Kinetic energy of the ball is (mv²) / 2, where m is the mass and v is the velocity
So plugging in the mass and the velocity into the kinetic energy expression, you get:
Kinetic energy of the ball = (mv²) / 2
(0.3125/32) times (132)² divided by 2 = 85 ft-lbs
Kinetic energy of the ball = 85 ft-lbs
For this we want to use Boyle's Law. Boyle’s law states that the pressure and volume of a fixed quantity of a gas are inversely proportional under constant temperature conditions. The formula for this is P1V1 = P2V2. We want to solve this out so it equals V2 (Volume 2). So P1V1 / P2 = V2. Then plug in your values for the variables. So (101)(4.2) / 235 = V2; so 424.2 / 235 = V2. The final volume equals 1.81. I hope this helps, If not I am very sorry.
E S *
The "E" represents Earth, "S" represent Sun, and the "*" represents the nearest star(which is Proxima Centauri).
The main thing to worry about here is units, so ill label everything out.
D'e,s'(Distance between earth and sun) = .<span>00001581 light years
D'e,*'(Distance between earth and Proxima) = </span><span>4.243 light years
Now this is where it gets fun, we need to put all the light years into centimeters.(theres alot)
In one light year, there are </span>9.461 * 10^17 centimeters.(the * in this case means multiplication) or 946,100,000,000,000,000 centimeters.
To convert we multiply the light years we found by the big number.
D'e,s'(Distance between earth and sun) = 1.496 * 10^13 centimeters<span>
D'e,*'(Distance between earth and Proxima) = </span><span>4.014 * 10^18 centimeters
</span>
Now we scale things down, we treat 1.496 * 10^13 centimeters as a SINGLE centimeter, because that's the distance between the earth and the sun. So all we have to do is divide (4.014 * 10^18 ) by (<span>1.496 * 10^13 ).
Why? because that how proportions work.
As a result, you get a mere 268335.7 centimeters.
To put that into perspective, that's only about 1.7 miles
A lot of my numbers came from google, so they are estimations and are not perfect, but its hard to be on really large scales.</span>
