O EQUILIBRIUM O PRICLES
1. ind the angle of tilt q with the horiontal so that the contact force at B will be one-half that at for the smooth clinder. (3/15)
q?, contact force at B will be one-half that at tangent tangent 45q 45q 45q 45q q 45 mg 45q 45 45q q 45q B 1 2 B 1 2 45q 45q mg q
q?, contact force at B will be one-half that at B 1 2 or 45q 45q mg mg 45q B 1 2 0 1 sin( 45q ) cos(45q ) 2 sin( 45q ) tan( 45q ) 1 cos(45q ) 2 45q 26.57 q 18.43 0 1 tan( 45q ) 2 45q 26.57 q 18.43 1 2
2. he 40-kg block rests on the rough surface. Length of the spring is 180 mm in the position shown. Unstretched length of the spring is 200 mm. Determine the coefficient of friction required for the equilibrium.
m 40-kg, l 180 mm, l 0 200 mm, m? spring spring spring k f 20 2500 m 0 W cos20 0 0.20.18m 50 20 W mg40 (9.81) 392. 4 392.4cos20 368.74 0 spring f W sin 20 0 50f 392.4sin 20 0 f 184.21, 184.21 f f m m 0.5 368.74
3. BC is a cable passing over a frictionless pulle at B where a force is applied. Let h 1 12 cm and h 2 24 cm. he length of the cable BC is 50 cm. Determine the magnitude and the direction of force such that the tension in the cable is 65.
h 1 12 cm, h 2 24 cm. he length of the cable l BC 50 cm, BC 65 determine. 2 2 2 2 a 12 50 24 2 2 144 2500100 576 100 2068, 20.68 cm sin q 12 0.58, q 35.45 20.68 sin 24 0.82, 54.94 50 20.68 0 29.32 cos 65cos35.4565cos54.94 0 2 12 cm 24 cm 0 sin 65sin 35.4565sin 54.94 0 90.29 sin 15.51, tan 0.17 cos 9.75, 91.61, a 65 q 50- cos 90.29 65, 90.29 cos
4. 4 kg sphere rests on the smooth parabolic surface. Determine the normal force it eerts on the surface and the mass m B of block B needed to hold it in the equilibrium position shown.
d tanq d 2 2.5 d tanq 2(2.5) d tanq 5(0.4) 2 q 63.43 m 4 kg, determine the normal force it eerts on the surface and the mass m B of block B. mg q d d 60 q tangent 0 cos60 sin 63.43 0, 1.79 0 19.62 1.79 sin 60 cos63.434(9.81) 0 39.24 (opposite direction to that shown), 35.12 2 39.24
pulle m 4 kg, determine the normal force it eerts on the surface and the mass m B of block B. 1 2 35. 12 B m B g 35. 12 m B 35.12 3. 58 kg 9.81
5. he cable and pulle sstem shown is used to hoist a weight W. If cables B and C have breaking strengths of 900 and cable DE has a breaking strength of 450, determine the largest weight W that ma be lifted.
cables B and C have breaking strengths of 900, cable DE has a breaking strength of 450, determine the largest weight W that ma be lifted
B h r r200 mm h120 mm C C 6. he clinder of mass 1 kg having a ver small diameter is held against a semi-clinder with a much larger diameter b two identical springs, which are fied to points C and C on the ground. he springs are unstretched when at point. Knowing that the small clinder is in equilibrium at point B, what is the spring constant?
m 1 kg, springs are unstretched when at point, small clinder is in equilibrium at point B, what is the spring constant? h B r r200 mm h120 mm C C
7. hree cables are used to hold a balloon as shown. Knowing that the balloon eerts an 800 vertical force at, determine the tension in each cable.
balloon eerts an 800 vertical force at, determine the tension in each cable ( 0,5.6, 0) m B ( 4.2,0,0) m C (2.4, 0, 4.2) m D (0,0, 3.3) m B B C D C B C D n 800 j n n B C D D B C D 0 4.2i 5.6 j 7 2.4i 5.6 j 4.2k 7.4 5.6 j 3.3k 6.5 B D C
balloon eerts an 800 vertical force at, determine the tension in each cable 0 4.2 7 B 4.2 7 2.4 C 7.4 B 2.4 7.4, C B 0 0.54 C B D 4.2 7.4 0 C 4.2 7.4 3.3 D 6.5 C, 3.3 6.5 D D 0 1.12 C C 0 5.6 7 B 5.6 7.4 C 5.6 6.5 D 800 0 5.6 7 B 0.54 C 5.6 7.4 C C 371.46 5.6 6.5 D 1.12 B C 800 200.59, 2.15 D C 800 416.04
8. small peg P rests on a spring that is contained inside the smooth pipe. When the spring is compressed so that s 0.15 m, the spring eerts an upward force of 60 on the peg. Determine the point of attachment (,, 0) of cord P so that the tension in cords PB and PC equals 30 and 50, respectivel. P s B 0.4 m 0.2 m C 0.3 m
s 0.15 m, spring 60 ( ), (,, 0)? P ( 0,0,0.15) m B (0, 0.4, 0) m C ( 0.3,0.2,0) m spring PB PC P 0, spring 60 0.4 j 0.15k k PB PBnPB 30 0.427 P 28.10 j 10.54k PC P 0.3i 0.2 j 0.15k PCnPC 50 0.39 38.46i 25.64 j 19.23k P n P P i j 0.15k 2 2 2 0.15 a B PB 0.4 m PB 30 PC 50 spring P (, s 0.2 m,0) m PC 0.3 m C
s 0.15 m, spring 60 ( ), (,, 0)? 0 0 38.46 P 0 a 28.1025.64 P 0 a 0 6010.5419.23 0.15 P 0 a P 38.46i 2.46 j 30.23k P P from from from 38.46 2 P P 0.19, 0.012, 0 m, 2 2 2.46 30.23 48.98 P 30.23 0.15 P a P 38.46 P a P 2.46 P a P, 38.46,,,, P P 2.46 0.19 30.23 a 0.243 0.012 m B m PB PB 30 PC 50 spring P P PC C
9. Cables B and C can sustain a maimum tension of 500 and the pole can sustain a maimum compression of 300. Determine the maimum weight of the lamp that can be supported in the position shown. he force in the pole acts along the ais of the pole.
