sphys2017

Need some help with question 12 and 13. I got 12 right and I just used my intuition. It seemed obvious that if the left side had 8/15 of the weight then it the center of mass was 7/15 away from it(maybe that's faulty reasoning?) . The verbal explanation given to me explained it in terms of torque and I didn't understand it. Also it may sound stupid but why is the answer to 13 A and not B?

ChipB

The center of mass is defined to be the point where the torques due to the various components of weight of an object = 0. Remember torque = force (in this case weight) times moment arm distance. Let's call the location of the CM as being distance D as measured from point Y. There are two moment armsacting about the CM to consider: the one acting at point Y has a force of 800N and has a moment arm length from the CM of D, so the torque this force presents at point D is Dx800N in the clockwise direction. The torque due to the 700N load at point X has a moment arm length of (L-D), so presents a torque to point D of 700(L-X) in the counter-clockwise direction. By convention counter-clockwise torques are considered positive and clockwise is negative. The sum of these two torques acting about point D must equal zero (that's the definition of the center of mass):

$\displaystyle \sum T = 700(L-X)-800X = 0$

Solve for X.

As for question 13 - it doesn't matter whether you weigh both ends of the bed at the same time or not - it's static, and so its weight doesn't change, and neither does the center of mass. Hence you get the same readings whether you use two scales on one.