Question

onstants Part A To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure If the satellite has a mass of 4000 kg, a radius of 4.6 m, and the rockets each add a mass of 220 kg, what is the required steady force of each rocket if the satellite is to reach 34 rpm in 5.0 min, starting from rest? (Figure 1) Express your answer using two significant figures Figure 1 of1 End view of cylindrical satellite Submit vio equest Ans we X Incorrect; Try Again; 6 attempts remaining Provide Feedback Next >

Answer 1

We know that torque is given by:

torque = I*alpha

and

torque = rxF = r*F*sin theta

since force is applied at 90 deg to the radius, So sin 90 deg = 1

Now

r*F = I*alpha

F = total force required = I*alpha/r

I = moment of inertia of cylindrical satellite + four engines = 0.5*m*r^2 + 4*M*r^2

m = mass of satellite = 4000kg,

M = mass of rocket = 220 kg

r = radius of satellite = 4.6 m, So

I = 0.5*4000*4.6^2 + 4*220*4.6^2 = 60940.8 kg-m^2

Now Using 1st kinematic equation, to find angular acceleration

w = w0 + alpha*t

alpha = (w - w0)/t

w0 = 0 rad/sec

w = 34 rpm = 34*2*pi/60 = 3.56 rad/sec

t = 5 min = 5*60 = 300 sec

So,

alpha = (3.56 - 0)/300 = 0.0119 rad/sec^2

Now Using above values:

F = I*alpha/r

F = 60940.8*0.0119/4.6

F = 157.65 N

Now since there are four engines, so force exerted by each engine will be

Fnet = F/4 = 157.65/4 = 39.4125 N

Fnet = 39 N (in two sig figures)

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