A Level Maths: Mechanics Pulley Question

🧠 A Level Maths: Mechanics — The Pulley Question Everyone Trips On

Let’s be honest — pulley problems look friendly. Two blocks, a bit of string, a smooth pulley. Easy marks, right?
Then you start drawing forces and suddenly it’s chaos. Signs flip, equations don’t match, and you’re wondering if the string’s haunted.

We’ve all been there.

This topic pops up in every A Level Mechanics paper because it checks whether you actually understand Newton’s Second Law — not just how to quote it. You’ll meet it in M1, again in M2, and it links straight into equilibrium and motion on inclined planes later.
So let’s slow it down and really get the logic clear.

🔙 Previous topic:

“Go back to see how connection and tension prepare you for pulleys.”

⚙️ Step 1 — Getting the Picture Straight

Always, always start with a diagram.
If the question gives you one, redraw it anyway — it helps you own the setup.

Two blocks, A and B, joined by a light inextensible string over a smooth pulley. Block A is 2 kg. Block B? Lighter, but we don’t yet know how much.

If it’s released from rest, which way do they move?
Right — the heavier one goes down. So A rises, B falls. Mark your directions before you touch any equations.

(Trust me — one arrow wrong and everything unravels later.)

✏️ Step 2 — Finding the Acceleration

We’re told:

Released from rest → u = 0
Displacement s = 3 m
Time t = 2.5 s

We want acceleration.

That’s a classic SUVAT job: s = ut + ½at².

Plug it in:
3 = 0 × 2.5 + ½a(2.5)².

Bit of rearranging → a = 0.96 m/s².

Looks tidy. And it passes the quick-sanity check — less than 1 g, which makes sense for a two-mass system where one side’s only slightly heavier.

✅ Exam Tip:
“Show that” questions aren’t asking for magic — they want the journey. Lay out your working line by line. Even if you lose the decimal, you’ll still earn most of the marks because the logic is visible.

And keep that acceleration safe — we’ll need it in a second.

⚙️ Step 3 — The Forces Game

Now for the proper mechanics bit — using F = ma.
This is where half the class sighs, so breathe.

For block A (moving up):
T − 2g = 2a.

For block B (moving down):
mg − T = ma.

Same tension throughout the string, same magnitude of acceleration, opposite directions.

That’s the beauty of an ideal pulley — equal and opposite forces, perfectly linked motion.

🧠 Little pause here:
You might be tempted to dive straight into numbers. Hold off.
First, decide what you actually need. The question says: find the mass of block B.
So tension’s just an accessory right now.

To get rid of it, add the two equations together. The T’s cancel neatly.

(That’s always satisfying.)

2g − mg = 2a + ma.

Now throw in the numbers: g = 9.8, a = 0.96.

19.6 − 9.8m = 1.92 + 0.96m.

Simplify it:
17.68 = 10.76m.

So m ≈ 1.64 kg.

Nice round result, lighter than 2 kg, direction check still fits.

✅ Quick sanity check:
If m had come out heavier than 2, the motion direction would flip — that’s your built-in “sense check.”
Always ask yourself: Does the answer fit the physical story? If not, there’s probably a sign error hiding somewhere.

✏️ Step 4 — Why the String Details Matter

You’ll often see phrases like light and inextensible string or smooth pulley. They’re not there for decoration.

Light → ignore the string’s own weight.
Inextensible → both blocks share the same acceleration.
Smooth pulley → no friction, so tension stays the same on both sides.

Those three words make the whole setup workable. If any of them changed — say, a rough pulley — then the tensions would differ and the algebra would get messy fast.

Tiny detour:
I once had a student who ignored “inextensible” every single time. He’d end up with two different accelerations and still wonder why his system didn’t make sense. It’s small details like that which separate a 7-mark script from a 10-mark one.

Anyway — back to the question.

⚙️ Step 5 — Pulling It Together

Let’s recap what we’ve done so far, just to clear the board in your head.

Drew the diagram (arrows first).
Found acceleration using SUVAT → 0.96 m/s².
Applied F = ma to each block.
Cancelled tension, solved for m → 1.64 kg.
Checked the logic and the units.

If that all holds, you’ve earned almost every mark in the question.

✅ Common Mistakes Worth Dodging

Sign errors. Decide “up = positive” or “down = positive” before you start, and stick with it.
Skipping the diagram. Even if you can picture it mentally, drawing fixes direction errors.
Forgetting g = 9.8 (or 9.81). Use what the paper gives you; don’t switch halfway.
Losing T too early. Sometimes you need tension for the next part — check the wording before cancelling.

It sounds obvious, but under pressure these are the first things that go.

🧠 Step 6 — Building Intuition

Here’s the bit most people miss: pulleys aren’t really about algebra. They’re about logic.

If two masses are equal, nothing moves — equilibrium.
If one’s heavier, that side goes down.
If friction appears later, acceleration shrinks.

Every pulley question is just a remix of those three ideas. Once you see the pattern, they stop feeling like “gotcha” questions and start feeling predictable.

And — small note — check your units. Forces in newtons, masses in kilograms, acceleration in m/s². Mix them and the numbers may look right but they’ll be nonsense physically.

💬 Quick Checkpoint

Alright, quick pause.

We’ve:

Used SUVAT properly.
Applied Newton’s Second Law twice.
Eliminated tension logically.
Found mass and sanity-checked direction.

Everything connects — that’s mechanics done well.

Next time, you might meet a friction pulley or one on a slope. Same logic, just an extra term or two. Don’t panic when you see it; trace the forces and it’ll fall into place.

💡 Quick Recap Table

Concept	Key Takeaway
SUVAT	For constant acceleration, pick the one with your four knowns.
F = ma	Write separately for each object, same acceleration if connected.
Equal tension	Only true with light, smooth, inextensible string.
Logic check	Direction must fit the mass difference.
Show-that questions	Display every step clearly — the mark scheme rewards method.

🧠 Reflection

Pulley questions are a bit like puzzles — they look mechanical but they test your reasoning. Once you start drawing and talking yourself through the motion, it feels less like algebra and more like storytelling.
Heavier side down, lighter side up, balance through the string.

Honestly, the diagram does half the thinking for you.

🚀 Next Steps

If this still feels a bit shaky, build from here. Try one where friction’s added, or where the pulley isn’t smooth — you’ll see how each assumption changes the maths.

And if you’re revising seriously, take a look at our 👉 February A Level Maths revision course. We break these big mechanics ideas into bite-sized lessons so you can walk into your exam with that calm, “I’ve seen this before” confidence.

About the Author

S. Mahandru is Head of Maths at Exam.tips and has more than 15 years of experience in simplifying difficult subjects such as pure maths, mechanics and statistics. He gives worked examples, clear explanations and strategies to make students succeed.

🧭 Next topic:

“Move on to variable acceleration — where the motion changes.”