Conservation of Energy with a Simple Pendulum, Grade 10
Two ruler readings verify the law of conservation of energy. You do not need the mass and you do not need a stopwatch.
Most versions of this practical ask a class to watch a pendulum swing and describe the energy as "maximum here, minimum there". That is an observation, not a verification, and it proves nothing.
Here is the measurement that does. Release the bob from a measured height and note the height it reaches on the far side. Divide the second by the first. That ratio is the exact fraction of the mechanical energy the pendulum kept.
Why the ratio of two heights is the answer
At each end of a swing the bob is momentarily still. Its speed is zero, so its kinetic energy is zero, and every joule it has is gravitational potential energy.
| At the release point | Em = mgh |
|---|---|
| At the far side | Em' = mgh' |
Divide the second by the first:
Em' ÷ Em = mgh' ÷ mgh = h' ÷ h
The m cancels. The g cancels. You never need to weigh the bob and you never need to know the value of gravity. Two heights, measured with a ruler, give you the fraction of mechanical energy that survived the swing.
This is the same cancellation that lets you work out how fast a toy car is going at the bottom of a track without knowing its mass. Here it does something more useful: it turns a ruler into an energy meter.
This is not the period experiment
Worth settling before you start, because half your class will have seen the other one.
| The period experiment | This experiment |
|---|---|
| Times 20 swings with a stopwatch | Measures two heights with a ruler |
| Uses T = 2π√(L ÷ g) | Uses Ek + Ep = constant |
| Is about simple harmonic motion | Is about conservation of energy |
| Grade 12 | Grade 10 |
Same apparatus, completely different investigation. A great deal of material online for "conservation of energy pendulum" is actually the timing experiment, and a learner who has done that one has not touched conservation of energy at all.
Where this fits in the curriculum
| Subject | Physical Sciences |
|---|---|
| Grade | 10 |
| Term | 4 |
| Topic | Topic 7, Mechanics. Energy |
| Status | Not a prescribed experiment. See below |
| Marks | 64 on our worksheet. None is prescribed |
The Grade 10 energy topic contains three worked examples and no practical at all. The pendulum appears as a calculation on paper, with the instruction to ignore air friction.
So this method is ours, and we would rather say so. It uses the curriculum's own equations and it fills a gap the prescribed list leaves open.
Method
Setting up
- Clamp a bosshead near the top of a retort rod and tie the string to it. The string must pivot from one fixed point rather than sliding
- Tie the bob to the free end so it hangs 5 to 10 cm above the bench
- Mark the lowest point with tape, directly under the pivot
- Stand a ruler vertically behind the pendulum so heights can be read straight off it
Use non-stretch string. Cotton thread or fishing line. A stretchy string stores energy of its own and quietly ruins the result.
The measurement
- Pull the bob to one side with the string taut until it is a measured height h above its lowest point. About 20 cm works well
- Read h and write it down
- Release without pushing. Hold it still between two fingers and open them
- Read the height h' it reaches on the far side. Watch at eye level, and mark the turning point with a pencil if that helps
- Repeat five times and average both
- Divide h' by h
A worked set of numbers
| Measurement | Value |
|---|---|
| Bob | 25 mm brass, about 70 g |
| Release height, h | 0,200 m |
| Height on the far side, h' | 0,192 m |
The fraction of mechanical energy kept:
h' ÷ h = 0,192 ÷ 0,200 = 0,96, which is 96 per cent
And if you want it in joules, with m = 0,070 kg:
| Quantity | Working | Result |
|---|---|---|
| Em at release | mgh = 0,070 × 9,8 × 0,200 | 0,137 J |
| Em on the far side | mgh' = 0,070 × 9,8 × 0,192 | 0,132 J |
| Mechanical energy lost | mg(h − h') | 0,005 J |
| Speed at the lowest point | v = √(2gh) = √3,92 | 1,98 m·s-1 |
The joules are optional. The ratio is the result, and the ratio needed no mass at all.
