To find the speed at which the chamber must move, we can use the equation for centripetal acceleration:
a = (v^2) / r
Where:
a = acceleration
v = velocity
r = radius
We are given that the acceleration must be 4.45 times the acceleration due to gravity, which we can denote as g.
Therefore, a = 4.45g
We know the radius of the circle is 16.0 m.
Plugging in the values, we have:
4.45g = (v^2) / 16.0
To solve for v, we can rearrange the equation:
v^2 = 4.45g * 16.0
v^2 = 71.2g
Taking the square root of both sides, we get:
v = sqrt(71.2g)
Substituting the value of g as approximately 9.8 m/s^2, we can calculate the speed:
v = sqrt(71.2 * 9.8)
v ≈ sqrt(697.76)
v ≈ 26.43 m/s
Therefore, the chamber must move at approximately 26.43 m/s in order for the astronaut to be subjected to 4.45 times the acceleration due to gravity.
The national Aeronautics and Space administration (NASA) studies physiological effects of large accelerations on astronauts. Some of these studies use a machine known as a centrifuge. This machine consists of a long arm, to one end of which is attached a chamber in which the astronaut moves on a circular path, much like a model airplane flying in a circle on a guideline. The chamber is located 16.0 m from the center of the center of the circle. At what speed must the chamber move so that an astronaut is subjected to 4.45 times the acceleration due gravity?
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