Question

A see-saw made from 4 meter board sits on a pivot at its center. A child weighing 280 N sits 1.75 m away from the center. A second child who weighs 330 N sits on the other side such that the board remains horizontal and steady. (a) What is the torque about the pivot point due to the weight of the first child? (b) how far from the center does the second child sit? (c) What is the force (magnitude and direction) that the pivot applies to the board? Now you come and push on the end of the seesaw nearest the second child with a force of 110 N. You don’t push straight up, but at an angle of 25° from the vertical – tilted toward the center of the seesaw. The first child moves to maintain equilibrium. (d) Based on your intuition, which way should the child move? Towards or away from the center? (e) Calculate how far she is now from the center? (f) What is the force now (magnitude and direction) that the pivot applies to the board?

***Please help me with solving (e) and (f) with the equations so that I can learn how to do it. Thanks***

Answer 1

(a) Torque about the center for child 1 is given as, (assuming that the first boy is sitting on right hand side)

Here r is the distance from the center and F is the force acting on it.

This is in clockwise direction.

(b) Now the moment generated by first child is balanced by the moment generated generated by the second child. (The torque generated by second child is counter clockwise)

let x be the distance from the center where the second child sits.

So the second child sits at a distance of 1.48 m.

(c) The board will be applying a downward force on the pivot due to the weights of the children, Therfeore the reaction force, ie. the force applied by the pivot on the board will be in upward direction.

(d) Now we push up the second child with a force acting at 25 degrees from the vertical, ie, the counter clockwise torque generated at that end of see-saw will decrease (the external force generates a clockwise torque). So to balance that the clockwise torque generated on the other end of the see-saw should decrease so, the child on the right end of the sea-saw should move towards the center.