To calculate the magnitudes and directions of the forces exerted on the board at points A and B, we can use Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration, F = m * a.
1. Start by calculating the gravitational force acting on the diver. The gravitational force is given by the equation F = m * g, where m is the mass of the diver and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the mass of the diver is 58 kg, so the gravitational force acting on the diver is F_d = 58 kg * 9.8 m/s^2 = 568.4 N.
2. Since the diver and the diving board are in contact with each other, an equal and opposite force will be exerted by the diver on the board. Therefore, the force exerted by the diver on the board, F_bd, is also 568.4 N, but in the opposite direction.
3. Next, we need to calculate the gravitational force acting on the diving board. The gravitational force acting on the diving board can be calculated in a similar way as with the diver. The mass of the diving board is 35 kg, so the gravitational force acting on the diving board is F_db = 35 kg * 9.8 m/s^2 = 343 N.
4. Again, since the board and the Earth are in contact, an equal and opposite force will be exerted by the Earth on the board. Therefore, the force exerted by the Earth on the board, F_ew, is also 343 N, but in the opposite direction.
5. Now, let's calculate the net force acting on the board at point A. At point A, there are three forces acting on the board: F_bd (force exerted by the diver on the board), F_db (gravitational force acting on the board), and F_ew (force exerted by the Earth on the board). The net force at point A, F_netA, is the vector sum of these forces. Since the forces are acting in the same direction, we add them up: F_netA = F_bd + F_db + F_ew = 568.4 N + 343 N + 343 N = 1254.4 N. Therefore, the magnitude of the net force at point A is 1254.4 N, and the direction is in the same direction as the forces (upwards).
6. Similarly, we can calculate the net force acting on the board at point B. At point B, there are only two forces acting on the board: F_db (gravitational force acting on the board) and F_ew (force exerted by the Earth on the board). The net force at point B, F_netB, is the vector sum of these forces. Again, since the forces are acting in the same direction, we add them up: F_netB = F_db + F_ew = 343 N + 343 N = 686 N. Therefore, the magnitude of the net force at point B is 686 N, and the direction is in the same direction as the forces (upwards).
In summary, the magnitudes and directions of the forces exerted on the board at points A and B are as follows:
- Force at point A: Magnitude = 1254.4 N, Direction = Upwards
- Force at point B: Magnitude = 686 N, Direction = Upwards