The loss is the result, not the error
Every school treatment of this practical tells the class to ignore air resistance. Do not.
The law is precise about its condition: mechanical energy is conserved only when no outside force acts on the system. Textbooks state that and then instruct the reader to ignore air friction, which assumes away the exact thing the condition is about.
Your class is going to watch the pendulum die out over two minutes. Pretending it did not is a worse lesson than measuring it.
| What was lost | About 4 per cent of the mechanical energy per half swing |
| Where it went | Air resistance, and friction where the string turns at the pivot |
| What it became | Heat and sound |
| Was energy destroyed? | No. The total is conserved. Only the mechanical part fell |
That distinction is the law. A class that measures 96 per cent and can say where the other 4 per cent went has understood conservation of energy. A class told to assume 100 per cent has memorised a slogan.
The extension that costs nothing
Count the half swings until the height has halved. At 96 per cent per half swing that takes seventeen, and a class can predict it before testing it: 0,96 raised to the power of n equals 0,5.
It is the first exponential decay most of them will ever meet, and it comes out of a piece of string.
The mass cancels, and three bobs prove it in two minutes
Nothing in h' ÷ h contains the mass. Nothing in v = √(2gh) contains it either.
So a heavy bob and a light bob released from the same height should do exactly the same thing.
| Bob | Approximate mass | Height reached on the far side |
|---|---|---|
| 13 mm brass | 10 g | The same |
| 19 mm brass | 31 g | The same |
| 25 mm brass | 70 g | The same |
Ask the class to predict first. Most will pick the heaviest, some the lightest. Neither. A seven-fold difference in mass changes nothing at all.
Keep the string the same length between bobs. If the length changes, so does everything else, and the comparison is lost.
This is the same result as the coin and the paper dropped together, and as the loaded trolley on the inclined plane page. Three practicals, one conclusion: gravity does not care about mass.
One thing worth saying out loud about h
"The potential energy at the bottom is zero" is a choice, not a fact.
Gravitational potential energy is always measured from a reference level that you pick, and in this experiment we pick the lowest point of the swing. Measure h from the floor instead and every number changes.
It does not matter, because only the difference is ever used, and a difference does not depend on where you put the zero. But a learner who thinks potential energy has one true value will be confused the first time somebody measures from somewhere else.
What you need
| Item | Qty | Why |
|---|---|---|
| Retort stand base and rod | 1 | Something rigid to hang from |
| Bosshead, 16 mm | 1 | The pivot. Tie the string to this, not to the smooth rod, or it will slide |
| Pendulum balls, brass, 13 mm, 19 mm and 25 mm | 1 of each | Three masses from 10 g to 70 g. The three together are the mass demonstration |
| Tape measure, 5 m steel | 1 | Measuring h and h' |
| Digital stopwatch | 1 | Optional. The core measurement does not use one |
String is not on the list on purpose. Every school has some, and what matters is that it does not stretch. Cotton thread or fishing line, not elastic and not wool.
Do not buy a clamp with jaws for this. A plain bosshead is the right pivot and costs a fraction as much.
What you should see
- h' consistently a little smaller than h, run after run
- A ratio between about 0,90 and 0,99. Below 0,85 means a stretchy string or a slipping pivot
- Never a ratio above 1,00. The pendulum cannot gain energy
- All three bobs giving the same ratio, within measurement error
- The swing visibly smaller after ten or fifteen swings, and roughly half the height after seventeen half swings
If it does not work
| What happens | What caused it |
|---|---|
| h' varies wildly between runs | The bob is being thrown, not released. Hold it still between two fingers and open them |
| h' comes out bigger than h | The bob was pushed, or h was misread. This is physically impossible, so repeat it |
| The pendulum swings in a circle | It was released off to one side of the plane. Pull it back in line with the ruler |
| The ratio is well below 0,9 | A stretchy string, or the string is sliding at the pivot. Cotton or fishing line, tied to a fixed bosshead |
| The string slips at the top | It is tied to the smooth rod. Tie it to the bosshead |
| Nobody can read h' in time | Use a bigger release height and a bigger bob, or hold a pencil at the turning point and read afterwards |
| The whole stand rocks or walks | The base is too light for a swinging mass. Weigh it down or clamp it to the bench |
| The three bobs give different ratios | The string length changed between bobs. Same string, same length, only the bob changes |
Safety
Low hazard, with one thing that genuinely matters.
