What is the magnitude of the gravitational force between two 7 kg objects that are separated by 2 m

Guest Nov 14, 2014

#4**+8 **

To see the relationship between G and g, start with the general gravitational force equation as in the previous replies:

F = Gm1m2/r^{2}

Suppose mass 1 is very large compared with mass 2 and that it has a very large radius (like mass1 is the Earth, say, and mass 2 is a ball near the surface of the Earth), so r is effectively just the radius of mass 1.

Then Gm1/r^{2} = g is virtually constant when dealing with objects much smaller than mass1 and near the surface of mass1. The force equation then simplifies to:

F = m2*g

or just F = m*g if we let the mass of the small object be m.

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G is called the gravitational constant, whereas g is the gravitational acceleration.

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Alan
Nov 14, 2014

#1**+8 **

$$\\F=\frac{Gm_1m_2}{r^2}\\\\

F=\frac{9.8*7*7}{2^2}\\\\$$

and I guess the units have to be

$$\frac{m}{s^2}\times\frac{kg^2}{m^2}=kg^2/(ms^2)$$

You can finish it :)

Melody
Nov 14, 2014

#2**+8 **

Right formula, but wrong G Melody!

G = 6.6742*10^{-11} m^{3}/(kg.s^{2})

so:

Force = 6.6742*10^{-11}*7*7/2^{2} N

$${\mathtt{Force}} = {\frac{{\mathtt{6.674\: \!2}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{11}}\right)}{\mathtt{\,\times\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{7}}}{{{\mathtt{2}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{Force}} = {\mathtt{0.000\: \!000\: \!000\: \!817\: \!589\: \!5}}$$

Force ≈ 8.2*10^{-10} N

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Alan
Nov 14, 2014

#4**+8 **

Best Answer

To see the relationship between G and g, start with the general gravitational force equation as in the previous replies:

F = Gm1m2/r^{2}

Suppose mass 1 is very large compared with mass 2 and that it has a very large radius (like mass1 is the Earth, say, and mass 2 is a ball near the surface of the Earth), so r is effectively just the radius of mass 1.

Then Gm1/r^{2} = g is virtually constant when dealing with objects much smaller than mass1 and near the surface of mass1. The force equation then simplifies to:

F = m2*g

or just F = m*g if we let the mass of the small object be m.

.

G is called the gravitational constant, whereas g is the gravitational acceleration.

.

Alan
Nov 14, 2014

#5**0 **

thanks Alan,

I can see how that G is derived when you are talking about Earth and a small object close to the Earth's surface

BUT why is it the same constant when you are talking about two equally sized objects that could be anywhere in the universe?

I don't get it.

Melody
Nov 15, 2014

#6**+5 **

Newton's law of gravitational interaction says that the gravitational force between *any* two objects is proportional to the product of their masses divided by the square of the distance between them. The "G" is just the constant of proportionality, which is a universal constant that has to be determined experimentally.

On the other hand "g" is not a universal constant, in fact, it varies from place to place even on Earth!

(Not sure if this answers your question.)

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Alan
Nov 15, 2014