Cables B and C can sustain a maimum tension of 500 and the pole can sustain a maimum compression of 300. Determine the maimum weight of the lamp that can be supported in the position shown.
9. he crate weighing 580 is held on the incline b the wire B and b the horiontal force P which is directed parallel to the ais. Since the crate is mounted on casters, the force eerted b the incline on the crate is perpendicular 1.5 m 3 m to the incline. B E Determine the magnitude of P and the 2.2 m C P tension in wire B. 3 m O 4 m
W 580, force eerted b the incline on crate perpendicular to the incline, determine the magnitude of P and the tension in wire B 3sin 53.13,33cos53.13, 1.5m 53.13 2.4,1.2, 1.5m, B0,5.2, 1.5m C 0,3,0 m, D4,0,0 m, E 0,3, 1.5m 3 m 4 m W P 0 W 580 j PPk W P 1.5 m 3 m B E 2.2 m C 3 m O 4 m P
W 580, force eerted b the incline on crate perpendicular to the incline, determine the magnitude of P and the tension in wire B n n for n either r r i j k D/ C E/ C 4 3 1.5 6 j 4.5i 4.5i 6 j n 0.6i 0.8 j 7.5 or n cos53.13i sin 53.13 j 0.6i 0.8 j r r B/ B/ 0.6i 0.8 j 2.4i 4 j 1.5k 4.9 53.13 2.2 m 3 m 3 m 4 m B C O 1.5 m 3 m 4 m E r E / C r D / C n 53.13 P W P D
W 580, force eerted b the incline on crate perpendicular to the incline, determine the magnitude of P and the tension in wire B 0 0.6 2.4 i 0.8 580 4 j P 1.5 k 0 4.9 4.9 4.9 i 0.6 2.4, 2.4 4.9 2.94 j 0.8 580 4, 1.47 580, 395 4.9 k 2.4 2.94 P 1.5 4.9, P 120 W P 322 2.2 m 3 m B C 1.5 m 3 m O 4 m E r E / C r D / C D P
10. Straight bar B is fied in space. Spring CD has a stiffness of 3 /mm and its unstretched length is 200 mm. If there is no friction between collar C and bar B, determine the weight W of the collar that produces the equilibrium condition shown and the reaction between the collar and bar B.
k 3 /mm, l 0 200 mm, neglecting friction determine the weight W of the collar for equilibrium and the reaction between the collar and bar B
11. If W W B 1400, determine the force P, B and the reactions between the collars and bars.
W W B 1400, determine the force P, B and the reactions between the collars and bars
12. Smooth collars, B and C, each weighing 360, are connected b the wires B and BC and ma slide freel on the smooth rod having the shape shown. Determine the magnitude of the horiontal force P which must be applied to the collar to maintain equilibrium. DEG portion of the rod is parallel to -plane.
BD of collar W P our unknowns B BD of collar B BD of collar C W B CB W B B BC our unknowns C hree unknowns C
BD of collar C CB W C C (0;9;3) B (2;5;7) C (6;1;0) 1.5 m 4.5 m B.5 4.5 B 6 m 0 6 BC 810 1 B E W BC C 0 4i 4 j 7k BC 9 360 j i k C C 4 9 BC W BC C 360 0 0
BD of collar W P 0 B B W 360 j i P Pk B 360 i 720 j j B W 720 k P 0 0 720 P 0 P 720
13. Smooth collars and B are connected b the spring. Spring has a constant of 120 /cm and its unstretched length is 30 cm. Determine the magnitude of the force P which must be applied to the collar to maintain equilibrium and the reaction between the collar and bar. eglect the weight of the collars. ake (40;0;40) and B (0;20;80). Q B P 40 cm 40 cm 20 cm 80 cm 80 cm 30 cm
BD of collar P spring 30 cm 40 cm 40 cm 20 cm 80 cm 80 cm P Q B P P P j k i Pk Pi P cm B k j i B k j i k j i B k j i spring spring 3483.87 387 0 5 3 5 4 2400 0 1200 0 1200 0 0 5 4 5 3 2400 0 5 3 5 4 5 4 5 3 60 40 20 40 2400 1200 2400 40) (80 0) (20 40) (0 60 40 20 40 30) 120(60 30 cm q q 0 0 spring P Correct sense