The Thinking Experiment — Work & Energy

Work & Energy Concepts Simulator

Explore interactive scenarios. Adjust parameters, watch animated force arrows and energy bar charts, and apply the 5-step problem-solving method.

Select Scenario

Free Fall Parameters

FORCE COLORS Gravity (Fg) Normal (N) Friction (fk) Applied (F) Tension/Spring

Free Fall

Ball drops from rest — watch PEg convert to KE

Method: Ei = Ef

Work Equation

Select a scenario and run the simulation.

Kinetic Energy

0.000 J

KE = ½mv²

Grav. Potential

0.000 J

PEg = mgh

Elastic Potential

0.000 J

PEs = ½kΔx²

Total Energy

0.000 J

KE + PEg + PEs

External Work

0.000 J

WEXT (Non-conservative)

Step 1

Define the System

Object only? Object + Earth (adds PEg)? Object + Spring (adds PEs)?

Step 2

Identify Energy Types

KE (moving), PEg (height), PEs (spring), Eth (friction)?

Step 3 — Path A

Conservative Only → Use Ei = Ef

Mechanical energy is conserved. Ei = Ef.

Step 3 — Path B

Non-Conservative → Work-Energy Theorem

Use Ef = Ei + WEXT.

Step 4

Calculate Work

Use WEXT = F · d · cos θ.

Step 5

Solve for Unknown

Plug in values and check units (Joules).

Find speed at bottom (m=2kg, h=10m):

  1. System: ball + Earth.
  2. Ei = Ef
  3. PEg,i + KEi = PEg,f + KEf
    mgh + 0 = 0 + ½mv²
    196 = v² → v = 14 m/s

Find final speed (m=2kg, h=3m, ramp=6m, μ=0.2):

  1. WEXT = −fk·d = −20.4 J
  2. Ef = Ei + WEXT
  3. ½mv² = PEg,i + WEXT
    ½(2)v² = 58.8 − 20.4
    v = √38.4 = 6.2 m/s

Spring Launch (k=200, Δx=0.15):

  1. Ei = PEs,i = ½kΔx² = 2.25 J
  2. Ef = PEg,f = mgh
  3. Ei = Ef → h = 2.25/9.8 = 0.23m

Pendulum (L=1.5m, θ=40°): Find v at bottom

  1. h = L(1 − cosθ) = 1.5(1 − 0.766) = 0.35m
  2. System: ball + Earth (Tension does NO work)
  3. Ei = Ef → mgh = ½mv²
  4. v = √(2gh) = √(2·9.8·0.35) = 2.6 m/s

Work at an Angle (F=20N, d=4m, θ=30°):

  1. Identify components: Only Fx = F·cosθ does work.
  2. WEXT = F · d · cosθ
  3. WEXT = 20 · 4 · cos(30°)
  4. WEXT = 80 · 0.866 = 69.3 J