Posts Tagged Newton’s laws

Woolly writing is a symptom of woolly thinking Marcus Wilson Jun 18

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People who think well, write well. Woolly minded people write woolly memos, woolly letters and woolly speeches. David Ogilvy.

There’s nothing like reading through and marking students’ exam scripts. Mostly it is terribly boring, but sometimes it is enlightening. 

One of the questions I asked on an exam this semester involved getting the students to describe and explain what happens in a particular situation. The exact question is immaterial – but what the students had to do was to write sentences. It was clear that this task is very difficult for a good many of our students. Their responses are a reminder to me that we don’t specifically teach writing in our science degrees. 

Well, we do, to some extent, in some papers. Students have to write things. But we don’t have a specific course on how to write scientifically. Student answers were plagued by bad grammar and spelling, but, more worryingly, were vague and woolly*. There are a lot of physics words with very specific meanings, that can be used to describe the movement of something unambiguously. Force, centre-of-mass, momentum, angular acceleration, etc, all have well-defined meanings. Instead of containing such words, used correctly, many answers were couched in vague, ill-defined language, or (maybe worse still) used good-sounding physics words but incorrectly. 

There are two issues I see here:

1. Is it time we  taught students explicitly how to write? (In particular, how to write technically). 

2. Woolly writing is a sign of woolly thinking. A badly phrased response is indicative that the student hasn’t really got their head around what is going on. And that’s suggesting that there is learning still to do. It is easy to hide behind mathematical calculations if you don’t know what’s going on. But having to abandon the calculator and resort to descriptions may really show up how a student is really thinking.

I’ve come across the  ten tips for good writing from David Ogilvy (of Ogilvy and Mather advertising agency) on the BrainPickings website. Have a read. They seem obvious, and they’re not difficult steps to follow. But it’s clear that following them doesn’t come naturally.

*I’m not sure where the term ‘woolly’ comes from, but it evokes the image of something ill-defined like the surface of a sheep: where does the fleece stop and the air start? It’s hard to pin down anything definite. 

The ticker-tape car Marcus Wilson May 28

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Somewhere in the Cambridge / Hamilton vicinity is a car with no oil in it. I know this because on the way in to work this morning there was a trail of oil on the road.  The damp road surface led to it being very prominent. A splash of oil, being less dense than water, will sit as a thin film on the water surface and show some colourful patterns due to interference of light reflected from the top and bottom surfaces.  

What was also clear was that these splashes of oil were not placed at equal intervals. They were closer together at intersections, and well spaced along the main road (to the point that I couldn’t follow them at times). A reasonable conclusion is that the oil was dripping at a roughly constant rate (a roughly constant time between each drips). When the car was travelling fast, there was a long time between splashes. When the car was travelling slowly, they were close together (I could see that the car had clearly stopped at the roundabout in the centre of Cambridge, for example). On the assumption that the car was travelling at approximately the speed limit on most roads, I could have estimated the rate of dropping by measuring the distance between the drops. I might find physics fun, but I don’t find it so fun as to stop on the side of SH1 and get out a long tape measure with heavy traffic roaring past, so I’m afraid I don’t have an answer to this. Perhaps more worryingly for the car driver, the car was leaving behind evidence of whether it had really stopped at stop signs. 

The pattern of splashes reminded me a lot of our experimental introduction to kinematics at school. We used a ticker-tape machine. We had a cart that was placed on a ramp, and the cart pulled a stream of ticker-tape behind it. The tape went through a machine that stamped it with dots at a constant rate. If the dots were close together, it was because the cart was moving slowly; if they were far apart, it was because the cart was moving fast. By analyzing the dots afterwards we could work out the velocity of the cart at any point on its descent of the ramp and its acceleration. 

Nowadays you can do the same experiment with a camera and a bit of computer software to do all the calculations for you. It might be more efficient, but its probably not as constructive as ticker-tape in getting a student’s head around what distance, velocity and acceleration are. And it’s definitely not as fun as ticker-tape was.

A bigger splash Marcus Wilson Apr 26

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The crawling baby is now undertaking a series of physics experiments. His favourite is the investigation of vibrational modes on biscuit tins and their coupling to longitudinal waves in the atmosphere. But he’s also repeating Galileo’s (supposed) famous experiment in studying the free-fall acceleration of various objects. In this case the elevated position  is not the Leaning Tower of Pisa, but the spare bed, and the objects take the form of anything he can lay his hands on, including himself. But the one I’ll comment on today concerns energy transfer from rapidly moving objects to fluid. 

