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 need to consider the centripetal acceleration.
The centripetal acceleration can be calculated using the formula:
a = r * ω²
Where:
a = centripetal acceleration
r = radius of the station
ω = angular velocity
In this case, the radius of the station is given as 100 meters, and the station rotates at 2 revolutions per minute. To convert this to angular velocity, we need to multiply it by 2π (since there are 2π radians in a complete revolution) and divide by 60 (since there are 60 seconds in a minute).
ω = (2 revolutions/minute) * (2π radians/revolution) / (60 s/minute)
= (2 * 2π) / 60 radians/s
= 4π / 60 radians/s
Now we can calculate the centripetal acceleration:
a = (100 meters) * (4π / 60 radians/s)²
Simplifying the equation:
a = (100 meters) * (16π² / 3600 radians²/s²)
≈ 1.74 meters/s²
The person's weight on the inner surface of the station is equal to the product of their mass and the centripetal acceleration (assuming no other external forces are acting):
Weight = mass * a
Weight = mass * 1.74 meters/s²
Therefore, to calculate the person's weight, we need to know their mass.
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