Three bys trying to balance a seesaw

[Naldo6]

Three boys are trying to balance on a seesaw, which consists of a fulcrum rock, acting as a pivot at the center, and a very light board L = 3.52 m long, see figure below.

Two boys are already on either end. One has a mass of m1 = 53.0 kg, and the other a mass of m2 = 32.8 kg. How far from the center should the third boy, whose mass is m3 = 23.0 kg, place himself so as to balance the seesaw?

i know how to do it but with just to boys, but with three boys idont have the minimum idea... can anyone helps me?...

 

[alphysicist]

Three boys are trying to balance on a seesaw, which consists of a fulcrum rock, acting as a pivot at the center, and a very light board L = 3.52 m long, see figure below.

Two boys are already on either end. One has a mass of m1 = 53.0 kg, and the other a mass of m2 = 32.8 kg. How far from the center should the third boy, whose mass is m3 = 23.0 kg, place himself so as to balance the seesaw?

i know how to do it but with just to boys, but with three boys idont have the minimum idea... can anyone helps me?...

Solving the problem with two boys and three boys is done exactly the same way--there is just one more term in your equation. So try doing it the same way, and if you get stuck, please post your work so that we can help you.

 

[baba89]

I would approach this problem by first identifying the key factors involved in balancing the seesaw: the mass of each boy and the distance from the center. From there, I would use the principle of torque, which states that for an object to be in rotational equilibrium, the sum of the clockwise torques must be equal to the sum of the counterclockwise torques.

In this case, we can calculate the torque of each boy by multiplying their mass by their distance from the fulcrum. For the first boy, this would be 53.0 kg x d1, where d1 is the distance from the fulcrum. Similarly, for the second boy, it would be 32.8 kg x d2. Since we want the seesaw to be balanced, we can set these two torques equal to each other and solve for the distance of the third boy.

However, with three boys, we also have to take into account the torque of the third boy. To balance the seesaw, the sum of the clockwise torques must be equal to the sum of the counterclockwise torques. So, we would add the torque of the third boy, which would be 23.0 kg x d3, to the counterclockwise side. This would give us the equation:

53.0 kg x d1 + 32.8 kg x d2 = 23.0 kg x d3

To solve for d3, we would need to know the values of d1 and d2. These can be calculated using the fact that the total length of the seesaw is 3.52 m. So, d1 + d2 = 3.52 m. We can then substitute this value into the equation and solve for d3.

Once we have the value of d3, we can use it to determine the distance from the center that the third boy needs to place himself in order to balance the seesaw. This approach can be used for any number of boys on the seesaw, as long as we have the necessary information about their masses and distances from the fulcrum.

I hope this explanation helps you understand how to approach this problem as a scientist. Remember to always identify the key factors and use the relevant principles to solve the problem systematically.