Dr. Evil has captured justin Bleber! (again!) This time, he straps J.B. onto the

Question

Dr. Evil has captured justin Bleber! (again!) This time, he straps J.B. onto the end of his Grav-o-Tron 2, a 15-meter-long pole which rotates about its center, powered by tow rockets. Each rocket exerts a force of 100N, are placed at either end of the pole and is facing perpendicular to the pole so that both are causing a counter clockwise rotation. The force of friction on the Grav-o-Tron is negligible. The Grav-o-Tron 2 has a mass of 50 kg and J.B has of 60 kg. Find the net torque of the two rockets. Find the moment of Inertia of the pole and Justin Bleber, assuming that you can consider J.B. a "point particle". Find the angular acceleration of the system of the pole and Justin Bieber. Dr. Evil's nefarious plan is to kill J.B by the maximum "g-force" that a human body can withstand (in J.B.'s case this is about 5g, where g = 9.81 m/s^2]. Notice that this is really measuring the acceleration on J.B, not the force on him. The g-force has the same value as the centripetal[or radial] acceleration on Justin Bieber. At what (tangential) velocity will this g- force be exceeded? At what time will this g-force be exceeded if the Grav-o-Tron starts at rest?

Explanation / Answer

here,

force , F = 100 N

mass of Grav o ton , m1 = 50 kg

mass of JB , m2 = 60 kg

length of pole , l = 15 m

a)

the net torque of the two rockets , T = 2 * F * l/2

T = 2 * 100 * 15/2

T = 1500 N.m

b)

the moment of inertia , I = (m1 + m2) * (l/2)^2

I = ( 50 + 60) * ( 15/2)^2

I = 6187.5 kg.m^2

c)

let the angular accelration be alpha

I * alpha = T

6187.5 * alpha = 1500

alpha = 0.24 rad/s^2

d)

let the maximum speed be v

centripital accelration = 5 * g = v^2 /( l/2)

5 *9.8 = v^2 /( 7.5)

v = 19.2 m/s

the maximum speed is 19.2 m/s

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