Spring constant question

In summary, the conversation discusses using conservation of energy to determine the spring constant needed to fire a 10 g mass to a height of 100 m with no friction. The potential energy of the spring and the mass are compared, and it is determined that they are equal. The formula for potential energy of a spring is mentioned and integrating the force over displacement is suggested to prove it. The conversation also includes a correction for the compression distance and a reminder about the conservative nature of gravity.
  • #1
NoHeart
28
0
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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  • #2
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.
 
  • #3
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
 
  • #4
Read the question in terms of energy. What must be the force F=kx such that the work

[tex]W = \int_{0}^{0.10} kx dx [/tex]

done by it over 10cm is equal to the potential energy associated with an height of 100m above the surface of the earth?
 
Last edited:
  • #5
how do i find the potential energy of the spring if i don't know the spring constant?
 
  • #6
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
 
  • #7
U need to know the minimum velocity needed for the body to reach 100 m in a constant gravity field.

Daniel.
 
  • #8
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
 
  • #10
dextercioby said:
What?

Daniel.

You don't need to know the minimal velocity.

marlon
 
  • #11
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...
 
  • #12
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
 
  • #13
Okay,Marlon,gravity field is conservative,so you could use the PE,too_Okay.

Daniel.
 
  • #14
thank you so much, marlon. 10cm is .1 m, jeez! at least i know how to do this problem now...
 

What is the definition of spring constant?

The spring constant, also known as the force constant, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain distance.

How is spring constant calculated?

The spring constant is calculated by dividing the force applied to the spring by the displacement of the spring from its equilibrium position. Mathematically, it can be expressed as k = F/x, where k is the spring constant, F is the applied force, and x is the displacement.

What is the unit of spring constant?

The unit of spring constant depends on the unit of force and displacement used in the calculation. In the SI system, the unit of spring constant is newton per meter (N/m).

What factors affect the spring constant?

The spring constant is affected by several factors, such as the material and dimensions of the spring, the number of coils, and the temperature. Generally, stiffer materials and longer springs have higher spring constants.

Why is spring constant important in physics?

The spring constant is an important concept in physics because it helps us understand the relationship between force and displacement in a spring. It is also used in various applications, such as designing springs for different purposes and analyzing the behavior of mechanical systems.

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