Expert: Paul Klarreich - 1/28/2008

Question
my first online question lol, here goes, Suppose that 2J of work is needed to
stretch a spring from its natural length of 30cm to a length of 42cm
a) how much work is needed to stretch the spring from 35cm to 40cm?
b) how far beyond its natural length will a force of 30N keep the spring
stretched?

answer: a)1.04J  b)10.8cm

please show me how these answers are obtained im so lost, thx

Answer
Questioner:   Alan
Category:  Calculus
Private:  No
 
Subject:  Work Applied on Spring
Question:  my first online question lol, here goes, Suppose that 2J of work is needed to
stretch a spring from its natural length of 30cm to a length of 42cm
a) how much work is needed to stretch the spring from 35cm to 40cm?
b) how far beyond its natural length will a force of 30N keep the spring
stretched?

answer: a)1.04J  b)10.8cm

please show me how these answers are obtained im so lost, thx
...........................
Hi, Alan,

Sorry, but you may have to supply some information regarding the units, etc.  that relate Force and Work.  You will use these ideas, which involve too much investigation for me at this stage of life:

For the spring:

F = kd, where d is the displacement.
W = Fd, so

W = kd^2

Now W = 2 when d = 12, so you can substitute.

2 = k(12)^2

2 = 144 k

k = 1/72.

Now for your (a), I think you might do:

W(40) = kd^2 with d = 10.

W(40) = 100(1/72)

W(35) = kd^2 with d = 5:

W(40) = 25(1/72)

W(35 to 40) = W(40) - W(35) = 75/72.  (Is that your 1.09?)


b) how far beyond its natural length will a force of 30N keep the spring
stretched?
If we use our k = 72, then

F = kd  and

30 = (1/72)d

Now we are in a little trouble, so I will have to leave that to you.