To balance the seesaw, we need to ensure that the torque (moment) on both sides of the pivot point is equal. Torque is calculated by multiplying the force by the distance from the pivot point.
Let's denote:
- F_1 as the force exerted by the person with a mass of 70 kg.
- F_2 as the force exerted by the person with a mass of 30 kg.
- D_1 as the distance from the pivot point to the person with a mass of 70 kg.
- D_2 as the distance from the pivot point to the person with a mass of 30 kg.
Since the seesaw is balanced, the total torque on each side of the pivot is equal:
F_1 × D_1 = F_2 × D_2
Given that the board is 10 m long, and assuming the pivot is at the center of the board for simplicity (which means D_1 = D_2 = 5 meters), we can solve for the forces:
F_1 × 5 = F_2 × 5
Since we have the masses of the people, we can use the formula F = m × g, where m is the mass and g is the acceleration due to gravity (approximately 9.81 m/s^2 to calculate the forces:
F_1 = 70 × 9.81 N
F_2 = 30 × 9.81 N
Now, we can plug in these values to find the forces:
F_1 = 686.7 N
F_2 = 294.3 N
So, to balance the seesaw, the person with a mass of 70 kg should exert a force of approximately 686.7 N, and the person with a mass of 30 kg should exert a force of approximately 294.3 N.