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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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