HELP!! Need to find the magnitude of forces supporting a diving board?

Question

A diver of weight (N) is standing at the edge diving board of length L. The board is fixed to two pedestals(A and B) seperated by a distance D. Pedestal A is at the other end of the board and is the futherest away from the water and pedestal B is the pedestal closer to the water.

What are the magnitiudes and directions of the forces(Force1 from pedestal A and Force2 from pedestal B) supporting the diving board)?

What is the torque due to the divers weight about the pedestal closest to the water(pedestal B)?

Answer 1

First, draw a free body diagram.  It should consist of a horizontal line (the diving board) with three arrows (1 for the diver, 1 for support A, 1 for support B).  The arrow for the diver will be in the downward direction.  The arrow for A will be at the complete other end of the line (distance L from arrow for diver) and it will be in the upward direction (just assume a positive value, and the calculated answer will show if you're correct in your assumption).  The arrow for B will be in the upwards direction at a distance D from A.

To find the forces, you need 2 equations, because there are 2 unknowns.  There is no force in the horizontal (x) direction, so you're left with the sum of forces in the y-direction equation and the torque equation.

∑Force_y = 0 (no movement)

0 = -N + A + B => It's negative N because the arrow is downwards.

A + B = N  <----- 1 equation

Next, the torque equation, and we'll sum the moments around A.  Remember, Torque = Force x Distance from a point, in this case A.

∑Torque_A = 0 ----> We'll take the counter-clockwise direction to be the positive direction.

0 = N*L - B*D

N*L = B*D  -----> B = (N*L)/D

You substitute the answer for B into the first equation...

A + [(N*L)/D] = N

A = N - [(N*L)/D]

There's your answers.  Remember that you assumed A and B to be in the upwards direction.  In this case a positive answer means that the direction of the force is upwards.  A negative answer means that the direction of the force is downwards.

For these types of problems, ALWAYS REMEMBER TO DRAW A FREE BODY DIAGRAM!!!  It makes it so much easier to visualize the problem.