Lockdown Challenge: Rolling stones forever

Lockdown Challenge #41: Hammer time on the marble run

Every time you talk on the phone, you are using optical fibres. After a radio link, photons of light carry the data to everywhere on the planet, inside fibres of ultra-pure glass. The fibres are highly transparent, but the photons still get absorbed, halving every 15km. So optical fibres can’t do it on their own: you must have amplifiers too. Every 100km an erbium-doped fibre amplifier boosts the signal.

It’s the same with marbles. They set off down a long track, but after 3 or 4 metres they run out of puff. But not if you have marble amplifiers like the ThorHammer. This is a small wooden hammer – a kind of mini golf club. It sits poised with its light end resting just above the marble track, ready to go. Then, when it’s hit by a slow marble, the heavy end swings down and wallops the marble down the track.

To make the marble amplifier, you will need some marbles (15mm or 22mm), wood, some nails, and three or more 3m lengths of half-round channel like rainwater guttering. (112mm size is less than £2/m.) To make the hammers, find thin laths of wood, maybe 12 x 8mm or so, to make hammers 20cm long with a 4 x 2 x 2cm block of wood for the head.

Make the hammer bases by glueing two flat pieces of wood like floorboard at right angles. Then glue a block on the base that will put the hammer in right place. Next, you need to drill and then nail the hammer shaft in the middle so it just clears the track as it swings. Use washers to ensure it swings freely. A long thin nail in the top of the block, or maybe thin fence wire, will provide a rest for the hammer to nestle against when the head is raised in the ready position. Now set up the track on a flat surface, with a ramp to launch the marble. Keep the track flat with supports the same height as the hammer bases. Join the channel sections accurately with tape (no ridges please!).

Set up your two hammers spaced down the track. Set up the ramp to launch the incoming marble just fast enough to reach the first hammer. Now, with hammerheads raised, Launch! Roll-roll-trundle-trundle… biff-BIFF!-ROLL-roll-roll-trundle-trundle… biff-BIFF!-ROLL-roll-roll-trundle-trundle…

How does it work? The potential energy of the hammer, weight x height, provides the energy. When it collides with a marble of similar weight, the marble will ping off with much of that energy. At speed v a marble of mass m will have kinetic energy ⁷/₁₀ mv², from the hammer’s potential energy. Why not the famous ½ mv² for kinetic energy? Because ²/₇ of the marble’s kinetic energy goes into rotation when it’s rolling. So, the marble pings off slower than you might think.

Why do marbles on a flat track slow down? That’s down to friction. Rolling friction, admittedly, which is teeny-weeny, hundreds of times smaller than sliding friction. That’s why things that rotate a lot use roller or ball bearings.

What about a longer hammer? However long the hammer, the incoming marble needs to be slow: if it’s too fast, the hammer will miss it. But a longer hammer will be closer to the track for longer, which is helpful. But the hammer fall time goes like a pendulum, as the square root of length, only 2-3 times slower. If you make it too long, the marble will have rolled too far to be hit.

And finally… Can you make a longer track – three or four hammers? Can you use bigger marbles, or superballs maybe? And what about a track with bends?

If you liked this, you will find lots more fun science stuff in Neil Downie’s books, like ‘The Ultimate Book of Saturday Science’ from Princeton University, and for lots of other things (and a free copy of the ‘Exploding Disk Cannons’ book), visit www.saturdayscience.org

There is also the back catalogue of Lockdown Challenges from 2020 to choose from if you are looking for more options. The IET also has a host of resources that adults can use to engage children with the world of STEM.