Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 40.0s to speed up from rest to its top speed of 1 rotation every 1.40s . The astronaut is strapped into a seat 4.50m from the axis.
What is the astronaut's tangential acceleration during the first 40.0s?
How many g's of acceleration does the astronaut experience when the device is rotating at top speed? Each 9.80 of acceleration is 1 g.
To find the astronaut's tangential acceleration during the first 40.0s, we can use the equation:
tangential acceleration = change in tangential velocity / time
Given that the centrifuge takes 40.0s to speed up from rest to its top speed of 1 rotation every 1.40s, we can calculate the change in tangential velocity.
Change in tangential velocity = top speed - initial velocity
The initial velocity is 0 because the astronaut starts from rest.
Change in tangential velocity = 1 rotation / 1.40s - 0 = 1 rotation / 1.40s
Now, let's convert the rotation to meters since we have the distance of the astronaut from the axis. In one rotation, the astronaut moves a circumference equal to the distance around the axis.
circumference = 2 * π * radius
radius = 4.50m
circumference = 2 * π * 4.50m
circumference ≈ 28.27m
Therefore, in one rotation, the astronaut moves approximately 28.27m.
Now, let's calculate the tangential acceleration:
tangential acceleration = (1 rotation / 1.40s) / (40.0s)
tangential acceleration = (28.27m / 1.40s) / (40.0s)
tangential acceleration ≈ 0.602 m/s^2
So, the astronaut's tangential acceleration during the first 40.0s is approximately 0.602 m/s^2.
To calculate the number of g's of acceleration the astronaut experiences when the device is rotating at top speed, we need to convert the acceleration into g's.
1 g = 9.80 m/s^2
Divide the tangential acceleration by 9.80 m/s^2 to get the acceleration in g's:
acceleration in g's = tangential acceleration / 9.80 m/s^2
acceleration in g's ≈ 0.602 m/s^2 / 9.80 m/s^2
acceleration in g's ≈ 0.0614 g
Therefore, the astronaut experiences approximately 0.0614 g's of acceleration when the device is rotating at top speed.