Question

1. A ruler is placed on top of a wedge as shown. The markings on the ruler are spaced a distance d apart, and the ruler has a mass m. You are given two weights-one has a mass of 2m, and the other has a mass of 4m-and you are instructed to balance the ruler. a. Find all the locations and combinations of the weights, using either one or both, that will balance the ruler. b. Draw each combination on one of the diagrams below. The number of combinations does not necessarily match the number of diagrams. c. For each combination, compute the torque for each force in terms of m, g, and d, then calculate net torque.

Answer 1

(a) il '2m' asta d left of wedge. hall Im' aut 'd' right of wedge and 'um' at 'd left of wedge. (i) 'am' at 'd' right of wedge and 'um' - at ad left of wedge. 2 1 (m mass of ruler, shown at it's center of mass) (C) (1) Clockwise torque negative Counter clockwise torque positive Ruler TR = - mg x 2d. =-2 mgd. 2m → Izm = +2mg xd -- +2mgd. net torque, Inet = TR+ Tim = 0.

0 (11) TR= -mg x2d = -2mgd. Tam= - 2mg xd=- 2mgd. Tym = t4mg xd = + 4mgd . Thet = Tp + łzm tłum = (iii) TR = -mgx2d = - 2mgd. Tam = -2mx 3d = -6mgd. Tym = -4mx 2d = -8mgd. Tnet - TR + Tam tłum = -2mgd - Emad + d mad