Chapter 8 Problem 8.45 12 of 21 Constants To get a flat, uniform cylindrical sat

Question

Chapter 8

Problem 8.45

12 of 21

Constants

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure (Figure 1). Suppose that the satellite has a mass of 3800 kg and a radius of 3.0 m , and that the rockets each add a mass of 250 kg.

Part A

What is the steady force required of each rocket if the satellite is to reach 43 rpm in 7.0 min , starting from rest?

Express your answer to two significant figures and include the appropriate units.

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?

Constants

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure (Figure 1). Suppose that the satellite has a mass of 3800 kg and a radius of 3.0 m , and that the rockets each add a mass of 250 kg.

Part A

What is the steady force required of each rocket if the satellite is to reach 43 rpm in 7.0 min , starting from rest?

Express your answer to two significant figures and include the appropriate units.

F =

SubmitRequest Answer

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Figure

1 of 1

End view of cylindrical satellite

Explanation / Answer

Using torque balance on satellite

T = I*alpha = r*F

F = I*alpha/r

Now

I = moment of inertia of cylinder = 0.5*m*r^2

I = 0.5*3800*3^2 = 17100 kg-m^2

I1 = moment of interia of each rocket = m*r^2 = 250*3^2 = 2250 kg-m^2

Net moment of inertia = I + 4*I1 = 17100 + 4*2250 = 26100 kg-m^2

Now

wf = wi + alpha*t

alpha = (wf - wi)/t

wi = 0 rad/sec

wf = 43 rpm = 43*2*pi/60 = 4.50 rad/sec

t = 7 min = 420 sec

alpha = (4.50 - 0)/420 = 0.0107 rad/sec^2

r = radius of satellite = 3.0 m

So,

Fnet = Inet*alpha/r

Fnet = 26100*0.0107/3 = 93.09

Force on each rocket will be

F = Fnet/4

F = 93.09/4 = 23.27 N

In two significant digits

F = 23 N

Please Upvote. Let me know if you have any doubt.

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