15) A uniform ladder having a weight of 150. N rests against a wall, making an angle of 60.00 up from the ground. Both the ground and the wall are frictionless surfaces, requiring a rope tied near the bottom of the ladder to prevent the base of the ladder from slipping left and the top of the ladder from sliding down. If the rope can reach a maximum tension of 450 N prior to breaking, how far up the ladder can a 700.-N person climb? The ladder is 3.00 m long and the rope is attached 0.500 m from its base. An incomplete free-body diagram is provided: 3.0 m x = ? ladder person 60° rope

The forearm shown below is positioned at an angle with respect to the upper arm , and a 5.0- kg mass is held in the hand. The total mass of the forearm and hand is 3.0 kg, and their center of mass is 15.0 cm from the elbow. (a) What is the magnitude of the force that the biceps muscle exerts on the forearm for =60 ? (b) What is the magnitude of the force on the elbow joint for the same angle? (c) How do these forces depend on the angle ?

Check Your Understanding For the situation in described in Example 12.5, determine the values of the coefficient s of static friction for which the ladder starts slipping, given that is the angle that the ladder makes with the floor.

A wooden door 2.1 m high and 0.90 m wide is hung by two hinges 1.8 m apart. The lower hinge is 15 cm above the bottom of the door. The center of mass of the door is at its geometric center, and the weight of the door is 260 N, which is supported equally by both hinges. Find the horizontal force exerted by each hinge on the door.

A painter of mass 87.8 kg is 1.45 m from the top of a 6.67-m ladder. The ladder rests against a wall. Friction between the ladder and the wall is negligible. The ladders mass is 5.50 kg. Assume the ladder is set up according to Occupational Safety and Health Administration standards so that it makes a 75.5 angle with the floor. a. What is the minimum coefficient of static friction required for the painters safety? b. Would rubber ladder tips on dry concrete be safe?

If an odd number of forces act on an object, the object cannot be in equilibrium.

(a) What force must be exerted by the wind to support a 2.50-kg chicken in the position shown in Figure 9.33? (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? Figure 9.33

(a) What minimum coefficient of friction is needed between the legs and the ground to keep the sign in Figure 9.35 in the position shown if the chain breaks? (b) What force is exerted by each side on the hinge?

a) What is the mechanical advantage of a wheelbarrow, such as the one in Figure 9.24, if the center of gravity of the wheelbarrow and its load has a perpendicular lever arm of 5.50 cm, while the hands have a perpendicular lever arm of 1.02 m? (b) What upward force should you exert to support the wheelbarrow and its load if their combined mass is 55.0 kg? (c) What force does the wheel exert on the ground? Figure 9.24 (a) In the case of the wheelbarrow, the output force or load is between the pivot and the input force. The pivot IS the wheel's axle. Here, the output force is greater than the input force. Thus, a wheelbarrow enables you to lift much heavier loads than you could with your body alone. (b) In the case of the shovel, the input force is between the pivot and the load, but the input lever arm is shorter than the output lever arm. The pivot is at the handle held by the right hand. Here, the output force (supporting the shovel's load) is less than the input force (from the hand nearest the load), because the Input is exerted closer to the pivot than is the output

Explain the need for tall towers on a suspension bridge to ensure stable equilibrium.