Problems (Equilibrium of Particles)

Transcription

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2 1. he 4kg block rests on the rough surface. Length of the spring is 18 mm in the position shown. Unstretched length of the spring is 2 mm. Determine the coefficient of friction required for the equilibrium.

3 2. 4kg sphere rests on the smooth parabolic surface. Determine the reaction of the surface on the sphere and the mass m B required to hold it in the equilibrium position. 6 o m B A = m

4 3. he hoist shown is used to position heav workpieces in a lathe. If the cable between pulles A and B can support a maimum force of 1.2 k, all other cables can support a maimum force of 2.2 k, and bar CE can support a maimum compressive force of 2.6 k, determine the largest weight W that ma be lifted. ote that bar CE is a two force member which can support a force along its longitudinal ais.

5 4. he pail and its contents have a mass of 1 kg. If the length of cable ABC is 7 m, determine the horiontal distance for equilibrium. Also find the tension in the cable. he mass of the small pulle at B is small and can be neglected. 4 m A 1 m B C

6 5. he clinder of mass 1 kg having a ver small diameter is held against a semiclinder 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 A. Knowing that the small clinder is in equilibrium at point B, what is the spring constant? h r=2 mm h=12 mm A B r C C

7 6. A small peg rests on a spring that is contained inside the smooth pipe. he spring eerts an upward force of 284 on the peg. Determine the point of attachment A (,, ) of cord A so that the tension in cords B and C equals 13 and 84, respectivel..6 m B.4 m.2 m.3 m C A

8 7. he shear leg derrick is used to haul the 2 kg net of fish onto the dock. Determine the compressive force along each of the legs AB and CB and the tension in the winch cable DB. Assume the force in each leg acts along its ais.

9 8. Crate A weighing 58 rests on the inclined surface b the cable AB and force which is parallel to the ais. Determine the tension in the cable AB and force for equilibrium. Since the crate is mounted on casters, the force eerted b the incline on the crate is perpendicular to the incline. B 1.5 m 3 m 2.2 m C 3 m E A O 4 m D

10 9. If W A =W B =14, determine the force, AB and the reactions between the collars and bars.

11 1. he 1kg collar A rests on the smooth straight fied bar CD b the cable AB. Determine the tension in the cable and the reaction between the collar and bar CD. C

12 11. Collar A weighing 25, which can slide freel on the parabolic rod in plane, is held in equilibrium.4 m b the spring AB and force which is parallel to ais. he spring has a constant of 3 /m and its unstretched length is.1 m..6 m B O k=3 /m A.2 m =3 2 Determine the reaction between the collar and rod. eglect friction.

13 12. wo bodies weighing 15 and 2, respectivel, rest on a clinder and are connected b a rope as shown. ind the reactions of the clinder on the bodies, the tension in the rope and the angle q. Assume all surfaces to be smooth. rope W 1 =2 W 2 =15 9q q

14 SOLUIO 12 BD of article 1 1 sinq cosq 1 cosq sinq 9q q 1 q q W 1 =2 1 cos 2 cosq sinq 2 cosq cosq sinq 2 sinq q sin 2 q 2 sinq 2 sinq

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16 13. Smooth collars A, B and C, each weighing 36, are connected b the wires AB and BC and ma slide freel on the smooth rod having the shape shown. Determine the magnitude of the horiontal force which must be applied to the collar A to maintain equilibrium. DEG portion of the rod is parallel to plane.

17 BD of collar A W our unknowns A AB A BD of collar B BD of collar C W BA W CB B B BC our unknowns C hree unknowns C

18 BD of collar C W CB C C A (;9;3) B (2;5;7) C (6;1;) 1.5 m 4.5 m B B 6 m 1 B 6 E W BC C BC 4i 4 j 7k BC 9 36 j C i C k BC W BC C 36

19 .6 cos.6 sin q q q o k j i j W k j i k j i W BA BA B BA B B B B B BA BA CB BC B AB BC BD of collar B W BA BC B B E E B 6 m.5 m B q q

20 BD of collar A W A AB BA W 36 j A Ai k AB A 36i 72 j A j AB W 72k A 72 72

21 14. Smooth collars A and B are connected b the spring. Spring has a constant of 12 /cm and its unstretched length is 3 cm. Determine the magnitude of the force which must be applied to the collar A to maintain equilibrium and the reaction between the collar and bar. eglect the weight of the collars. ake A (4;;4) and B (;2;8). Q B A 4 cm 4 cm 2 cm 8 cm 8 cm 3 cm

22 BD of collar A A A spring 3 cm 4 cm 4 cm 2 cm 8 cm 8 cm Q A B j k i k i cm AB k j i AB k j i k j i AB k j i A A A A A A A A A spring spring ) (8 ) (2 4) ( ) 12(6 4 cm A 3 cm A q q A spring Correct sense

23 15. he 1kg collar A and 2kg collar B rest on the smooth fied bars b the cable AB and the force. Determine the magnitude of the force required to maintain equilibrium of the sstem. he force is parallel to the bar CE. AB 3. 5 m (;5;) m (;3;) m 3 m (;;4) m (4;;) m

24 16. Collar A weighing 17, which can slide freel on the quarter circle, is held in 4.5 m equilibrium b cable AB. a) Determine the tension in the cable. b) Determine the magnitude and 3.4 m 15 8 the components of the contact force acting on the collar from r =3.4 m the circle.