## extension of a spring

hey all, this is my first post, sorry for not introducing myself formally, but i am on a tight schedule, getting ready for my retakes.

my question is;

a 5kg monkey, initially at rest, starts climbing up the weightless rope at 0.2g. the top end of the spring is connected to a spring with k=10N/cm. what will be the extension of the spring? what will it be without the monkey?

i have done the first part of the question as follows;

0.2g + g = 1.2g
F= ma
F=5kg x 1.2g = 60N

F = -kx
x= F/-k
x = 60N/-10N/cm
x = -6cm=6cm

(please correct me if i'm wrong)

the part of the question i'm completely stuck on is the second bit; 'what will it be without the monkey?'

if anybody could point me out in the right direction with this part, it would be great. thank you

 PhysOrg.com science news on PhysOrg.com >> 'Whodunnit' of Irish potato famine solved>> The mammoth's lament: Study shows how cosmic impact sparked devastating climate change>> Curiosity Mars rover drills second rock target

Mentor
Blog Entries: 1
 Quote by procrastin the part of the question i'm completely stuck on is the second bit; 'what will it be without the monkey?'
That's an odd question. Are you sure it didn't say 'what would it be without the monkey climbing?'.

 Quote by Doc Al That's an odd question. Are you sure it didn't say 'what would it be without the monkey climbing?'.
yes i am sure. it may be a typo but i'm not risking not doing it without another opinion

Mentor
Blog Entries: 1

## extension of a spring

Well, without the monkey there would be no extension at all. (We're assuming that the spring is massless, of course.)

 ok i'll solve the question with the assumption that there is a typo. do u know if the previous part of he question i've answered is correct?

Mentor
Blog Entries: 1
 Quote by procrastin do u know if the previous part of he question i've answered is correct?
Yes, it's fine. (But I recommend thinking in terms of forces acting on the monkey, instead of directly in terms of acceleration.)

 do u mean like this; F1=ma=(5kg)(0.2g) F2=mg=(5kg)(g) Ftotal=ma+mg x=Ftotal/-k ?

Mentor
Blog Entries: 1
 Quote by procrastin do u mean like this; F1=ma=(5kg)(0.2g) F2=mg=(5kg)(g) Ftotal=ma+mg x=Ftotal/-k ?
I look at it like this. There are two forces acting on the monkey: the tension pulls up, the weight pulls down:

∑F = ma
T - mg = ma

Thus T = ma + mg.

And the tension is the force that extends the spring, so from Hooke's law: T = kx, or x = T/k.

Same thing, expressed a bit cleaner.

 i understand, thank you for your help <3