9.3 Stability  (Page 4/7)

A person carries a plank of wood 2 m long with one hand pushing down on it at one end with a force ${\text{F}}_1$ and the other hand holding it up at 50 cm from the end of the plank with force ${\text{F}}_2$ . If the plank has a mass of 20 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces ${\text{F}}_1$ and ${\text{F}}_2$ ?

A 17.0-m-high and 11.0-m-long wall under construction and its bracing are shown in [link] . The wall is in stable equilibrium without the bracing but can pivot at its base. Calculate the force exerted by each of the 10 braces if a strong wind exerts a horizontal force of 650 N on each square meter of the wall. Assume that the net force from the wind acts at a height halfway up the wall and that all braces exert equal forces parallel to their lengths. Neglect the thickness of the wall.

(a) What force must be exerted by the wind to support a 2.50-kg chicken in the position shown in [link] ? (b) What is the ratio of this force to the chicken's weight? (c) Does this support the contention that the chicken has a relatively stable construction?

Suppose the weight of the drawbridge in [link] is supported entirely by its hinges and the opposite shore, so that its cables are slack. (a) What fraction of the weight is supported by the opposite shore if the point of support is directly beneath the cable attachments? (b) What is the direction and magnitude of the force the hinges exert on the bridge under these circumstances? The mass of the bridge is 2500 kg.

Suppose a 900-kg car is on the bridge in [link] with its center of mass halfway between the hinges and the cable attachments. (The bridge is supported by the cables and hinges only.) (a) Find the force in the cables. (b) Find the direction and magnitude of the force exerted by the hinges on the bridge.

A sandwich board advertising sign is constructed as shown in [link] . The sign's mass is 8.00 kg. (a) Calculate the tension in the chain assuming no friction between the legs and the sidewalk. (b) What force is exerted by each side on the hinge?

(a) What minimum coefficient of friction is needed between the legs and the ground to keep the sign in [link] in the position shown if the chain breaks? (b) What force is exerted by each side on the hinge?

A gymnast is attempting to perform splits. From the information given in [link] , calculate the magnitude and direction of the force exerted on each foot by the floor.

Using the concept of torque, explain why a traffic cone placed on its base is in stable equilibrium, while a traffic cone placed on its tip is in unstable equilibrium.