How to Calculate the Mass of the Board in a Balanced Uniform Seesaw System
What is the mass of the board in a uniform seesaw system?
Given data:
Mass of the smaller boy on the right: 41 kg
Mass of the bigger boy on the left: 82 kg
Fulcrum located 4.0 m from the left end
Calculating the Mass of the Board
To determine the mass of the board in the uniform seesaw system, we can use the principle of torque balance.
Distance from the fulcrum to the left end = 4.0 m
Mass of the smaller boy on the right (m1) = 41 kg
Mass of the bigger boy on the left (m2) = 82 kg
For the system to be balanced, the torques on each side of the fulcrum must be equal. The torque (τ) can be calculated by multiplying the force (F) by the distance (d) from the fulcrum:
τ = F * d
Understanding the Calculation
Considering the torque balance equation, we have:
(m1 * g * d1) = (m2 * g * d2)
where g is the acceleration due to gravity (9.8 m/s²),
d1 is the distance from the fulcrum to the smaller boy,
d2 is the distance from the fulcrum to the bigger boy.
Since the fulcrum is located 4.0 m from the left end, we have:
d1 + d2 = 4.0 m
To solve for the mass of the board (m_board), we need to find the value of d1 and d2. Since the seesaw is uniform, we can assume that the mass is evenly distributed along the length. Therefore, the distances from the fulcrum to the boys are equal:
d1 = d2 = (4.0 m) / 2 = 2.0 m
Now we can substitute the values into the torque balance equation to find the mass of the board:
m_board = 20.5 kg
Therefore, the mass of the board in the uniform seesaw system is 20.5 kg.