SOLUTION: -find the mass and radius of three of the nine planets in our solar system. Be sure that the masses are expressed in kilograms and the radii are expressed in meters. -Using your

Algebra ->  Systems-of-equations -> SOLUTION: -find the mass and radius of three of the nine planets in our solar system. Be sure that the masses are expressed in kilograms and the radii are expressed in meters. -Using your       Log On


   

Question 45147: -find the mass and radius of three of the nine planets in our solar system. Be sure that the masses are expressed in kilograms and the radii are expressed in meters.
-Using your data, calculate the gravitational acceleration on each of the three planets you selected. Note: With the masses measured in kilograms and the radii in meters, the units of gravitational acceleration would turn out to be meters per squared seconds.
-Use the gravitational accelerations that you calculated in Step 2 to find the period of a 2 meter long simple pendulum on each of the three planets. Note: The length of a simple pendulum is normally expressed in meters, so it is sufficient to replace L with the number 2 in the period expression
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
Newton's law of universal gravitation is goverened by the following equation:
F=G%28m%5B1%5Dm%5B2%5D%29%2Fr%5E2
where F is the gravitational force fwelt between the two masses m1 and m2,
r is the distance between the centres of the two objects
G is the universal gravitational constant
let m1 be the mass of the planet and m2 be the mass of an object on the surface of that planet.
Now look at Newton's 2nd law:
F=ma
where "a" is an acceleration. If this is gravitational acceleration, we can call it g.
F=mg
also, we can call the mass m1, then
g=F%2Fm%5B1%5D
If we divide the top equation by m1, we achieve:
g=G%28m%5B2%5D%29%2Fr%5E2
The time period of a simple pendulum is governed by:
T=2%2Api%2Asqrt%28L%2Fg%29
Now substitute in your expression for g:
T=2%2Api%2Asqrt%28%28L%2Ar%5E2%29%2F%28G%2Am%5B2%5D%29%29
put in your values for r,m2,L and G to find the time period of the pendulum on that planet.
Note G=6.673x10^-11.
I hope this helps.
Adam
P.S. please visit my website, I only set it up lastnight and it may be of use to you. The address is http://geocities.com/quibowibbler