AP Physics 2: 1.3 Fields in Space. How long will it take PANCAKE to reach the plate?

AP Physics 2 | Fields in Space |

Language | English Language |

Science Practice 2 | Using math appropriately |

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

booster rocket is broken A rescue satellite finally appears ten

kilometers above the surface The satellite has a charged plate

that creates a uniform electric field of magnitude tend of

the sixth newton cool ums pancake has a mass of

one hundred kilograms It charges itself with six hundred micro

coolant and stands directly under the plate Acceleration due to

gravity on mars is four meters per second squared Well

the figure displays the situation with pancake treated as a

point charge How long will it take pancake to reach

the plate And here the angel answers any second All

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

about failing rockets and lack of food and water really

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

we were to get stuck maybe a rescue satellite come

save us In this case the charge from the satellite

is pulling up on our little pancake and the martian

gravity is pulling it down Thie first thing we have

to do is figure out the forces being applied to

the martian explorer will the upward force Being applied by

the satellite equals the charge times The magnitude of the

electric field and the force of gravity pulling pancake down

equals mass times gravity Well the electric force is positive

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

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

the gravitational force from the electric force But hold on

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

us how long this trip takes for that We need

to find pancakes Acceleration acceleration equals force divided by mass

so we can put our net force equation over master

to find the acceleration Now we can plug in the

numbers find the acceleration So here we go Six hundred

micro columns times ten to the sixth minus one hundred

kilograms times four meters per second Squared over one hundred

kilograms When we boil it all down gives us an

acceleration of two meters per second squared Alright we found

the acceleration We still have to figure out how long

it takes for pancake to reach the satellite and head

for home We know the acceleration is two meters per

second squared We know the distance of the satellite is

ten kilometers or ten thousand meters and we know that

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

we need an equation that involves time acceleration and distance

Well the one to go with is the distance or

displacement equation Distance equal starting velocity times time plus one

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

starting velocity is zero so we can knock the first

part of the equation out Now We know that ten

thousand meters equals one half two meters per second squared

times times square well solving for time were able to

see that it takes pancake one hundred seconds to reach

the sweet embrace of the rescue satellite The right answer

is the houston pancake is headed home Goes down sticking