Why Does Hooke's Law Seem Contradictory in Calculating Spring Energy?

In summary, the conversation discusses the discrepancy between the equations mg=(1/2)*x*k and F=mg=kx, both of which relate to energy and Hooke's law. The speaker asks for clarification on why these equations seem to contradict each other. The conversation also mentions using energy considerations to determine the change in x of the weight, and emphasizes the importance of following a specific procedure in order to do so accurately. The expert suggests that the discrepancy may be due to the force not being constant, and asks if the speaker is familiar with differential calculus.
  • #1
tallwallyb
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Homework Statement
Given a vertical spring with spring constant k=53N/m, a 2.5kg weight is hung from it. What is the change in x of the weight. (USE HOOKE'S LAW and compare it to using ENERGY.
Relevant Equations
F = kx
PEs = (1/2)kx^2
PEg = (mgh)
On the energy part, I keep getting mg=(1/2)*x*k, which is contradictory to Hooke's law F=mg=kx. What is going on?
 
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  • #2
Please show how you applied energy considerations. Suppose you were given the spring and mass and you wanted to measure "the change in x of the weight." What procedure will you follow to do that? That procedure is important because it will inform your use of energy considerations.
 
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  • #3
tallwallyb said:
On the energy part, I keep getting mg=(1/2)*x*k, which is contradictory to Hooke's law F=mg=kx. What is going on?
I'm guessing you divided E by x expecting to get F. But the equation energy = force x displacement only works if the force is constant.
Are you familiar with differential calculus?
 
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1. What is the difference between force and energy in relation to springs?

Force is a physical quantity that describes the push or pull on an object, while energy is the ability of an object to do work. In the context of springs, force refers to the amount of tension or compression applied to the spring, while energy refers to the potential or kinetic energy stored within the spring.

2. How does the force applied to a spring affect its energy?

The force applied to a spring directly affects its energy. When a force is applied to a spring, it causes the spring to compress or stretch, storing potential energy. The more force applied, the more the spring will compress or stretch, resulting in a higher potential energy.

3. Can a spring have both potential and kinetic energy?

Yes, a spring can have both potential and kinetic energy. When a spring is compressed or stretched, it has potential energy. When the spring is released, it converts this potential energy into kinetic energy as it returns to its original shape.

4. How does the spring constant affect the force and energy of a spring?

The spring constant, also known as the stiffness of the spring, determines how much force is needed to stretch or compress a spring by a certain distance. A higher spring constant means that more force is required to stretch or compress the spring, resulting in a higher potential energy.

5. What factors can affect the force and energy of a spring?

The force and energy of a spring can be affected by various factors, including the material and shape of the spring, the amount of force applied, and the environment in which the spring is used. Additionally, the temperature and age of the spring can also impact its force and energy.

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