Physics Help Forum Weight question

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 Mar 23rd 2017, 02:16 AM #1 Junior Member   Join Date: Mar 2017 Posts: 3 Weight question 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? Last edited by sphys2017; Mar 23rd 2017 at 02:22 AM.
 Mar 23rd 2017, 07:28 AM #2 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,326 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.

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