Problem Involving Work Required for Stretching Spring

[chocolatelover]

Hi,

Could someone please help me with this problem?

Homework Statement

A spring has a natural length of 20 cm. If a 25 N force is required to keep it stretched to a length of 30 cm, how much work is required to stretch it from 20 cm to 25 cm?

Homework Equations

w=lim a to b f(x)dx
work=(force)(distance)

The Attempt at a Solution

int. from 0 to 10 kxdx=25N
25=[1/2kx^2]0 to 10
25=1/2k(10)^2
25=50k
k=.5

int. from .05 to .10 (.5)xdx

Could someone please tell me if this is correct so far?

Thank you very much

 

[chaoseverlasting]

No, its not right. You've almost hit it. You know $$F=kx$$ Now, you know 25N force is required to hold it at 30 cm. Plug these values in and find k from here. Be careful about the unit and convert everything to SI before plugging the values in.

The second part asks you to find the work done, you know $$W=\int F(x)dx$$.
This gives you $$W=\frac{1}{2}kx^2$$ Apply the limits as you did, and use the value of k found above, and you have your answer.

 

[chocolatelover]

Thank you very much

Would the limit be from 0 to 10?

Also, I was thinking that maybe I should have used the formulas f/d=k and w=1/2kd^2

Would that also work, since the force isn't constant?

Thank you very much

 

[chocolatelover]

Does this look right?

.30-.20=.10m
f(.10)=25
k=250m

.25-.10=.15
.20-.10=.10

w=int. .10 to .15(250xdx)
=1.56J

Thank you very much