SOLUTION: I am having a hard time with this word problem:The force of attraction between two bodies varies directly with the product of their masses and inversely with the square of the dist

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Question 522528: I am having a hard time with this word problem:The force of attraction between two bodies varies directly with the product of their masses and inversely with the square of the distance between them. The force of attraction is 6 pounds when masses of 64 slugs and 108 slugs are 24 feet apart. Find the force of attraction when two masses are 25 slugs each and 60 feet apart.
I know for varies directly the equation would be x=ky and the inversely is z=k/w my problem is I have a hard time pulling out the numbers and putting them in the right part of the equation.
Any help will be appreciated. Thank you
Found 2 solutions by Earlsdon, Edwin McCravy:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with:
F+=+k%2AM%5B1%5D%2AM%5B2%5D%2Fd%5E2 Find the value of k by substituting M%5B1%5D+=+64, M%5B2%5D+=+108, d+=+24 and F+=+6
6+=+%28k%2A64%2A108%29%2F%2824%29%5E2 Solve for k.
k+=+6%2A%2824%29%5E2%2F%2864%2A108%29
k+=+0.5 Now the equation is:
F+=+0.5%2AM%5B1%5D%2AM%5B2%5D%2Fd%5E2 To find F, substitute M%5B1%5D+=+25, M%5B2%5D+25, and d+=+60.
F+=+0.5%2A25%2A25%2F%2860%29%5E2
F+=+0.0868pounds.

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Rule:

Quantity that varies = k·%28%22directly%28s%29%22%29%2F%28%22inversely%28s%29%22%29

>>...The force of attraction between two bodies varies...<<
That's the quantity that varies.  We'll call it F. That goes on
the left of the equal sign.

>>...directly with the product of their masses...<<
So the two masses go on top on the right of the equal sign.  We 
will call them m1 and m2.

>>...and inversely with the square of the distance between them...<<
That's the inversely.  We'll call it d². It goes on the bottom on the 
right. So we have:

              F = k·%28m%5B1%5Dm%5B2%5D%29%2Fd%5E2

That's the incomplete formula.  We must find k before we have the
complete formula:

>>...The force of attraction is 6 pounds when masses of 64 slugs and 108 slugs are 24 feet apart.<<
We substitute F=6, m1=64, m2=108, d=24 

              6 = k·%2864%2A108%29%2F24%5E2
              6 = k·12
              6%2F20 = k
              0.5 = k

Now we have k.  Now we substitute 0.5 for k in this:

              F = k·%28m%5B1%5Dm%5B2%5D%29%2Fd%5E2

              F = 0.5·%28m%5B1%5Dm%5B2%5D%29%2Fd%5E2

And that is the complete formula.  Now that we have the complete
formula, we are ready to use it.  Here is what we are to use it to
find:

>>..Find the force of attraction when two masses are 25 slugs each and 60 feet apart..<<
We substitute m1 = 25, m2 = 25, d = 60

              F = 0.5·%28m%5B1%5Dm%5B2%5D%29%2Fd%5E2

              F = 0.5·%2825%2A25%29%2F60%5E2

              F = 0.5·625%2F3600

              F = 0.5·25%2F144
       
              F = 1%2F2·25%2F144

              F = 25/288 = .0868 pounds.

Edwin