His method takes the form of sitting in the bath and whacking the surface in such a manner as to create the largest splash of water. What he needs to work out is the relationship between the area of the object hitting the water (his hand), the speed at which he strikes the surface, and the height to which the splash goes.

Fluid dynamics is governed by a collection of dimensionless numbers that relate various quantities. The most commonly used is probably the Reynolds number, which is the ratio of the intertial force to the viscous force on an object. A high Reynolds number shows that intertial effects are prevelant; a low Reynolds number shows that viscous effects dominate.  In baby’s case, he probably needs to look at the Froude number. This tells us that gravitational-velocity effects depend on the dimensionless term v/sqrt(gL), where v is the velocity of an object, g the acceleration due to gravity (9.8 m/s2) and L is a characteristic length. The pattern of flow obtained, for example the height h of the splash in terms of the length scale L,  is likely to be a function of the Froude number. So, if we want the height of the splash, we can say that h/L = f(v/sqrt(gL)) which tells us h  = L f( v /sqrt(gL) ) where f is some function to be determined. We’d expect it to be an increasing function – if we increase v we’d expect  h to increase – and if we did the experiment on the moon where g was lower we’d expect h to increase too. 

A series of experiments should tell us whether such a relationship indeed holds for whacking the surface of the water with a hand of length L, at a speed v, and the form of the function f. We shall collect the data over the next couple of weeks and hope to have a paper  published soon. 

Turning moments Marcus Wilson Apr 16

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 The last couple of weeks has seen a few changes in the house as Benji has finally mastered crawling. Being a rather LARGE baby, he’s been the last of his coffee-group babies to become mobile, but now he’s got it worked out he’s away at high speed. No peaceful sunbathing for the chickens or the neighbour’s cat now. 

So, one thing we’ve had to do is to work out what he can get into, up, along, through, etc, that we’d rather him not. The freestanding coat stand, for example, we’ve now bracketed to the wall. Our bookcases are secured anyway from an earthquake point of view, there are some bits of furniture that aren’t. I mean, you can’t practically bracket down a chair, can you? With a couple of pieces, I’ve had a quick go at working out whether he could, in principle, pull them over. 

To pull over something on four legs, you need to shift its centre of mass so that it crosses the line between the two legs that are touching the floor  - then gravity will ensure that it falls over. That generally means pulling it towards you. (Pushing just pushes it into the wall). What is of importance is the turning moment you apply to the object about the two nearest legs, compared with the turning moment that is generated by gravity. If you win, then over comes the object. The turning moment about the point is the product of the force applied, multiplied by the perpendicular distance between the force and the point.  Basically, then, the greater the force applied, the larger the turning moment, and the greater distance between where the force is applied and the contact point between the legs and the ground, the greater the turning moment. Thus an adult will be able to tip over a piece of furniture much more effectively by pulling at the top, rather than pulling a quarter of the way up. (This acts in our favour when considering Bubble’s abilities.)

Assuming aforementioned child doesn’t CLIMB the object (and he’s not doing that yet), it’s a simple estimate as to how far up he can pull from. But how hard can he pull? 

 It’s tough to pull more with a force more than your own weight, unless you have your feet clamped to the floor. The reason is that at some point the friction between one’s feet and the floor is insufficient to keep your feet in one place. Try pushing a heavy box along a polished floor while wearing socks. The box might stay put, and it’s your feet that do the sliding. 

So that gives us an estimate of how much force he could reasonable pull with. Therefore we can work out the turning moment, and compare it with that generated by gravity the other way. That’s fairly easy too – estimate the weight of the object and where the centre of mass is in relation to the legs and do the multiplication. A heavy object, with legs wide apart – a light one with only a small footprint on the ground, like our CD rack, will go over rather more easily.

So, at present, I’d be surprised if he’s able to tip anything that has to the potential to cause real damage. But that will change.

It’s what the learner knows… Marcus Wilson Mar 22

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 On the door of her office, Alison Campbell has a sign that says "the biggest factor in learning is what the learner already knows". Or something like that. In other words, students build upon an existing foundation when they make sense of the world. This can be very helpful, or very unhelpful, depending on whether that foundation is correctly laid. One of the roles of a teacher (I would say one of the hardest roles of a teacher) is to identify where there are cracks in those foundations before the student starts building too much upon it. If that doesn’t happen, the student is likely to run into something that just doesn’t fit with what he or she already knows, or thinks she already knows, and it’s going to cause them problems. 


as the saying goes. (I haven’t been able to track down the origin of this quote – some attribute it to Mark Twain but I think others disagree. Can anyone help?)

