Question

The gravitational attraction between two masses varies inversely as the square of the distance between them. If the attraction force between them is 75 lbs. when the bodies are eight feet apart, find the attraction when the masses are twelve feet apart.

Answer 1

this is just a ratio and proportion problem...do you know the equation for inverse proportion?

Answer 2

no my notes for this is just way too confusing

Answer 3

i'll make it simple...

\(\Large F_{g} = \frac{k}{d^2}\)

where \(F_{g}\) = gravitational force
k = proportionality constant
d = distance between the objects


you understand that so far?

Answer 4

yea

Answer 5

good...so in the first part of the problem..."If the attraction force between them is 75 lbs. when the bodies are eight feet apart,"

what is given to you?

Answer 6

yes

Answer 7

yes? i was asking what is the given in the first part of the problem :P hahaha..so what's given? gravitational force? proportionality constant? distance?

Hint: there are 2 given values

Answer 8

uhh gravitational force

Answer 9

right! what else?

Answer 10

between 2 masses inversely as a square

Answer 11

no no..that's the condition for the proportion..just look here ""If the attraction force between them is 75 lbs. when the bodies are eight feet apart,"

Answer 12

oh yea...we have to find the attraction when they are 12 feet apart

Answer 13

physics :)

Answer 14

focus on "If the attraction force between them is 75 lbs. when the bodies are eight feet apart," first...don't look at the other parts of the problem

Answer 15

@AravindG it's ok...it's proportion haha

Answer 16

ok

Answer 17

so what are the 2 given values in there?

Answer 18

71 and 8

Answer 19

75 and 8*

and what is 75? what is 8?

by that i mean if it is attraction force, distance or proportionality constant

Answer 20

distance?

Answer 21

which is the distance?

Answer 22

75 or 8?

Answer 23

75

Answer 24

check the problem again..

"If the ATTRACTION FORCE between them is 75 lbs. when the bodies are eight FEET APARTt,"

Answer 25

oh sorry haha 8

Answer 26

right! and 75 is?

Answer 27

the proportionality constant

Answer 28

check what i capitalized there...

Answer 29

the Force

Answer 30

good! so we substitute force and distance to the equation i said earlier...

\(\LARGE F_{g} = \frac{k}{d^2} \rightarrow 75 = \frac{k}{(8)^2}\)

you're gonna look for k..how do you think you can do that?

Answer 31

Hint: "cross" multiply

Answer 32

uh multiply by its reciprocal??? lol ireallydk

Answer 33

hmm close...whose reciprocal?

Answer 34

k/(8)^2

Answer 35

and what do you mean multiply by reciprocal? multiply by 8^2/k?

Answer 36

yes

Answer 37

hmm well that would cancel out the k right? but you want k...so you'll just multiply both sides by 8^2 got it?

Answer 38

right

Answer 39

so your k = 72(8^2)

you might wanna use the calculator

Answer 40

4608

Answer 41

so that becomes your k...moving on to the second part of the problem..." find the attraction when the masses are twelve feet apart." what is the given value this time?

Answer 42

12

Answer 43

but wasnt that 72 supposed to be 75

Answer 44

what 72?

Answer 45

72(8^2)

Answer 46

oh..sorry typo!!! :))) do it (75)(8^2) hehe sorry

Answer 47

so..on to the second part of the problem?

Answer 48

k=4800

Answer 49

okay..we'll need that k for later...so back to what we were talking about...what do you think is 12? distance? attraction? proportionality constant?

Answer 50

12 is definitely the distance

Answer 51

right! and what are we looking for?

Answer 52

the attraction force

Answer 53

GOOD! :D and we have proportionality constant already right? so we substitute!

\(\LARGE F_{g} = \frac{k}{d^2} \rightarrow F_{g} = \frac{4800}{(12)^2}\)

Answer 54

ohh koolio understandable

Answer 55

got it now? :)

Answer 56

so now we have to divide?

Answer 57

yuppp :)

Answer 58

so that going to be 33.33

Answer 59

you got it! :)

Answer 60

THANK YOU SOOOOOO MUCHHH you a LIFESAVER

Answer 61

hehe it was nothing :"> haha

Answer 62

have a blessed day

Answer 63

you too ^_^