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🏗️ Newton’s Laws: Lifts, Contact Forces, Blocks and Tension Problems
🏗️ Newton’s Laws: Lifts, Contact Forces, Blocks and Tension Problems
Right — today we’re doing Newton’s Laws in the “real mechanics” way, not the perfectly polished version from textbook pages. Lifts, tension, blocks pushing each other, strings pulling things around corners — this is where the diagrams finally start feeling like physics.
And somewhere in this, your A Level Maths understanding shifts from “equations on paper” to actually modelling what objects do — the kind of insight you only build through steady A Level Maths tips that focus on real motion.
Newton’s Laws are simple; it’s the situations that twist themselves into knots. So we’re slowing the pace, letting the messy working breathe, and building confidence piece by piece.
🔙 Previous topic:
Our work on Moments: Non-Uniform Rods, Beams and Equilibrium leads naturally into this, because once you’re confident balancing forces and turning effects, Newton’s Laws problems start to feel far more structured and predictable.
📘 Where Newton’s Laws Questions Usually Appear
Exam boards love these problems because they reveal whether a student can model forces consistently.
Expect setups like:
- lift accelerating up or down
• two blocks connected by a string
• a block pushing another block
• tension in a light, inextensible string
• reaction forces at walls or floors
• forces at angles creating vertical and horizontal components
It’s never the algebra that breaks students — it’s the diagram discipline.
🧩 Typical Problem Setup
Imagine two blocks on a smooth horizontal surface. Block A of mass m is connected by a light string over a pulley to block B of mass M hanging vertically.
We want acceleration and the tension in the string.
Forces you’ll often see:
- weight of each mass → mg and Mg
• tension in the string → same throughout (light, inextensible)
• normal reaction from the surface
• sometimes friction, depending on the variant
Everything comes back to Newton’s 2nd Law:
Resultant force = mass × acceleration.
🖼️ Required Diagram
🧠 Key Ideas Explained
🪜 Step One — Treat Each Block as Its Own Universe
This is the step students skip when they’re nervous.
Each block gets its own free-body diagram and its own equation of motion.
Even when blocks are connected, they don’t share forces — they share the acceleration.
That’s the key insight: the constraint of the string synchronises acceleration, not forces.
Write “same acceleration” on your diagram. It prevents half the classic mistakes.
🎢 Step Two — Know When Tension Helps and When It Fights You
Tension always pulls towards the string.
On a horizontal block, it might be the only horizontal force.
On a hanging block, it fights gravity.
Where misconceptions explode is assuming tension must equal weight — nope. That is only true in equilibrium, not in motion.
Most real Newton’s Laws questions live in this gap between static intuition and dynamic truth.
⏫ Step Three — Lifts: Where Normal Reaction Reveals Everything
Lifts are exam-board favourites because the same diagram can give:
- a normal reaction bigger than mg (accelerating up)
- a normal reaction smaller than mg (accelerating down)
- normal reaction equal to mg (moving at constant speed)
The relationship usually comes from something like:
We might write R – mg = ma when accelerating upward.
Rearrange depending on direction of motion.
And ignore “weight felt” wording — it’s just the normal reaction pretending to be a sensation.
Somewhere in this section, the whole topic suddenly feels clearer — the kind of shift you get when A Level Maths revision made simple focuses on spotting positive and negative directions before you start plugging numbers in.
🔗 Step Four — Blocks Pushing or Pulling Each Other (Internal Forces)
Two blocks in contact?
Push the first one, and a contact force appears between them.
But here’s the trick: the internal force is equal and opposite on each block, but the accelerations stay the same.
This is Newton’s 3rd Law in the most exam-friendly form.
You solve by treating both blocks as a system first, then isolating one block to find the contact force.
It’s elegant when drawn correctly — chaotic when not.
🎣 Step Five — Strings, Pulleys & Tension Consistency
If the string is:
- light
- inextensible
- over a smooth pulley
…then tension is the same everywhere.
But if any of those assumptions break, tension changes — and examiners love asking whether students noticed.
Even with consistent tension, each block will have unique forces acting on them.
And yes, you always write two equations, not one.
⚖️ Step Six — Positive Direction Isn’t a Guess
Before you write anything, choose up or down (or left or right) as positive.
Stick to it ruthlessly.
Half of Newton’s Laws errors come from silently switching sign conventions mid-question.
Once direction is declared, every force follows that sign rule — even if it “feels wrong.”
