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Posts Tagged Newton’s laws

Apparent forces Marcus Wilson Apr 01

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A couple of weeks ago I had the misfortune to be on a bus which had an accident. I wasn't hurt, because I was safely seated, which is more than I can say for one unfortunate passenger who was still on his way to his seat at the time. It wasn't a high-speed event – I'd guess we were doing about 10 km/h. We had just pulled away from a bus stop, when a car that had been parked a few metres in front of the bus decided to pull out into the road right in front of us. The driver hits the breaks hard, and, as a result, the fellow passenger ends up in a heap on the floor at the front of the bus. 

While the cause of the crash I would say rests firmly with the driver of the car that pulled out, that's little comfort to the poor guy with blood dripping from a wound on his head, down the back of his shirt, which is probably now dyed a nice shade of maroon. Standing on buses is pretty dangerous, even at low speed. I do think the driver should have waited till everyone was seated before pulling away. 

So, from a physics perspective, what happened? One can explain this in two ways. There's the 'inertial' approach, as explained by the witness on the side of the road: The bus stopped, but the guy standing, who has inertia, carried on. Then there's my viewpoint, from inside the bus. Everything experiences a sudden acceleration forward. This causes the passenger to lose his balance, and down he goes. 

This forward acceleration, from the perspective of the person on the bus, is called an apparent force. It arises because the frame-of-reference, the bus, isn't an inertial frame. That is, it's accelerating (or, in this case, decelerating). It's called 'apparent' because the person on the side of the road wouldn't see it in this way; it only becomes apparent if the observer is in the accelerating frame of reference. It might be termed an 'apparent' force, but for the person on the bus it's a very real push forwards, one that splatted him on the floor and would have given the bus cleaners a more interesting job that usual.  It's the same kind of thing as centrifugal force (yes, the 'f' word), which one experiences when going round corners. To the person in the object that is doing the moving, the force is a very real thing (ask the racing car driver). But to everyone else, it doesn't actually exist. 

Apparent forces are pretty hard to teach (I've just been doing it), but I think the key is really to emphasize that they are there only to the observer who is in the accelerating frame. 

What happened to the passenger? Against the advice of everyone around him, including me, he refused to be taken to a medical centre, which was only a few hundred metres from the place of the incident, and insisted on carrying on the journey to his destination. Possibly if he'd been able to see the back of his head he might have thought differently. One shudders to think of the consequences at 50 km/h. Seat belts in buses? Yes please. 

 

 

 

 

Oh dear Mr Kohli Marcus Wilson Feb 11

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Wow! That was a real nailbiting finish to the first test. Well done to the New Zealand bowlers to hold their nerve as India's batsmen got close. There was some great bowling, and also some great batting at times. Maybe the difference between the teams was that New Zealand in that final innings made fewer tactical blunders. 

I'm sure every armchair pundit has their own opinion of where the match was won and lost, but one that stands out for me is Virat Kohli's lapse of concentration against Neil Wagner. Aggressive batting is great to watch, but it has to give way to common sense if you want to stay at the crease. Trying a pull shot at a ball that isn't terribly high and  w-i-d-e outside off stump would be a suspect choice of shot even in a Twenty20 game, bad in any Test match, and downright appaling in a test that was as closely balanced as this one. What did he expect to happen? 

Anyone who has ever faced fast bowling will know that there are some basic laws of physics going on. What's of great importance in determining where the ball will end up after hitting your bat is the relative motion of the ball with respect to the bat, and the angle of incidence of the ball on the bat. The ball doesn't go in the direction that you hit it. Since it's carrying momentum (and a fair bit of it), what you do when you apply a force with the bat is that you change the ball's momentum. It's the change in momentum, not the final momentum itself, that's equal to the impulse (force times time) that you give to the ball. These things are vector quantities, that is, they have directions.  If you don't hit the ball in the exact opposite direction to where it is coming from, the final momentum of the ball won't be in the direction in which you hit it (apply a force on it). 

