To solve this problem, we can use the conditions of equilibrium, which state that the net force and net torque acting on an object must be zero.
Let's consider the forces and torques acting on the diving board. We have the weight of the person (force due to gravity acting downwards) and the weight of the diving board (also force due to gravity acting downwards). These forces can be represented as:
1. For the person: F_person = m_person * g
2. For the diving board: F_board = m_board * g
The supports exert an upward force on the diving board to balance the gravitational forces. Let's call these forces F_1 and F_2 for the left and right supports, respectively.
To find the force of each support, we can analyze the torques acting on the diving board. Torque is the product of the force exerted on an object and the distance from the point of rotation (in this case, the supports).
The torque exerted by each support is given by torque = force * distance. Considering the left support, the torque is:
Torque_1 = F_1 * r_1
where r_1 is the distance of the left support from the center of the diving board.
Similarly, for the right support, we have:
Torque_2 = F_2 * r_2
where r_2 is the distance of the right support from the center of the diving board.
Since the torques must be balanced for equilibrium, we can write:
Torque_1 + Torque_2 = 0
Substituting the expressions for torque, we get:
F_1 * r_1 + F_2 * r_2 = 0
To find the force of each support, we need to solve this equation. Let's substitute the given values into the equation:
m_person = 60 kg
m_board = 30 kg
r_1 = 1.5 m
r_2 = 2.5 m (half the length of the diving board)
Now we can solve:
60 kg * 9.8 m/s^2 * 1.5 m + 30 kg * 9.8 m/s^2 * 2.5 m = 0
Simplifying the equation, we find:
88.2 N * 1.5 m + 294 N * 2.5 m = 0
132.3 N*m + 735 N*m = 0
867.3 N*m = 0
Since this equation cannot be satisfied, it indicates an error in the setup. It suggests that the net torque is not zero, and therefore, the diving board is not in equilibrium. Please check the values again and make sure all the forces and distances are correct.