Direction isn’t emotional. It’s bookkeeping.
🧱 Step Seven — Combining Newton’s 1st, 2nd & 3rd Laws Without Overthinking
1st Law → equilibrium → resultant force = 0
2nd Law → motion → resultant force = ma
3rd Law → interaction forces → equal and opposite
Most questions blend all three:
• 1st Law on one block
• 2nd Law on another
• 3rd Law between them
Newton would be proud if students realised he never expected them to memorise anything — he expected understanding.
🌍 Real-World Link
Pulling a trolley with a strap, a lift starting suddenly, pushing two boxes across a floor, handling loads with ropes — you’ve lived Newton’s Laws without noticing.
Mechanics simply slows the world down so the forces become visible.
🚀 Next Steps
If you want Newton’s Laws problems — lifts, strings, blocks pushing blocks, all the awkward tension setups — to feel predictable rather than chaotic, the A Level Maths Revision Course that builds confidence walks you through the modelling habits, direction choices, diagram discipline and reasoning templates exam boards expect you to master.
📏 Recap Table
• Draw each block separately
• Tension is consistent only in ideal strings
• Normal reaction reveals lift behaviour
• Contact forces follow Newton’s 3rd Law
• Direction choice must be fixed
• Use one equation per block
Author Bio – S. Mahandru
I’m a mechanics teacher who thinks of moments like tiny stories about balance — shift a weight here, adjust a support there, and the whole system reveals what it wants to do. Once students see that equilibrium is more about intuition than algebra, the topic suddenly feels far less mysterious and far more satisfying.
🧭 Next topic:
After getting comfortable with Newton’s Laws and how forces drive motion in lifts, blocks, and tension setups, the natural next step is Work, Energy & Power: Efficiency, Resistance & Real Exam Questions, where those same forces start translating into energy changes and real-world performance.
❓ Quick FAQs
Why do we bother drawing each block separately? I mean… can’t we just treat the whole system as one thing?
Honestly, yes — sometimes treating it as one thing is quicker, and I even encourage it… but only after you’ve drawn the separate diagrams. Each block has its own little world of forces acting on it, and the moment you skip that step, weird things start happening. You mix signs. You forget where tension goes. You treat friction like it magically applies to both. And then you’re four lines in thinking “hang on— why doesn’t this make sense?”
The separate diagrams force you to slow down long enough to see the structure: who pulls whom, who resists what, where acceleration actually points. Once you’ve got that, combining them is easy, almost obvious. But if you jump straight to the combined system, you lose the internal story — and that “internal story” is usually where the marks live. Treat them separately first, even if you don’t feel like it. Future-you will be grateful.
Why does the normal reaction get bigger or smaller in lifts? It feels weird — shouldn’t my weight just be my weight?
Yes — and that’s the exact misconception that tangles everyone. Your actual weight never changes; it’s mg whether you’re in a lift or on the Moon. What changes is the push from the floor. And that push — the normal reaction — is just the lift trying to keep you moving the way it’s moving.
If the lift shoots upward, it has to shove harder on you to give you the same upward acceleration. If it slows down while going up, the shove relaxes a bit. And if it drops suddenly, the floor barely touches you — that odd flutter in your stomach? That’s just R dipping below mg for a moment.
Students often overthink this, but really, R is a mood ring for the lift’s motion: hard shove = accelerating up, soft shove = accelerating down, no shove = free fall (which hopefully never appears outside the exam paper). Once you separate R from “how heavy I feel,” lift problems calm right down.
Tension keeps confusing me. Why does it change when the setup changes? Isn’t a string just… a string?
I wish it were that simple. Think of tension less like a fixed quantity and more like the string doing whatever it must to keep itself un-stretched. That’s its entire personality. Nothing else.
If two blocks accelerate, tension adjusts to make that possible while keeping the string length constant. If one block is heavier, the system shifts around until the acceleration and tension fit the constraints. And here’s the messy bit students rarely say out loud: tension isn’t “decided by” the string — it’s decided by the equations of motion on each block.
Different masses? Tension settles somewhere between their weights. Add friction? Tension rebalances again. Put the system on an incline? It changes once more. It’s reactive, not constant. Honestly, once you stop expecting tension to behave nicely — like a polite houseguest — and start treating it as a force that negotiates between both ends of the string, everything clicks. The diagrams begin telling the story, and tension stops feeling mystical.