Physic Labs

Newtonian mechanics

Interaction forces and momentum conservation

Recognize that forces two bodies exert on each other are equal and opposite, and investigate momentum conservation in an isolated system. Measure both bodies’ momentum before and after impact, and verify pbefore=pafterp_{before} = p_{after}.

Middle school

⚠ Collisions are simulated only; do not launch or strike real objects, which may cause injury.

Equipment

  • Two spheres in a one-dimensional collision
  • Mass, initial-velocity, restitution, and slow-motion sliders

Procedure

  1. Vary masses and velocities before impact

    Set m₁, m₂, v₁, and v₂ with the sliders, choose e = 1, and press Collide again to view the slow-motion impact. Read total momentum before and after; change a mass or velocity and repeat to confirm the total momentum remains the same. Reduce e to 0 to compare a perfectly inelastic collision: momentum is still conserved, but kinetic energy is not. Compare the observed quantities with pbefore=pafterp_{before} = p_{after}.

  2. Compare the interaction forces

    Run the slow-motion collision and inspect both force vectors at the same instant. Compare magnitude, direction, and the body acted on to check F⃗12=−F⃗21\vec F_{12} = -\vec F_{21}; the pair acts on different bodies.

  3. Distinguish momentum and kinetic energy

    Keep masses and initial velocities fixed, lower restitution e from 1 to 0, and rerun. Read total momentum and kinetic energy before and after impact; identify which quantity is conserved in each case. Compare the observed quantities with pbefore=pafterp_{before} = p_{after}.

Simulation

Experiment history

Newton stated the third law in the Principia in 1687: when two bodies interact, the forces they exert on each other are equal in magnitude, opposite in direction, and act on different bodies. This distinguishes an interaction pair from two balancing forces on one body. Collisions and contact forces illustrate that the law applies to each interaction pair, regardless of which object is moving. Together with the second law, the third law leads to momentum conservation for an isolated system: internal forces cancel when the system is considered as a whole, and zero net external force leaves total momentum unchanged. Momentum can therefore be conserved in an inelastic collision even while kinetic energy decreases. The interaction forces, system momentum, and kinetic energy must be distinguished when interpreting a simulation.

Related physicists

Isaac Newton

Related library topics

Newton’s third lawConservation of momentumElastic collisions