# Slowing down time to think [about strain energy]

Let me take you bungee jumping.  I should declare that I am not qualified to do so, unless you count an instructor’s certificate for rock-climbing and abseiling, obtained about forty years ago.  For our imaginary jump, pick a bridge with a good view and a big drop to the water below and I’ll meet you there with the ropes and safety gear.

It’s a clear early morning and the air is crisp and fresh – ideal for throwing yourself off a bridge attached to a rope.  The rope is the star of this event.  It’s brand new, which is reassuring, and arrived coiled over my shoulder.  A few days ago, I asked you how much you weigh – that’s your real weight fully clothed, at least I hope that’s the number you gave me otherwise my calculations will be wrong and you’ll get wet this morning!  I have calculated how much the rope will stretch when it arrests your free-fall from the bridge parapet; so, now I am measuring out enough rope to give you an exciting fall but to stop you short of the water.  I’m a professor of structural materials and mechanics so I feel confident of getting this bit right; but it’s a long time since I worked as an abseiling instructor so I suggest you check those knots and that harness that we’ve just tightened around you.

You’ve swung yourself over the parapet and you’re standing on the ledge that the civil engineers conveniently left for bridge jumpers.  The rope is loosely coiled ready with its end secured to a solid chunk of parapet.  As you alternate between soaking up the beautiful view and contemplating the chasm at your feet, you wonder why you agreed to come with me.  At this moment, you have a lot of potential energy due to your height above the sparkling water [potential energy is your mass multiplied by your height and gravitational acceleration], but no kinetic energy because you are standing motionless.  The rope is relaxed or undeformed and has zero strain energy.

Finally, you jump and time seems to stand still for you as the fall appears to be happening in slow motion.  The air begins to rush past your ears in a whoosh as you build up speed and gain kinetic energy [equal to one half your mass multiplied by your velocity squared].  The bridge disappeared quickly but the water below seems only to be approaching slowly as you lose height and potential energy.  In reality, your brain is playing tricks on you because you are being accelerated towards the water by gravity [at about 10 metres per second squared] but your total energy is constant [potential plus kinetic energy unchanged].  Suddenly, your speed becomes very apparent.  The water seems very close and you cry out in surprise.  But the rope is beginning to stretch converting your kinetic energy into strain energy stored by stretching its fibres [at a molecular level work is being done to move molecules apart and away from their equilibrium position].  Suddenly, you stop moving downwards and just before you hit the water surface, the rope hurls you upwards – your potential energy reached a minimum and you ran out of kinetic energy to give the rope; so now it’s giving you back that stored strain energy [and the molecules are relaxing to their equilibrium position].  You are gaining height and speed so both your kinetic and potential energy are rising with that squeal that just escaped from you.

Now, you’ve noticed that the rope has gone slack and you’re passing a loop of it as you continue upwards but more slowly.  The rope ran out of strain energy and you’re converting kinetic energy into potential energy.  Just as you work out that’s happening, you run out of kinetic energy and you start to free-fall again.

Time no longer appears to stationary and your brain is working more normally.  You begin to wonder how many times you’ll bounce [quite a lot because the energy losses due to frictional heating in the rope and drag on your body are relatively small] and why you didn’t ask me what happens at the end.  You probably didn’t ask because you were more worried about jumping and were confident that I knew what I was doing, which was foolish because, didn’t I tell you, I’ve never been bungee jumping and I have no idea how to get you back up onto the bridge.  How good were you at rope-climbing in the gym at school?

When eventually you stop oscillating, the rope will still be stretched due to the force on it generated by your weight.  However, we can show mathematically that the strain energy and deformation under this static load will be half the values experienced under the dynamic loading caused by your fall from the bridge parapet.  That means you’ll have a little less distance to climb to the parapet!

Today’s post is a preview for my new MOOC on ‘Understanding Super Structures’, which is scheduled to start on May 22nd, 2017.  This is the script for a step in week 2 of the five-week course, unless the director decides it’s too dangerous.  By the way, don’t try this home or on a bridge anywhere.

# Revisiting closed systems in nature

It is the beginning of the academic year and once again I am teaching introductory thermodynamics to engineering undergraduate students and my MOOC entitled ‘Energy: Thermodynamics in Everyday Life‘ is running in parallel.  Last week after my lecture on thermodynamic systems, a student approached me to ask whether the universe is a closed and isolated system.  It’s an interesting question and the answer is depends on the definition of universe.   In thermodynamics, we usually define a boundary to delineate the system of interest as everything inside the boundary and everything else are the surroundings.  The system and surroundings taken together are the universe (see my post ‘No beginning or end‘ on February 24th, 2016).  If the universe is defined as the system then there are no surroundings; hence the system cannot exchange energy or matter with anything which is the definition of a closed and isolated system.

Physicists often refer to the observable universe, or define the universe as everything we can observe.  We are aware that we cannot observe everything.  Hence, it is reasonable to suppose that the observable universe exchanges energy and matter with the unobservable space beyond it, in which case the observable universe is an open system.  We could also consider the concept that we are part of multiverse and our universe is only one of many, in which case it seems likely that is not isolated, i.e. it can exchange energy, and perhaps it is open, i.e. it can exchange both energy and matter with other parts of the multiverse.

