1) A seesaw consisting of a uniform board of mass M and length l supports a father and daughter with masses mf and md, respectively, as shown in Figure 12.8. The support (called the fulcrum) is under the center of gravity of the board, the father is a distance d from the center, and the daughter is a distance l/2 from the center.

Determine the magnitude of the upward force n exerted by the support on the board.

Determine where the father should sit to balance the system.

What If? Suppose we had chosen another point through which the rotation axis was to pass. For example, suppose the axis is perpendicular to the page and passes through the location of the father. Does this change the results to parts (A) and (B)?

2) A person holds a 50.0-N sphere in his hand. The forearm is horizontal. The biceps muscle is attached 3.00 cm from the joint, and the sphere is 35.0 cm from the joint. Find the upward force exerted by the biceps on the forearm and the downward force exerted by the upper arm on the forearm and acting at the joint. Neglect the weight of the forearm.

3) A uniform horizontal beam with a length of 8.00 m and a weight of 200 N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of 53.0° with the beam. If a 600-N person stands 2.00 m from the wall, find the tension in the cable as well as the magnitude and direction of the force exerted by the wall on the beam.

4) A uniform ladder of length l rests against a smooth, vertical wall. If the mass of the ladder is m and the coefficient of static friction between the ladder and the ground is 0.40, find the minimum angle at which the ladder does not slip.

What If? What if a person begins to climb the ladder when the angle is 51°? Will the presence of a person on the ladder make it more or less likely to slip?

5) In the arrangement shown in Fig below, what is the minimum coefficient of friction to prevent the 8.0kg mass from sliding?

6) Place a 7.0m uniform, 150N ladder against a frictionless wall at an angle of 75°. What are the reaction forces at the ground and wall and the minimum coefficient of friction of the ground?

7) A 20kg beam 4.0m long is pivoted at a wall and supported by a cable as shown in Fig below. What is the force at the wall and the tension in the cable?

8) Set up a 300N strut 14m long with a cable as shown in Fig below. Find the tension in the cable and the reaction force at the pivot.

9) Consider a non-uniform bar of 200N weight and 4.0m length suspended horizontally between two walls where the angles between the walls and cables are 37° and 50°. What are the tensions in the cables?

10) A uniform rod PQ of length 7m and mass 12kg is pivoted at the point R where PR is 2.5m. Calculate the mass of the particle that must be attached at P to maintain the rod in a horizontal position.

11) A uniform beam AB of mass 40kg and length 12m is supported in a horizontal position at C and D, where AC = 1.5m and DB = 1m. A man of mass 80Kg stands on the beam at the point E where EB = 2.5m. Find the reactions at C and D.

Examiners always suggest that a diagram is VITAL.

12) A non-uniform beam AB of mass 20kg and length 12m has an object of mass 40kg placed at a point 8m from A. The beam is in equilibrium in a horizontal position resting on a support C at the midpoint of AB. Find the position of the center of mass.