Question

how can we estimate the gravitational force of attraction between two people sitting side by side on a bench? How does this force compare with gravitational force exerted on each of them by the earth(weight)?

Answer 1

I suppose you could "estimate" it by taking the product of their two masses, and about 7*10^-5...?

\[\Large \begin{array}{l}
g = G\frac{{{m_1}{m_2}}}{{{r^2}}}\\
= 6.673 \times {10^{ - 11}} \cdot \frac{{{m_1}{m_2}}}{{{r^2}}}\\
{m_1} = {m_2} = 60{\rm{kg}}\\
r = 0.01{\rm{m}}\\
{r^2} = 0.000001{\rm{m}}\\
6.673 \times {10^{ - 11}} \times \frac{{3600}}{{0.000001}}\\
= 6.673 \times {10^{ - 11}} \times 3600000000 = 0.240228\\
3600 \cdot 7 \times {10^{ - 5}} = 0.252
\end{array}\]

Answer 2

But to be honest I think this is a pretty askew question =)

Answer 3

This is a common question in "physics 101". Teachers like to get across the idea that gravitational forces exist between all things having mass, albeit these forces are usually negligible.

Answer 4

Oh yes, I was referring to the asking to "estimate" the attraction. Unless by "estimate" they mean actually work it out to the best of your abilities, since this is in itself an estimation at best.

Answer 5

(One small thing. In the formula fsm has written above, he starts with g = .... It should be the force, F = .... )

Answer 6

the answers i have to it is
10^-6N
is there anyway to find that out?

Answer 7

You'll need to set the radius and mass of the two people. This data isn't given, so a precise answer cannot be found.

Answer 8

but how do we estimate this value?

Answer 9

But the distance used in the calculation above isn't perhaps the best approximation. The distance between their center of masses is likely to be closer to 1 m than 0.01 m.

Answer 10

and the weight is greater by a factor of 10^9 ?
what value of masses should we estimate? 50-80kg?

Answer 11

Sure. 70 kg is as good as any other point estimate.

As has been pointed out above, the purpose of the exercise isn't the precise number, but showing it is so much less than the gravitational force of the earth.

Answer 12

Haha yeah, everything about my example was a bit awful. Apologies.