A person inside a rotating space station of radius 100 meters experiences artificial gravity. Calculate the person's weight on the inner surface of the station if the station rotates at 2 revolutions per minute.
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To calculate the person's weight on the inner surface of the station, we can use the equation for centripetal acceleration:
a = (v^2) / r
Where:
a = centripetal acceleration
v = tangential velocity
r = radius
First, we need to find the tangential velocity of the person inside the rotating space station. The tangential velocity is given by:
v = (2πr) / T
Where:
v = tangential velocity
π = pi (approximately 3.14159)
r = radius
T = time for one revolution (in seconds)
Given that the space station rotates at 2 revolutions per minute, T can be calculated as:
T = (1 minute) / (2 revolutions/minute) = 0.5 minutes/revolution = 30 seconds/revolution
Now we can calculate the tangential velocity:
v = (2π * 100m) / (30s) = (200π m) / (30s)
Next, we can calculate the centripetal acceleration:
a = [(200π m) / (30s)]^2 / 100m = [(40000π^2) m^2/s^2] / 100m = 400π^2 m/s^2
Finally, we can calculate the person's weight using Newton's second law of motion:
F = m * a
Where:
F = force (weight)
m = mass of the person
a = centripetal acceleration
Since the acceleration due to gravity is typically denoted as "g," we can calculate the person's weight as:
F = m * g
m * g = m * a
So, the person's weight on the inner surface of the station is:
Weight = m * a = m * 400π^2 m/s^2
Note: We can't provide an exact numerical value for the person's weight without knowing the mass of the person. But with this equation, you can calculate it once the mass is provided.
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