Release a pendulum from a measured height and follow its energy through one swing. You’ll predict the bottom speed, measure it from slow-motion video, see how high the bob comes back up, and then test where the missing energy went.
🎯 Goals
- Predict a pendulum’s bottom speed from its release height, then measure it and compare.
- Measure how much of the starting PE shows up as KE at the bottom and as PE on the far side.
- Draw energy bar charts that account for 100% of the energy at three moments in the swing.
- Find where the missing energy went by testing a change in how much the air pushes back.
🧰 Materials
🧵String, about 1.3 m long
🏗️A rigid support to hang it from: a ring stand with a long rod, or a ceiling or door-frame hook. It must not wobble.
🏋️A bob: a hooked 200–500 g mass or another dense weight
📏Two meter sticks and masking tape (one vertical for heights, one horizontal for the speed gate)
📱A phone that records slow motion (120 or 240 fps) and a way to hold it still
⚖️A scale that reads in grams
🗂️An index card and tape (Day 3)
🧮Calculator
📓Physics notebook
📏 Constraints
- Use the same bob and the same string length (1.00 m from pivot to the center of the bob) for every trial.
- Release the bob from rest at 0.10 m, 0.20 m, and 0.30 m above its lowest point. No pushing, no throwing.
- Get the bottom speed from slow-motion video at 120 fps or higher (or a photogate, if your teacher provides one). Regular 30 fps video is too coarse.
- Show every calculation with units: mass in kg, height in m, speed in m/s, energy in J.
- Safety: the support must be secure, nobody stands in the swing plane, and the bob is released only after the person holding it calls “ready.”
1
Build the pendulum.
Hang the bob from your rigid support so the string is 1.00 m from the pivot to the center of the bob. Make sure the bob swings freely and the support doesn’t wobble when it moves.
⚠️ Clear the swing path and keep everyone out of the swing plane. If the support moves at all, fix it before you release anything.
2
Mass the bob and set up a height stick.
Find the bob’s mass in kilograms. Stand a meter stick upright behind the swing with its 0 mark level with the bob’s center when it hangs at rest. Put tape marks at 0.10 m, 0.20 m, and 0.30 m. The bottom of the swing is your zero level, just like in Activity 4-1-3.
3
Set up the speed gate and the camera.
Tape two marks on a horizontal meter stick behind the bottom of the swing, exactly 0.20 m apart and centered on the lowest point. Put your phone on a stable stand at bob height, straight on, and as far back as you can while zooming in. Record at the highest slow-motion fps your phone offers and write that number down.
⚠️ Don’t film from above or below. Parallax shifts the bob against the marks and makes your speed wrong.
4
Predict the bottom speed for each release height.
If no energy were lost, mgh at the top would become ½mv² at the bottom. Solve for v for each height before you measure anything.
Predict It
Ideal case, no energy lost. Use g = 9.8 N/kg.
5
Practice one release from 0.20 m.
Hold the bob against the 0.20 m mark, call “ready,” and let go without pushing. Record it, then open the video and step through it frame by frame so you know how to find the moment the bob crosses each gate mark.
📓 Physics Notebook
Before you collect data, predict: will the real KE at the bottom be more than, equal to, or less than the PE at the top? How high will the bob come back up on the far side? Explain your thinking in a sentence or two.
6
Release the bob from 0.10 m and record the swing.
Frame the video so it shows the bottom gate and the far-side height stick. Release from rest without a push. Capture the pass through the gate and the peak of the first swing on the far side.
7
Count the frames the bob takes to cross the 0.20 m gate.
Step through the video one frame at a time. Count from the frame where one point on the bob (always the same point) reaches the first mark to the frame where it reaches the second mark.
8
Read the far-side height.
Find the frame where the bob is highest on the far side and read its height h₂ from the meter stick. Do three runs at this height and average your frame counts and your h₂ values.
9
Repeat for 0.20 m and 0.30 m.
Same bob, same string, same camera spot, three runs each.
10
Calculate Table A (down) and Table B (back up).
Gate time t = frames ÷ fps. Speed v = 0.20 m ÷ t. Then KE = ½mv² and PE = mgh. For Table B, because m and g are the same on both sides, the fraction of PE returned is just h₂ ÷ h₁.
Table A: from the top to the bottom
How much of the starting PE is still motion at the bottom?
Table B: from the bottom back up
How much of the starting energy comes back as height?
What good data looks like
Most groups find that about 80–100% of the starting PE shows up as KE at the bottom, and that the bob comes back to about 90–98% of its release height. If you see more than 100% anywhere, that’s a measurement problem, not extra energy. Recount frames, recheck the gate width, and check your camera angle.
📓 Physics Notebook
Look at your three release heights. Does the percentage of energy that stays kinetic change much as the height changes? Does the bob always return to the same fraction of its release height? What does that tell you about the energy lost per swing?
DAY 3Account for the Energy 11
Build an energy bar chart for your 0.20 m release.
Show the energy at the top, the bottom, and the far side as percentages of the starting energy. Use your Table A and Table B percentages, and let thermal energy be whatever is left.
Energy Bar Builder
Use your 0.20 m results. Every bar is a percent of the starting energy. Take the KE percent from Table A and the PE percent from Table B. Thermal is whatever is left.
■ Potential■ Kinetic■ Thermal
1. Top of the swing (released from rest)
Fixed for you: all PE, no KE, no thermal energy yet.
3. Far side, at the top of the first swing
12
Predict, then test where some of the energy goes.
Tape an index card to the bob. First hang it edge-on (slicing through the air), then flat (catching the air). Release from 0.20 m each time and measure h₂ with the same video method. Write your prediction in the table before you test.
📓 Physics Notebook
Write a claim, evidence, and reasoning paragraph. Claim: where did the missing energy go? Evidence: numbers from your tables and your card test. Reasoning: why does that evidence point to your claim?
13
Assemble your energy ledger.
Put your Table A, Table B, card test, bar chart, and written explanation together. Make sure every number has units and every calculation is shown.
Question 1
Using Table A, what percent of the starting PE was still kinetic at the bottom? How does your measured speed compare with the √(2gh) prediction you made on Day 1?
Question 2
Using Table B, how much of the energy came back as height? Why does the bob always come back a little lower than where it started?
Question 3
Use your card test to explain at least one place the missing energy went. Why isn’t the energy actually gone?
Question 4
Would you expect a heavier bob to return closer to its release height or farther from it? Use √(2gh) and your card test in your answer.
📤 Turn In
- Energy conversion data: completed Table A and Table B with units and calculations shown
- Your Day 1 predictions and your card-test table
- Energy bar chart for the 0.20 m release, showing 100% at all three moments
- Claim–evidence–reasoning explanation of where the missing energy went
- Written answers to the four Conclusion questions