- #1
eurekameh
- 209
- 0
Is this answer wrong? I think they've made a mistake in the work done by the spring, which I think should be (1/2)(135)(0.5)^3?
Solve the Work-Energy Problem: Is There a Mistake?
- Thread starter eurekameh
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- Work-energy
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SUMMARY
The discussion centers on the work-energy problem, specifically addressing the calculation of work done by a spring. The correct formula for the potential energy of a spring is confirmed as U = (1/2) k x^2, where k is the spring constant and x is the displacement. The work done by the spring is derived using the integral of the spring force, leading to the same result: W = (1/2) k x^2. This validates the original answer and clarifies the misunderstanding regarding the work calculation.
PREREQUISITES- Understanding of Hooke's Law and spring constants
- Familiarity with integral calculus
- Knowledge of potential energy concepts
- Basic principles of work-energy theorem
- Study the derivation of work done by variable forces
- Explore advanced applications of Hooke's Law in mechanical systems
- Learn about energy conservation in spring systems
- Investigate the relationship between work and kinetic energy
Students of physics, mechanical engineers, and anyone interested in understanding the principles of work and energy in spring systems.
Is this answer wrong? I think they've made a mistake in the work done by the spring, which I think should be (1/2)(135)(0.5)^3?
- #2
Steely Dan
- 319
- 0
No, the potential energy of a spring is indeed [itex]U = \frac{1}{2} k x^2[/itex]. If you want to think of it as work, then know that the spring force is [itex]F = k x[/itex], so the work done is
[tex]W = \int F dx = \int k x dx= \frac{1}{2} k x^2,[/tex]
which is the same answer.
[tex]W = \int F dx = \int k x dx= \frac{1}{2} k x^2,[/tex]
which is the same answer.