92the endProb. 5.91 if the gate weighs 1000 lb. Fig. P5.91 3 ft C D B D 2 ft 5 Prob. prismatically shaped gate placed 5.92 Solve.93 A 5.91 if the gate weighs 1000 lb. at the end of a freshwater chan- nel is supported by a pin and bracket at A and rests on a frictionless support at Bgate placed located at a freshwater chan5.93 A prismatically shaped . The pin isat the end of adistance h 5 0.10 m below d 0.75 m 257 ...
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