What is NOT an example of Reflection
2 answers:
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Answer:
(a) E=0 : 0 cm from the center of the sphere
(b) E= 227.8*10³ N/C : 10.0 cm from the center of the sphere
(c)E= 911.25*10³ N/C : 40.0 cm from the center of the sphere
(d)E= 411.84 * 10³ N/C : 59.5 cm from the center of the sphere
Explanation:
If we have a uniform charge sphere we can use the following formulas to calculate the Electric field due to the charge of the sphere
: Formula (1) To calculate the electric field in the region outside the sphere r ≥ a
:Formula (2) To calculate the electric field in the inner region of the sphere. r ≤ a
Where:
K: coulomb constant
a: sphere radius
Q: Total sphere charge
r : Distance from the center of the sphere to the region where the electric field is calculated
Equivalences
1μC=10⁻⁶C
1cm= 10⁻²m
Data
k= 9*10⁹ N*m²/C²
Q=16.2 μC=16.2 *10⁻⁶C
a= 40 cm = 40*10⁻²m = 0.4m
Problem development
(a)Magnitude of the electric field at 0 cm :
We replace r=0 in the formula (2) , then, E=0
(b) Magnitude of the electric field at 10.0 cm from the center of the sphere
r<a , We apply the Formula (2):
E= 227.8*10³ N/C
(c) Magnitude of the electric field at 40.0 cm from the center of the sphere
r=a, We apply the Formula (1) :
E= 911.25*10³ N/C
(d) Magnitude of the electric field at 59.5 cm from the center of the sphere
r>a , We apply the Formula (1) :
E= 411.84 * 10³ N/C
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