What If? Lab
What if a table were very grippy?
A magnet can pull a paperclip across a table. But what if the table were very grippy, like rubber? Try it in Olly's lab!
A magnet only slides a paperclip toward it when its pull beats the grip of the table. Make the table four and a half times grippier and the clip 6 cm away stays put. But the magnet's reach shrinks by only about a fifth. Find out why.
A steel clip on a table moves only when the magnetic force, which falls off roughly as 1/r⁷ for a small magnet, exceeds static friction μmg. Because the force is so steep, raising μ from 0.2 to 0.9 cuts the reach only from 6.5 to 5.2 cm: reach scales as μ^(−1/7).
The big question
Olly puts a paperclip on a smooth table. He brings a magnet near. Zip! The clip slides to the magnet.
What if the table were very grippy? Would the clip still slide?
Put a paperclip on a table and slowly bring a magnet toward it. At some distance the clip suddenly jumps and slides to the magnet. Before that moment, something was holding it still: the grip of the table, called friction.
So what if the table were very grippy, like a rubber mat? Would the magnet still pull the clip in, and from how far away? In this lab you can change the table's grip and find out.
Two forces compete on the clip: the magnet's attraction and static friction, which can rise up to a maximum of μs times the normal force before the clip moves (OpenStax).
The question: if the coefficient of friction rose from 0.2 to 0.9, how would the distance from which the magnet can pull the clip change? The answer depends on how steeply magnetic force falls with distance.
Try the experiment
Make a prediction
The table gets much, much grippier. How far away can the magnet now pull a clip from?
The table becomes four and a half times as grippy. What happens to the magnet's reach, the distance it can pull clips in from?
μ rises from 0.2 to 0.9. How does the reach r*, where the magnetic pull equals the maximum static friction, change?
- It shrinks a lot, to under a quarter
- It shrinks a little, by about a fifth
- It does not change at all
| Control | In our world | What if… | Range |
|---|---|---|---|
| Table grip (friction) · How strongly the table holds the clip still. The magnet's pull has to beat this grip. | 0.2 | 0.9 | 0.1–1 |
| Paperclip distance · How far the clip is from the middle of the magnet. On the grippy table, try moving it to 5 cm. | 6 cm | — | 1.5–30 cm |
| Magnet strength · How strong the magnet is. The lab uses a 2.5 cm neodymium block (16). | 16 A·m² | — | 0.05–50 A·m² |
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Established fact
A still object starts to slide only when the push or pull beats its grip.
Static friction holds an object still by matching the force on it, up to a limit. Pull harder than that limit and the object starts to slide.
Static friction adjusts to oppose an applied force up to f_s(max) = μsN; beyond it, the object moves (OpenStax).
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What the model shows
In the model, the grippy table holds the clip still at 6 cm.
In this model, at 6 cm the magnet pulls with 1.66 mN. That beats a 0.2 table's grip (0.981 mN) but not a 0.9 table's grip (4.41 mN).
Model (m = 16 A·m², r = 6 cm): pull 1.66 mN; friction 0.981 mN at μ = 0.2 (ratio 170%, moves) and 4.41 mN at μ = 0.9 (ratio 37.7%, stays).
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What the model shows
A much grippier table makes the magnet's reach only a little shorter.
In the model, making the table 4.5 times grippier shrinks the magnet's reach only from 6.5 cm to 5.2 cm, because the pull grows so fast as the clip gets closer.
Since F ∝ 1/r⁷ in the model, r* ∝ μ^(−1/7): μ from 0.2 to 0.9 moves the reach from 6.5 to 5.2 cm.
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Established fact
Rubber on dry concrete is very grippy. Teflon is very slippery.
Typical grip numbers for starting to slide: about 1.0 for rubber on dry concrete, 0.5 for metal on wood and 0.04 for Teflon on steel.
Approximate static coefficients (OpenStax): rubber on dry concrete 1.0, metal on wood 0.5, shoes on wood 0.9, Teflon on steel 0.04.
