A (lightweight) pallet has a load of ten identical cases of tomato paste (see Fig. 7–39), each of which is a cube of length . Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.
In order to watch this solution you need to have a subscription.
This is Giancoli Answers with Mr. Dychko. We are asked to find the center of mass in the horizontal plane so we can take a top-down view of this pallet of boxes and the crane operator is gonna position their hook above the center of mass so that the pallet doesn't tip over. So we'll take the origin to be in the bottom-left corner say, and we'll calculate our distances relative to this point here. So we'll consider the x and the y components separately. So in the x-direction, the center of mass is 5 times m multiplied by the center of mass of these particles which is gonna be l over 2; the length of one block is l and center of mass of each of these particle's is gonna be midway between the boxes because the boxes have uniform density. And then we'll add to that this mass of 3m and that mass is positioned 1.5l away from the left hand side so that's 1.5l here and then there's gonna be mass of 2m positioned at 2.5l away from the left side and all of that gets divided by the total mass of 10 boxes times the mass of one box and that gives 1.2l is the center of mass in the x-direction. So it's gonna be somewhere approximately here and we expect it to be closer to the left than to the right because we can see that there's so much more mass on the left side of this pallet. When you are doing calculations, you should always do a reality check on your answers and see if it makes intuitive sense and if we have had some answer that was greater than 1.5, we would probably question our calculation. And for the y-direction, we expect some number that's gonna be more than 1.5, somewhere closer to this top-edge than the bottom because we can see so many boxes are piled up at the top here. So we have a single mass at a position of l over 2 center of mass of this particular box is the length of a box divided by 2 and then plus 2 masses at a position of 1.5l from the bottom of the edge and then there's 3, 4, 5, 6, 7 masses positioned with a center of mass 2.5l away from the bottom and all that gets divided by a total mass of 10 and that gives 2.1l. So the center of mass is gonna be 1.2 times the length of a box from the left side with a y-coordinate of 2.5l above the bottom. So these are the coordinates from the bottom-left corner.
Find us on:
