Question

You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M, length L) that can be moved so that the pivot is a distance d from the center of the board. This will allow riders to achieve static equilibrium even if they are of different mass, as most people are. You have decided that each rider will be positioned so that his/her center of mass will be a distance xoffset from the end of the board when seated as shown.You have selected a child of mass m (shown on the right), and an adult of mass n times the mass of the child (shown on the left) to test out your prototype.

Answer 1

In designing a balanced seesaw, we use the principles of static equilibrium and rotational mechanics, ensuring the net force and net torque on the system are zero. The mass of riders and their distances from the pivot determine their respective torques. It's crucial to consider the seesaw's center of mass and adjust the positions of the riders to maintain balance.

Step-by-step explanation:

Understanding the Seesaw and Static Equilibrium

To create a family-friendly seesaw in static equilibrium, one must consider the mass and placement of the riders.

For two children to balance on a seesaw, their respective weights must exert forces around the pivot such that the torques are equal and opposite.

This involves applying the principles of rotational mechanics and the conditions for static equilibrium, which are that the net force and the net torque on the system must both be zero.

For instance, if a seesaw is designed with a uniform board of length 3.0 m and a pivot 1.50 m to one side, we must adjust the position of the riders accordingly.

The lighter child, who sits further from the pivot, and the heavier child, closer to the pivot, create a balance by ensuring that their torques about the pivot point are equal in magnitude but opposite in direction. If one child is off the board, the location of the pivot or the position of the child must be adjusted.

When considering the seesaw's design for static equilibrium, it's important to factor the center of mass of the seesaw, which may not be at the geometric center.

Furthermore, the system’s mass and weight can be represented as acting through a single point, the center of gravity.

This simplification helps in calculating the balance by assessing the moments about the pivot point.