ShmoopTube

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Thank you We sneak and here's your shmoop dooz your

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brought to you by pancakes for when you want deserve

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for breakfast We've been there The planetary access non combustion

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automatic kinetic explorer and cake has been sent to mars

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to search for signs of primitive life Pancake is about

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to blast off back to earth when it realizes it's

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booster rocket is broken A rescue satellite finally appears ten

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kilometers above the surface The satellite has a charged plate

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that creates a uniform electric field of magnitude tend of

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the sixth newton cool ums pancake has a mass of

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one hundred kilograms It charges itself with six hundred micro

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coolant and stands directly under the plate Acceleration due to

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gravity on mars is four meters per second squared Well

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the figure displays the situation with pancake treated as a

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point charge How long will it take pancake to reach

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the plate And here the angel answers any second All

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right we'd love to go to mars but let's talk

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about failing rockets and lack of food and water really

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doesn't make it sound all that much fun But if

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we were to get stuck maybe a rescue satellite come

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save us In this case the charge from the satellite

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is pulling up on our little pancake and the martian

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gravity is pulling it down Thie first thing we have

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to do is figure out the forces being applied to

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the martian explorer will the upward force Being applied by

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the satellite equals the charge times The magnitude of the

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electric field and the force of gravity pulling pancake down

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equals mass times gravity Well the electric force is positive

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and the gravitational force is negative Since they're acting in

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opposite directions we'll figure out the net force We subtract

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the gravitational force from the electric force But hold on

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a second Just finding the force isn't going to tell

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us how long this trip takes for that We need

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to find pancakes Acceleration acceleration equals force divided by mass

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so we can put our net force equation over master

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to find the acceleration Now we can plug in the

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numbers find the acceleration So here we go Six hundred

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micro columns times ten to the sixth minus one hundred

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kilograms times four meters per second Squared over one hundred

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kilograms When we boil it all down gives us an

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acceleration of two meters per second squared Alright we found

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the acceleration We still have to figure out how long

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it takes for pancake to reach the satellite and head

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for home We know the acceleration is two meters per

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second squared We know the distance of the satellite is

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ten kilometers or ten thousand meters and we know that

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we're dealing with kinnah matics at this point All right

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we need an equation that involves time acceleration and distance

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Well the one to go with is the distance or

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displacement equation Distance equal starting velocity times time plus one

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half acceleration times times square that'll do with rick The

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starting velocity is zero so we can knock the first

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part of the equation out Now We know that ten

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thousand meters equals one half two meters per second squared

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times times square well solving for time were able to

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see that it takes pancake one hundred seconds to reach

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the sweet embrace of the rescue satellite The right answer

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is the houston pancake is headed home Goes down sticking

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