## Torques on a Seesaw: A Tutorial

**Learning Goal: **To make the connection between intuitive understanding of a seesaw and the standard formalism for torque.

This problem deals with the concept of torque, the “twist” that an off-center force applies to a body that tends to make it rotate.

Use your intuition to try to answer the following question. If your intuition fails, work the rest of the problem and return here when you feel that you are more comfortable with torques.

**A) Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child, Jacques, simply sinking **to** the ground. Given that Jacques, whose weight is W, is sitting at distance L to the left of the pivot, at what distance L_{1} should Marcel place Gilles, whose weight is w, to the right of the pivot to balance the seesaw?**

**B) Find the torque τ about the pivot due to the weight w of Gilles on the seesaw.Express your answer in terms of L_{1} and w.**

**C) Determine **Σ*τ***, the sum of the torques on the seesaw. Consider only the torques exerted by the children. Express your answer in terms of W, w, L, and L_{1} **

**.**

**D) Where should Marcel position Jacques to balance the seesaw? Express your answer in terms of L _{2}, L_{3}, W, and w.**

**E) With what force in the rightward direction, F _{x}, should Marcel push? If you think the force should be toward the left, your answer F_{x} should be negative. Express your answer in terms of W, L_{end}, w, L_{2}, L_{3}, and h.**

## Answer ( 1 )

A) Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child, Jacques, simply sinking to the ground. Given that Jacques, whose weight is

is sitting at distanceW,to the left of the pivot, at what distanceLL1should Marcel place Gilles, whose weight is, to the right of the pivot to balance the seesaw?w=> L1 =

LW/wB) Find the torque

τabout the pivot due to the weightwof Gilles on the seesaw.Express your answer in terms of L1 andw.=>τ= -L1wC) DetermineΣτ, the sum of the torques on the seesaw. Consider only the torques exerted by the children. Express your answer in terms ofW,w,L, and L1.=> Σ

τ=0 = WL-wL1D) Where should Marcel position Jacques to balance the seesaw? Express your answer in terms of L2, L3, W, andw.=> w(L2+L3)/w

E) With what force in the rightward direction, Fx, should Marcel push? If you think the force should be toward the left, your answer Fx should be negative. Express your answer in terms ofW, Lend, w, L2, L3, and h.=> Fx=[

wLend-w(L2+L3)]/h