Chapter 8 Problem 8.45 12 of 21 Constants To get a flat, uniform cylindrical sat
ID: 2034165 • Letter: C
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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Figure1 of 1
End view of cylindrical satelliteExplanation / 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
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