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Energy, Momentum & SHM — Visual Lab
Module 3. Two carts slide toward each other on a frictionless track. Momentum survives every crash; kinetic energy doesn't. Set the masses and velocities, choose an elastic bounce or a perfectly inelastic stick, and the lab computes — and animates — the exact outcome. Then flip to a spring or pendulum to watch energy slosh between kinetic and potential.
Two big conservation laws run this module. Momentum \(\big(p = mv\big)\) is conserved in every collision — the total before equals the total after, no matter what. Mechanical energy is conserved only when nothing dissipates it: an elastic collision keeps all its kinetic energy, while a perfectly inelastic one (the carts stick) loses the most possible to heat and sound. The same energy bookkeeping — \(KE = \tfrac12 mv^2\) trading with \(PE\) — drives the back-and-forth of simple harmonic motion. Drive the lab below and watch the numbers stay honest.
Collision Forensics Lab
Set mass and velocity for each cart, pick elastic or perfectly inelastic, and press Run. Watch the carts collide and read the conserved momentum next to the kinetic energy lost. Flip the top switch to the SHM view to drive a mass-spring or a pendulum, with live period and a kinetic-vs-potential energy split.
What you're seeing
- Two carts on a frictionless track. Each carries an arrow showing its velocity; the bigger mass is drawn larger. Positive velocity points right, negative points left.
- Momentum is always conserved. The readout shows the total \(p = m_1v_1 + m_2v_2\) before and after — they match for every collision, elastic or not.
- Kinetic energy is the tell. "KE lost" is exactly \(0\) for an elastic bounce and positive for an inelastic stick — that lost energy went to heat and sound.
- Elastic vs. inelastic. Elastic carts rebound at the velocities the elastic formulas predict; inelastic carts lock together and move at the common \(v_f\).
- The SHM view. A spring or pendulum oscillates in real time; the energy bar shows the live split between kinetic and potential, while the total stays fixed.
Try this
- Equal masses, elastic, one at rest. Set \(m_1 = m_2\), \(v_2 = 0\), elastic. Run it: the moving cart stops dead and the target leaves with the original speed — the classic "velocity swap."
- Same setup, but inelastic. Switch to inelastic. They stick and crawl off at half the speed — and exactly half the kinetic energy is gone.
- Heavy hits light. Make \(m_1\) much bigger than \(m_2\), elastic. The light cart rockets off at nearly twice the heavy cart's speed.
- SHM: change the amplitude. On the spring, raise \(A\). The period \(T\) doesn't budge — \(T = 2\pi\sqrt{m/k}\) ignores amplitude — but the total energy \(\tfrac12 kA^2\) climbs.
- SHM: change the pendulum length. Lengthen \(L\) and watch \(T\) grow as \(\sqrt{L}\). Changing the bob mass does nothing to the period.
Worked Examples
Two moves this module asks for most: tracking momentum and energy through a perfectly inelastic collision, and reading the energy split off a spring oscillator.
Example 1 — A sticky collision: find \(v_f\) and the kinetic energy lost
A \(2\) kg cart moving \(+4\) m/s catches up to a \(3\) kg cart moving \(+1\) m/s and the two stick together. Find their common speed and the kinetic energy lost.
- Momentum before. \(p = m_1v_1 + m_2v_2 = 2(4) + 3(1) = 8 + 3 = 11\) kg·m/s.
- Stick → one mass moving at \(v_f\). Momentum is conserved: \((m_1 + m_2)\,v_f = 11\), so \(v_f = \dfrac{11}{5} = 2.2\) m/s.
- Kinetic energy before. \(KE_i = \tfrac12(2)(4)^2 + \tfrac12(3)(1)^2 = 16 + 1.5 = 17.5\) J.
- Kinetic energy after. \(KE_f = \tfrac12(5)(2.2)^2 = 12.1\) J. So \(KE\) lost \(= 17.5 - 12.1 = 5.4\) J.
Example 2 — A mass on a spring: period and energy split
A \(1\) kg block on a spring of constant \(k = 100\) N/m oscillates with amplitude \(A = 0.2\) m. Find the period, the total mechanical energy, and the block's maximum speed.
- Period. \(T = 2\pi\sqrt{\dfrac{m}{k}} = 2\pi\sqrt{\dfrac{1}{100}} = 2\pi(0.1) \approx 0.63\) s.
- Total energy. All of it is spring \(PE\) at the turning point: \(E = \tfrac12 kA^2 = \tfrac12(100)(0.2)^2 = 2\) J.
- Fastest at the center. At \(x = 0\) all energy is kinetic: \(\tfrac12 m v_{\max}^2 = 2\), so \(v_{\max} = \sqrt{\dfrac{2(2)}{1}} = 2\) m/s.
- Check the trade. Anywhere in between, \(KE + PE = 2\) J exactly — the energy bar in the lab shows this split live.
AP Physics · enrichment — not a TEKS-graded course. The Texas Essential Knowledge and Skills (TEKS) define the state-graded Physics course; AP Physics is a separate, College-Board–aligned enrichment track offered here for scholars who want a calculus-adjacent, university-style treatment of mechanics. Nothing on this page is scored toward a TEKS grade or a STAAR EOC.
The skills below map to the AP Physics 1 framework — energy, momentum, and simple harmonic motion — not to a TEKS standard. Treat it as practice and exploration, not a graded requirement.
Key Vocabulary
The precise words a physicist uses to describe what the lab is doing.
The product \(p = mv\). The total momentum of an isolated system is conserved in every collision — before equals after.
Energy of motion, \(KE = \tfrac12 mv^2\). It depends on speed squared, so it grows fast with velocity.
A collision in which kinetic energy is conserved. Objects bounce apart with no energy lost to heat or sound.
A collision where the objects stick together. Momentum is still conserved, but the maximum possible kinetic energy is lost.
Work \(W = Fd\cos\theta\) transfers energy; power \(P = W/t\) is the rate of doing it. Only the force component along the motion does work.
Oscillation driven by a restoring force proportional to displacement. Period \(T = 2\pi\sqrt{m/k}\) (spring) or \(2\pi\sqrt{L/g}\) (pendulum).
AP Physics 1 — Energy, Momentum & Oscillations
This lab targets the energy, linear momentum, and simple harmonic motion units of the AP Physics 1 framework: applying conservation of momentum to one-dimensional collisions, distinguishing elastic from inelastic, tracking kinetic and potential energy, and modeling oscillators. It is enrichment — not a TEKS standard.
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AP Physics is enrichment, offered alongside the TEKS-graded math and science courses. Content aligns with the College Board AP Physics 1 framework and is not part of any TEKS standard or state assessment. "AP" is a trademark of the College Board, which does not endorse this site.