Can the Total Energy in a Spring Be Rearranged?

• JustinLiang
In summary, the conversation discusses rearranging the equation for total energy in a spring and the factors that affect it, such as the maximum force and amplitude. It is mentioned that the equation may be incorrect if the force applied is not equal to the weight of the attached mass.
JustinLiang

Homework Statement

Since the total energy in a spring is
(1/2)kA^2

Can we rearrange this...
given k=F/x
(1/2)(FA^2/x)

Since x is also the amplitude, we have:
(1/2)(FA)
(1/2)(mgA)

I am pretty sure this is wrong, but why?

Thanks

JustinLiang said:

Homework Statement

Since the total energy in a spring is
(1/2)kA^2

Can we rearrange this...
given k=F/x
(1/2)(FA^2/x)

Since x is also the amplitude, we have:
(1/2)(FA)
yes, where F is the max force in the spring and A is the absolute value of x.
(1/2)(mgA)
Only if F = mg, as when a mass is attached from a hanging spring and released.

1. What is total energy in a spring?

Total energy in a spring refers to the potential and kinetic energy that is stored in a spring when it is stretched or compressed. It is the sum of the elastic potential energy and the kinetic energy of the spring.

2. How is total energy in a spring calculated?

The total energy in a spring can be calculated using the formula E = ½kx², where E is the total energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

3. What factors affect the total energy in a spring?

The total energy in a spring is affected by the spring constant (k), the displacement of the spring (x), and the mass of the object attached to the spring. It is also affected by external factors such as friction and air resistance.

4. What is the relationship between total energy and amplitude in a spring?

The total energy in a spring is directly proportional to the square of the amplitude. This means that as the amplitude increases, the total energy in the spring also increases.

5. How does the total energy in a spring change over time?

The total energy in a spring remains constant as long as there are no external forces acting on it. However, as the spring oscillates, the potential energy and kinetic energy exchange with each other, resulting in a constant total energy value.

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