# Spring constant question

#### NoHeart

with no friction- what spring constant would fire a 10 g mass to a height of 100 m. the spring is compressed to 10 cm.

i know k=F/x but i don't know how to find the force for this problem, because i need to find the acceleration and there is no time unit given. any help???

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#### jamesrc

Gold Member
You don't really need to consider the force. What is the potential energy stored in the spring before it is released? What is the potential energy of the mass when it reaches its maximum height? What is the relationship between those two quantities? I hope you see what I'm getting at.

#### marlon

Use conservation of energy. The potential energy of a spring that has been compressed over a distance x is kx²/2

You also know that at the 'end' of the motion, the object must be 100m above the horizontal. This corresponds to a potential energy of mg100 (due to gravity)...

regards
marlon

#### quasar987

Homework Helper
Gold Member
Read the question in terms of energy. What must be the force F=kx such that the work

$$W = \int_{0}^{0.10} kx dx$$

done by it over 10cm is equal to the potential energy associated with an height of 100m above the surface of the earth?

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#### NoHeart

how do i find the potential energy of the spring if i don't know the spring constant?

#### marlon

NoHeart said:
how do i find the potential energy of the spring if i don't know the spring constant?
like i said, the potential energy is kx²/2. You can prove this formula by integrating the force wtr displacement x, but that's not necessary.

You will need this formula to find k...

marlon

#### dextercioby

Homework Helper
U need to know the minimum velocity needed for the body to reach 100 m in a constant gravity field.

Daniel.

#### marlon

dextercioby said:
U need to know the minimum velocity needed for the body to reach 100 m in a constant gravity field.

Daniel.
Nope, that is not necessary...

marlon

Homework Helper
What?

Daniel.

#### marlon

dextercioby said:
What?

Daniel.
You don't need to know the minimal velocity.

marlon

#### NoHeart

thanks so much for the help everyone, i hope i'm understanding now...
so the potential energy of the object when it reaches a height of 100m is mgh, .01kg x 10m/s^2 x 100m=10Nm=10J
is the potential energy of the object equal to the potential energy of the spring? if so, i have 10Nm=(k(1m)^2)/2 and k=20N/m
please tell me i'm at least on the right track...

#### marlon

NoHeart said:
so the potential energy of the object when it reaches a height of 100m is mgh, .01kg x 10m/s^2 x 100m=10Nm=10J
That is correct

is the potential energy of the object equal to the potential energy of the spring?
yes indeed, that's the clue of the story

if so, i have 10Nm=(k(1m)^2)/2 and k=20N/m
please tell me i'm at least on the right track...
Beware, the compression is 10 cm NOT 1m !!!

marlon

#### dextercioby

Homework Helper
Okay,Marlon,gravity field is conservative,so you could use the PE,to kay.

Daniel.

#### NoHeart

thank you so much, marlon. 10cm is .1 m, jeez! at least i know how to do this problem now...