I need help with number 10 please. Ans: slowing down since and have opposite sig

Question

I need help with number 10 please.
Ans: slowing down since and have opposite signs (c) At what time will the grindstone momentarily stop? Ans: 13s (d) After how much time will the grindstone have rotated five revolutions? Ans: 32s 10. Astronauts undergo "high g" training in a centrifuge where they can be subjected to forces up to 11 times their body weight. They sit in a pod that is attached to a long metallic arm 15.0m in radius and spun around in a circle at a high speed. (a) At what constant angular velocity must an astronaut be spun to be subjected to a radial acceleration that is 11 times that of gravity? Give answer in rad's and rev/min Ans: 2.68 rad/s, 26 rev/min (b) For your answer in part(a), the angular velocity is constant. Since “ linear acceleration" consists of two components "radial" and " tangential". Explain why the linear acceleration in the situation is all radial Ans: a)= constant =0 a, = 0 since a,= r (c) What is the linear speed of the astronaut under these condition of part (a) Ans: 40m/s (d) Assume in a given run of the centrifuge, the astronaut accelerates uniformly from rest to the angular velocity computed in part(a) in 120s. What is the tangential acceleration? Give your answer in m Ans: 0.33 m/ 11. An astronaut undergoes a centrifuge experiment. He sits in a pod that is attached to a long metallic arn 15.0m in radius and spun around in a circle at a high speed. At time Os the pod is at rest and the pod then xperiences a constant angular acceleration of 0.045a rad

Explanation / Answer

10)

centriptala cceleration a = r*w^2

r = distance from central axis to astronaut = 15 m

a = 1.1*9.8

1.1*9.8 = 1.5*w^2

w = 2.68 rad/s^2

2pi rad = 1 revolution

1 rad = (1/(2pi)) revolution

1 min = 60 s

1s = (1/60)min

w = 2.68 rad/s = 2.68*(1/(2pi)) *60 rev/min

w = 26 rev /min

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(b)

linear acceleration a = sqrt(atan^2 + arad^2)

arad = r*w^2

atan = r*alpha

alpha = angular acceleration = dw/dt

since w (angular speed) is constant

dw = 0

atan = 0

linear acceleration = arad

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(c)

linear speed v = r*w = 15*2.68 = 40 m/s^2

=================

(d)

tagential acceleration atan = r*alpha

alpha = (wf - wi)/t = (2.68 - 0)/120 = 0.0223 rad/s^2

atan = r*alpha = 15*0.0223 = 0.33 m/s^2

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