EQUILIBRIUM OF PARTICLES

PROBLEMS

1. Determine the force P required to maintain the 200-kg engine in the position for which =30o. The diameter of the pulley at B is negligible.

2. The pail and its contents have mass of 60 kg. If the cable is 15 m long, determine the distance y of the pulley for equilibrium. Neglect the mass of the pulley. Also find the tension in the cable.

2 m

A

B

C

y

10 m

3. 4-kg sphere rests on the smooth parabolic surface. Determine the reaction of the surface on the sphere and the mass mB required to hold it in the equilibrium position.

A

mB

x

y

0.4 m

60o

y=2.5x2

4. The 40-kg block rests on the rough surface. Length of the spring is 180 mm in the position shown. Unstreched length of the spring is 200 mm. Determine the coefficient of friction required for the equilibrium.

5. Two bodies weighing 150 N and 200 N, respectively, rest on a cylinder and are connected by a rope as shown. Find the reactions of the cylinder on the bodies, the tension in the rope and the angle . Assume all surfaces to be smooth.

ropeW1=200 N

W2=150 N

6. A car is to be towed using the rope arrangement shown. The towing force is required is 3000 N. Determine the minimum length l of rope AB so that the tension in either rope AB and AC does not exceed 3750 N.

7. Determine the tensions in cables AB, AC, and AD.

xy

z

8. Determine the compression in each of the three legs of the tripod subjected to the vertical 2-kN force. The weight of the legs is negligible compared with the applied load.

9. Smooth collars A, B and C, each weighing 360 N, are connected by the wires AB and BC and may slide freely on the smooth rod having the shape shown. Determine the magnitude of the horizontal force P which must be applied to the collar A to maintain equilibrium. DEFG portion of the rod is parallel to xy-plane.

10. The 100-kg collar A rests on the smooth straight fixed bar CD by the cable AB. Determine the tension in the cable and the reaction between the collar and bar CD.

C

11. Crate A weighing 580 N rests on the inclined surface by the cable AB and force P which is parallel to the z-axis. Determine the tension in the cable AB and force P for equilibrium. Friction between surface and crate is negligible.

P

A

1.5 m

4 m

3 m

2.2 m

x

y

zDO

C

B

E