A slippery table
On a slippery table, the clip slides easily.
The magnet's pull is stronger than the table's grip. So the clip zips over to the magnet.
The lab uses a strong neodymium block magnet and a steel paperclip 6 cm away, on a slippery table with a grip (friction coefficient) of 0.2.
In the model, the magnet pulls on the clip with 1.66 thousandths of a newton (mN), and the table can only hold back with 0.981 mN. The pull is 170% of the grip, so the clip slides in. The 'reach' readout says the magnet can pull clips in from as far as 6.5 cm.
With magnet strength m = 16 A·m² (a 2.5 cm neodymium block in the model), clip distance r = 6 cm and μ = 0.2, the model gives a field of 14.8 mT at the clip, a pull of 1.66 mN and a maximum friction of 0.981 mN for the 0.5 g clip. The ratio is 170%, so the clip moves.
The reach, where pull equals grip, is 6.5 cm. Inside it, every clip is pulled in.
Make the table grippy
Now Olly makes the table very grippy, like a rubber mat.
The magnet pulls just the same. But now the table holds the clip tight, and it does not move!
Now raise the table's grip to 0.9, four and a half times as grippy. The magnet still pulls with 1.66 mN, but now the table can hold back with 4.41 mN. The pull is only 37.7% of the grip, so the clip stays put.
Slide the clip closer. At 5 cm the pull jumps to 5.96 mN, stronger than the grip, and the clip zips in. The reach is now 5.2 cm: smaller, but only by about a fifth.
At μ = 0.9 the maximum static friction is 4.41 mN. The pull at 6 cm is unchanged at 1.66 mN, only 37.7% of it, so the clip stays. The reach falls to 5.2 cm; at 5 cm the pull is 5.96 mN (135% of the grip) and the clip moves.
Friction rose by a factor of 4.5, yet the reach shrank only from 6.5 to 5.2 cm, a factor of about 1.24.
Why the reach barely shrinks
A magnet's pull gets weak very fast as you move away. It gets strong very fast as you move closer.
So the clip only has to be a little closer for the pull to win again.
A magnet's pull fades extremely quickly with distance. In the model, moving the clip from 6 cm to 5 cm makes the pull more than three times stronger.
So when the table grips harder, the magnet doesn't need to be much closer to win again. That's why a grippy table shrinks the magnet's reach only a little. The model treats the clip as a tiny ball of iron, and real clips, being long and thin, can be pulled from a bit farther.
On a small magnet's axis the field is B = (μ₀/4π)(2m/r³). The clip's induced magnetization is proportional to B, and the force to B·dB/dr, so F ∝ m²/r⁷. Setting F equal to μ·m_clip·g gives a reach r* ∝ (m²/μ)^(1/7): multiplying μ by 4.5 divides r* by 4.5^(1/7) ≈ 1.24.
The model's simplifications: an ideal point dipole (poor within a few magnet lengths), a clip treated as a soft-iron sphere, equal static and sliding friction, and motion only along the axis. Real clips magnetize more easily along their length, so real reaches can be larger, though they scale the same way.
Grip in the real world
Different things grip each other in different ways.
Rubber on dry concrete grips a lot. Teflon on steel is very slippery. Grip helps keep things from sliding.
Scientists measure grip with a number called the coefficient of friction. OpenStax lists some typical values for things just starting to slide: about 0.5 for metal on wood, 0.9 for shoes on wood, and 1.0 for rubber on dry concrete. Teflon on steel is only 0.04.
Things are usually harder to start sliding than to keep sliding. Our model uses one number for both, which is one of its simplifications.
OpenStax's table of approximate coefficients gives static and kinetic values: rubber on dry concrete 1.0 and 0.7, metal on wood 0.5 and 0.3, shoes on wood 0.9 and 0.7, Teflon on steel 0.04 and 0.04. Static friction is a responsive force that matches the applied force up to μsN; beyond that the object moves, and kinetic friction, usually smaller, takes over.
The model uses a single coefficient for starting and sliding, so it misses the sudden 'jump' that happens when a clip breaks free and the friction drops.
