Conservation of Linear Momentum: The Trolley Explosion Experiment
The Law of Conservation of Linear Momentum states that the total linear momentum of an isolated system remains constant. An isolated system is one with no net external force acting on it, and that word carries the whole law: momentum is not conserved in general, only when nothing outside the system is pushing on it. In this Grade 12 experiment two trolleys are pushed apart by a spring. They start at rest, so the total momentum before is zero, and if the law holds the total afterwards must also be zero. It is a prescribed formal assessment for CAPS Physical Sciences, Term 1, marked out of 40.
Where this fits in the curriculum
| Subject | Physical Sciences |
|---|---|
| Grade | 12 |
| Term | 1 |
| Topic | Mechanics, momentum and impulse |
| Status | Prescribed experiment for formal assessment (SBA) |
| Marks | 40 |
| Time needed | 50 minutes |
The aim
To investigate whether the total linear momentum of an isolated system is conserved, using two trolleys pushed apart by a spring.
The physics behind it
Momentum is mass multiplied by velocity, and it is a vector, so direction counts. The total momentum of a system is the sum of the momentum of everything in it.
Before the spring is released, both trolleys are at rest. Neither has any momentum, so the total momentum of the system before the explosion is zero.
If momentum is conserved, the total afterwards must also be zero. Two trolleys are now moving, so the only way their momenta can add to zero is if they are equal in magnitude and opposite in direction. The heavier trolley must move more slowly, by exactly the ratio of the masses.
Why you measure distance instead of velocity
This is the part that catches learners out, and it is worth three marks in the assessment.
The experiment never measures a velocity, and it never measures a time. There is no stopwatch and no ticker tape timer.
Both trolleys start moving at the same instant. You then adjust the buffers at each end until the two trolleys strike them at the same instant, which you check by listening for a single knock rather than two. Once that is true, both trolleys have travelled for exactly the same length of time.
Since distance, velocity and time are related by x = vt, equal times mean the distances are directly proportional to the velocities. So the distance each trolley travels can stand in for its velocity.
That is why the results are recorded in arbitrary units: mass in trolley units, distance in centimetres, and momentum as the two multiplied together. The numbers are not in kg·m·s⁻¹ and they do not need to be. What the experiment tests is whether the two sides cancel, and a ratio answers that just as well as an SI unit does.
What you need
Apparatus
| Item | Qty |
|---|---|
| Dynamics trolleys, one with a spring plunger | 1 pair |
| Dynamic track | 1 |
| Slotted mass set, to match one trolley mass | 2 |
| Metre ruler | 1 |
You supply
Two solid blocks to act as buffers, and a level surface if you are not using a track.
No timer of any kind is required.
Method
- Place the two trolleys on the track back to back, with the spring plunger of one pressed against the other.
- Mark the starting position of each trolley. This is the line you measure from.
- Place a buffer at each end of the track.
- Release the plunger. The trolleys move apart and each hits its buffer.
- Listen. Two separate knocks means the buffers are in the wrong place. Move them and try again.
- Repeat until you hear one single knock. Both trolleys are now arriving at the same instant.
- Measure how far each trolley travelled, from its starting mark to its buffer, in centimetres. Do not round off.
- Record each trolley's mass in trolley units. A plain trolley is 1 unit. A trolley carrying an equal added mass is 2 units.
- Work out each momentum as mass in units multiplied by distance in centimetres, giving one direction a negative sign.
- Add the two together. This is the total momentum after the explosion, and it should come out at or near zero.
- Repeat for a 1 : 2 mass ratio twice, then for a 2 : 2 ratio.
Step 6 is the experiment. A class will spend most of the lesson on it and that is time well spent, because every reading afterwards depends on the times being equal.
What you should see
The light trolley travels about twice as far as the heavy one. With a 1 : 2 mass ratio the distances come out at roughly 2 : 1 and the two momenta cancel.
A worked set of readings:
| Run | A mass | A distance | A momentum | B mass | B distance | B momentum | Total after |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 125 cm | +125 | 2 | 62 cm | −124 | +1 |
| 2 | 1 | 123 cm | +123 | 2 | 61 cm | −122 | +1 |
| 3 | 2 | 61 cm | +122 | 2 | 61 cm | −122 | 0 |
Zero exactly is not the target. A total of +1 against distances of 125 cm is a discrepancy of under 1 %, which is a very good result on a school bench. A learner who reports exactly zero on all three runs has usually worked backwards from the answer.
Conclusion
The total linear momentum of the system before the explosion, which was zero, is equal to the total linear momentum after it. Momentum is therefore conserved in an isolated system.
A conclusion that only restates the aim will not earn full marks. It has to say what was found, and it has to match the learner's own readings. A learner whose totals came out well away from zero and who says so honestly, then identifies the reason in the evaluation, earns the marks.
Safety precautions
There are no chemicals and no electricity in this practical, which makes it one of the safest in the Grade 12 range.
- Keep fingers clear of the spring plunger as it releases
- The trolleys leave the track at speed. Run the experiment away from the edge of the bench
- Nobody stands at the end of the runway
If it does not work
| What you see | What caused it |
|---|---|
| The totals are nowhere near zero | The buffers are wrong. Go back to the single knock step. This is the cause nine times out of ten |
| One trolley barely moves | The plunger pushed off centre, or that trolley's wheels are stiff |
| Results drift across repeats | The track is not level, or its surface is dented. Check by letting a trolley sit on it |
| The light trolley travels much more than twice as far | The added mass does not actually equal one trolley. Weigh it |
| Totals are consistently positive or negative | A systematic error, usually a starting mark measured from a different edge of the trolley each time |
| Distances are hard to repeat | Somebody is rounding to the nearest centimetre. The assessment says explicitly not to |
How the 40 marks are made up
| Section | Marks |
|---|---|
| Results table | 10 |
| Interpretation and discussion, four questions | 9 |
| Conclusion | 3 |
| Evaluation | 4 |
| Application | 14 |
| Total | 40 |
The three marks most often lost are on the question asking why distance can be used instead of velocity. Learners who did not understand why the buffers had to be adjusted cannot answer it. The second most common loss is leaving the direction off a velocity in the application question, because momentum is a vector and the whole point is that the two are opposite.
If you have time
A collision instead of an explosion. Run one trolley into a stationary one and check whether momentum is still conserved. It is, but you now need a way to measure the velocities, because the trolleys no longer travel for equal times. That is where a ticker tape timer or an air track earns its keep.
Newton's cradle shows the same principle in a form learners remember. Pull one ball back and one flies out. Pull two back and two fly out. Momentum on its own does not explain why one ball cannot come out at twice the speed, and working out why brings conservation of kinetic energy into the discussion.
Free worksheet and marking memo
Both free, no sign up, straight to the PDF.
- Learner worksheet, 40 marks, with the results grid and the discussion, conclusion, evaluation and application questions set out for the formal assessment
- Marking memorandum, with the mark allocation, model answers, a worked application question and a note on the six places learners most often drop marks
Buy this experiment
We are putting together a complete Conservation of Momentum Kit for Grade 12 with the trolleys, the track, the masses and a printed teacher guide in one box. Coming shortly.
There is no refill for this one. Nothing in the box is used up, and the trolleys and track will outlast most of the equipment in a school lab. In the meantime every item in the apparatus table above is sold separately.