HOMEWORK 2

EQUILIBRIUM OF PARTICLES

Homework 2

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

Homework 2

2. The collar A of mass m may slide freely on the horizontal frictionless rod. The spring attached to the collar has a stiffness of 10 N/cm and it is undeformed when the collar is directly below support B. Determine the magnitude of the force P required to maintain equilibrium.

9 cm

12 cm

B

A P

m

Homework 2

3. A scale is constructed using the 10 kg mass A, the 2 kg pan P and the pulley and cord arrangement. Cord BCA is 2 m long. If s = 0.75 m, determine the mass D in the pan. Neglect the size of the pulley.

Homework 2

4. The pipe is held in place by the vice. If the bolt exerts a force of 250 N on the pipe in the direction shown, determine the forces FA and FB that the smooth contacts at A and B exert on the pipe.

Homework 2

Homework 2

5. Determine the mass of each of the two cylinders if they cause a sag of s = 0.5 m when supported from the rings at A and B. Note that s = 0 when the cylinders are removed.

Homework 2

6. Two particles weighing 800 N and 200 N are held in

equilibrium on frictionless perpendicular surfaces by a cable

which makes an angle q with the horizontal.

a) Determine the normal forces acting from the surfaces on

the particles,

b) Tension in the cable,

c) Angle q .

7. pail and its contents have a mass of 10 kg. If the

length of cable ABC is 7 m, determine the horizontal

distance x for equilibrium. Also find the tension in the

cable. The mass of the small pulley at B is small and can

be neglected.

Homework 2

1 m

4 m

x

A

B C

8. Straight bar AB is fixed in space. Spring CD has a stiffness of

3 N/mm and its unstretched length is 200 mm. If there is no

friction between collar C and bar AB,

Homework 2

determine the weight W

of the collar that

produces the equilibrium

condition shown and the

reaction between the

collar and bar AB.

x

y

z

9. Determine the tensions in cables AB, AC, and AD for equilibrium.

Homework 2

10. Determine the stretch in each of the two springs

required to hold the 20 kg crate in the equilibrium position

shown. Each spring has an unstretched length of 2 m and a

stiffness of k = 300 N/m.

Homework 2

11. Determine the force in each cable used to lift the 9.50 Mg surge arrester at constant velocity.

Homework 2

12. If the maximum allowable tension in cables AB and AC is 2000 N, determine the maximum height z to which the 800 N crate can be lifted.

W=800 N y x

1.5 m

2 m

2 m z

A

B

C

z 3 m F

F

Homework 2

What horizontal force must be applied?