Acceleration on an Inclined Plane, Grade 10
A ramp is a way of slowing gravity down until you can measure it.
Drop a ball one metre and it hits the floor in 0,45 seconds. A school stopwatch started and stopped by hand is about 0,2 s late at each end, so a class trying to time that fall is mostly measuring its own reflexes.
Tilt the same fall onto a ramp and nothing about the physics changes. It just runs slower. At about 10 degrees the acceleration drops from 9,8 to roughly 1,7 m·s-2, the trolley takes well over a second to cover a metre, and a stopwatch can handle it comfortably.
That is Galileo's method, and it is the entire reason the inclined plane exists as a piece of physics apparatus. It is not a shape. It is diluted gravity.
The two formulas, and that is all there is
Because the trolley starts from rest, x = ½at². Rearranged:
a = 2x ÷ t²
And on a ramp, only part of gravity acts along the slope:
a = g sin θ, which rearranges to g = a ÷ sin θ
Measure a distance, measure a time, measure the slope, and you have the acceleration due to gravity. A Grade 10 class can measure g with a plank, a tape measure and a stopwatch, and almost none of them are ever shown that they can.
You do not need a protractor
sin θ is the height of the raised end divided by the length of the ramp. That is what a sine is.
| Measure | With |
|---|---|
| The height of the raised end | The tape measure |
| The ramp length, along the slope | The same tape measure |
| sin θ | Divide the first by the second |
The angle in degrees never enters the calculation. A ramp 1,50 m long raised 0,26 m gives sin θ = 0,173, and 0,173 is the only number you need. It happens to be about 10 degrees, and knowing that changes nothing.
Measure the ramp along the slope, not along the floor. The slope is the hypotenuse and it is the longer of the two. Getting this wrong is the commonest reason a class ends up with a value of g that is too low.
Where this fits in the curriculum
| Subject | Physical Sciences |
|---|---|
| Grade | 10 |
| Term | 3 |
| Topic | Topic 7, Mechanics |
| Status | Not a prescribed experiment. See the note below |
| Marks | 52 on our worksheet. None is prescribed |
Grade 10 has no prescribed inclined plane practical. The curriculum gives free fall and g = 9,8 m·s-2 and never offers a way to measure either. There is one prescribed experiment in the whole of Topic 7 and it is a walking exercise with a stopwatch.
So this method is ours, and we would rather say so than dress it up as prescribed. It is a good practical, it uses the curriculum's own numbers, and it fills a gap the prescribed list leaves open.
Method
- Raise one end of the ramp about 0,25 m over a 1,5 m length. Gentle. If the trolley reaches the bottom in under a second, lower it
- Measure the ramp along its slope, and the height of the raised end. Write both down
- Mark a start line and a finish line as far apart as the ramp allows. Longer is better, and the reason is below
- Hold the trolley at the start line and let go without pushing. Start the stopwatch on the release
- Stop the watch as the trolley crosses the finish line
- Repeat at least five times and average the times
- Calculate a, then work back to g
One person should release and time. If one learner lets go and another starts the watch, you have added a second reaction time to the measurement.
A worked set of numbers
| Measurement | Value |
|---|---|
| Ramp length along the slope, x | 1,50 m |
| Height of the raised end | 0,26 m |
| sin θ = 0,26 ÷ 1,50 | 0,173 |
| Average of five timed runs | 1,33 s |
The acceleration:
a = 2x ÷ t² = 2(1,50) ÷ (1,33)² = 3,00 ÷ 1,77 = 1,70 m·s-2
And the acceleration due to gravity:
g = a ÷ sin θ = 1,70 ÷ 0,173 = 9,8 m·s-2
That is the accepted value, from a plank and a stopwatch. A class that lands between about 8,5 and 10,5 has done this well.
The mistake almost every version of this practical makes
Do not use a ball.
A steel ball and a dynamics trolley are routinely offered as alternatives, as though the two were interchangeable. They are not, and the difference is large.
