Kepler's third law hypothesizes that for all the small bodies in orbit around the
same central body, the ratio of (orbital period squared) / (orbital radius cubed)
is the same number.
<u>Moon #1:</u> (1.262 days)² / (2.346 x 10^4 km)³
<u>Moon #2:</u> (orbital period)² / (9.378 x 10^3 km)³
If Kepler knew what he was talking about ... and Newton showed that he did ...
then these two fractions are equal, and may be written as a proportion.
Cross multiply the proportion:
(orbital period)² x (2.346 x 10^4)³ = (1.262 days)² x (9.378 x 10^3)³
Divide each side by (2.346 x 10^4)³:
(Orbital period)² = (1.262 days)² x (9.378 x 10^3 km)³ / (2.346 x 10^4 km)³
= 0.1017 day²
Orbital period = <u>0.319 Earth day</u> = about 7.6 hours.
Hello
This question requires us to deal with the football as a projectile. Therefore, we will assume that the ball is caught at the same height from which it was thrown.
To see how far the ball will travel, we use the formula for the range of a projectile that is:
Range = [(initial velocity)^2 * sin(2*angle to horizontal)]/g
Given that the initial velocity is 16 m/s, the angle to the horizontal is 25 and g is 9.81 m/s^2, R works out to be:
almost 20.0 m
The distance the receiver will have to run will be:
20 - 16.5 = 3.5 m
The time of the ball's flight will be equal to the time the receiver has to get to the ball. The ball's flight time is given by:
time = [2 * (initial velocity) * sin(angle from horizontal)] / g
time = 1.38 seconds
Therefore, the receiver's speed must be:
3.5 / 1.38 = 2.54 m/s
Not sure if this is right but I think it’s TRUE sorry if it’s wrong....
The energy stored in the membrane is ![6.44\cdot 10^{-14} J](https://tex.z-dn.net/?f=6.44%5Ccdot%2010%5E%7B-14%7D%20J)
Explanation:
The capacitance of a parallel-plate capacitor is given by
![C=\frac{k\epsilon_0 A}{d}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7Bk%5Cepsilon_0%20A%7D%7Bd%7D)
where
k is the dielectric constant of the material
is the vacuum permittivity
A is the area of the plates
d is the separation between the plates
For the membrane in this problem, we have
k = 4.6
![A=4.50\cdot 10^{-9} m^2](https://tex.z-dn.net/?f=A%3D4.50%5Ccdot%2010%5E%7B-9%7D%20m%5E2)
![d=8.1\cdot 10^{-9} m](https://tex.z-dn.net/?f=d%3D8.1%5Ccdot%2010%5E%7B-9%7D%20m)
Substituting, we find its capacitance:
![C=\frac{(4.6)(8.85\cdot 10^{-12})(4.50\cdot 10^{-9})}{8.1\cdot 10^{-9}}=2.26\cdot 10^{-11} F](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B%284.6%29%288.85%5Ccdot%2010%5E%7B-12%7D%29%284.50%5Ccdot%2010%5E%7B-9%7D%29%7D%7B8.1%5Ccdot%2010%5E%7B-9%7D%7D%3D2.26%5Ccdot%2010%5E%7B-11%7D%20F)
Now we can find the energy stored: for a capacitor, it is given by
![U=\frac{1}{2}CV^2](https://tex.z-dn.net/?f=U%3D%5Cfrac%7B1%7D%7B2%7DCV%5E2)
where
is the capacitance
is the potential difference
Substituting,
![U=\frac{1}{2}(2.26\cdot 10^{-11} F)(7.55\cdot 10^{-2})^2=6.44\cdot 10^{-14} J](https://tex.z-dn.net/?f=U%3D%5Cfrac%7B1%7D%7B2%7D%282.26%5Ccdot%2010%5E%7B-11%7D%20F%29%287.55%5Ccdot%2010%5E%7B-2%7D%29%5E2%3D6.44%5Ccdot%2010%5E%7B-14%7D%20J)
Learn more about capacitors:
brainly.com/question/10427437
brainly.com/question/8892837
brainly.com/question/9617400
#LearnwithBrainly
M = molar mass of the helium gas = 4.0 g/mol
m = mass of the gas given = 18.0 g
n = number of moles of the gas
number of moles of the gas is given as
n = m/M
n = 18.0/4.0
n = 4.5 moles
P = pressure = 2.00 atm = 2.00 x 101325 Pa = 202650 Pa
V = Volume of balloon = ?
T = temperature = 297 K
R = universal gas constant = 8.314
Using the ideal gas equation
P V = n R T
(202650) V = (4.5) (8.314) (297)
V = 0.055 m³