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This is college Physics Answers through Shaun Dychko. A cork is pounded right into the peak of a jug of wine through a force of 120 newtons and also the diameter that the cork is 2.00 centimeters and also the diameter of the bottom that the jug is 14.0 centimeters and this bottom pops off and we are meant come calculate exactly how much force past the 120 newtons used is on the bottom the the jug? for this reason we convert these centimeters into meters although it turns out that"s no really necessary since we are just splitting the squares of this numbers and so it simply matters that the units space the same yet I walk it the end of a issue of habit. For this reason we understand that the pressure where the cork is will be exact same as the pressure at the bottom the the jug and also I have written push as force divided by area here. For this reason this is the F 1, which is the force applied to the cork split by the area that the cork and also that"s walk to same the force applied to the bottom of the jug, F 2, split by the area that the bottom the the jug, A 2. So we want to recognize what F 2 is and so we"ll main point both sides by A 2 to settle for it climate switch the political parties around. For this reason F 2 is F 1 time A 2 end A 1; the area that the bottom the the jug will be π times the radius of the circular bottom squared and the radius is half the diameter and then exact same for the A 1—same formula— yet d 1 instead of d 2. The π"s cancel and also so do these denominators which will end up being 4 after girlfriend square the denominators; castle cancel and we room left v F 1d 2 squared over d 1 squared. For this reason that"s 120 newtons applied times 14.0 time 10 to the minus 2 meters— diameter of the bottom the the jug—squared separated by 2.00 times 10 to the minus 2 meters—for the cork—squared and that"s 5880 newtons. And to discover the extra force, we take 120 newtons far from that and this is the amount by which the pressure on the bottom the the jug over the force applied and that"s 5760 newtons.
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