Calculate stored elastic energy, launch velocity, flight distance, and force for stretched rubber bands. Includes band selection and projectile analysis.
Rubber bands store elastic potential energy when stretched, and release it to launch projectiles, power model cars, or snap back with surprising force. Understanding the energy stored in a stretched rubber band connects physics concepts like Hooke's law, energy conservation, and projectile motion. It is a simple system, but it captures several useful mechanics ideas at once.
This calculator computes the elastic potential energy stored in a stretched rubber band, the force at maximum extension, the launch velocity of a projectile, and the estimated flight distance including angle optimization. It accounts for the non-linear stress-strain behavior of rubber with both linear and hyperelastic models.
Whether you're designing a rubber band car for a science competition, building a slingshot, teaching physics concepts, or just curious how much energy your rubber band gun stores, this tool provides quantitative answers with educational context. It also helps you compare how extension length, stiffness, and projectile mass affect the result before you test anything in the real world.
Rubber band physics involves non-linear forces, energy transfer efficiency, and projectile dynamics. This calculator handles the math for science projects, competitions, and curious minds, making it easier to estimate launch energy and range without trial and error. It is helpful when you want a first estimate before building or testing a setup.
Energy (linear): E = ½kx² where x = extension. Force: F = kx. Launch velocity: v = √(2E/m) × η (efficiency). Range: R = v²sin(2θ)/g. For non-linear rubber: E = ∫F(x)dx.
Result: 0.56 J stored, 15 cm extension, 4.74 m/s launch, 2.29 m range
A rubber band with k=50 N/m stretched 15 cm stores 0.56 J. Launching a 5g projectile at 45° gives ~4.7 m/s velocity and ~2.3 m range.
Rubber's elasticity comes from entropy-driven polymer chain recoil. When stretched, the long polymer chains uncoil from random conformations into aligned configurations. The restoring force is primarily entropic — the chains "want" to return to their higher-entropy random state.
For small deformations, this behaves like a spring: F = kx and E = ½kx². At larger deformations, rubber stiffens dramatically (strain hardening). The full stress-strain curve for rubber follows hyperelastic models like Mooney-Rivlin or Ogden, which account for the non-linear behavior.
When the band releases, stored energy converts to kinetic energy of the projectile (and the band itself). For an ideal massless band: ½kx² = ½mv², giving v = x√(k/m). Real bands have mass, so some energy goes into accelerating the band — roughly ⅓ of the band's KE is wasted.
Rubber band cars store energy by winding bands around an axle. The energy budget is: E_stored = ½kx², delivered as torque over many rotations. Key optimization: use multiple thin bands for better efficiency, gear ratios to match torque to load, and minimize friction. The current distance record for rubber-band-powered cars exceeds 100 meters.
A standard #64 rubber band stretched to 2x its length stores about 0.1-0.3 J. Larger bands (like #107) can store 1-3 J. This is enough to launch a small projectile 5-20 meters.
Only approximately and at small extensions (<50% of natural length). At larger stretches, rubber bands stiffen non-linearly. For accurate results, the force-extension curve should be measured directly.
45° in vacuum/no-drag. With air resistance (which matters for light projectiles), the optimal angle drops to ~35-40°. For heavier projectiles, 45° is close to optimal.
Good rubber bands can be stretched to 5-7× their natural length before breaking. However, repeated stretching to max causes fatigue — practical limit is 3-4× for repeated use.
About 50-80% of stored energy transfers to the projectile. Losses go to: heat in the rubber, air resistance, band mass energy, and vibration. Thick bands waste more energy accelerating themselves.
Hang a known mass from the band and measure extension. k = mg/x. Example: 100g hanging produces 5 cm extension → k = 0.1×9.81/0.05 = 19.6 N/m.