In order to balance the stick on the pivot, the total "moments" must be equal on both sides. A "moment" is (a weight) x (its distance from the center).
for the 5N weight: Moment = (5N) x (3 cm) = 15 N-cm
for the 12N weight: Moment = (12N) x (5 cm) = 60 N-cm
Sum of the moments trying to pull the stick down on that side = 75 N-cm
Whatever we hang on the other side has to provide a moment of 75 N-cm in the other direction. We have a 25N weight. Where should we hang it ?
(25N) x (distance from the pivot) = 75 N-cm
Distance from the pivot = (75 N-cm) / (25 N)
<em>Distance from the pivot = 3 cm </em>
To convert km to AU, we divide 225,000,000 km by the factor of 1.5 x 10^8 = 150,000,000 km. This gives us 225,000,000 / 150,000,000 = 1.5 AU. Therefore, the distance between Earth and Mars in AU is 1.5 AU.
The AU is not equivalent to a light-year. A light-year is equivalent to around 9.5 x 10^12 kilometers.
A trace gas is a gas which makes up less than 1% by volume of the Earth's atmosphere, and it includes all gases except nitrogen (78.1%) and oxygen (20.9%). The most abundant trace gas at 0.934% is argon.
We add the values on each of the riders:
300 + 20 + 8
= 328 grams