To pull a cricket ball through midwicket means that your bat's got to be pointing somewhere towards mid-on when you make contact with it. Try doing that when you're stretching out for a ball that's w-i-d-e outside off stump and you'll get the idea of why this shot was never going to work. Guiding it to the point boundary would have been a whole lot safer and effective, but then I'm sure Mr Kohli is well aware of that now. 

 

 

 

Scholarship Physics, 2013-style Marcus Wilson Jan 24

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Last year, Sam Hight and I made a collection of videos on tackling the 2012 Scholarship Physics exam. Well, to be precise, Sam did the videoing, editing, and distribution, and I just did the exam. The key thing, though, was that I did the exam 'live'. I was seeing the questions for the first time. I didn't give myself a few days to work out carefully composed and presented answers, like some of the slick model answers you find online. The idea was to give students an idea of what scholarship is like to do (answer: hard!)  but also how I think through a physics problem and come up with my solutions. Often what is lacking on a 'slick' model answer is any indication of how the writer 'knew' to tackle the question in the way she did. (Answer to that one – probably because she'd spend a few days looking at it, or wrote the exam question in the first place – neither terribly helpful to a student.)

By popular request, I did the same yesterday. Video camera in front of me, whiteboard, three hours with a scholarship paper. My conclusion? The 2013 paper was hard-as. (You can see for yourself here.) I'd rate it a good step up from the 2012 one. To be fair, different people have different strengths. It may have been that there was a 'bad' lot of questions for me in the 2013 paper, but it might have been a 'good' lot for someone else. I'd love to hear your thoughts on this one – do you think it's harder?

One thing I noticed was there was a lot of algebra and calculation in the 2013 paper, and there wasn't so much in 2012. The question about the A-frame ladder had a derivation involving three simultaneous equations to solve. But I got it! In the end. 

Sam and I will get the videos distributed in due course, probably via PhysicsLounge  http://physicslounge.org   If nothing else, you can watch me fumble around with a couple of questions which, 24 hours on, I realize weren't as difficult as I was trying to make them out. But if I showed you the answer today, it would be slick, and you'd be stuck wondering how I came up with it.  

Will they be helpful? You decide. If not, you can always have a good laugh at me squaring a number twice because I wasn't paying attention to what I'd written, and getting my notation in a muddle.  Whatever, I'd like to offer my congratulations to those who landed Scholarship Physics in 2013, because you most certainly deserve it!

Is it OK to bungle the science if the end message is good? Marcus Wilson Oct 23

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On Saturday morning I held a session for school students preparing to sit the 2013 Scholarship Physics exam. My intention is to help them prepare for this. It's a tough exam, aimed at rewarding the best school students in the various subjects. I talked through the principles behind answering various types of question, e.g. 'estimate' questions, mathematical questions, 'explain' questions and so forth, drawing heavily from previous exam papers. One of the questions we talked about was from the 2010 paper. Students were asked to critique the voice-over on a well-aired road safety ad of the time. (You can find the ad here - isn't YouTube wonderful?).

I won't go into the physics here, partly because I've already done it in a previous blog entry. Suffice to say that the advert will get approximately zero out of ten for scientific accuracy. However, it does get its central message across rather well, I think: Excessive speed causes crashes. So, I think it's reasonable to ask the question: "Is this a good advert?". We had a brief discussion on this on Saturday. There are several points that could be made. In defence of the ad, it does, I think, what it is designed to do – get people to think about how fast they drive.

But does it do more harm than good? It certainly doesn't promote scientific literacy by using science concepts incorrectly. We've already seen numerous examples of how lack of science understanding among the public can lead to outrageous decisions being made by politicians who rely on the public vote: governments drag their feet on tackling climate change (coz it will hit the voters in their pocket – not a smart political move) and in Hamilton we've had a narrow squeak over fluoridation – fortunately in the latter case the science won and a citizen's referendum has overturned a ridiculous decision made by the Hamilton City councillors. 

But the science can sometimes be hard to explain well. After I gave him what I thought was a clear, concise and accurate statement of what I thought the advert should say, my father-in-law replied on Saturday afternoon "no wonder they've done another explation – it's easier to understand" (or words to that effect).  Yes…but…it's not right.

Tricky one this.

