What is the molar mass of an ideal gas if a 0.800 g sample of this gas occupies a volume of 200. mL at 50.0 oC and 720. mm Hg?
1 answer:
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Answer:
The orbital speed of Dactyl is
Explanation:
The orbital speed can be determined by the combination of the universal law of gravity and Newton's second law:
(1)
Where G is gravitational constant, M is the mass of the asteroid, m is the mass of the moon and r is the distance between them
In the other hand, Newton's second law can be defined as:
(2)
Where m is the mass and a is the acceleration
Then, equation 2 can be replaced in equation 1
(2)
However, a will be the centripetal acceleration since the moon Dactyl describe a circular motion around the asteroid
(3)
(4)
Therefore, v can be isolated from equation 4:
(5)
Finally, the orbital speed can be found from equation 5:
Notice, that it is necessary to express r in units of meters.
⇒
Hence, the orbital speed of Dactyl is
Answer:
The maximum radius the asteroid can have for her to be able to leave it entirely simply by jumping straight up is approximately 1782.45 meters
Explanation:
Whereby the height the astronaut can jump on Earth = 0.500 m, we have the following kinematic equation;
v² = u² - 2·g·h
Where;
v = The final velocity
u = The initial velocity
g = The acceleration due to gravity ≈ 9.8 m/s²
h = The height she jumps
At the maximum height, = 0.500 m, she jumps, v = 0, therefore, we have;
0² = u² - 2·g·
u² = 2 × 9.8 × 0.5 = 9.8
u = √9.8 ≈ 3.13
u = 3.13 m/s
Her initial jumping velocity ≈ 3.13 m/s
Escape velocity,
Where;
M = The mass of the asteroid
G = The Universal gravitational constant = 6.67408 × 10⁻¹¹ m³/(kg·s²)
r = The radius of the asteroid
The average density of the Earth = 5515 kg/m³
The mass of the asteroid, M = Density × Volume = 5515 kg/m³× 4/3 × π × r³
The escape velocity, she has, ≈ 3.13 m/s is therefore;
Therefore, the maximum radius of the asteroid can have for her jumping velocity to be equal to the escape velocity for her to be able to leave it entirely simply by jumping straight up = r ≈ 1782.45 meters.