Question

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 2800 kg and a radius of 3.0 m , and that the rockets each add a mass of 250 kg.

What is the steady force required of each rocket if the satellite is to reach 30 rpm in 7.0 min , starting from rest?

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

Answer 1

We know that torque is given by:

Torque = F*r = I*alpha

I = moment of inertia of system = 0.5*M*r^2 + 4*m*r^2

M = mass of satellite = 2800 kg

m = mass of each rocket = 250 kg

r = radius = 3 m

So,

I = 0.5*2800*3^2 + 4*250*3^2 = 21600 kg-m^2

alpha = angular acceleration = dw/dt

alpha = 30 rpm/7.0 min

30 rpm = 30rev/min*(2*pi*rad/1 rev)*(1 min/60 sec) = 3.14 rad/sec

7 min = 420 sec

So,

alpha = 3.14/420 = 7.48*10^-3 rad/sec^2

Now

Fnet*r = I*alpha

Fnet = I*alpha/r

Fnet = 21600*7.48*10^-3/3

Fnet = 53.86 N = force on all rockets

Force on each rocket = Fnet/4 = 53.86/4

Force on each rocket = 13.46 N = 13 N (In two significant figures)

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