Newton's Second Law: Force, Acceleration and the Trolley Experiment
Newton's Second Law states that when a net force is applied to an object of mass m, the object accelerates in the direction of that force. The acceleration is directly proportional to the net force and inversely proportional to the mass. Written as an equation, Fnet = ma. This page explains the law, shows how to draw the free body diagrams it depends on, and gives the Grade 11 prescribed experiment that tests it, including the one mistake that turns a straight-line graph into a curve.
Where this fits in the curriculum
| Subject | Physical Sciences |
|---|---|
| Grade | 11 |
| Term | 1 |
| Topic | Mechanics, Newton's laws |
| Status | Prescribed experiment for formal assessment |
| Marks | 40 |
What the law actually says
Newton's First Law tells you that an object keeps doing what it is doing unless a net force acts on it. The Second Law tells you what happens when one does.
Three things follow from Fnet = ma, and all three are examined:
- The acceleration is in the same direction as the net force
- Double the net force and you double the acceleration. They are directly proportional
- Double the mass and you halve the acceleration. They are inversely proportional
The word that carries the marks is net. It is not the force you apply, it is the sum of every force acting, including friction and the normal force. Which is why the next section matters.
Free body diagrams
A free body diagram shows one object on its own, with every force acting on it drawn as an arrow, and nothing else.
Three rules that account for most of the lost marks:
- One object per diagram. If two objects are connected, draw two diagrams
- Only forces acting ON the object. Not forces it exerts on other things
- Label every arrow, and make the lengths roughly proportional to the sizes
A worked example: the trolley and the hanging mass
This is the setup in the experiment below, and it is the one learners find hardest, because there are two objects and they are connected by a string.
The trolley, on the bench:
- Weight Mg straight down
- Normal force N straight up from the bench
- Tension T forward, along the string
The weight and the normal force cancel, so the net force on the trolley is just T. That gives T = Ma.
The hanging mass, in the air:
- Weight mg straight down
- Tension T straight up
It accelerates downwards, so mg − T = ma.
Solve the two together and you get a = mg ÷ (M + m) and T = Mmg ÷ (M + m).
The experiment
Investigate the relationship between force and acceleration.
Apparatus
| Item | Qty |
|---|---|
| Dynamics trolley | 1 |
| Bench pulley, clamps to the table edge | 1 |
| Set of mass pieces | 1 |
| Stopwatch | 1 |
| Tape measure | 1 |
Plus string, plasticine, and a smooth bench at least 2 m long.
Method
- Clamp the pulley to the edge of the table.
- Put the trolley on the table, tie the string to its front end, run the string over the pulley and let it hang.
- Press a small piece of plasticine onto the front of the trolley as a buffer.
- Compensate for friction. Add small pieces of plasticine to the hanging string until the trolley moves at constant speed after a small push. Once it is right, do not move it again.
- Hold the trolley still and hang a mass piece from the string.
- Mark the start and measure the distance to the pulley. At least 2 m.
- Release the trolley and time the run. Three readings, averaged.
- Calculate the acceleration.
- Add another mass piece and repeat, at least four times.
- Draw the two free body diagrams and work out the net force on the trolley for each run.
- Plot acceleration against net force and describe the graph.
Why the friction step is not optional
Step 4 is the one classes rush and it is the one that decides the result. Adding plasticine until the trolley coasts at constant speed means the friction force is exactly balanced, so the only unbalanced force left is the tension. Every calculation afterwards assumes that.
Too little plasticine and the trolley slows. Too much and it speeds up on its own. You want it to keep going at whatever speed you gave it.
Working out the acceleration
You never measure acceleration directly. You measure a distance and a time:
Δx = viΔt + ½a(Δt)²
The trolley starts from rest, so vi = 0, leaving a = 2Δx ÷ (Δt)²
The mistake that turns the graph into a curve
This is the single most useful thing on this page, and no printed method warns you about it.
When you hang a mass from the string, two things accelerate: the trolley on the bench and the mass in the air. They are joined, so they move together. That gives you two different forces:
| What it is | Is it the net force on the trolley? | |
|---|---|---|
| mg | The weight of the hanging mass | No. It drives the whole system |
| T | The tension in the string | Yes. This is what pulls the trolley |
Every mass piece you add increases the driving force and the total mass being accelerated. So acceleration does not keep up, and a plotted against mg bends over.
With a 0,50 kg trolley over a 2,00 m run:
| Hanging mass | mg | Acceleration | a ÷ mg | Tension T | a ÷ T |
|---|---|---|---|---|---|
| 0,05 kg | 0,49 N | 0,89 m·s⁻² | 1,82 | 0,445 N | 2,00 |
| 0,10 kg | 0,98 N | 1,63 m·s⁻² | 1,67 | 0,817 N | 2,00 |
| 0,15 kg | 1,47 N | 2,26 m·s⁻² | 1,54 | 1,131 N | 2,00 |
| 0,20 kg | 1,96 N | 2,80 m·s⁻² | 1,43 | 1,400 N | 2,00 |
Against mg the ratio falls steadily, which is a curve. Against T it is constant, which is a straight line through the origin.
The gradient is 1 ÷ M, so a class that measures the gradient has effectively weighed the trolley off a graph.
One thing to be careful about
Work the tension out from the masses, using T = Mmg ÷ (M + m). If a learner instead calculates T as M × a using their own measured acceleration, the graph is straight by construction and proves nothing at all.
What you should see
A straight line through the origin. Acceleration is directly proportional to the net force, which is Newton's Second Law.
If it does not work
| What you see | What caused it |
|---|---|
| The graph curves | Acceleration was plotted against the hanging weight instead of the tension. See above |
| The line misses the origin | Friction was not fully compensated. Redo the plasticine step |
| The trolley slows before it arrives | Not enough plasticine, or a stiff wheel |
| The trolley creeps forward on its own | Too much plasticine. Take some off |
| Times vary wildly between readings | Reaction time, roughly 0,2 s. Use the longest run the bench allows |
| The trolley veers sideways | The string is not pulling straight. Line the pulley up with the trolley |
On reaction time, honestly
A hand-operated stopwatch carries about 0,2 s of error. On a 2 s run that is 10 %, and it enters the acceleration twice because the time is squared.
Use the longest run your bench allows. A 3 s run halves the percentage error against a 1,5 s one. This is worth discussing with the class rather than hiding, because the evaluation question asks for exactly this kind of answer.
How the 40 marks are made up
| Section | Marks |
|---|---|
| Method, variables and friction compensation | 8 |
| Results table | 8 |
| Free body diagrams and net force | 8 |
| Graph | 10 |
| Conclusion and evaluation | 6 |
The graph carries the most marks and the free body diagrams are the hardest. Between them they are nearly half the assessment.
If you have time
This experiment holds the mass constant and changes the force. Do the reverse: keep the force constant and load the trolley with mass pieces. Acceleration should be inversely proportional to mass, so a graph of a against 1 ÷ M comes out straight. Between the two you have the whole of F = ma.
Free worksheet and marking memo
Both free, no sign up, straight to the PDF.
- Learner worksheet, 40 marks, with the planning, results table, free body diagram space and graph questions set out for the formal assessment
- Marking memorandum, with a fully worked sample set, the mark allocation and a note on the six places learners most often drop marks
Buy this experiment
We are putting together a complete Newton's Second Law Kit for Grade 11 with the trolley, bench pulley, masses, stopwatch and tape measure in one box, plus a printed teacher guide and the marking memo. Coming shortly.
Most schools already own a trolley and a stopwatch. What they usually do not have is a bench pulley that clamps to the table edge, and without one this practical is very difficult to set up properly. Every item above is sold separately.