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A spring has natural length 20 cm. Compare the work $ W_1 $ done in stretching the spring from 20 cm to 30 cm with the work $ W_2 $ done in stretching it from 30 cm to 40 cm. How are $ W_2 $ and $ W_1 $ related?
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Calculus 2 / BC
Chapter 6
Applications of Integration
Section 4
Work
Campbell University
Oregon State University
Harvey Mudd College
Boston College
Lectures
02:20
A spring with a force cons…
04:19
A spring has a natural len…
02:33
02:39
For the following exercise…
03:01
A force of 10 pounds stret…
02:00
Suppose that 2 J of work i…
04:09
Suppose that 2 $\mathrm{J}…
So what is the relationship between 2 of 1 so we're moving the spring by 2 times and each time we have its corresponding work? That'S done by moving the spring by the hooks law. The force is always k x and the work is always integral over. The force and 2 is from x, 212 x, 22 and the once from x, 112 x 12, and we plug in all this value, because x, 11012 s 0.1, k, x, dx and for double 2 x 21 is .1 and x 22.2. So what we have all we have is k times: half of it, squared the ratio is equals to 0.1 0.2 over k times have squared from 0 to 0.1. So, to simplify this expression, we're going to have the ratio equals to 3, which implies 2 is 3 times so 3 times.
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