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# A spring has a natural length of 40 cm. If a 60-N force is required to keep the spring compressed 10 cm, how much work is done during this compression? How much work is required to compress the spring to a length of 25 cm?

## $$0.3125 \mathrm{J}$$

#### Topics

Applications of Integration

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

Okay, So first, let's recall the Hooks Law because we're modeling a spring and key here in hopes Love stands for Spring Constant, which is a positive brew number. So by the question, we have K times zero in three months. Her one, too, said That's Theo the start position. Once the immunization it was trying to fly. Then why skaters to fitting so over function will be after that Sequels 2 50 X and for the work for the work recalled that the work equals the force. So the integral lower the force That's the work. And from the starting position A to the ending position B. So here we just apply over the force function and, uh, would plug in two positions. So we're gonna have the work equals two 0 to 01 by two for the X d s. And, uh, that equals to 1 25 x squared from 1 25 0 to 0.5 And that's roughly equals two zero points. Three

University of Illinois at Urbana-Champaign

#### Topics

Applications of Integration

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp