A student of mass M0 and another student of mass 2.5 * M0 sit at opposite ends of a board of length Lb and negligible mass. The board is free to pivot about a support at its center. At the instant shown above, the board is horizontal.
Derive an expression for the magnitude of the net torque exerted on the students-board system about the support at the instant shown in the figure. Express your answer in terms of M0, Lb, and physical constants, as appropriate.
The students want to be able to balance the board horizontally without the students touching the ground. They figure out that one student needs to move closer to the support while the other student remains at the end of the board. Which student should move closer to the support: the student of mass M0 or the student of mass 2.5 * M0? Briefly explain your reasoning.
Derive an expression for the distance that the student indicated in the last question should move. Express your answer in terms of M0, Lb, and physical constants, as appropriate.
Determine the magnitude of the force exerted on the board after the student has moved and the board is balanced horizontally. Express your answer in terms of M0, Lb, and physical constants, as appropriate.
