The bar AB is uniform and has a mass of 50.0 kg. At the moment shown, the rod has an angular velocity of 4.00 rad/s and spring is stretched by 0.30 m. The force constant of the spring is 25.0 N/m.a) Determine whether or not the bar will reach the horizontal position.b) If the bar becomes horizontal, calculate its angular velocity at that position. If not, calculate the angle the bar makes with the horizontal when it comes to rest momentarily. The bar AB is uniform and has a mass of 50.0 kg.At the moment shown, the rod has an angularvelocity of 4.00 rad/s and spring is stretched by0.30 m. The force constant of the spring is 25.0 N/m.a) Determine whether or not the bar will reachthe horizontal position.b) If the bar becomes horizontal, calculate itsangular velocity at that position. If not,calculate the angle the bar makes with thehorizontal when it comes to rest momentarily.Smooth0.6m1.8™BA

Given that, Mass of bar AB = 50 kg Angular velocity of rod = 4 rad/sec Spring is stretched by 0.3 mTotal energy = [Rotational kinetic energy+ Potential energy+ Spring energy] Spring energy = 12kx2where, k = spring constantRotational kinetic energy=12Iw2Potential energy=mghEi(initial energy)=12×ml23w2+mgh+12kx2Ei=12×50×1.82×423+50×9.8×0.9+12(25×0.32)Ei=432+441+1.125Ei=874.125 kJ Let bar AB will be in horizontal direction, From Pythogoras rule, x=1.82+1.8+0.62x=3m Extension of the spring, xf=x-0.6+0.3xf=3-0.3xf=2.7m Ef=12Iw2+12kxf2Ef=12Iw2+1225×2.72Ef=12Iw2+91.125By the law of conservation of energy,Ei=Ef=12Iw2=Ei-91.125w2=874.575-91.12550×1.82×2×3w=5.39 rad/sec

Answered: The bar AB is uniform and has a mass of…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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The bar AB is uniform and has a mass of 50.0 kg.
At the moment shown, the rod has an angular
velocity of 4.00 rad/s and spring is stretched by
0.30 m. The force constant of the spring is 25.0 N/
m.
a) Determine whether or not the bar will reach
the horizontal position.
b) If the bar becomes horizontal, calculate its
angular velocity at that position. If not,
calculate the angle the bar makes with the
horizontal when it comes to rest momentarily.

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