Question

Newton's law of universal gravitation states that force,F, is inversely proportional to the square of the distance between two masses.When the distance between two masses is (r) km,the force is 120N.Find the force when the distance is increased by 200%.

Answer 1

i just need to know how to solve the increase by 200% part.

Answer 2

\[F_{g} =\frac{M*m}{r^2} = 120 \]
when r is increased by 200%: 200% 2 = 2*r
\[\frac{M*m}{(3r)^2} = \frac{M*m}{9r^2} = \frac{1}{9}*F_{g} = \frac{120}{9}\]

Answer 3

hey i don't quite get it.the equation i formed is F=k/d^2.

Answer 4

OOps I forgot the\[G\]
but you find the same thing anyway

Answer 5

then i got k=120r^2 after substituting in r into d^2 and 120 into F.

Answer 6

but i don't know how to substitute in the 200% part.can u explain the solution using my equation ?

Answer 7

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Answer 8

then i substitute it into d^2 ?

Answer 9

exactly :-D then just factor it out

Answer 10

the equation is like this: F=k(1/r^2). being inversely proportional since distance is now 200% more, or thrice as much, putting into the equation, u get F=k(1/(3r)^2) and therefore the equation now relates to 120/9.

Answer 11

but then how did u get (3r)^2? i thought its supposed to be (2r)^2?

Answer 12

3r^2 is r increased by 200%

\[r + (\frac{200}{100)}r = r + 2r = 3r\]

Answer 13

OHHHH i got it.THANKS DUDE :)

Answer 14

See ya man.

Answer 15

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