How long would it take to fall through the Earth?

This is a classic calculation, and one that’s surprisingly tricky: suppose you could bore a hole all the way through the Earth. If you jumped in, how long would it take you to fall through and come out of the other side?

If you’re taking A-level physics you know pretty much everything you need to do the calculation for yourself, but there are a few fiddly little problems you need to deal with along the way. Most importantly: if you’re falling through the Earth, only some of it is below your feet. The rest of it is above your head, and the force of gravity from that part is pulling you not downwards but upwards. So working out the forces isn’t as simple as you might hope, but you do get something back: when you start picking away at the maths, you’ll find that what happens when you reach the centre of the planet is pretty important.

Have a think about how you’d tackle the problem yourself, then take a look at this video from MinutePhysics.

Tip of the hat to Alom Shaha for pointing us to this.

Engineering principles: keep it simple

We’re developing a neat little workshop based around catapults, bits of which have sneaked out into the world in test events over the last couple of months. The core of the challenge is the simplest possible catapult we could dream up, which uses a paper cup, elastic band and a plastic spoon to fire a table tennis ball at least five metres. It’s tremendously satisfying, but it’s not quite enough on its own for the workshop.

My Mark II Catapult uses the same basic ingredients, but pivots the spoon on a kebab stick bearing. It’s even more satisfying, but a little more fiddly to make and – annoyingly – slightly less effective in range.

This morning: the Mark III Catapult, which uses the elastic band as a torsion spring. It’s fiddly to make, pushes the limits of cardboard cup rigidity even more than the other designs, and…

…is almost completely ineffective.

Back to the drawing board, with one key engineering principle ringing in our ears: keep it simple.

Turns out motor racing might be useful after all

The Formula 1 Championship is a strange beast. I’m not alone in having become thoroughly bored with the political wranglings around it, and I’ve drifted far enough away that I no longer even recognise most of the team names. So it’s something of a surprise to learn that the engineering work going on behind the scenes might still be – whisper it – relevant and useful.

Click for animated diagram of an internal combustion engine, from the excellent Animagraffs.com.

Burning petrol in a car engine is fairly mad in the grand scheme of things, partly because internal combustion engines are horribly inefficient. They typically bumble along around the 20 or 25 per cent thermal efficiency mark: only one fifth or so of the energy input (in the form of petrol) is turned into useful work. That’s not necessarily a great surprise if you look at everything that’s going on inside an engine –  click the picture for a brilliant Animagraffe page illustrating the four-stroke engine cycle. Car engines get hot, and that heat isn’t doing anything to propel you down the road.

Diesel engines can head up towards 40% efficiency, but even as recently as 2014 it was big news when Toyota managed to hit 38% for a petrol engine, which I think is the one currently in their latest Prius hybrid.

So a rumour that the Mercedes and Ferrari F1 teams have petrol engines that achieve somewhere around 47% efficiency is eye-catching. They’re managing this thanks to German engine component supplier Mahle, whose design adds a secondary combustion chamber linked to the main cylinder head. The spark plug ignites a fuel-rich mixture in that secondary chamber, blasting a turbulent jet of burning gases into the leaner mixture in the cylinder. That leads to more complete combustion, and hence a more efficient engine overall.

Now, internal combustion engines are at their most efficient when they’re operating under load (ie. accelerating) and with the throttle full open (ie. accelerating hard). Which is more like the typical situation for Formula 1 engines than a daily commute, bumbling along in nose-to-tail traffic. So gains at the racing circuit don’t necessarily mean as much on the public road. Nevertheless, the thought that there are still major gains to be wrung out of old engine technology is surprising, and encouraging. Maybe we’ll see some of these ideas in road cars in the not-too-distant future?

Read more about the ‘Turbulent Jet Ignition” technology in this excellent Ars Technica article.

In fact, engine technology remains a huge field of research. Here’s engineer Hannah Petto giving a behind-the-scenes peek of the engine test facilities at Caterpillar’s engine research site, here in the UK, outside Peterborough:

The racing teams may have all the showy glamour, but there’s similar sorts of work going on for construction and agricultural machinery.

Not-so-coincidentally, the Think Physics office is currently reverberating to the sound of power tools and hydraulic hammers, as the building here at Northumbria University is being partially rebuilt to accommodate – amongst other things – a new engine test facility similar to the one Hannah shows in the film. It’ll be used to help deliver the new Automotive Engineering degree course we have starting up here from September this year.

The future may rest in electric vehicles, but we’re a long way from done with internal combustion.

