Complete question:
In the movie The Martian, astronauts travel to Mars in a spaceship called Hermes. This ship has a ring module that rotates around the ship to create “artificial gravity” within the module. Astronauts standing inside the ring module on the outer rim feel like they are standing on the surface of the Earth. (The trailer for this movie shows Hermes at t=2:19 and demonstrates the “artificial gravity” concept between t= 2:19 and t=2:24.)
Analyzing a still frame from the trailer and using the height of the actress to set the scale, you determine that the distance from the center of the ship to the outer rim of the ring module is 11.60 m
What does the rotational speed of the ring module have to be so that an astronaut standing on the outer rim of the ring module feels like they are standing on the surface of the Earth?
Answer:
The rotational speed of the ring module have to be 0.92 rad/s
Explanation:
Given;
the distance from the center of the ship to the outer rim of the ring module r, = 11.60 m
When the astronaut standing on the outer rim of the ring module feels like they are standing on the surface of the Earth, then their centripetal acceleration will be equal to acceleration due to gravity of Earth.
Centripetal acceleration, a = g = 9.8 m/s²
Centripetal acceleration, a = v²/r
But v = ωr
a = g = ω²r
Therefore, the rotational speed of the ring module have to be 0.92 rad/s
Answer:
the required minimum magnitude of the force F is 21 N
Explanation:
Given the data in the question,
m = 5 kg
width = 60 cm
height = 80 cm
Let force is F represent in the image below,
so when the block about to rotate normal shifted to edge of cube
mg(w/2) = Fh
F = mg(w/2) / h
we know that g = 9.8 m/s²
we substitute
F = (5 × 9.8 ( 60/2)) / 70
F = (5 × 9.8 × 30 ) / 70
F = 1470 / 70
F = 21 N
Therefore, the required minimum magnitude of the force F is 21 N
Answer:
The rotational kinetic energy takes 0.430 seconds to become half its initial value.
Explanation:
By the Principle of Energy Conservation and the Work-Energy Theorem we know that flywheel slow down due to the action of non-conservative forces (i.e. friction), the energy losses are equal to the change in the rotational kinetic energy. That is:
(1)
Where:
- Energy losses, measured in joules.
,
- Initial and final rotational kinetic energies, measured in joules.
By definition of rotational kinetic energy, we expand the equation above:
(2)
Where:
- Moment of inertia of the flywheel, measured in kilograms per square meter.
,
- Initial and final angular speed, measured in radians per second.
If we know that ,
and
, then the initial angular speed is:
(3)
(4)
Under the assumption that flywheel is decelerating uniformly, we get that the time taken for the flywheel to slowdown is:
(5)
If we know that ,
and
, then the time needed is:
The rotational kinetic energy takes 0.430 seconds to become half its initial value.