Question
A force of pounds is required to hold a spring stretched 0.3 feet beyond its natural length. How much work (in foot - pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length?
A force of pounds is required to hold a spring stretched 0.3 feet beyond its natural length. How much work (in foot - pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length?
Answers
A force of 10 pounds stretches a spring 2 inches. Find the work done in stretching this spring 3 inches beyond its natural length.
Okay, we're told that the amount of force required to stretch a particular spring S fee is given by force is equal to nine S. Um And that's given in pounds. And we want to determine the work done to stretch it to stretches particular spraying to two ft. Um And so we know that work is given by the integral of the relaxed length of the spring, which we're going to notice zero to the stretch length of two ft of the force, which is nine S. Integrating with respect to us. So this is actually going to be equal to um oops equal to nine over to S squared, evaluated zero and at two. So this is going to be 18 foot pounds of work.
Okay, Someone skin spring prompts. So we'll do f equals K X for Hook's Law. Now that we have that we can determine what are K value is gonna be by plugging in our force and are expecting you. I went ahead and did fraction for the I'm sorry, that should be one of over five. And so we can find that K is gonna equal 500. Just what? High value. But then we go ahead. And just for the sake of giving this to you once again, your work is from A to B k x t X. So then you'll have one half k x squared, going from A to B, and in this case, R K value is gonna be 500 well of one half 500. And then, since the X is the only thing variable, I'm gonna go ahead and put kind of a parentheses from R B squared minus or a C weird. In this case, we're going from 0 to 4/5. So really, this is just gonna be minus zero, then 4/5 squared, which will end up equaling 160
Thanks, please. So how you need to set up the secondary role that this time it's going to go from four inches, which was 1/3 of but to an additional three wishes. That is 1/3 of plus 1/4 because three inches, this one for three inches. Okay. Your account for this one was four inches. This one is the three inches. Great. My gives us seven over people. Nice swim in an integrated. No, it's already stretched that size 27 And we know that cane I was 300 before. We're going to integrate 324. Hey, as you know, 200 for a constancy. Just pull that out. 324 times I'm x squared over Teo evaluated between one over and seven Ord. I don't know how to do this part. Plug in the 1st 1 Minus plugging. The 2nd 1 you're gonna get 304 times one hand. Come on. 49 over. One word for that. Yeah, I think this one over nine 1 37.1 Ah, NCIS. This is work. It's going to be four pounds. Just us. The one that we were given home. Fuck. Hey, I hope that's all. Yeah. Growing
Okay. Recalled the books law that after that six kids and the definition of work devil equals two. That's the ex from Axl. That's cool. Okay, so plug in the data. We have 12 equals to 12 0 to 1 k x. T s. So that gives us cakes, Tony before and we're asking The working man is a stretch. The spring. 29 inches. Be honest, natural wings. And we know that one fetus, 12 inches. So what's nine inches deserve 175 feet. Okay, so the work equals to 0.20 point 75 24 x b s escapes when people here and that equals to 6.75 seat bones.