This is not really thermodynamics in everyday life.  However, the occurrence of closed systems in nature appears to interest a lot of people to judge from the visits to my previous posts on this topic.  See ‘Closed Systems in Nature?‘ on  December 12th, 2012; Is Earth a closed system? Does it matter? on December 10th, 2014; and ‘No Closed Systems in Nature‘ on August 12th, 2015. For more about system boundaries, see my post entitled ‘Drawing Boundaries‘ on December 19th, 2012.

# Popping balloons

Balloons ripe for popping!

Each year in my thermodynamics class I have some fun popping balloons and talking about irreversibilities that occur in order to satisfy the second law of thermodynamics.  The popping balloon represents the unconstrained expansion of a gas and is one form of irreversibility.  Other irreversibilities, including friction and heat transfer, are discussed in the video clip on Entropy in our MOOC on Energy: Thermodynamics in Everyday Life which will rerun from October 3rd, 2016.

Last week I was in Florida at the Annual Conference of the Society for Experimental Mechanics (SEM) and Clive Siviour, in his JSA Young Investigator Lecture, used balloon popping to illustrate something completely different.  He was talking about the way high-speed photography allows us to see events that are invisible to the naked eye.  This is similar to the way a microscope reveals the form and structure of objects that are also invisible to the naked eye.  In other words, a high-speed camera allows us to observe events in the temporal domain and a microscope enables us to observe structure in the spatial domain.  Of course you can combine the two technologies together to observe the very small moving very fast, for instance blood flow in capillaries.

Clive’s lecture was on ‘Techniques for High Rate Properties of Polymers’ and of course balloons are polymers and experience high rates of deformation when popped.  He went on to talk about measuring properties of polymers and their application in objects as diverse as cycle helmets and mobile phones.

# Engaging learners on-line

Filming at Quarry Bank Mill

The Everyday Engineering Examples page of this blog continue to be very popular.  More than 70 engineering schools in the USA have signed up to use this approach to teaching engineering science as part of the ENGAGE project.  The lesson plans on that page assist instructors to deliver traditional lectures that are engaging and effective.  Now, we have transferred the approach to online delivery in a MOOC that was designed to support undergraduate learning as well as to increase public engagement and understanding of engineering science.

The MOOC entitled ‘Energy: Thermodynamics in Everyday Life‘ was completed by more than 960 learners from about 35 countries who ranged in age from 13 to 78 years old with a correspondingly wide range of qualifications in terms of both subject and level.  I believe that this is the first MOOC to use Everyday Engineering Examples within a framework of the 5E lesson plans and it seems to have been effective because the completion rate was 50% higher than the average for FutureLearn MOOCs.

We also included some experiments for MOOC learners to do at home in their kitchen.  Disappointingly only a quarter of learners performed the experiments but surprisingly almost half of all learners(46%) reported that the experiments contributed to their understanding of the topics.  This might be because results and photos from the experiments were posted on a media wall by learners.  There was also a vibrant discussion throughout the five-week course with a comment posted every 8 minutes (or more than 6,500 comments in total).

More than half the undergraduates (53%) who followed the MOOC did not continue to attend the traditional lectures and roughly the same percentage agreed or agreed strongly that the MOOC could replace the traditional lecture course with only 11% disagreeing.  So maybe the answer to my question about death knell for lectures [see my post ‘Death Knell for the lecture?‘ on October 7th, 2015] is that I can hear the bell tolling.

I gave a Pecha Kucha 20×20 on these developments at an International Symposium on Inclusive Engineering Education in London last month, which is available as a short video.

# Writing backwards

My regular readers will know that I am a fan of the 5E instructional method and in particular combining it with Everyday Engineering Examples when teaching introductory engineering courses to undergraduate students. Elsewhere in this blog, there is a catalogue of lesson plans and examples originally published in a series of booklets produced during a couple of projects funded by the US National Science Foundation. Now, I have gone a step further and embedded this pedagogy in a Massive Open Online Course (MOOC) on Energy! Thermodynamics in Everyday Life. If you follow the MOOC, you’ll find some new worked examples that I explain while writing ‘backwards’ on a glass board. My film unit are very proud of the ‘backwards’ writing in these examples, which they tell me is an innovation in education filming-making. Our other major innovation is laboratory exercises that MOOC participants can perform in their kitchens. Two of these are based on everyday experiences for most participants: boiling water and waiting for a hot drink to cool down; the third is less everyday because it involves a plumber’s manometer. In each case, I am attempting to move people around Honey and Mumford’s learning cycle, which is illustrated schematically in the figure, i.e. having an experience, reviewing the experience, concluding from the experience and the planning the next steps. The intention is that students progress around the cycle in the taught component, then again in the experiments.

If you want to have a go at the one of experiments, then the instructions for the first one are available here. Alternatively you could sign up for the MOOC – its not too late!  But if you don’t want to follow the course then you can stil watch some excerpts on the University of Liverpool’s Stream website, including the backwards written examples.

Sources:

Atkin, J.M. and Karplus, R., 1962. Discovery of invention? Science Instructor, 29 (5), 45–47.

Honey P, Mumford A. The Manual of Learning Styles 3rd Ed. Peter Honey Publications Limited, Maidenhead, 1992.