ShmoopTube

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Alright here's your shmoop du jour brought to you by skyscrapers their [Skyscrapers in Chicago city]

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impressive feats of engineering and we love to look at them you know with our

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feet planted firmly on the ground the Willis Tower in Chicago is the tallest

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building in the U.S. at 527 meters the 1,700 feet to reach the top floors [Willis Tower shown to be 1,729 feet]

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tourists take a one-minute trip up an elevator that quickly accelerates to a

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high speed and intrepid schmooper weighs himself before getting on the elevator [Shmoop employee weighing himself before getting on the elevator]

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and finds that the scale reads 500 n Newtons as the elevator begins its ascent

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at constant acceleration he sees that the scale reads 950 Newton if the [Scale reading 950 N]

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elevator descends with a constant acceleration equal to 1/2 the upward

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acceleration what will the scale read on the ride

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down and here are the potential answers... ok well we're dealing with three

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separate forces here we have the normal force before we're even on the elevator [Luke Skywalker fighting Darth Vader]

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the force when we're moving up in the elevator and the force when we're going

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down all right well let's deal with the normal force first when we're on the

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ground gravity pushes us down and the floor pushes us up these two forces [Gravity pushing down and the floor pushing up on a woman]

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balance each other out.. if they didn't we'd float above the floor or crash

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through it'd be kind of cool we're happy to report that the Willis Tower

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has very sturdy floors that push back against gravity and we don't see anyone [Man stood in a glass window looking down from a skyscraper]

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floating in Chicago so it appears the forces balance out so all this means

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that the normal force minus mass times gravity equals zero well we're in luck

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because we know the amount of force pushing down on the schmooper is 500 [White ball lands on 29 black on a roulette wheel]

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Newtons and we can calculate his mass since mass times gravity equals Newtons

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we can rearrange the equation so we have mass equals Newton's divided by gravity

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for our sake here we'll also round gravity up to ten meters a second

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squared when we plug in the numbers we find that his mass is 50 kilograms now [Re-arranged equation to find the mass]

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when the elevator starts going up the force of gravity is still balanced out

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by the force of the elevator floor but this time instead of equaling zero the [Man going up an elevator in the tower]

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forces interact to equal mass times acceleration upwards all right well now

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we can solve for upward acceleration all we have to do is subtract mass times

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gravity from Newtons on the upward ride and divide that by mass okay some quick

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calculations and we'll find that acceleration upward is nine meters per [Equation for acceleration upward shown as 9 meters per second squared]

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second squared now we know that when the elevator starts slowing down the downward

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acceleration is half of the upward acceleration well the downward force

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equals negative mass times acceleration and downward acceleration equals

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one-half of upward acceleration so the downward force minus mass times gravity

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equals negative mass times half of upward acceleration all right we're

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almost there I promise now we solve for the downward force which again equals [Woman waving her finger]

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mass times gravity minus mass times one-half upward acceleration well we

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multiply 50 kilograms by five point five meters per second squared and we get an

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answer of 275 Newtons so the correct answer is option C let's quickly touch

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on the other answer choices we could have knocked a and D out of the running [Boy on his phone gesturing at his laptop screen]

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right away we know that there's a downward force in action here since

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gravity never stops so there's no way a is correct and we know that the force [Young girls jumping up and down]

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during the slowdown will be less than the force standing in place on the

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ground so D would never work either and we also know that next time we go to [Man attempts to float in mid-air and falls down]

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Chicago we'll stick to ground level attractions a super tall building in a

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place called the windy city, yeah we don't even like to climb step ladders [Man looking up at Willis Tower with a step ladder]

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and look out below....whoa boy!

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