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StoneMask
Group Title
Please answer this, because I am suffering horrible calculusrelated feelings of self doubt, shattered dreams, and existential dread.
Suppose that 2J of work is needed to stretch a spring from its natural length of 30cm to a length of 42cm.
(a) I've already solved this, and every time someone else has posted both a and b, they only answer a and for some reason ignore that b exists.
(b) How far beyond its natural length will a force of 30N keep the spring stretched?
Hooke's Law: F = kx
k = 138.9
The answer is 10.8cm.
Explain step by step because I feel more stupid the longer I spend on these godforsaken problems. Explain in integral form.
Please.
 one year ago
 one year ago
StoneMask Group Title
Please answer this, because I am suffering horrible calculusrelated feelings of self doubt, shattered dreams, and existential dread. Suppose that 2J of work is needed to stretch a spring from its natural length of 30cm to a length of 42cm. (a) I've already solved this, and every time someone else has posted both a and b, they only answer a and for some reason ignore that b exists. (b) How far beyond its natural length will a force of 30N keep the spring stretched? Hooke's Law: F = kx k = 138.9 The answer is 10.8cm. Explain step by step because I feel more stupid the longer I spend on these godforsaken problems. Explain in integral form. Please.
 one year ago
 one year ago

This Question is Closed

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
whats question a?
 one year ago

StoneMask Group TitleBest ResponseYou've already chosen the best response.0
(a) How much work is needed to stretch the spring from 35cm to 40cm? I am only posting this for you in the hopes it will give you useful information. I have already solved this problem, so if you try to tell me its answer, there isn't a point and it will only depress me further.
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
isnt it just \(F=kx\) for part b ?
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
you use hookes law for b
 one year ago

StoneMask Group TitleBest ResponseYou've already chosen the best response.0
Can you work that out for me, because I've tried working that out, checking it against W = Fd, etc. etc. and I keep getting the wrong answer. Oh yeah, and the answer to part b is 10.8cm. Doing what you said gives me .22
 one year ago

StoneMask Group TitleBest ResponseYou've already chosen the best response.0
F = kx; 30 = 138.9x; x = .2159(...) So I thought hey, maybe I plug it into b for the integral from a to b. \[W = \int\limits_{a}^{b} f(x)dx\] to get\[\int\limits_{0}^{.22} 138.9(x)dx\] but it came out as 3.239740821 when I integrated it. I also tried finding W = Fd in comparison to F = kx. W/d = 30; .2159(...) = x. I can't compare them at all. It's useless.
 one year ago

StoneMask Group TitleBest ResponseYou've already chosen the best response.0
I also tried checking the equation against previous equations in the problem. Nothing works. I can hardly find any examples of this problem on the internet, and the ones I can find don't answer b, as I mentioned. What do I do? what is there to do?
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
are you sure that the answer you got for a is correct?
 one year ago

StoneMask Group TitleBest ResponseYou've already chosen the best response.0
1.04J. If I'm wrong, tell me why. The book says it's 1.04J. So I don't know.
 one year ago

StoneMask Group TitleBest ResponseYou've already chosen the best response.0
a doesn't matter, like I said. It's b that's giving me an existential crisis.
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
because a is related to b; so it does matter
 one year ago

StoneMask Group TitleBest ResponseYou've already chosen the best response.0
They're separate problems. a solves for a variable depending on two limits in a definite integral, so it completely changes the result. It isn't connected to b in any way other than that it uses the spring constant. I'm not aware of a ratio law or anything. Please correct me if I'm wrong. I would literally love to hear why.
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
lol i found that on google as well
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
and i got a retarded answer; that is not the same as the answer given by the asker..
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
http://answers.yahoo.com/question/index?qid=20081015165946AAcZCdL this looks exactly the same; but the answer is different to stonemask answer
 one year ago

okaywhynot Group TitleBest ResponseYou've already chosen the best response.2
\[2=\int\limits\limits_{0}^{0.12}F(x)dx=\int\limits_{0}^{0.12}kxdx=\frac{ k(0.12)^{2} }{ 2 }\] \[k=277.78\] 30=277.78x x=.108m or 10.8cm You had k wrong.
 one year ago

StoneMask Group TitleBest ResponseYou've already chosen the best response.0
How did I get the right answer for a with a wrong k? :( Thank you, also, @okaywhynot. This was a dark time in my life.
 one year ago
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