Final answer:
In order to find the mass of the board, we need to consider the torque balance on the seesaw. By calculating the torque on the left side and equating it to the torque on the right side, we can determine the distance at which the smaller boy is sitting. In this case, the smaller boy is sitting completely off the board, resulting in a mass of 0 kg for the board.
Step-by-step explanation:
To find the mass of the board, we need to consider the torque balance. Torque is the product of force and distance. In this case, the torque on the left side is counterbalanced by the torque on the right side. We can use the formula: mass * distance to calculate the torque.
Let's consider the torque on the left side first. The mass of the bigger boy is 79 kg and the distance from the fulcrum is 3.0 m. So the torque on the left side is 79 kg * 3.0 m = 237 Nm. Since the seesaw is balanced, the torque on the right side should be the same. The torque on the right side is the product of the mass of the smaller boy (37 kg) and the distance to the fulcrum (unknown). So we can solve the equation: 37 kg * distance = 237 Nm to find the distance. Solving for distance, we get distance = 237 Nm / 37 kg = 6.405 m. Now we can calculate the distance of the board by subtracting the distance of the smaller boy from the total length of the seesaw: 3.0 m - 6.405 m = -3.405 m. Since distance cannot be negative, this means that the smaller boy is sitting completely off the board. Therefore, the mass of the board is 0 kg.