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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?

## The relationship between $W_{2}$ and $W_{1}$ is given by:$W_{2}=3 W_{1}$

#### Topics

Applications of Integration

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

So what is the relationship between Dublin two of that one? So we're moving this spring by two tires, and each time we have, it's responding. Ward. That's done by moving this spring. But hooks law. The force is always cats, and the work is always integral over the force. And number two is from Ah, 2112 That's 22 and then once from that's one once that's one, too. And we plug in all this value because X 11 is Cyril. That's one, too. It's terrible. One text e X and for double two, that's 21 is 0.1. That's too, too. Is there one? Two? It's the S. So what we have, what we have is okay, comes have about squared. The ratio is close to 0.12 Terrible to over K. Times haven't square from 0 to 0.1. Justify this expression? We have the racial eagles to three, which implies number two. It's three times to people, so three times work

University of Illinois at Urbana-Champaign

#### Topics

Applications of Integration

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp