Derive the expression for the work done by the ideal spring

In summary, the ideal spring is a theoretical model used in physics to describe the behavior of real springs, simplifying calculations and allowing for a better understanding of spring mechanics. The equation for the work done by an ideal spring is W = (1/2)kx^2, where W is the work, k is the spring constant, and x is the displacement from the equilibrium position. The work done by an ideal spring is directly proportional to the spring constant, meaning that as the spring constant increases, so does the work done. The work done by an ideal spring can be negative if the displacement is in the opposite direction of the applied force. Finally, the work done by an ideal spring is equal to the change in potential energy stored
  • #1
Alexanddros81
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4

Homework Statement


Derive the expression for the work done by the ideal spring on the slider when the
slider moves from A to B. Assume that the free length of the spring is (a) ##L_0 = b##;
and (b) ##L_0 = 0.75b##

Fig P14_5_6.png


Homework Equations

The Attempt at a Solution


Pytels_Dynamics100.jpg


Can you check if my solution is correct?
 

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  • #2
Looks reasonable.
 

1. What is the ideal spring and why is it important?

The ideal spring is a theoretical model used in physics to describe the behavior of real springs. It is important because it simplifies calculations and allows us to understand the fundamental principles of spring mechanics.

2. What is the equation for the work done by an ideal spring?

The equation for the work done by an ideal spring is W = (1/2)kx^2, where W is the work, k is the spring constant, and x is the displacement from the equilibrium position.

3. How is the work done by an ideal spring related to the spring constant?

The work done by an ideal spring is directly proportional to the spring constant. This means that as the spring constant increases, the amount of work done also increases.

4. Can the work done by an ideal spring be negative?

Yes, the work done by an ideal spring can be negative if the displacement is in the opposite direction of the force applied. This can occur if the spring is compressed or stretched beyond its equilibrium position.

5. How is the work done by an ideal spring related to the potential energy stored in the spring?

The work done by an ideal spring is equal to the change in potential energy stored in the spring. This means that as the spring is compressed or stretched, the potential energy stored in the spring increases or decreases, respectively.

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