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You cn soe the contect answers after 7-0Q pin "9x10" Nr*/C7 8.054 10 12€?/Nm?10 ptsQueston ?Aspring of length 58 cm and spring constant K 189 N/m i ...

Question

You cn soe the contect answers after 7-0Q pin "9x10" Nr*/C7 8.054 10 12€?/Nm?10 ptsQueston ?Aspring of length 58 cm and spring constant K 189 N/m i $ fixedat one end and has - mass 1.1 kg atuached to Its erd (ree end: The spring cn oscillate on horizontal table without anv Iriction: The spring pulled to the right by 16 cm: and then" released Calculate the kinenic energy the mass when it is at cm from the mean position; and going towrds the Mean posltion Write Your answer in term

You cn soe the contect answers after 7-0Q pin "9x10" Nr*/C7 8.054 10 12€?/Nm? 10 pts Queston ? Aspring of length 58 cm and spring constant K 189 N/m i $ fixedat one end and has - mass 1.1 kg atuached to Its erd (ree end: The spring cn oscillate on horizontal table without anv Iriction: The spring pulled to the right by 16 cm: and then" released Calculate the kinenic energy the mass when it is at cm from the mean position; and going towrds the Mean posltion Write Your answer in terms of joules; Previous Next No new data IO sqve Last checked at 2-13pm Submli 0



Answers

(II) Draw a graph like Fig. 11 for a horizontal spring whose spring constant is 95 $\mathrm{N} / \mathrm{m}$ and which has a mass of 55 $\mathrm{g}$ on the end of it. Assume the spring was started with an initial amplitude of 2.0 $\mathrm{cm} .$ Neglect the mass of the spring and any friction with the horizontal surface. Use your graph to estimate $(a)$ the potential energy, $(b)$ the kinetic energy, and
$(c)$ the speed of the mass, for $x=1.5 \mathrm{cm} .$

So there is an object off and this problem object off mass m and it disconnected by a spring. It is kept like this. Sorry for this. On the let's face, it ties to a fixed support. And then they're saying that this support, which is Jed, just fixed. The object is fixed for the spring and the massive spooled at a distance. So the mass has pulled to some distance and the masses pulled by a distance. It say's stretch initially ex not from this initial position. So it philosophy it back and forth and simple harmonic motion. Obviously, at this point, at this point, the spring will have elastic potential energy, which is maximum half gain or X squared. And this object will come moment, Lee to arrest them for the kinetic energy is going to be zero. So kinetic energy is zero. And the elastic potential energy at this point is this. When it comes to the middle point here, it will have zero elastic pretension and evil. Kinetic energy is going to be half m B square and then it will come to some place here and we'll continue our starting back and forth. So we need to draw the potential energy. So since potential energy is given by half key X squared, sir, it has got a parabolic function. So well, Joy draft for this here like this. So the graph is going to look like this, You know, a parable like function here and this is you affects and on this side is going to be displacement, so they're just resumed. Their disappoint is X not, which is the maximum displacement. So now we can have the object starting from here. And then let's say somewhere in the middle, you know this position will be kinetic energy, and then this will reflect there's potential energy. So the object then released will gain kinetic energy and loose potential energy until it races. They could be in position at this point where it will have maximum kinetic energy and maximum speed. Then it continues to move toward the left. You know, in this election losing can it take energy and gaining potential energy until unless it Lee reached the same point on the left, which is X, not our disposition. And the motion reverses. So it will continue in this austerity motion between exit goes to zero and X equals two extensions in the graph. You know, off the object, the potential energy you versus exits looks like

Okay in this coach and we have to show that the kinetic energy is equal to. Uh huh. one out of six. Am I be scared? And the frequency is given us, frequency is given us who investigate is equal to K. O. Donnell M plus M. Mode of three. Okay myself any lament? We have given us myself in element. They were equal to mm dish which is equal to M. D. By brian and velocity of the limits velocity of element which is V. Dish equal though. Why are we out of and and we know that the kinetic energy kinda take energy can be written as one out of two M dish redish scare. So we can write the kind of take energy are the element do you buy is able to one out of two into M. O. D. Ed the way into y out of it. We scared. And the total energy total energy can be written as can you take energy of the sub drink spring is equal to him. Integration from 0 to 1. The kinetic energy of the element debate. So therefore the kinetic energy of the suffering is equal to Integration from 0 to 1. One of the two sp will put the bolivar kinetic an idea of the element which is mm out of L. D. Buy into. Why out of L. We scared do you buy? So this can be written as Yes I am. And we are constant weekend. Take it out of the uh huh. Into the to L. Cube Integration from 0 to 1. Why scared do you buy? So therefore the kinetic energy of the sibling can be written as one out of six M. We scared. And the total kinetic energy of the system is the some of the kinetic energy of the suffering and the suspended mass which are given this. So the kinetic energy of the total kinetic energy is equal to some off some afghan tick energy of the sitting, which is one out of six a.m. We scared. Plus the suspended mass. Can I take a Nigerian suspended mass, which is one out of two mm. We skate so by taking one out of two common, we can write it M. Plus him out of three into we scare. So the frequency pregnancy omega scale can be written as get out of geo toph M plus M. Out of three.

We know that s net of the net force. It was to minus off K, effective into its on the time period. T equals two to fight RuPaul's Emma Horn gay sector. So is the no missions of the spring are x one on next to then they must satisfy its one plus x two to be able to be 0.200 m. Now, when we consider the Net force at equilibrium that this F net at it really Agrium, that should be equal to zero. So we get cable next one equal to get two extra because the U neh Tik four should be zero. And once spring, the one big K one it will do to growing 00 Newton per meter must be stretched three times. Done. Que two equal do 600 Nugent perimeter because this is too and this is six. So it should be said the spring. But K one should be stretched three times with respect to this. No, the some of the long missions, some of long nations, is it builds to 0.200 m and therefore what happens? One spring stretches 0.150 m on the other stretches 0.50 m. Why, You know thus one should be three times more than this. Yes, three dimes. Therefore, the equilibrium lengths would be oneness 0.350 m on the other oneness. 0.250 m. So these are the equilibrium lengths. So when you moved to this second part of the be part of it, we know that when the block is displaced after distance X to the right, the net force off the locus minus K one. It's one plus X plus kids to X two Minuses! I'm dizzy. Will shoot minus off que one x one minus gave two x two minus. Hey, want plus Kato into its This is the net force. So from the result of Barbie, the tone of the square brackets zero. So this becomes zero Hanks. The net force comes down toe. So what happens so f net will be equal to minus off K one plus Kate to into it. So the effective spring constant that s k effective equal to okay. One last Katie on the beat it Oh, vibration. You know, vibration is given by the formula to buy Good off and my phone effective at 0.100 Katie A one 8.0 Newton barometer and that is equals to 0.702 seconds. So this is the time.


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