Question

PLEASE help! I am so desperate LOL

1: A 75.0 kg astronaut is training for accelerations that he will experience upon reentry. He is placed in a centrifuge (r = 20.0 m) and spun at a constant angular velocity of 15.0 rpm (revolutions per minute). He is then slowed and brought to a stop in 2.0 minutes.
(1a) Find the magnitude and direction of the centripetal acceleration and force when he is spinning at constant angular velocity.

(2a) How many g’s is the astronaut experiencing when moving at constant angular velocity?

(3a) Find the torque that is needed to bring the centrifuge to a stop knowing the centrifuge has a mass of 5500.0 kg (ignore all other forces) and the force is applied at the edge of the centrifuge (20.0 m radius). Hint: torque is based on the change of linear velocity.

2: An astronaut lands on an alien planet. He places a pendulum (L = 0.200 m) on the surface and sets it in simple harmonic motion, as shown in this graph.

(2a) What is the period and frequency of the pendulum’s motion?

(2b) How many seconds out of phase with the displacements shown would graphs of the velocity and acceleration be?

(2c) What is the acceleration due to gravity on the surface of the planet in m/s2? Determine the number of g-forces.

Answer 1

1a) The magnitude and direction of the centripetal acceleration can be found using the formula a = ω²r. 1b) The centripetal force can be found using the formula F = ma. 2a) To find the number of g's the astronaut is experiencing, we can divide the centripetal acceleration by the acceleration due to gravity.

Step-by-step explanation:

1a)

The magnitude of the centripetal acceleration can be found using the formula a = ω²r, where ω is the angular velocity and r is the radius. Substituting the given values, we have a = (15.0 rpm)²(20.0 m) = 4500 m/s². The direction of the centripetal acceleration is towards the center of the centrifuge.

1b)

The centripetal force can be found using the formula F = ma, where m is the mass of the astronaut and a is the centripetal acceleration. Substituting the given values, we have F = (75.0 kg)(4500 m/s²) = 337,500 N. The direction of the centripetal force is also towards the center of the centrifuge.

2a)

To find the number of g's the astronaut is experiencing, we can divide the centripetal acceleration by the acceleration due to gravity, which is 9.8 m/s². Therefore, the astronaut is experiencing approximately 4500 m/s² / 9.8 m/s² ≈ 459 g's.