Mrs. Archer spent her Saturday running a bunch of errands. She started out by
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Artificial gravity is created by rotating the cylinder
So here we can say that the acceleration is due to centripetal acceleration
So here we know that the formula of centripetal acceleration is given by
so here we know that
now we will plug in all values
So above is the radius of the cylinder
Now to find the diameter
so its diameter is 194.8 m
To solve this problem it is necessary to apply the concepts related to the conservation of momentum and conservation of kinetic energy.
By definition kinetic energy is defined as
Where,
m = Mass
v = Velocity
On the other hand we have the conservation of the moment, which for this case would be defined as
Here,
m = Total mass (8Kg at this case)
Mass each part
Initial velocity
Final velocity particle 2
Final velocity particle 1
The initial kinetic energy would be given by,
In the end the energy increased 100J, that is,
By conservation of the moment then,
Replacing we have,
(1)
In the final point the cinematic energy of EACH particle would be given by
(2)
So we have a system of 2x2 equations
Replacing (1) in (2) and solving we have to,
200J=\frac{1}{2}4*(V_1^2+(10-V_1)^2)
PART A:
Then replacing in (1) we have that
PART B: