Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The

Question

Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 30 s to speed up from rest to its top speed of 1 rotation every 1.3 s. The astronaut is strapped into a seat 6.0 m from the axis. (a) What is the astronaut's tangential acceleration during the first 30 s? (b) How many g's of acceleration does the astronaut experience when the device is rotating at top speed? Each 9.8 m/s^2 of acceleration is 1 g. A 75 kg steel file cabinet is in the back of a dump truck. The truck's bed is slowly tilted with angle theta. The coefficient of static friction mu_s between the cabinet and the truck's bed is 0.50, and the coefficient of static friction mu_k is 0.30. (a) Suppose the cabinet is not moving at first. Draw a free body diagram isolating the cabinet and clearly demonstrate the direction of the forces applied on the cabinet. (b) What is the value of theta at which the cabinet begins to slide? (c) What is the magnitude of the frictional force on the cabinet if theta = 30 degree? (d) What is the magnitude of the acceleration of the cabinet when theta = 30 degree?

Explanation / Answer

part a:

tangential acceleration=change in tangential speed/time

=((1/1.3)-0)/30 rotations per sec^2

=0.16111 rad/s^2

part b:

top speed=1/1.3 rotations per second

=4.8322 rad/s

then acceleration =angular speed^2*radius

=4.8322^2*6=140.16 m/s^2

=14.3 g

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