Question

Suppose that 3 J of work is needed to stretch a spring from its natural length of 24 cm to a length of 38 cm.
(a) How much work is needed to stretch the spring from 28 cm to 33 cm? (Round your answer to two decimal places) <-- got 65/98=0.66 J, incorrect
(b) How far beyond its natural length will a force of 40 N keep the spring stretched? (Round your answer one decimal place.) <-- got 19.60 cm, incorrect

I will definitely give a medal if somebody can help me find the correct answer. I'll try to type my steps here in a moment

Answer 1

Ok so first I set 3 Joules equal to this integral:

\[\huge 3= \int\limits_{0m}^{0.14m} kx dx\]

Answer 2

if my memmory is ok, F of the spring is kx. \[W=\int\limits_{0}^{14} kx*dx\]

Answer 3

f(x) = kx is Hooke's Law for springs, where k is the spring constant (Newton/meters here)

Answer 4

Oh, forgot to pass cm to m

Answer 5

first you have to find k

Answer 6

I went ahead and subtracted out the differences for the following:
38 cm - 24 cm = 14 cm = 0.14 m
28 cm - 24 cm = 4 cm = 0.04 m
33 cm - 24 cm = 9 cm = 0.09 m

Answer 7

so take it out of the integral: 3=k*0,14
k=3/0,14

Answer 8

I got k = 10000/49 N/m

Answer 9

\[\frac{k(0.14)^2}{2}\]

Answer 10

the lower bound is just 0

Answer 11

so integral\[\int\limits_{0}^{0,14}x dx= 1/2 x ^{2}|_{0}^{0,14}=0,14^{2}/2\]

Answer 12

(3*2)/0.0196 = 306.122

ack originally I had (2*2)/(0.0196)

Answer 13

0,0098

Answer 14

\[W = 0,0098\int\limits_{0}^{0,05}xdx\]

Answer 15

ohh sry, not from 0, from 0,04

Answer 16

and to 0,09

Answer 17

0.04 to 0.09, yes

What's your k constant you got?

Answer 18

0,0098

Answer 19

I currently have ~306 N/m

Answer 20

0.0098 N/m seems unreasonably small no?

Answer 21

ya, but we got it right i think

Answer 22

so 0,0098(0,09^2 -0,04^2/2)

Answer 23

0.0098 = ? (/me looks to see where you might have gotten that value from)

Answer 24

Woot I got it! 15000/49 \(\approx\) 306 N/m

This means 0.99 J and 13.1 cm are the answers. I'll give you a medal regardless for being kind enough to try to help :-)

Answer 25

yes, i was wrong k=306,122