Amazing facts
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Starting to slide is harder than keeping on sliding.
It usually takes more force to start something sliding than to keep it sliding: static friction is bigger than sliding friction.
For most surface pairs μs > μk; OpenStax lists rubber on dry concrete at 1.0 static and 0.7 kinetic.
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A magnet's pull fades very fast as you move away.
In the model, moving a clip from 6 cm to 5 cm from the magnet more than triples the pull on it.
With F ∝ 1/r⁷, a 17% shorter distance gives (6/5)⁷ ≈ 3.6 times the force, matching the model's 1.66 → 5.96 mN.
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Teflon is one of the most slippery things on the list.
Teflon sliding on steel has a friction coefficient of only about 0.04, much less than shoes on wood at 0.9.
OpenStax gives μs ≈ μk ≈ 0.04 for Teflon on steel, compared with 0.9 and 0.7 for shoes on wood.
Words to know
- friction
- the grip between two surfaces that resists sliding
- static friction
- the friction that holds a still object in place until the push or pull gets big enough
- coefficient of friction
- a number that says how grippy two surfaces are together
- magnetic field
- the region around a magnet where it can push or pull on magnetic materials
- newton
- the unit of force; a millinewton (mN) is a thousandth of a newton
- reach
- in this lab, the farthest distance from which the magnet can pull a clip in
Discovery challenge
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When does the clip start to slide?
When does the paperclip start to slide toward the magnet?
The clip begins to move when…
- When the magnet pulls harder than the table grips
- As soon as the magnet is in the room
- Only when the table is wet
Show the answer
When the magnet pulls harder than the table grips
When the magnet's pull is stronger than the grip.
When the magnet's pull is bigger than the most the table's grip can hold back.
…the magnetic force exceeds the maximum static friction, μsN.
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On the very grippy table, does the clip 6 cm away move?
In the lab, with a grip of 0.9, does the clip 6 cm away move?
At μ = 0.9 and r = 6 cm, is the pull larger than the grip?
- No, it stays still
- Yes, it zips in
- It slides away from the magnet
Show the answer
No, it stays still
No. The table holds it tight.
No: the pull is only 37.7% of the grip.
No: 1.66 mN against 4.41 mN, a ratio of 37.7%.
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The table gets much grippier. What happens to the magnet's reach?
Making the table 4.5 times grippier changes the magnet's reach from 6.5 cm to about…
With μ raised from 0.2 to 0.9, the model's reach becomes about…
- 5.2 cm
- 1.4 cm
- 6.5 cm
Show the answer
5.2 cm
It gets a little shorter: about 5.2 cm.
About 5.2 cm: only about a fifth shorter.
5.2 cm, since r* ∝ μ^(−1/7) and 4.5^(1/7) ≈ 1.24.
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Which is the most grippy?
Which pair of surfaces has the highest friction coefficient in the textbook list?
Which pair has the largest static coefficient in OpenStax's table?
- Rubber on dry concrete
- Metal on wood
- Teflon on steel
Show the answer
Rubber on dry concrete
Rubber on dry concrete is the grippiest here.
Rubber on dry concrete, about 1.0.
Rubber on dry concrete, μs ≈ 1.0 (metal on wood 0.5, Teflon on steel 0.04).
Experiments to try
- Watch Try it What If? Lab What if a magnet were farther away? A magnet's pull fades astonishingly fast. In our model, a neodymium magnet yanks a paperclip in from 5 centimeters away. Move the clip to 10 centimeters, just twice as far, and the magnetic field is one eighth as strong, but the pull on the clip is 128 times weaker, far too weak to slide it across the table.
- Watch Try it What If? Lab What if magnets became stronger? A magnet's pull fades very fast as you move away. In our model, a ceramic magnet can't budge a paperclip 5 centimeters away, but a magnet three times stronger pulls it right in. Yet its reach grows by much less than its strength.