I ran into an example of this while marking some third year assignments this week. Students were tackling a problem in which a mechanism was rotating. Now, to the large majority of the class, it is clearly evident that something of mass m moving in a circle of radius r at speed v has a  force on it of m times v squared divided by r. They did it till they were sick of it at school, and it has stuck. The problem is, that they are WRONG. What!, you cry, but that’s correct isn’t it? F=mv2/r for circular motion. Yes, but ONLY when the speed v is CONSTANT. If it isn’t, there’s another term to consider. 

Now, the interesting thing from my point of view is that I though that the students were over this misconception. I’d talked about it in class, and even done a couple of formative multiple choice questions with them in lecture time that showed me (so I thought) that they appreciated this subtlety. But, when the pressure was on with an assignment, a great many students abandoned what we’d talked about in class and reverted back to what they perceived as their foundation knowledge. 

So what went wrong with my formative assessment? Did it come too early after the discussions on the subject? Were my multiple choice questions just poorly written. I need to go back and have a rethink on this. At least I’ve identified that a problem still remains, via the assignment, which is a good thing as it gives some time to talk about the issue again before the exam (and before the students leave and try applying F=mv2/r inappropriately in the design of some safety-critical piece of machinery.)



Is maths real? Marcus Wilson Mar 21

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 A friend has just started a Bachelor of Arts degree here at Waikato. As part of her first year study, she’s chosen to do a Philosophy paper. Apparently, one of the questions that has been posed, is "Is maths real?". 

Well, what is real? You certainly can’t put ‘maths’ in a box and give it to someone. like you could with a chair or a chicken. But does it have more substance than just some made-up statements about how to add things or describing how large angles are?  I’ve often wondered, for example, whether it would be possible to have a universe in which the value of pi was four. In our universe, it isn’t. But is pi, the ratio of the circumference of a circle to its diameter, necessarily 3.14159265…in all universes?  I don’t know. I guess it depends on what a circle is. 

So is physics real?  I would think that it is more real than maths. I mean, physics is supposed to describe reality. Gravity is gravity. Objects attract each other proportional to their masses and inversely proportional to the distance between them. That’s what happens. It’s hard to be a physicist if you’re not a positivist, or at least have strong positivist leanings. In other words, if you don’t believe that there is a real world out there that we can know about, and that we can find out about this world objectively (e.g. by doing experiments), you are going to struggle to be a physicist. (It is true that quantum theory throws a spanner in the works at this point. The quantum world is weird indeed -an example here – and raises big issues about what is real.) 

Recently, I was at a teaching seminar that seemed to be populated mostly be social scientists. In social science, a common paradigm is social constructivism, or namby-pamby waffle as it is known by positivists. In social constructivism, what the world is is constructed in one’s mind, and that what you can find out about it inevitably depends upon how go about finding out about it. In other words, everything is relative. 

So, back to the point. Where does maths sit in all of this? I’m not sure it does. It’s hard to believe that maths depends on your point of view. It doesn’t matter how you look at it, 1 + 2 doesn’t equal 4, and it never will. But neither does it fit well with reality, either. 1 + 2 would be 4 in any universe, wouldn’t it?  Maybe maths sits in some strange space of its own, separate from ties with this universe but not ‘made up’ in anyone’s head. So what is it? Er, that’s getting too close to philosophy for my liking.  I await my friend’s response with interest. 

Perhaps the best answer is to say that maths is as real as philosophy. 


Blackwater rafting Marcus Wilson Mar 08

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 I’ve had my brother visiting from the UK, which has been a good excuse for doing some of the touristy things in the area. I wasn’t taken by the prospect of zorbing, but we did give blackwater rafting a go in the Ruakuri cave at Waitomo. I’ve always wanted a go at that – and it’s strange how you can have something a touch less than an hour’s drive from you and you don’t do it.  But that’s been corrected now. Essentially, the concept isn’t desperately complicated: you sit in a truck inner-tube and float down the river – the complicating factor being that the river is underground. 

I was surprised how much water was flowing through the cave, given the lack of rain in recent weeks. The guides were saying that it’s low, but it was still plenty enough for a rafting exercise. One highlight, if it can be called that when in the dark, is the waterfall jump – when you jump backwards off the top of a small (2 metres?) waterfall and land in your ring in the pool below. Just what exactly happens on the impact of an adult-laden inner tube flat with the water I’m not sure – it being rather dark, but it certainly was wet. Having done the jump, we accumulated further down the cave and got very splashed by those still jumping, so I’d say there was some considerable water displacement  going on.

