Question

i give medals!
Two men each have a mass of 90 kg. If the gravitational force between them is 8.64 10^-8 N, how far apart are they?

A. 3.2 m
B. 4.0 m
C. 5.0 m
D. 2.5 m

Answer 1

What's the formula for the force between two masses using the gravitational constant?

Answer 2

I found it, it's\[F=G\frac{m_1m_2}{r^2}\]

Answer 3

You know the masses and the force, you should memorize \(G = 6.67\times 10^{-11}\frac{N\cdot m^2}{kg^2}\)... though I didn't, I looked it up.

Answer 4

You want to know the distance, so\[F=G\frac{m_1m_2}{r^2}\]Multiply each side by \(r^2\)\[r^2 F=G\frac{m_1m_2\cancel{r^2}}{\cancel{r^2}}\]Divide each side by \(F\)\[\frac{r^2\cancel{F}}{\cancel{F}}=G\frac{m_1m_2}{F}\]Which gives you\[r^2=G\frac{m_1m_2}{F}\]You want the distance between them \(r\), not \(r^2\) which is \(r\times r\)
so you have to find the square root\[r=\sqrt{G\frac{m_1m_2}{F}}\]

Answer 5

how do i know what to plug in?
like, which number is matched to which variable.
like, what number does g= , m1= , m2= , & f= ? @doc.brown

Answer 6

The stuffy answer is:
Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

Answer 7

\(F\) means force, in this case force due to gravity.
\(m_1\) and \(m_2\) are the two masses, or man-one and man-two here.
\(r\) is the distance between them, they use \(r\) meaning radius because they figured this stuff out with the movement of the planets.
Gravity is really weak, I mean really really weak. Think about the whole planet pulling on a metal ball. It should be a huge force, but you can overpower a planet worth of force and pick that ball up. SO we scale the force way down by multiplying by 0.0000000000667, which is a constant scalar everywhere in the universe. They call it big G.

Answer 8

so would it be set up \[r=\sqrt9.8 \times \ \frac{ 180 }{ 8.64 }\]

Answer 9

@doc.brown

Answer 10

Close, you're multiplying by little g, the force of gravity on you on the surface of the Earth.
You want big G, the universal constant.\[G=6.67\times 10^{-11}\frac{N\cdot m^2}{kg^2}\]

Answer 11

i dont think i did it right.
I got .95? @Isaiah.Feynman

Answer 12

Use your calculator

Answer 13

i got 8.25/8.64
the simplified to .95? @Isaiah.Feynman

Answer 14

\(m_1\times m_2\)
not +