Question

The National Aeronautics and Space Administration (NASA) studies the 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 sits. The other end of the arm is connected to an axis about which the arm and chamber can be rotated. The astronaut moves on a circular path, much like a model airplane flying in a circle on a guideline. The chamber is located 14.0 m from the center of the circle. At what speed must the chamber move so that an astronaut is subjected to 4.72 times the acceleration due to gravity? _____________________ m/s

Answer 1

Answer:

$v=25.46m/s$

Explanation:

The equation for centripetal acceleration of an object that moves in a circle of radius r at velocity v is:

$a_{cp}=\frac{v^2}{r}$

So we can write this velocity as $v=\sqrt{a_{cp}r}$

Our chamber is r=14m from the center of the trajectory, and we want our centripetal acceleration to be 4.72g, where g is $9.81m/s^2$, so with these values we have:

$v=\sqrt{4.72gr}=\sqrt{4.72(9.81m/s^2)(14m)}=25.46m/s$