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Basic Math Help

tical

tical

Rising Star
BGOL Investor
Fam, I'm reviewing some basic math concepts for my upcoming MCAT test and I can't figure out a series of similar problems. Unfortunately math was never my strong suit...


Here's the problem given:
Universal Gravitation Equation

F=GMm/R^2

Problem ask if you reduce the radius "by a factor of 2" what does that do to "F"?

ANSWER: it increases by a factor of 4

This is what i know or think I know F is proportional to GMm and F is inversely proportional to R^2 looks like this:

F~GMm
F/R^2

Thus if you reduce R^2 it increases F.

Does anyone "How" mathematically you derive that answer? "F" increases by a factor of 4

Thanks
 
You can't substitute F for GMm because F = (GMm/R^2) but F will increase when the radius decreases since it is in the denominator

the only way i can think of that you could derive an answer mathematically would be to use proofs since all you have is an undefined value for 'R'
 
This looks to be a physics equation. Assuming that M and m, which I am assuming to be mass of object 1 and mass of object 2, remains the same, G, being a constant, and the only two variables change are R and F, then your reasoning is correct. From manipulating the original equation, R^2=(G*M*m)/F. By replacing R with (1/2)R, you yield, ((1/2)R)^2=(1/4)R^2. Since it is not proper to have fractions in your denominator, you would multiple 4 to both sides of the equation and hence produce: 4F=(G*M*m)/(R^2). That will bring you to the conclusion that F will increase by a factor of 4.
Hope that helps.
 
This looks to be a physics equation. Assuming that M and m, which I am assuming to be mass of object 1 and mass of object 2, remains the same, G, being a constant, and the only two variables change are R and F, then your reasoning is correct. By replacing R with (1/2)R, you yield, ((1/2)R)^2=(1/4)R^2. Since it is not proper to have fractions in your denominator, you would multiple 4 to both sides of the equation and hence produce: 4F=(G*M*m)/(R^2). That will bring you to the conclusion that F will increase by a factor of 4.
Hope that helps.
 
Gods_Debris said:
You can't substitute F for GMm because F = (GMm/R^2) but F will increase when the radius decreases since it is in the denominator
Click to expand...

Thanks for the reply,

I understand that F will increase as the radius decreases as I stated in the Original Post. My question is does anyone know "how" to derive it mathematically? Because sometimes the question ask if R^2 is reduced by a factor of 40,10,.5, 3,4 or increase by a factor of 40,10,.5,3,4 etc how does that effect "F". Thus i need to understand mathematically how to derive/express it
 
a1rimrocka said:
You mean aside from substituting random numbers for the variables and divide R by 2 the second time? :lol:
Click to expand...

Exactly, I could substitute random numbers.However, when they ask what happen if its reduced by a factor of 467?:hmm: You better understand how to mathematically manipulate the formula to see how it effects "F"
 
tical said:
Thanks for the reply,

I understand that F will increase as the radius decreases as I stated in the Original Post. My question is does anyone know "how" to derive it mathematically? Because sometimes the question ask if R^2 is reduced by a factor of 40,10,.5, 3,4 or increase by a factor of 40,10,.5,3,4 etc how does that effect "F". Thus i need to understand mathematically how to derive/express it
Click to expand...
This might help though I think the reasoning it is based on is Mathematically unsound.
dademon said:
This looks to be a physics equation. Assuming that M and m, which I am assuming to be mass of object 1 and mass of object 2, remains the same, G, being a constant, and the only two variables change are R and F, then your reasoning is correct. By replacing R with (1/2)R, you yield, ((1/2)R)^2=(1/4)R^2. Since it is not proper to have fractions in your denominator, you would multiple 4 to both sides of the equation and hence produce: 4F=(G*M*m)/(R^2). That will bring you to the conclusion that F will increase by a factor of 4.
Hope that helps.
Click to expand...
 
Grandpa_bfaf78_777622.gif
 
GMm/[R-(2,4,6,8... etc. etc.)]^2 seems to be the more Mathematical answer since the phrase is 'factor' of 2 i.e. any number that can be divided by two without leaving any remainder. don't see any mention of quotients or multiples so I don't think you should be dividing or multiplying to solve. just a mention of inverse effect of number size in the denominator should suffice (said mathematical proof)
 
*Reads thread title, looks at replies, reads thread title again. Thinks to self, "basic math" ? Pours drink.*
 
F is inversely proportional to r^2. As one gets bigger, the other gets smaller.

BTW, that's not basic math, that's calculating the gravitational force between two masses.
 
Gods_Debris said:
GMm/[R-(2,4,6,8... etc. etc.)]^2 seems to be the more Mathematical answer since the phrase is 'factor' of 2 i.e. any number that can be divided by two without leaving any remainder. don't see any mention of quotients or multiples so I don't think you should be dividing or multiplying to solve. just a mention of inverse effect of number size in the denominator should suffice (said mathematical proof)
Click to expand...

Fam does this sound right

"r" reduced by a factor of 2 can be rewritten as: r=r/2
Once we have that we plug it into the formula accordingly


F=GMm/(r/2)^2
F=GMm/(r^2/4)
F=GMm4/(r^2)

Giving you an increase of the Gravitational force between the two bodies by a factor of 4
 
d-weezy said:
F is inversely proportional to r^2. As one gets bigger, the other gets smaller.

BTW, that's not basic math, that's calculating the gravitational force between two masses.
Click to expand...

Yeah. To me, THIS is "basic math": 8(-9)+11(6)=-6. Y'all cats trying to calculate how to send people to Neptune and shit! On a serious note, good luck with the MCAT, OP.:cool:
 
Last edited:
woodchuck said:
Yeah. To me, THIS is "basic math": 8(-9)+11(6)=-6. Y'all cats trying to calculate how to send people to Neptune and shit! On a serious, good luck with the MCAT, OP.:cool:
Click to expand...

:lol::lol:

Fam thanks...I haven't been able to sleep proper going on a month now..this shit is stressing me the fuck out!:smh:
 
tical said:
Fam does this sound right

"r" reduced by a factor of 2 can be rewritten as: r=r/2
Once we have that we plug it into the formula accordingly


F=GMm/(r/2)^2
F=GMm/(r^2/4)
F=GMm4/(r^2)

Giving you an increase of the Gravitational force between the two bodies by a factor of 4
Click to expand...

What i was thinking to.
 
Jackal said:
F=GMm/(R/2)^2

F=GMm/(R^2/2^2)

F=GMm/(R^2/4)

F=4GMm/R^2

F=4(GMm/R^2)


If that makes any sense?
Click to expand...

Jackal said:
What i was thinking to.
Click to expand...


It's also how I was able to eventually derive it...Ofcourse it gets worst..then they want you to combine

Universal Gravitational Force with Centripetal Force to figure out how much velocity and/or radius is needed to keep a satellite in orbit in under 1 min:angry:
 

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