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(6 points) Recall, according to Hooke"s law the force required to stretch spring feet beyoud Its natural leugth f(c) spring has natural length of CI and the wo...

Question

(6 points) Recall, according to Hooke"s law the force required to stretch spring feet beyoud Its natural leugth f(c) spring has natural length of CI and the work requiredl to stretch the spring from CMt0 Ct is 0.24 huow: Mluch work required to stretch the spring from cin t0 10 cm?' Don"t forget to do the following Convert to the #ppropriate units_ Tnke into account the Hatutal length_ Include units on your final nnsWUE.

(6 points) Recall, according to Hooke"s law the force required to stretch spring feet beyoud Its natural leugth f(c) spring has natural length of CI and the work requiredl to stretch the spring from CMt0 Ct is 0.24 huow: Mluch work required to stretch the spring from cin t0 10 cm?' Don"t forget to do the following Convert to the #ppropriate units_ Tnke into account the Hatutal length_ Include units on your final nnsWUE.



Answers

In Exercises $3-6,$ compute the work (in joules) required to stretch or compress a spring as indicated, assuming a spring constant of $k=800 \mathrm{Nm}$
Stretching from equilibrium to 12 $\mathrm{cm}$ past equilibrium

7.35. So we have a spring with a spring constant of 65 Newman's per meter. So what we'd like to do is draw a graph of the forest versus distance and then find the work if we take the spring and stretch it from three centimeters from its equilibrium position to six and 1/2 centimeters. So let's start by Sprint sketching the force here. We know that for a spring the forces just directly proportional to the display the amount of stretcher compression by the constant of proportionality is the spring constant. So if we have X one and x two, those are three and six and 1/2 centimeters that our force will be k x one k x to here. And so the work if we have a lot of force versus distance, is the area under that curves. This case the curve is a straight line. So this is a trap is little region and we can compute the area it pretty easily. Um, if we didn't know this, we could, you know, if they weren't in some shape, that's easy. Thio compute. We could, uh, directly integrated, but we don't need to in this case, So we just used the But we know from geometry about areas of trap is oi ds and that will be equal to the work x one. And so then all we need to do now is put in the numbers for this and you want to make sure to, uh, for X one, for example. Needs to be quite 03 meters, uh, so that you get units of jewels. So otherwise you'd have Newton Newton centimeters per meter, and that's that's not really a standard unit of energy. So you don't want to do that. So, being careful about the units, we find that this takes 0.11 jewels of work.

The formula for work is w is equal to that interval from a to B of halfbacks DX were f of X is force. So in this case, we are stretching Hey spring from 5 to 15 centimeters. So are limits and integration is going to be from five. Um hi Sun readers without the 0.5 meters to 0.15 meters and our forces going to be K Times X and kay in this case is 800 will be 800 eggs the ex. So this is going to be equal to 400 x squared the violator from 0.50 point 15 and this is going to be equal to eight. Your boss?

So it is given here F. three x 2 x. Lord and 10" needed to strategy Find the work done in is touching the Spain to Atlanta off 16 age. Right. It's a load is given initial displacement is given and final displacement is Cuban. Lord is three x 2 X. So Lord is proportional to uh displacement. X initial is an inch. That's finalist 16". So how we can solve this problem? So D. W. Or a unit work done. Can we return as ex D. F. Right and be a serious three x 2 works. Either we can write X. DF or also we can write FDX in this case FBX is valid. Mhm So king bed two X and dX. So integrating this you can see this value will be integrated. So ogden will be integration of three x 2 x dx X limited 10 inch to 16 inch mm This is nothing but three x 2. Expire by two. Now put down the values and let's see the answer. It will be three by four which is constant once outside X square X. where 16 spirits to 56 and 10 spares 100. So this is three x 4 into 156. Okay, Final answer is 117 for the part be pregnant in stretching. They're going 16 inch. So now to the for the part of me it is asking stretching this thing 16" which means X final will be for this case then Plus stretching which is 16 which is 2016. This this is vaccination and this is stretched part So for this work done will be formula is Him three by two, sorry, T before X square X final upon X initial. So as a final in this case is 26 initially. Okay, so we get the value 26 Experience six 76- Tennis Paris 100. So answer will be T before into 57 six. This is cancel out. The final answer will be what protected?

We have our formula for work which is integral from a to B ah function of X, the ex where FX is the force. So in this case, we are compressing Ah, a spring from equilibrium to four centimeters past. So which means we're going from zero to negative 0.4 meters and our force is going to be K X and in this case, are chaos 800. So this is going to be 800 eggs, the ex ability. And did your That is going to be 400 x squared and I were balloting from zero to negative 0.4 Though this needs our answer is going to be equal to zero point six or jewels.


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