Question

4. A device used to expose fighter pilots to high g’s that they might experience in action incorporates a small cockpit on the end of a 50 ft. long radial shaft that is attached to the cg. of the cockpit. The cockpit and pilot weigh 600 lb total. If there is a motor that provides a torque of 1000*sqrt(t) ft-lb to the system, calculate the following:
   1. How fast does the cockpit have to travel to produce 6 g’s?
   2. How long does the system take to get to that speed?

Answer 1

The assumptions in this case are

• There are no efffects of wind resistance whatsoever
• The cockpit rotates in a horizontal plane

Given,

• length of rod r = 50 ft
• Requred acceleration f = 6g = 6*32.1 ft/s2 = 192.6 ft/s2

Thus from laws of centrifugal acceleration, we get

So linear velocity is 1.963*50 = 98.15 ft/s

Now it is said that the torque acting is 1000*sqrt(t). Thus from there we can proceed as

[torque is product of force and radius]

[ Force is product of mass and acceleration]

[Given total mass is 600 lb]

[ changing linear acceleration to angular acceleration by dividing by the length of the rod]

Now let us assume that the angular velcoity of the capsule is 0 rad/s at 0 s, and 1.963 rad/s at t seconds. Then using them as integration limits we get

Thus the required angular velocity is 1.963 rad/s, or linear velocity is 98.15 ft/, and the time taken will be 4 minutes and 29 seconds

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