Hookes Law and Spring Constant: Explaining the Integral

In summary, the conversation is about the use of the spring constant "k" and Hookes law in calculating the potential energy, U, of a spring. The person is confused about the presence of the ^2 in the formula and is asking for clarification. Another person explains that the ^2 comes from calculating the area of a triangle and provides a visual demonstration. They also clarify that the function for force, F, is equal to kx and the primitive function for kx is (kx^2)/2, which can be used to calculate the integral.
  • #1
Alec
25
0
Hello, I'm having some problems with the spring constant "k" together with Hookes law. U=1\2kx^2

Could someone please explain how you get that integral?
If you insert it in a diagram and calculate the area as a triangle you would get 1/2kx. Where does the ^2 come from?
 
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  • #2
No, you don't!
Draw the triangle again.
How long is its base, and how long is its height?
 
  • #3
Alright, my bad :rolleyes: I missed that it's (kx * x)/2
Now, another question.
The function for F = kx.
The primitiv function for kx = (kx^2)/2 right? Because then you could calculate it as an integral?
 

What is Hooke's Law?

Hooke's Law is a physical principle that states the force required to extend or compress a spring is directly proportional to the distance it is stretched or compressed. This relationship is represented by the equation F = -kx, where F is the force, k is the spring constant, and x is the displacement.

What is the spring constant?

The spring constant, also known as the force constant, is a measure of the stiffness of a spring. It is represented by the letter k and is measured in units of newtons per meter (N/m). A higher spring constant indicates a stiffer spring, meaning it requires more force to stretch or compress it.

How is Hooke's Law related to the integral?

The integral is used to calculate the work done by a variable force, such as the force required to stretch or compress a spring. In the context of Hooke's Law, the integral of the force-displacement equation (F = -kx) is used to calculate the potential energy stored in a spring.

What is the significance of the negative sign in Hooke's Law equation?

The negative sign in the equation F = -kx indicates that the force and displacement are in opposite directions. This means that when the spring is stretched, the force is directed towards the equilibrium position, and when the spring is compressed, the force is directed away from the equilibrium position. This is known as the restoring force, as the spring always wants to return to its equilibrium state.

How can Hooke's Law be applied in real-life situations?

Hooke's Law has various applications in everyday life, such as in car suspension systems, door hinges, and pogo sticks. It is also used in engineering and construction to determine the appropriate size and strength of springs in various structures and machines.

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