A seesaw consisting of a uniform board of mass M and length ( supports at rest a father and daughter with masses m, and m respectively, as shown in the figure. 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 - from the center. A balanced system. (a) Determine the magnitude of the upward force n exerted by the support on the board. SOLUTION Conceptualize Let us focus our attention on the board and consider the gravitational forces on the father and daughter as forces applied directly to the board. The daughter would cause -Select- support, whereas the father would cause -Select-- Categorize Because the text of the problem states that the system is at rest, we model the board as a rigid object in -Select- however, we could also simply model the board as a particle in equilibrium. rotation of the board around the rotation. Because we will only need the first condition of equilibrium to solve this part of the problem, Analyze (Use the following as necessary: m, m M, and g.) Define upward as the positive y-direction and substitute the forces on the board into the equation F = 0: = 0 6Pw - b'w - u Solve for the magnitude of the force n: (1) n= (b) Determine where the father should sit to balance the system at rest. SOLUTION Categorize This part of the problem requires the introduction of torque to find the position of the father, so we model the board as a rigid object -Select- Analyze (Use the following as necessary: m, m, M, and t.) The board's center of gravity is at its geometric center because we are told that the board is uniform. If we choose a rotation axis perpendicular to the page through the center of gravity of the board, the torques produced by n and the gravitational force about this axis are -Select- Substitute expressions for the torques on the board due to the father and daughter into the equation i = 0: Solve for d: Finalize We can obtain this same result by evaluating the angular acceleration of the system and setting the angular acceleration equal to-Select- te

A seesaw consisting of a uniform board of mass M and length ( supports at rest a father and daughter with masses m, and m respectively, as shown in the figure. 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 - from the center. A balanced system. (a) Determine the magnitude of the upward force n exerted by the support on the board. SOLUTION Conceptualize Let us focus our attention on the board and consider the gravitational forces on the father and daughter as forces applied directly to the board. The daughter would cause -Select- support, whereas the father would cause -Select-- Categorize Because the text of the problem states that the system is at rest, we model the board as a rigid object in -Select- however, we could also simply model the board as a particle in equilibrium. rotation of the board around the rotation. Because we will only need the first condition of equilibrium to solve this part of the problem, Analyze (Use the following as necessary: m, m M, and g.) Define upward as the positive y-direction and substitute the forces on the board into the equation F = 0: = 0 6Pw - b'w - u Solve for the magnitude of the force n: (1) n= (b) Determine where the father should sit to balance the system at rest. SOLUTION Categorize This part of the problem requires the introduction of torque to find the position of the father, so we model the board as a rigid object -Select- Analyze (Use the following as necessary: m, m, M, and t.) The board's center of gravity is at its geometric center because we are told that the board is uniform. If we choose a rotation axis perpendicular to the page through the center of gravity of the board, the torques produced by n and the gravitational force about this axis are -Select- Substitute expressions for the torques on the board due to the father and daughter into the equation i = 0: Solve for d: Finalize We can obtain this same result by evaluating the angular acceleration of the system and setting the angular acceleration equal to-Select- te