A-Level Physics teachers: your thoughts welcome

A few months ago, we made a film of an A-level core practical: measuring g via the free-fall method. Many teachers responded to our invitation to comment, and to our shameless request for recommendations for funders. Well… that worked. Thanks for your kind words, and thanks to your kind words we’re making more of these films. We’re not yet revealing the funder, but we can reveal the first three (or four) practicals we’re filming. We’d also like your help again.

We’re filming next weekend, 21st/22nd May, and we’d be delighted if these films could reflect your experience with practicals you’ve completed, your thoughts about ones you’ve yet to teach, and so on. We’ve a crack team of advisors and supporters already involved, but nothing beats the broad experience of teachers across the UK (and internationally).

So: here are the outlines of the films we’re planning to make. Please leave a comment below if you’ve any pertinent thoughts. It’s extremely helpful if you sign your comments with your real name, and note your affiliations (ie. school, that you’re a teacher / head of department / examiner etc) if appropriate. As before, the films are intended primarily to support teachers, but may be of use to students for revision purposes.

Laser diffraction

• Introduction to traditional two-slit diffraction apparatus, with recap of explanation.
• Plotting slit/screen distance vs. slit spacing.
• Discussion of laser safety issues and suppliers.
• Suggestions around practicalities, and the value of the practical for exploring issues of experiment design.
• Alternative arrangement using a wire rather than traditional double slit.
• Second alternative using diffraction gratings and vertical arrangement.
• (possibly – this film’s already getting quite long!) third alternative using diffraction from a CD, as suggested by OCR.
• Discussion of historical context and significance.

Finding the EMF and internal resistance of a battery

• Conceptual basis of internal resistance; review of relationship between EMF, terminal potential difference, current and internal resistance.
• Apparatus, using multimeters, variable resistor, bare wire contacts.
• Variations, including array of known resistors; switched contact; analogue meters.
• Comparison of internal resistance of different battery types.
• Discussion of value of this practical for exploring key lab skills, including careful but quick working.

Discharging a capacitor through a resistor

• Using a data logger to explore capacitor behaviour.
• Initial verification of $$V = V_0 e^{-t/RC}$$; demonstrating that voltage decay half-life is constant, and the time taken to decay to $$1/e$$ of the original value.
• Manipulation of $$V = V_0 e^{-t/RC}$$ to a form comparable with $$y = mx + c$$; processing and plotting data accordingly.
• Low-budget version of practical using voltmeter and stopclock, and with hand-processing of data.
• Extend the practical to finding the value of an unknown capacitor.
• Discussion of error.

Force on a current-carrying conductor in a magnetic field

• The standard ammeter and balance arrangement.
• Sequence of
• Determining magnetic field strength.
• Alternative arrangement with U-shaped wire segment.

Thanks in advance for all your comments and suggestions. Inevitably, we won’t be able to incorporate everything everybody suggests, but if you’ve come across a brilliant way of covering one of these practicals which we’ve not mentioned above, or have thoughts on aspects your students find particularly challenging – we’ll do our best to incorporate your ideas.

Final note: this post was written by Jonathan. Hello. I’m the film-maker behind all these videos, and while I am technically a physicist, I last saw most of these practicals in my own A-level studies more than 25 years ago. Any glaring howlers in the above are due to my misunderstanding of the scripts, and you can be reasonably confident that the many teachers involved in the filming will politely roll their eyes before we commit film-based crimes against physics.

Watch this marble run with magnets

Brilliantly inventive. See if you can work out how all the different mechanisms work – there are some amazing and subtle ideas in here. Great stuff.

Tip of the hat to Joe for spotting this as it hit Digg this afternoon.

Computer training opportunities in Newcastle

Two outstanding computing events are coming to Newcastle in the next few weeks:

The Raspberry Pi Foundation’s flagship teacher training experience, Picademy is a two-day extravaganza of all things “Pi in the classroom”. There doesn’t seem to be a course outline for what’s covered, but the events are very well-regarded by previous attendees.

The course is free, and being held on various dates at Google Digital Garage, Newcastle City Library. For more information and to apply for a place, see the Raspberry Pi website.

Apply very soon – the first dates are almost upon us!

BBC Micro:Bit Drop-in day

Micro:Bit boards are being distributed (free of charge) to every year 7 student in the country, assuming your school signed up to the scheme. The school also receives  a class set of boards, a few for teachers, and a few spare units for breakages.

There’s such a wealth of stuff around Micro:Bit it can be hard to know where to start. Most of the teacher training events have passed, but there’s a teacher / student / family drop-in style workshop event right here at Northumbria University on Saturday 25th June. So if you have a Micro:Bit and want some ideas or help, or if you’re trying to work out what to do when yours arrives, or if you’re plain curious – this could be your chance.

Free, but registration required (through the link above)