 

 

 

The 2013 Nobel Prize in Physics goes to…. Marcus Wilson Oct 09

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….Well, what do you think? No surprises this year.  Francois Englert and Peter Higgs have been awarded this year's Nobel Prize in physics for the theoretical 'discovery' of the Higgs mechanism. The citation, however, I find very interesting:

for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted funamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider.

First of all, can one 'discover' something theoretically? Sure, one can predict the presence of something theoretically, but can it be discovered by a piece of theoretical analysis? I'll let you debate the semantics of 'discovery'. 

Then, note how the prize isn't given for the discovery of the Higgs Boson.  The word 'boson' doesn't get a mention at all, in fact, though it is implied by the words 'predicted fundamental particle'.  The boson is merely a piece of experimental evidence  - a rather key piece, it has to be said, given it's the only thing about the Higgs mechanism that is really observable – but still only a piece of evidence for the Higgs mechanism. It is the explanation of the origin of mass that is the notable thing here.

Well, actually, not quite. Note how the citation is for "…a mechanism that contributes to our understanding of the origin of mass…" It stops short of saying that the Higgs mechanism explains it. Is there more to come?

Then finally the experimental credit is given. The Nobel Prize isn't generally awarded to large teams of people. The ATLAS and CMS teams are vast indeed (see the list of authors on the ATLAS and CMS Higgs Boson discovery papers here and here) but these teams are rightfully given credit for their part in confirming the Higgs mechanism.

So, well done to you all. 

Gravity goes downwards Marcus Wilson Aug 06

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Yesterday afternoon I was engaged in a spot of DIY – putting up some shelves. Even for me, as someone who takes to DIY like a duck to mountaineering, it’s a fairly simple task, and I’m pleased to say that I got there without the ‘do’ in DIY turning into ‘destroy’. With the help of my trusty stud-finder (Karen – who has a knack of locating those invisible studs behind plasterboard walls just be tapping), I managed to locate two studs by drilling just three holes. The rest of the job took only four tools – a drill, a pencil, a screwdriver and the all-important spirit level.

I’ve always been fascinated by just how simple a tool the spirit level is. It does a fantastic job of getting things level (level enough for general domestic purposes, anyway), just by using a bubble of air in a liquid. The physical principle by which it works is hardly taxing – the bubble (the lack of fluid) rises to the highest point in its tube, as the liquid sinks down as low as possible to minimize its potential energy. A similarly simple method – the plumb line – gets things vertical – though a second tube turned by 90 degrees on the spirit level turned through 90 degrees can do the same task. 

In fact, it is hard to imagine a complicated machine to find where ‘vertical’ is. If one assumes that ‘up’ is the opposite direction to the force of gravity, one simply has to measure the direction of the force of gravity, and hanging something on a string is the most obvious method to do it. Sure, one can get technical and enclose the thing in a pipe so that wind doesn’t get to it, and so forth, but the basic weight-on-a-string is simple and effective. 

There are some hiccups to think about, however. One needs to be sure what one actually means by ‘vertical’ and ‘horizontal’. The force of gravity isn’t precisely towards the centre of the earth at all places on the earth’s surface. A weight on a string will be affected by the presence of nearby mountains, or large-scale variations in the geology underneath the surface. A quick estimate based on Newton’s law of gravitation and the size of mount Te Aroha, for example, suggests that houses in Te Aroha town might have their vertical distorted by a few thousands of a degree. Not a great deal but enough to be detectable with half-decent equipment.

But is the vertical really out? If the definition of a vertical is "the direction of the acceleration due to gravity" then, no, it isn’t. If one is putting up shelves in Te Aroha and wants them horizontal (so that a ball placed on the shelf stays on the shelf) one wants them at 90 degrees to the local force of gravity. If that means a few thousands of a degree different from what you’d get in Hamilton, then so be it. It just depends on your definition of ‘up’.

[And, of course, it is more than a few thousands of a degree different from Hamilton anyway - being 44km away on a sphere of 6400km radius, that's about 0.4 of a degree due to location.] 

 

Woolly writing is a symptom of woolly thinking Marcus Wilson Jun 19

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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.

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