Compute the mass of the marble?

[Max CR]

Homework Statement

The gravitational attraction between a 20 kg cannonball and a marble separated center to center by 30 cm is 1.48 x 10^-10 N. Compute the mass of the marble.

Homework Equations

The Attempt at a Solution

Mc = 20 kg
L = 30 cm = 0.3 m.
Fg = 1.48 x 10^-10 N
Mm = ?

Fg = G x mM/r^2
1.48 x 10^-10 N = 9.8 m/s^2 x 20 kg x m/0.3 m^2=
1.48 x 10^-10 N/2177.78 = 2177.78 m/2177.78 =
6.796 x 10^-14 kg

 

[CompuChip]

Fg = G x mM/r^2
1.48 x 10^-10 N = 9.8 m/s^2 x 20 kg x m/0.3 m^2

I almost agree up to there. Two questions: what are you squaring when you write 9.8 m/s^2 and 0.3 m^2? And what is G in that formula?

The rest of your post is just numerics, of which I can only guess what they came from. Can you be more specific as to what you did? For example, first do the calculation with the variables only and plug in the value only later, or at least indicate your steps (now we calculate ... = 2177.78, and plug it into ...)

Just from my intuition, I would say 10^(-14) kg is a bit light for a ball of marble.

 

[Max CR]

G in that formula is gravity. Gravity is measured as 9.8 m/s^2. THanks! I know hte answer but I need to know how to get to it.

 

[CompuChip]

G in that formula is gravity. Gravity is measured as 9.8 m/s^2.

Not quite. What we measure is g = G M_\mathrm{earth} / r_\mathrm{earth}^2 \approx 9.81 m/s^2. G is the gravitational constant which is quite something else (check your textbook).

THanks! I know hte answer but I need to know how to get to it.

So you don't know the answer
Once you have found the correct value of G, please try carefully writing down the formula (brackets!), indicating your steps (21777 doesn't mean anything to me) and check your units (m/s^2 * kg^2 / m^2 is not N).

 

[Max CR]

Ok I see now. So I ahve this so far and am getting the wrong answer.

Fg = G x mM/r^2

1.48 x 10^-10 N = 6.6726 m/s^2 x 20 kg x m/(0.3m)^2

1.48 x 10^-10 N/1482.8 m. = 1482.8 m./1482.8 m. =

9.98 x 10^-14 kg

This is not correct. What did I do?

 

[CompuChip]

The 6.6726... part is correct (rounded) but you are still missing a 10^{-11}, also the unit is not m/s^2 but m^3 / (kg s^2).

See http://www.google.nl/search?q=G

 

[Max CR]

Ok. I get it now thanks!

 

[CompuChip]

Good

Please remember to be careful about your quantities (people don't (just) drag along the units in their calculations because it's so much fun ) and to write clearly (for example, between the second and third step write something like: "I calculate 6.6726 m/s^2 x 20 kg /(0.3m)^2 = 1.48 x 10^-10 / 1482.8 N/m, so ...")