The Thinking Experiment

Conservation of Mechanical Energy

Drop an object through photogates, track the transformation between potential and kinetic energy, and verify that mechanical energy is conserved.

Learning Objective

Track PE, KE, and ME at six heights during free fall. Verify that their sum stays constant — energy is transformed, never lost.

Step 1 · Set Up

Set the mass of the falling object. The top photogate is fixed at the release height. Move the lower photogate to each measurement height.

Step 2 · Drop & Record

Press Drop Ball. The timer starts when the ball passes the top photogate and stops at the lower one. Click Record Data Point to save the trial.

Step 3 · Analyze

After recording all 6 points, examine the energy bar chart and line graph. Does ME stay constant? What pattern do PE and KE follow?

Free-Fall Setup

Move the lower photogate and drop the ball to build your data table.

Height1.000 m
Fall Time— s
Trials0 / 6

Controls

Data Table

Point h (m) t (s)
A——
B——
C——
D——
E——
F——

Energy at Each Point

Grouped bar chart — PE (blue), KE (orange), ME (green) at each recorded point.

Energy vs. Height

As height decreases, PE converts to KE — but ME stays constant.

🔮 Predict First

Before dropping the ball, predict: at half the original height, will the ball have half the original PE? Will it have half the maximum KE? Think carefully!

📊 Read the Bar Chart

Look at the green bars (ME). Are they all roughly the same height? If PE drops by some amount between two points, how much does KE increase?

🧪 The Transfer Pattern

On the line graph, find the height where PE = KE. At that height, each form of energy equals exactly half of the total. Why?

The Model

Gravity does work on the falling object. Potential energy converts to kinetic energy:

\(PE = mgh \qquad KE = \tfrac{1}{2}mv^2\)

Mechanical energy is their sum:

\(ME = PE + KE = \text{constant}\)

For free fall from rest:

\(v_f = g \cdot t \qquad (v_0 = 0)\)

Key Insights

  • Reference point: Height h is measured from the lowest point (h = 0 at Point F).
  • At the top: All energy is PE, KE = 0.
  • At the bottom: All energy is KE, PE = 0.
  • Conservation: \(\Delta PE + \Delta KE = 0\) — any PE lost becomes KE gained.

Why Does It Work?

Gravity is a conservative force — the work it does depends only on start and end positions, not the path. No energy is "used up"; it just changes form.

Teacher Demonstration

Auto-run the complete experiment with step-by-step annotations. Use this to walk through the lab with your class or demonstrate the conservation principle.

Demonstration View

Press "Run Demo" to start the automated walkthrough.

Trials0 / 6
Height— m
Velocity— m/s
ME— J

Energy at Each Point

Energy vs. Height

Demo Controls

Demo Data

Pt h (m) v (m/s) PE (J) KE (J) ME (J)
A—————
B—————
C—————
D—————
E—————
F—————

Move the lower photogate and drop the ball to build your demonstrative data table.

💡 Key Misconception

Students often think energy is "used up" during a fall. Emphasize that PE transforms into KE — the total doesn't change. Point at the green ME bars.

📐 The Math Connection

Show that setting \(mgh = \frac{1}{2}mv^2\) and solving for v gives \(v = \sqrt{2gh}\) — mass cancels! All objects fall the same way regardless of mass.

🌊 Air Resistance Toggle

Turn on air resistance to show ME decreasing. Ask: "Where does the energy go?" (thermal energy, sound). This bridges to non-conservative forces.

Conservation of Energy

\(ME = PE + KE = mgh + \tfrac{1}{2}mv^2\)

For free-fall from rest at height \(h_0\):

\(mgh_0 = mgh + \tfrac{1}{2}mv^2\)

Solving for speed at any height:

\(v = \sqrt{2g(h_0 - h)}\)

Lab Verification

Using photogates, we measure time for free fall. Since v₀ = 0:

\(v_f = g \cdot t\)

Combined with the height of the lower photogate, we can calculate PE and KE independently and verify:

\(\Delta PE + \Delta KE = 0\)