If the collar p is given a constant acceleration a 27g to...

If the collar P is given a constant acceleration $a = 2.7g$ to the right, the pendulum will assume a steady-state deflection $\theta = 39^\circ$. Determine the stiffness $k_T$ of the torsional spring which will allow this to happen. The torsional spring is undeformed when the pendulum is in the vertical position. Set $m = 3.3 \, kg$ and $L = 930 \, mm$. Answer: $k_T = \text{_____} \, Nm/rad$

Transcript

00:01 This question we are given here color so that color p is given given that constant acceleration so is constant acceleration constant acceleration and here a which is equal we are given here that 3 multiple over g to the right here to the right here and the pendulum let us assume that steady state deflection so teta which is equal we are given here at 30 degree let's determine the stiffness here let's determine the stiffness that k k t of the torsional spring which is allowed this happen and torsional spring is und deform it when the pendulum is vertical position so here we can write here can write a body diagram of the pendulum here of that neat moment of the point b here we can write nate moment about point p about point p is zero nate moment around point p is zero now we can clearly here from that we can write suppose the pendulum and here that's suspended we know that this went on this pendulum delta downward goes md acting here ma is acting on that we know that we clearly see that there's stiffness k t here stiffness k t here we have l sine theta and here we have l co so here we can write here right here that net moment so m a while you divided by 2 here we can write cost theta minus we can write m g multibra we can write l divided by 2 sine theta plus we can write m wali blah by a here we can write cost theta minus we can write m d l s sin theta minus we can write k t by theta which is equal to 0 here we can write theta which is equal to 30 degree theta which is equal to 30 degree and we know that theta which is equal to 30 degree where we can write pi divided by 180 we just simplify and we can write pi divide 6 radian we can write k t multiplicity molecule by theta so here we we can write ktties by by , which is equal to we can write 3 divided by 2 here we can write m a multiple by l multiply by can write four which is equal we can write 3 divided by 2 here we can write m g l multiple by sine theeta and we know that a which is equal to 3 multiplied by g and now we just substitute value so here we can write k t which is equal to 60 by pi and here we can write 3 divided by 2 m g l multiple we can write 3 koss theta minus we can write sin theta now again we just simplify and we can write here answer is 90 whatever 2 pi here we have m g l multiple we can write 3 multiple costeta minus sine theta again we just simplify and because we know that theta value we are given here is 30 degree theta is 30 degree we are substituting and we just simplify and we can write here answer is 3 multiple by and mdr.

03:44 So this is the final answer...

Question

Please give Ace some feedback