Question

A boy and a girl are playing on a teeter totter. The boy is three times as massive as the girl. If the boy is sitting 0.5 meters away from the pivot point, how far away should the girl sit such that the two can sit balanced, horizontally?

Answer 1

To balance on a teeter totter with the boy being three times as massive and sitting 0.5 meters from the pivot, the girl must sit 1.5 meters from the pivot.

Step-by-step explanation:

To solve the problem of balancing the boy and the girl on a teeter totter, we need to use the principle of moments, also known as the principle of torque. The principle states that for the system to be in equilibrium, the clockwise moments must equal the anticlockwise moments. The moment is calculated as the product of the force (mass × gravitational acceleration) and the distance from the pivot point.

In this case, the force exerted by the boy is three times that of the girl since his mass is three times greater. Thus, if the boy is sitting 0.5 meters from the pivot, to achieve balance, the girl must sit at a distance that is three times greater from the pivot point. If we let x represent the distance at which the girl sits, the equation for equilibrium would be:

Boy's moment = Girl's moment

3 × mass of girl × 0.5 = mass of girl × x

1.5 = x

Therefore, the girl should sit 1.5 meters away from the pivot to maintain a balanced, horizontal position on the teeter totter.