- Watch Try it What If? Lab What if there were no friction? Friction is the grip between two surfaces. It slows a wooden block sliding down a ramp and stops it on the floor. Switch friction off in our model and the block races down faster and then slides along the floor forever.
- Watch What If? Lab What if there were no magnets? You can see magnets holding pictures on a fridge, but most magnets are hidden. They sit inside electric motors, speakers and the generators that make electricity, and a compass needle is a magnet too. Imagine a world with no magnets and follow what might stop working.
- Watch What If? Lab What if every surface were slippery? Friction is the grip between surfaces. It lets you walk, hold a pencil and stop a bike. Imagine a world where every surface was as slippery as ice, and follow what would happen to walking, writing and driving.
Explore next
- Watch Try it What If? Lab What if a magnet were farther away? A magnet's pull fades astonishingly fast. In our model, a neodymium magnet yanks a paperclip in from 5 centimeters away. Move the clip to 10 centimeters, just twice as far, and the magnetic field is one eighth as strong, but the pull on the clip is 128 times weaker, far too weak to slide it across the table.
- Watch Try it What If? Lab What if magnets became stronger? A magnet's pull fades very fast as you move away. In our model, a ceramic magnet can't budge a paperclip 5 centimeters away, but a magnet three times stronger pulls it right in. Yet its reach grows by much less than its strength.
- Watch Try it What If? Lab What if there were no friction? Friction is the grip between two surfaces. It slows a wooden block sliding down a ramp and stops it on the floor. Switch friction off in our model and the block races down faster and then slides along the floor forever.
- Watch What If? Lab What if there were no magnets? You can see magnets holding pictures on a fridge, but most magnets are hidden. They sit inside electric motors, speakers and the generators that make electricity, and a compass needle is a magnet too. Imagine a world with no magnets and follow what might stop working.
- Watch What If? Lab What if every surface were slippery? Friction is the grip between surfaces. It lets you walk, hold a pencil and stop a bike. Imagine a world where every surface was as slippery as ice, and follow what would happen to walking, writing and driving.
- Watch Try it What If? Lab What if gravity disappeared? Gravity is the pull that makes a dropped ball fall and keeps your feet on the ground. Switch it off in our model and watch what a ball does instead, then find out why astronauts float.
- Watch Try it What If? Lab What if water were denser? Water pushes up on anything you put in it. A heavier, denser liquid pushes up harder. In our model, a block that sinks in water floats in a pretend liquid twice as dense, with only 60 percent of it under the surface.
- Watch Try it What If? Lab What if wheels were square? A square wheel on a flat road lifts its axle up and down with every corner. In our model it bounces almost 9 centimeters and loses most of its motion at each bump. On a road of curved humps, though, the same square rolls perfectly smoothly.
For parents & teachers
What children will learn
- An object at rest starts to slide only when the force on it beats the maximum static friction.
- A magnet's pull weakens very quickly with distance.
- Because the pull changes so steeply, even big changes in friction change a magnet's reach only a little.
- Models simplify: this one treats a paperclip as a tiny iron ball and uses one friction value.
Recommended ages: 12 to 17 · About 15 minutes
Talk about it
- Where else do you see a force that has to 'win' against friction before anything moves?
- Why might a long, thin paperclip be pulled from farther away than the model says?
- How could you make a magnet's reach bigger without changing the table?
Try at home or in class
- Place a paperclip on a smooth table and slide a fridge magnet slowly toward it. Mark where the clip first jumps. Repeat on a rubber mat or a towel and compare the distances.
- Try two different fridge magnets on the same towel. Which changes the jump distance more: the magnet or the surface? (Use fridge magnets: strong magnets can pinch fingers, and small magnets must be kept away from young children.)
Key vocabulary: friction, static friction, coefficient of friction, magnetic field, newton, reach
Where these facts come from
- University Physics Volume 1, §6.2 Friction , OpenStax
- University Physics Volume 2, §12.7 Magnetism in Matter , OpenStax
Checked, not yet human-reviewed. Last updated October 26, 2026. Spotted a mistake? Tell us.