- A 70 g brass ball on a metre of string is heavy enough to hurt. Nobody stands in the plane of the swing
- Weigh down or clamp the retort base. A swinging mass will walk a light stand across a bench
- Never release the bob towards a window, a face or the front of the class
- Check the knot before every run. A bob that comes off mid-swing travels a long way
- Keep the swing small. Twenty centimetres of height is plenty, and a bigger swing is neither safer nor more accurate
No chemicals, nothing hot, no goggles.
How the 64 marks are made up
| Section | Marks |
|---|---|
| Where the energy is at each point of the swing | 8 |
| The measurement, five runs and the ratio | 10 |
| Why the ratio is the answer, and what cancels | 10 |
| The missing energy, and where it went | 11 |
| The calculation in joules | 9 |
| Does the mass matter? | 10 |
| Conclusion | 6 |
No mark allocation is prescribed for this practical. The worksheet and this split are ours, as is the method.
The most valuable question on the sheet asks for the difference between "the total energy is conserved" and "the mechanical energy is conserved". Very few learners can separate the two, and the whole law lives in that gap.
The mark most often dropped is a unit conversion: 70 g is 0,070 kg, and a learner who uses 70 gets 137 J instead of 0,137 J.
If you have time
Try a very light bob, like a cork or a ball of paper. The ratio falls noticeably, because air resistance is a bigger deal relative to a small weight. That is the outside force made visible, and it is a better argument than any explanation.
Compare a smooth pivot with a rough one. Loop the string over a pencil instead of tying it to the bosshead and watch the ratio drop.
Ask why a grandfather clock needs winding. A pendulum clock loses a few per cent of its mechanical energy every swing, exactly like this one, and the weight that you wind up is what puts it back. The clock is this experiment, running for a week.
Free worksheet and marking memo
Both free, no sign up, straight to the PDF.
- Learner worksheet, 64 marks, with the five-run measurement table, the derivation of h' ÷ h, the missing-energy questions, a full calculation in joules and the three-bob comparison
- Marking memorandum, with worked answers, what to do about a ratio below 0,85, and the five answers that look right and score nothing
Related practicals
- Acceleration on an inclined plane, Grade 10. The other way to measure gravity in a classroom, on the same retort stand
- Ticker tape and motion graphs, Grade 10. Same topic block, motion rather than energy
- Work, energy and power, Grade 12. Where kinetic and potential energy are done properly, with the work-energy theorem
- Vertical projectile motion, Grade 12. Free fall, and the equations of motion
- Newton's Second Law, Grade 11. Where the mechanics block goes next year
Buy this experiment
We are putting together a Conservation of Energy Kit for Grade 10 with the retort stand, rod, bosshead, all three brass bobs, a tape measure and a stopwatch in one box, plus a printed teacher guide and the marking memo. Coming shortly.
The three brass bobs are the part worth buying. Thirteen, nineteen and twenty-five millimetres is roughly ten, thirty and seventy grams, and having all three is what turns "the mass cancels" from a claim into a two-minute demonstration. They are on one product page and the set of three costs less than R170.
The pivot is a plain bosshead at R42, not a clamp. The string ties straight to it, and a clamp with jaws costs seven times as much and does the job worse.
The retort stand runs four of our published practicals, this one, the inclined plane, endothermic and exothermic reactions in Grade 11 and titration in Grade 12. Worth buying once.