A spring stores ½kx², the area under its F–x line
"A spring stores ½kx², the area under its F–x line" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the lesson "Potential energy of a spring" in Work, Energy and Power. Press Play (it runs at quarter speed). The block squeezes the spring, stops for an instant, and is pushed back out at the same speed. Drag the time slider to pause it mid-squeeze and read the bars. Spring energy is ½kx², the area under the F–x line, not ½kx. The maximum compression x_m = v√(m/k) grows in step with the speed. JEE Main asked 44 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Potential energy of a spring in Work, Energy and Power. Change the values and watch what happens.
In JEE Main
42 shifts analysed
44 questions from Work, Energy and Power across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT § "The Potential Energy of a Spring"
- An ideal spring obeys Hooke's law, F_s = −kx, where x is the extension or compression from the natural length and k is the spring constant (N m⁻¹).
- The potential energy stored in a spring deformed by x is V(x) = ½kx², the same for extension and compression by the same amount.
- A stiffer spring (larger k) stores more energy for the same deformation.
- On a smooth surface, a block of speed v pushing a spring comes to rest at maximum compression x_m where ½mv² = ½kx_m², so x_m = v√(m/k).
- Energy in a mass-spring system shifts between kinetic and potential forms; the kinetic energy is greatest at the natural length and zero at maximum deformation.
- The work done by the spring force over a complete cycle (returning to the starting deformation) is zero, as expected for a conservative force.
Questions
3 answers
- What does the "A spring stores ½kx², the area under its F–x line" simulation show?
- Press Play (it runs at quarter speed). The block squeezes the spring, stops for an instant, and is pushed back out at the same speed. Drag the time slider to pause it mid-squeeze and read the bars.
- Does JEE Main ask questions from Work, Energy and Power?
- Yes. JEE Main asked 44 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Potential energy of a spring" in Work, Energy and Power (Class 11 Physics).
Embed this simulation
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