Problems (Equilibrium of Particles)
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- Archibald Warner
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2 1. he kg block rests on the rough surface. Length of the spring is 18 mm in the position shown. Unstretched length of the spring is mm. Determine the coefficient of friction required for the equilibrium.
3 . kg sphere rests on the smooth parabolic surface. Determine the reaction of the surface on the sphere and the mass m required to hold it in the equilibrium position. 6 o m =.. m
4 3. wo particles weighing 8 and are held in equilibrium on frictionless perpendicular surfaces b a cable which makes an angle q with the horiontal. a) Determine the normal forces acting from the surfaces on the particles, b) ension in the cable, c) ngle q. cable
5 . he clinder of mass 1 kg having a ver small diameter is held against a semiclinder with r= mm h=1 mm a much larger diameter b two h r identical springs, which are fied to points C and C on the ground. he springs are unstretched when C at point. Knowing that the small clinder is in equilibrium at C point, what is the spring constant?
6 . wo bodies weighing 1 and, 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. ssume all surfaces to be smooth. rope W 1 = W =1 9q q
7 SOLUIO D of article 1 1 sinq cosq 1 cosq sinq 9q q 1 q q W 1 = 1 cos cosq sinq cosq cosq sinq sinq q sin q sinq sinq (1)
8 D of article sin 9 q cos9 q 9 q 9 q cos sin 9q q 9q W =1 9q cos cos cos sin 9 q sin9 q 1 9 q cos9 q sin9 q 9 q 1 9 q sin 9 q 1 sin9 q 1 sin 9 q () (1)=() tanq sinq 1sin 9 q sinq cosq 1 cos q q o 1, 1 16, 9
9 6. It is aimed to hold the 8 k load in equilibrium b the wire that passes from the ring at C. In order to do this, another force parallel to the plane is applied to the ring. Determine the tension in the wire and the vector epression of load. 1 m 1 m O 8 m 9 m 1 m C
10 7. Determine the compression in each of the three legs of the tripod subected to the vertical k force. he weight of the legs is negligible compared with the applied load.
11 8. Crate weighing 8 rests on the inclined surface b the cable and force which is parallel to the ais. Determine the tension in the cable 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. 1. m 3 m. m C 3 m E O m D
12 9. If W =W =1, determine the force, and the reactions between the collars and bars.
13 1. he 1kg collar rests on the smooth straight fied bar CD b the cable. Determine the tension in the cable and the reaction between the collar and bar CD. C
14 11. he 1kg collar and kg collar rest on the smooth fied bars b the cable and the force. Determine the magnitude of the force required to maintain equilibrium of the sstem. he force is parallel to the bar CE. 3. m (;;) m (;3;) m 3 m (;;) m (;;) m
15 (;;) m Coordinates of point C (;3;) m m 3 m 3 m m E (;;) m (;;) m CE 6. m m m (.1,.3, )
16 (.1,.3, ) (;;) m Coordinates of point G (;3;) m 3. m 3 m 3 m (;;) m (;;) m (, 1.131,.) D m
17 (.1,.3, ) (, 1.131,.) W D of particle G i cos i i k. 67i k , sink k, W D m m
18 (.1,.3, ) (, 1.131,.) W D of particle C sin i, cos i k, W i k i k cos i sin. 6i k m m 3 m E
19 1. Collar weighing 17, which can slide freel on the quarter circle, is held in. m equilibrium b cable. a) Determine the tension in the cable. b) Determine the magnitude and 3. m 1 8 the components of the contact force acting on the collar from r =3. m the circle.
20 1 8 3., 3.,, 3., D of particle 1 8 i k W 17 3i k , 17, 3. m. m W 1 8 r =3. m
21 13. Smooth collars, and C, each weighing 36, are connected b the wires and C 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 to maintain equilibrium. DEG portion of the rod is parallel to plane.
22 W D of collar our unknowns D of collar D of collar C W W C C our unknowns C hree unknowns C
23 D of collar C W C C C (;9;3) (;;7) C (6;1;) 1. m. m.. 6 m 1 6 E W C C C i 7k C 9 36 C i C k 81 9 C W C C 36
24 .6 cos.6 sin q q q o k i W k i k i W C C C D of collar W C E E 6 m. m q q
25 D of collar W W 36 i k 36i 7 W 7k 7 7
26 1. Smooth collars and are connected b the spring. Spring has a constant of 1 /cm and its unstretched length is 3 cm. Determine the magnitude of the force 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 (;;) and (;;8). Q cm cm cm 8 cm 8 cm 3 cm
27 D of collar spring 3 cm cm cm cm 8 cm 8 cm Q k i k i cm k i k i k i k i spring spring ) (8 ) ( ) ( 6 3) 1(6 cm 3 cm q q spring Correct sense
Problems (Equilibrium of Particles)
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.
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