Physic Labs

Newtonian mechanics

Gravitational and elastic potential energy

Explore two forms of potential energy: gravitational and elastic. Measure how mass, height, spring constant, and deformation affect each, then verify Ug=mghU_g = mgh and Us=12kx2U_s = \frac{1}{2}kx^2.

Middle school

Equipment

  • Virtual mass m with adjustable weight
  • Ideal spring with stiffness k
  • Sliders for m, h, k, x and energy display

Procedure

  1. Measure gravitational potential energy

    Use the "Mass m" and "Height h" sliders to place the object at different heights; watch the UgU_g energy bar change. Record two (m, h) pairs and check the proportion Ug=mghU_g = mgh: doubling h doubles UgU_g.

  2. Measure elastic potential energy

    Drag the "Deformation x" slider to compress or stretch the spring and vary "Stiffness k". Record UsU_s at two values of x and check Us=12kx2U_s = \frac{1}{2}kx^2: doubling x quadruples the energy.

  3. Compare and predict

    Preset k or m and predict the x or h needed to make the two energies equal (mgh=12kx2mgh = \frac{1}{2}kx^2). Test your prediction in the simulation and comment on the shapes: UgU_g is linear in h while UsU_s is a parabola in x. Use "Pause" to read values precisely.

Simulation

Experiment history

The concepts of work and energy took shape during the 17th–19th centuries. Galileo noted that a falling body gains speed in proportion to the height it descends, and Huygens argued that a pendulum rises to exactly the height it lost — an early form of energy conservation. In 1678 Robert Hooke published the spring law F=−kxF = -kx, the basis for computing energy stored in deformation. In the 19th century engineers such as Coriolis and Rankine standardized the terms "kinetic" and "potential" energy; William Rankine proposed the name potential energy in 1853. In Lagrangian and Hamiltonian mechanics, potential energy became central: knowing UU as a function of coordinates determines the forces and the equations of motion.

Related physicists

Isaac NewtonGalileo Galilei

Related library topics

Gravitational and elastic potential energy