A rolling object has to spend some of its energy on spinning, so less is left for moving forwards and it accelerates more slowly. For a solid ball rolling without slipping:
a = (5/7) g sin θ, which is 28,6 per cent less than a sliding object on the same ramp
| What you release | Its acceleration |
|---|---|
| A block sliding with no friction | g sin θ |
| A trolley on light wheels | Very close to g sin θ |
| A solid ball | 0,71 g sin θ |
| A hollow ball | 0,60 g sin θ |
| A solid cylinder, or a full tin | 0,67 g sin θ |
Run the same 1,50 m ramp with a solid ball and you measure 1,21 m·s-2 instead of 1,70. Divide by sin θ and you get g = 7,0.
A class that gets 7,0 will blame friction. Friction is not the problem. The ball is spinning, and a trolley's wheels are light enough that almost none of its energy goes into them.
Turn it into the best question of the lesson
Release a ball and a trolley from the same line at the same moment. The trolley wins, clearly and every time.
Ask why. It is not friction and it is not mass. A class that works out that the ball is spending energy on spinning has understood something most matric learners have not.
Reaction time is the error, and a longer run is the only fix
A hand on a stopwatch is roughly 0,2 s late, twice. That error does not shrink when you repeat a short run.
| Run length | Time | 0,2 s as a share of it |
|---|---|---|
| 20 cm | about 0,5 s | 40 per cent |
| 1,5 m | about 1,3 s | 15 per cent |
| A long, gentle ramp | 3,0 s | 7 per cent |
Averaging removes random error. Reaction time is largely systematic, because most people are late in the same direction at both ends, and the two only partly cancel.
So time one long run several times, rather than five short distances three times each. The five-distance version generates fifteen readings, every one of them shorter and therefore worse than a single full-length run.
Keep the five distances as a graphing exercise, because plotting x against t² and getting a straight line is genuinely worth doing. But take the number that goes into g from the long run.
Comparing surfaces, done honestly
The usual version covers the ramp with different materials and compares the accelerations. That works, but it buries a small friction effect inside a number that is mostly gravity.
A cleaner measurement: for each surface, raise the ramp slowly until the trolley just begins to move on its own.
| Surface | Angle at which it just starts to move |
|---|---|
| Bare board | Smallest |
| Cloth | Larger |
| Rubber matting | Largest |
That angle measures the friction and nothing else. There is no stopwatch in it, so there is no reaction time, and it is the most repeatable reading in the whole practical.
Grade 11 turns this into the coefficient of static friction. At Grade 10, "steeper before it moves means more friction" is exactly the right amount of the idea.
What you need
| Item | Qty | Why |
|---|---|---|
| Digital stopwatch | 4 | The whole measurement. One per group |
| Tape measure, 5 m steel | 2 | Does the protractor's job as well as its own. Height and slope length |
| Retort stand base and rod | 1 | Holding the raised end at a steady, repeatable height |
| Dynamics trolley, pair | 1 pr | Use a trolley, not a ball. Light wheels, so almost no energy goes into spin |
| Dynamic track | 1 | Straight and smooth. A plank works; a track works better and does not warp |
| Mass set | 1 | For the extension: does a heavier trolley accelerate differently? |
A plank, a shelf board or a length of skirting will do for the ramp. It needs to be straight and smooth, and nothing else.
Not supplied, and not needed: a protractor, because the tape measure replaces it, and a ball, because using one as the main object gives you g = 7,0.
