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anonymous
 one year ago
c. When the center of Earth is 2 × 1011 meters from the center of Mars, the force of gravity between the two planets is about 64.32 × 1014 newtons. The mass of Earth is about 6 × 1024 kilograms, and the mass of Mars is about 6.4 × 1023 kilograms. Using these values, estimate the gravitational constant.
anonymous
 one year ago
c. When the center of Earth is 2 × 1011 meters from the center of Mars, the force of gravity between the two planets is about 64.32 × 1014 newtons. The mass of Earth is about 6 × 1024 kilograms, and the mass of Mars is about 6.4 × 1023 kilograms. Using these values, estimate the gravitational constant.

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phi
 one year ago
Best ResponseYou've already chosen the best response.1do you have a formula for G ?

midhun.madhu1987
 one year ago
Best ResponseYou've already chosen the best response.0The universal law of gravitation states that: \[F = GMm \div d ^{2}\] where F = Gravitational Force G= Universal Gravitational constant M = Mass of Earth m = Mass of mars d = distance between the 2 objects

midhun.madhu1987
 one year ago
Best ResponseYou've already chosen the best response.0You can find G by substituting other values..

midhun.madhu1987
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437838350097:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the formula I'm using for G is G=Fg d2/m*M

phi
 one year ago
Best ResponseYou've already chosen the best response.1now put in numbers in place of the symbols

phi
 one year ago
Best ResponseYou've already chosen the best response.12 × 1011 meters from the center of Mars, the force of gravity between the two planets is about 64.32 × 1014 newtons. The mass of Earth is about 6 × 1024 kilograms, and the mass of Mars is about 6.4 × 1023 kilograms. \[ G = \frac{F_g \cdot d^2}{m\cdot M}\\ G= \frac{64.32\cdot 10^{14} \ N \cdot (2\cdot 10^{11})^2 \ m^2}{6\cdot10^{24} \cdot 6.4\cdot 10^{23} \ kg^2} \] are you sure about the force being 64.32 x 10^14 (normally the leading number would be 6.432)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry typo, I meant 6.432

phi
 one year ago
Best ResponseYou've already chosen the best response.1so the expression is \[ G= \frac{6.432\cdot 10^{14} \ N \cdot (2\cdot 10^{11})^2 \ m^2}{6\cdot10^{24} \cdot 6.4\cdot 10^{23} \ kg^2}\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1first, square 2*10^11 which is 2*10^11 * 2 * 10^11 or, reordering 2*2 * 10^11*10^11 I assume you know 2*2 is 4 what is 10^11 * 10^11 ?

phi
 one year ago
Best ResponseYou've already chosen the best response.110*10 is 100 or using exponents \( 10^1 \cdot 10^1 = 10^2 \) or 100*100= 10000 using exponents \(10^2 \cdot 10^2 = 10^4 \) do you see a pattern ? if you have the same base (and we do, it is 10) then when you multiply them, you add their exponents

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ G= \frac{6.432\cdot 10^{14} \ N \cdot 4\cdot 10^{22} \ m^2}{6\cdot10^{24} \cdot 6.4\cdot 10^{23} \ kg^2} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1Let's just do the "numbers" (the leading coefficients) what is (6.432*4)/(6*6.4) ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok. now let's do the top exponent part 10^14 * 10^22 = ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1now do the bottom exponent part. what do we get ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1so we now have \[ 0.67 \cdot \frac{10^{36}}{10^{47}} \] when you divide numbers with the same base, do top exponent  bottom exponent can you do that ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0divide the top by the bottom?

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, but to do that you do 3647 to get the new exponent

phi
 one year ago
Best ResponseYou've already chosen the best response.1for example \[ \frac{100}{10} = 10 \] using exponents \[ \frac{10^2}{10^1} = 10^{21} = 10^1 = 10 \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1the answer is 10 ^ new exponent the new exponent is 36  47

phi
 one year ago
Best ResponseYou've already chosen the best response.1so we now have \[ 0.67 \cdot \frac{10^{36}}{10^{47}} \\ 0.67 \cdot 10^{11} \] now we put the answer in standard form. we want 6.7 instead of 0.67 to do that we multiply by 10. and then divide by 10, like this \[ 0.67 \cdot 10 \cdot \frac{10^{11}}{10^1} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.10.67*10 is 6.7 we have \[ 6.7 \cdot \frac{10^{11}}{10^1} \] can you do the 10 part? remember : top exponent  bottom exponent

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes 10^12 so the answer is 6.7 x 10^12

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now I need to rewrite the formula to solve for one of the mass values

phi
 one year ago
Best ResponseYou've already chosen the best response.1if you start with \[ G = \frac{F_g \cdot d^2}{m\cdot M} \] multiply both sides by m (which means write m * on both sides) can you do that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how would I do that?

phi
 one year ago
Best ResponseYou've already chosen the best response.1multiplying by a letter (like "m") is easy... you write m on both sides example, say you have x=y and you multiply both sides by m. you write mx = my

phi
 one year ago
Best ResponseYou've already chosen the best response.1like this \[ mG = m\frac{F_g \cdot d^2}{m\cdot M}\] you can write the righthand side as \[ mG =\frac{m}{m} \frac{F_g \cdot d^2}{ M}\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1if it were numbers: 2/2 or 3/3 or 7/7 ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes. anything divided by itself is 1 (which is why I did what we did) so we have \[ mG =\frac{m}{m} \frac{F_g \cdot d^2}{ M} \\ mG =1\cdot\frac{F_g \cdot d^2}{ M} \\ mG =\frac{F_g \cdot d^2}{ M}\] 1 times anything is the anything, which is how we get the last line

phi
 one year ago
Best ResponseYou've already chosen the best response.1now multiply both sides by \(\frac{1}{G} \)

phi
 one year ago
Best ResponseYou've already chosen the best response.1it is clearer if you use G (not g) on the left side on the left side you have \[ \frac{mG}{G} \] what happens to the G/G ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1and what does 1* m simplify to ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1so you have \[ m= \frac{F_g \cdot d^2}{ M}\cdot \frac{1}{G} \] on the right side, to multiply fractions, you multiply top*top and bottom * bottom

phi
 one year ago
Best ResponseYou've already chosen the best response.1in other words you get \[ m=\frac{F_g \cdot d^2}{G\cdot M} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1the bottom could also be written M*G. you can change the order when multiplying
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