Question

Consider a diving board of length 8.0 m. The right end of the board lies directly above a pool. The mass of the diving board is 23.0 kg and is supported by two legs. The first leg is located 0.1 meters from the left side of the board and the second leg is located 2.1 m from the left side of the board. If a diver of mass 60.0 is standing at the right end of the board what is the force of the left leg on the board?

Note that if the left leg is pushing upward on the board we will consider the force positive while a downward pulling force on the board is considered negative.

Answer 1

To find the force exerted by the left leg on the diving board, we use static equilibrium principles. The diver's weight and the board's weight are countered by the support forces of the legs. The left leg exerts a downward force of -1947.387 N.

Step-by-step explanation:

The scenario presented involves calculating the force exerted by the left leg on the diving board when a diver is standing on the right end of the board. We can approach this problem by using the principles of static equilibrium, where the sum of all forces and the sum of all torques (moments) about any point must equal zero. To solve for the force that the left leg exerts, we must consider the weight of the board, the weight of the diver, and the location of the supports.

First, let's calculate the weight of the board (WB) and the weight of the diver (WD):

• WB = mass of board × gravity = 23.0 kg × 9.81 m/s2 = 225.63 N
• WD = mass of diver × gravity = 60.0 kg × 9.81 m/s2 = 588.6 N

Since the board is uniform, the center of gravity is in the middle, at 4.0 meters from either end. We will choose the left leg as the pivot point to simplify calculations, as it eliminates the force by the left leg in the torque equation since its torque would be zero at the point of application.

Now, let's calculate the torques around the left leg (`0.1m` from the end):

• Torque due to the weight of the board = (225.63 N)(4.0 m - 0.1 m) = 880.494 Nm (counter-clockwise)
• Torque due to the diver = (588.6 N)(8.0 m - 0.1 m) = 4642.74 Nm (clockwise)
  
  

To maintain equilibrium, the net torque should be zero. Therefore, the support at 2.1 meters from the left must provide a counter-clockwise torque to balance the torques:

• (Force by right leg)(2.1 m - 0.1 m) = 880.494 Nm + 4642.74 Nm
• (Force by right leg) = 5523.234 Nm / 2.0m
• (Force by right leg) = 2761.617 N

Finally, we calculate the force that the left leg exerts using the balance of forces in the vertical direction:

• Force by left leg + Force by right leg - WB - WD = 0
• Force by left leg = WB + WD - Force by right leg
• Force by left leg = 225.63 N + 588.6 N - 2761.617 N
• Force by left leg = -1947.387 N

Thus, the left leg exerts a downward (negative) force of 1947.387 N on the board.