A diving board length 5.60m that weighs 250N is supported by two pillars. One pillar is at the left end of the diving board,the other is distance 1.55m away .

Find the magnitude of the force exerted by the left pillar when a 90.0kg diver stands at the far end of the board.
Find the magnitude of the force exerted by the right pillar when a 90.0kg diver stands at the far end of the board.

To find the magnitude of the force exerted by each pillar, we can analyze the forces acting on the diving board.

First, let's identify the forces at play:

1. Weight of the diving board (Wb) = 250N
2. Weight of the diver (Wd) = mass of the diver (m) * acceleration due to gravity (g)
- mass of the diver (m) = 90.0kg
- acceleration due to gravity (g) = 9.8m/s²

Now, let's analyze the forces:

1. Forces acting on the diving board:
- Weight of the diving board acting downward (Wb) = 250N
- Force exerted by the left pillar (Fl) acting upward
- Force exerted by the right pillar (Fr) acting upward

2. Forces acting on the diver:
- Weight of the diver acting downward (Wd)

Since the diving board is at rest, the sum of all the forces acting on it must be zero.

In the vertical direction:
Sum of forces upward = Sum of forces downward

Fl + Fr = Wb + Wd

Now, let's calculate the values:

1. Weight of the diver (Wd):
Wd = m * g
= 90.0kg * 9.8m/s²
= 882N

2. Sum of forces downward:
Sum of forces downward = Wb + Wd
= 250N + 882N
= 1132N

Therefore, the sum of the forces exerted upward by both pillars is 1132N.

Since the diving board is symmetrical, the forces exerted by each pillar are equal. Therefore, we can divide the sum of forces by 2 to find the magnitude of the force exerted by each pillar.

Magnitude of the force exerted by the left pillar (Fl) = 1132N / 2 = 566N
Magnitude of the force exerted by the right pillar (Fr) = 1132N / 2 = 566N

Hence, the magnitude of the force exerted by the left pillar is 566N, and the magnitude of the force exerted by the right pillar is also 566N.