What you should see
- Times that agree within about 0,3 s across five runs on the same ramp
- A value of g between roughly 8,5 and 10,5 with a trolley
- A value near 7,0 if a ball was used. That is the spin, not a mistake
- The trolley beating the ball, released together, every single time
- A steeper starting angle on rougher surfaces
If it does not work
| What happens | What caused it |
|---|---|
| g comes out around 7 | A ball was used instead of a trolley. The spin, not friction |
| g comes out well below 7 | Real friction, or a warped board. Check the wheels spin freely |
| g comes out too low and the ramp looked fine | The ramp was measured along the floor instead of along the slope. The slope is longer, so sin θ came out too big |
| Times vary by more than 0,3 s | The trolley is being pushed, or the watch anticipated. One person releases and times |
| Times are under a second | The ramp is too steep and reaction time is now most of the measurement. Lower it |
| The trolley veers off the side | A twisted board or misaligned wheels. A strip of masking tape as a guide rail helps |
| The trolley will not move at all | The ramp is too shallow for the friction present. Raise it slowly until it just moves, and record that angle. It is a result |
| g comes out above 9,8 | Usually a timing error, or the start line was crossed with the trolley already moving |
Safety
Very low hazard. No chemicals, nothing hot, no goggles.
- Put a hand or a book at the bottom of the ramp. A trolley leaving the end at 2 m·s-1 travels a long way
- Nobody stands at the bottom, and nobody stops a moving trolley with a foot
- Check the ramp is stable before releasing anything. A board balanced on a stack of books slides
- Secure any masses on the trolley. A loose mass leaving a moving trolley is the only thing in this practical that can actually hurt someone
- Keep bags off the floor around the ramp
How the 52 marks are made up
| Section | Marks |
|---|---|
| Why a ramp at all, including timing free fall | 7 |
| The measurements and the average | 9 |
| The calculation, a and then g | 10 |
| How close did you get, and why not closer | 8 |
| The ball and the trolley | 9 |
| Friction, measured by the starting angle | 5 |
| Conclusion | 4 |
No mark allocation is prescribed for this practical. The worksheet and this split are ours, as is the method.
The hardest question on the sheet asks what happens to g if the ramp is measured along the floor instead of the slope. The answer is that sin θ comes out too big, so g comes out too small.
The most valuable question asks whether the ball is slower because of friction. It is not, and a learner who refuses that answer has understood the practical.
If you have time
Load the trolley with masses and run it again. The acceleration does not change. Gravity pulls harder on a heavier trolley and the heavier trolley is correspondingly harder to accelerate, and the two cancel exactly. It is the same result Galileo got from the tower, on a bench.
Change the angle and plot a against sin θ. A straight line through the origin, and its gradient is g. This is a better way to get g than a single ramp, because it averages out over several angles.
Race a full tin against an empty one down the ramp. The empty one wins, and working out why is the rolling correction all over again.
Free worksheet and marking memo
Both free, no sign up, straight to the PDF.
- Learner worksheet, 52 marks, with the free fall calculation, your own ramp measurements, the route from a to g, the ball and trolley comparison and the friction question
- Marking memorandum, with a full worked sample, how to mark a value of g that came out at 7,0, and the four answers that look right and score nothing
Related practicals
- Ticker tape and motion graphs, Grade 10. The same measurement with a ticker timer instead of a stopwatch, and where the three motion graphs are built
- Conservation of energy with a pendulum, Grade 10. Same term, same stopwatch, and the other classroom route to g
- Newton's Second Law, Grade 11. Where the ramp and the trolley go next year, with a measured force added
- Static and kinetic friction, Grade 11. Where the starting-angle comparison becomes a coefficient of friction
- Vertical projectile motion, Grade 12. Free fall done properly, with the equations of motion
Buy this experiment
This is the cheapest practical in the Grade 10 mechanics range to run, and the only one a school with no budget can do properly this week. A plank, a tape measure and a stopwatch is the whole apparatus list.
The stopwatches and the tape measures are the lines worth buying, because the same set runs this practical, the ticker tape walking method and the pendulum. Four stopwatches covers a class of thirty working in groups.
The trolley and track are worth buying once and using for three years. The same pair runs this practical and the ticker tape one in Grade 10, Newton's Second Law in Grade 11 and conservation of momentum in Grade 12. Four published practicals off one purchase.
You do not need a protractor and you should not use a ball. The tape measure gives you sin θ directly, and a ball will hand you 7,0 where the answer is 9,8.