(Solved): Learning Goal: To make the connection between intuitive understanding of a seesaw and the standard ...

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. (Figure 1) 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. Part 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? Express your answer in terms of $L,W$, and $w$. Now consider this problem as a more formal introduction to torque. The torque of each child about the pivot point is the product of the child's weight and the distance from the pivot to the child's center of mass (center of gravity.) The sign of the torque is taken to be positive by convention if it would cause a counterclockwise rotation of the seesaw. The distance is measured perpendicular to the line of force and is called the moment arm. Part B Find the torque $?$ about the pivot due to the weight $w$ of Gilles on the seesaw. Express your answer in terms of $L_1$ and $w$.