Lesson 7 of 10 · 10 min
Potential energy of a spring
NCERT § "The Potential Energy of a Spring"
The dart gun's spring, compressed 5 cm, fires a 20 g dart at 10 m/s. Anu compresses it twice as far. Will the dart go twice as fast?
The lesson in notes
In short
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.