A diving board 3.00 m long is supported at a point 1.00 m from the end, and a diver weighing 500 N stands at the free end (Fig. E11.11). The diving board is of uniform cross section and weighs 280 N. Find the force at the support point.

Verified step by step guidance

1. Identify the forces acting on the diving board: the weight of the diver (500 N) acting downward at the free end, the weight of the board (280 N) acting at its center of gravity (1.5 m from the pivot), and the reaction force at the support point.
2. Set up the torque equilibrium equation about the support point. The sum of the torques around the support point must be zero for the board to be in equilibrium.
3. Calculate the torque due to the diver's weight: Torque_diver = 500 N * 2.00 m.
4. Calculate the torque due to the board's weight: Torque_board = 280 N * 0.50 m (since the center of gravity is 0.50 m from the support point).
5. Set the sum of the torques equal to zero and solve for the reaction force at the support point: Reaction_force * 0 m = Torque_diver + Torque_board. Rearrange to find the reaction force.

Key Concepts

Torque

Torque is the rotational equivalent of force, calculated as the product of force and the distance from the pivot point. In this problem, the diver and the board create torques around the support point, which must be balanced to find the force at the support. Understanding torque is crucial for analyzing rotational equilibrium in systems like the diving board.

Equilibrium

Equilibrium in physics refers to a state where all forces and torques are balanced, resulting in no net motion. For the diving board, both translational and rotational equilibrium must be considered. The sum of forces and the sum of torques around the support point must be zero to solve for the force exerted at the support.

Center of Mass

The center of mass is the point where the mass of an object is concentrated and acts as if all the mass were located there for the purpose of calculating torque. For the uniform diving board, its center of mass is at its midpoint. This concept helps in determining the torque due to the board's weight, which is essential for solving the problem.