As a physicist, one is obliged to do some estimates of this. What is going on here? The falling person needs to be brought to a halt by the buoyancy force of the ring in the water. That involves working out how much water is being displaced by the ring and perhaps doing a bit of calculus. It’s rather complicated because of the ring’s shape – things would be rather simpler if the ring were a cube. With a bit more time – maybe in a later post, I’ll have a go at estimating this, but I have other more pressing commitments like lectures to give.  

So for now I’ll just comment that next time I’ll be taking a tape measure and high speed low light camera into the cave.




Weight and lift: Chicken style Marcus Wilson Jan 31

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For reasons best known to their small chicken-brains, Harriet and Henrietta have decided to abandon the coup and roost in a tree. Maybe this is because it is rather hot in the coup at night, or possibly because a neighbour’s cat enjoys sitting outside the coup at six in the morning. (One day that cat is going to push his luck too far and find out what sixteen chicken-claws and two beaks feel like.)  Whatever the reason, they feel that a tree is the better place.

They manage to hop and waddle up their separate trees without too much problem and sit out on branches as thin as they dare go about three metres off the ground, presumably happy that they are safe up there for the night. Getting down again in the morning is more interesting. Henrietta usually chooses the same route down as up, through the low branches. But Harriet, suffering delusions of  aeronautical ability, takes a more direct approach. And believe me you don’t want to be in her flight path when she launches.

Her flight-time is beyond the ability to time with a stop-watch, but I’d say this morning it was about one second. Given that she has dropped, I reckon, about three metres, she can’t be generating much lift. A quick estimate can be made at this point.

First, recall that motion can be separated out into the vertical component and horizontal component. Under constant force (in this case gravity plus lift), the components don’t affect each other. That means we can use simple kinematics to work out her acceleration. For an object accelerating from rest, the distance it travels in a time ‘t’ is given by half times ‘a’ times ‘t’ squared, where ‘a’ is the acceleration.  If distance is about three metres, time about one second, then we obtain an acceleration of about 6 metres per second squared. 

That’s made up of gravity (10 metres per second squared) minus the contribution due to lift. This means the lift she’s generating with her barely coordinated flapping equates to about 4 metres per second squared. In other words, she’s managing to lift only about half her weight. Little wonder she has to climb the tree to get up it.




The sneeze jet Marcus Wilson Jan 07

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Undiscovery in physics Marcus Wilson Nov 28


With the recent undiscovery of Sandy Island I’ve begun wondering what other things might be ripe for undiscovery. Wasps, for example. Wouldn’t it be great if we realized that there wasn’t actually any evidence for the existence of wasps after all. Their discovery had been just a mistake made by an entomologist back in the depths of history. We can all tell our children not to worry about them – they don’t exist. Our chickens would love to see the neighbour’s cat undiscovered (as would we – at least from our garden).  I’m sure a variety of places might feature strongly too. Hamilton is bound to be on the list of some people; but, I can assure you, the last time I looked it was still there.

I don’t think in physics there has been a great deal of undiscovery in the last few centuries. I struggle to think of any real undiscoveries.  Sure, there have been changes to our thinking. For example, relativity superseded Newtonian physics, but it would be wrong to say that Einstein undiscovered Newton’s Laws of motion. The latter are still a cornerstone of physics – but their applicability has been reduced to the realm where things aren’t travelling close to the speed of light. That would be more like discovering the coastline of Sandy Island is a bit different to what the maps have it. One might say that the Michelson-Morley experiment undiscovered the aether, but in reality the aether had never been discovered – it was just a well-accepted hypothesis. Likewise Joule’s experiments with heat put pay to the idea that heat was a fluid, but since no-one had claimed (supported by real evidence)  to have observed this fluid, it wasn’t really an undiscovery either.

Underlying modern science (by which I mean Galileo and beyond) is experimental evidence. No change in understanding of science, in any discipline, is going to happen without well collected and well analyzed data. This makes undiscovery of something (by which I mean overturning of some knowledge, theory or principle that has been believed based upon evidence, as opposed to mere hypothesis) unlikely. There have been a few instances of reports of new things that have been made prematurely, with unreliable evidence, such as cold fusion and faster-than-light neutrinos, and these have been embarrassing for the groups concerned and undiscovered very rapidly.  But undiscovery here has happened because they were never properly discovered in the first place.

That said, neither was Sandy Island properly discovered. My spell-checker’s underlining of the word undiscovery may be for good reason.

I’d love to hear readers’ thoughts on this one. Is there any piece of modern science that has been genuinely undiscovered?





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