Spring Constant Force Problem Help

[Thana]

Homework Statement

If you apply a greater force, will the spring constant remain the same, increase, or decrease?

Relevant Equations

PEe=1/2kx^2

I'm leaning towards the same, or maybe increase. I actually have no clue.

 

[kuruman]

Homework Statement: If you apply a greater force, will the spring constant remain the same, increase, or decrease?
Relevant Equations: PEe=1/2kx^2

I'm leaning towards the same, or maybe increase. I actually have no clue.

What is your reasoning for that? Say it in your own words.

 

[Thana]

When you increase the force the spring compresses more, so the spring Constant increases? Spring Constant is the resistance.

 

[PeroK]

The term constant in spring constant is a clue!

 

[kuruman]

When you increase the force the spring compresses more, so the spring Constant increases? Spring Constant is the resistance.

Resistance to what? What equation comes to mind that involves the spring constant? What is the definition of each term in this equation?

 

[Thana]

F=-k/x is hooke's law.
force, spring Constant, and displacement. so if we set x=2 and solve for k if force is 2 and 4, the k would be 1 and 2, so it increases?

 

[haruspex]

F=-k/x is hooke's law.

No, F=-kx

so if we set x=2 and solve for k if force is 2 and 4, the k would be 1 and 2, so it increases?

How can the same extension applied to the same spring result in two different forces?

 

[deajohn]

If spring is linear, then F = kx and k is the same, a constant. Greater force gives greater deflection but k is constant and the same, as long as it is a linear spring.

 

[kuruman]

If spring is linear, then F = kx and k is the same, a constant. Greater force gives greater deflection but k is constant and the same, as long as it is a linear spring.

Actually F=-kx. The negative sign is important because it says that the force F is always opposite to the displacement x, i.e. the force is restoring.

 

[Lnewqban]

F=-k/x is hooke's law.
force, spring Constant, and displacement.

The value of the spring constant is found experimentally.
For linear springs, it is a constant of proportionality between force on the spring and its deformation.

Please, see:
https://en.wikipedia.org/wiki/Hooke's_law#Formal_definition

 

[Mister T]

so if we set x=2 and solve for k if force is 2 and 4, the k would be 1 and 2, so it increases?

How can the force change from 2 to 4 if the value of x stays constant? Are you picturing in your mind the spring?

 

[Mister T]

Actually F=-kx

Not if by F you mean the magnitude of ##\vec{F}##. The correct expression is ##F_x=-kx##.

 

[kuruman]

Not if by F you mean the magnitude of ##\vec{F}##. The correct expression is ##F_x=-kx##.

"F" in F = - kx is the symbol standing for a one-dimensional vector and can be positive when x < 0 or negative when x > 0. This convention is also the case in other 1-D equations such as
x = x₀ + v₀ t + ½ a t²
where all the algebraic variables except t represent one-dimensional vectors that can have positive or negative values.

Strictly speaking, you are right. However, it is customary to omit the subscript when vectors are either parallel or antiparallel. In the case of F = - kx, the minus sign locks "antiparallel" in the expression.