A planetary space probe is in the shape of a cylinder. To protect it from heat o

Question

A planetary space probe is in the shape of a cylinder. To protect it from heat on one side (from the Sun's rays), operators on the Earth put it into a "barbecue mode," that is, they set it rotating about its long axis. To do this, they fire four small rockets mounted tangentially as shown in the figure (Figure 1) (the probe is shown coming toward you). The object is to get the probe to rotate completely once every 20.0s , starting from no rotation at all. They wish to do this by firing all four rockets for a certain length of time. Each rocket can exert a thrust of 70.0N . Assume the probe is a uniform solid cylinder with a radius of 2.50m and a mass of 2000kg and neglect the mass of each rocket engine.

Determine the amount of time the rockets need to be fired.

Explanation / Answer

The linear speed is

vf = 2 pir/ T = 2 pi ( 2.50 m)/20 s = 0.785 m/s

angular speed i s

wf= vf/r = 0.785 m/s/ 2.5 m= 0.314 rad/s

The relation between torque and angular accleration is

T = I alpha

4 ( F r) = I alpha

4 ( Fr) = (1/2) mr^2 alpha

4 (70 N) ( 2.5 m) = ( 1/2) ( 2000 kg) ( 2.5 m)^2 alpha

alpha = 0.112 rad/s^2

From the rortational kinematic eqaution

wf = wi + alpha (t)

0.314 rad/s = 0 + ( 0.112 rad/s^2) t

t = 2.8 s

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