Final answer:
In order for the seesaw to be balanced, the torques on both sides of the fulcrum must be equal.
Step-by-step explanation:
In order for the seesaw to be balanced, the torques on both sides of the fulcrum must be equal. Torque is calculated by multiplying the force applied to an object by the distance from the pivot point. In this case, we can use the equation:
Torque = Force x Distance
Since we know the torques on both sides of the fulcrum are equal, we can set up the equation:
Force1 x Distance1 = Force2 x Distance2
Where Force1 and Force2 are the forces applied by the two children, and Distance1 and Distance2 are the distances from the children to the fulcrum. We can solve for the unknown force by rearranging the equation:
Force2 = (Force1 x Distance1) / Distance2
Using the given information, we can substitute the known values:
Force2 = (40 kg x 3.0 m) / 1.50 m
Simplifying the equation gives us:
Force2 = 80 kg
Therefore, the mass of the board is 80 kg.