In January I had a go at the 2014 Scholarship Physics Exam, as I've done for the last couple of years. Sam Hight from the PhysicsLounge came along to help (or was it laugh?) The idea of this collaboration is that I get filmed attempting to do the Scholarship paper for the first time. This means, unlike some of the beautifully explained answers you can find on YouTube, you get my thoughts as I think about the question and how to answer it. Our hope is that this captures some of the underlying thinking behind the answers – e.g. how do you know you're supposed to start this way rather than that way? What are the key bits of information that I recognize are going to be important – and why do I recognize them as such? So the videos (to be put up on PhysicsLounge) will demonstrate how I go about solving a physics problem (or, in some cases, making a mess of a physics problem), rather than providing model answers, which you can find elsewhere. We hope this is helpful.
One of the questions for 2014 concerned friction. This is a slippery little concept. Make that a sticky little concept. We all have a good idea of what it is and does, but how do you characterize it? It's not completely straightforward, but a very common model is captured by the equation f=mu N, where f is the frictional force on an object (e.g. my coffee mug on my desk), N is the normal force on the object due to whatever its resting on, and mu (a greek letter), is a proportionality constant called the coefficient of friction.
What we see here is that if the normal force increases, so does the frictional force, in proportion to the normal force. In the case of my coffee mug on a flat desk*, that means that if I increase the weight of the mug by putting coffee in it, the normal force of the desk holding it up against gravity will also increase, and so will the frictional force, in proportion.
Or, at least, that's true if the cup is moving. Here we can be more specific and say that the constant mu is called 'the coefficient of kinetic friction': kinetic implying movement. But what happens when the cup is stationary? Here it gets a bit harder. The equation f=mu N gets modified a bit: f < mu N. In other words, the maximum frictional force on a static object is mu N. Now mu is the 'coefficient of static friction'. Another way of looking at that is that if the frictional force required to keep an object stationary is bigger than mu N, then the object will not remain stationary. So in a static problem (nothing moving) this equation actually doesn't help you at all. If I tip my desk up so that it slopes, but not enough for my coffee mug to slide downwards, the magnitude force of friction acting on the mug due to the desk is determined by the component of gravity down the slope. The greater the slope, the greater the frictional force. If I keep tipping up the desk, eventually, the frictional force needed to hold the cup there exceeds mu N, and off slides the cup.
What this means is that we when faced with friction questions, we do have to think about whether we have a static or kinetic case. Watch the videos (Q4) you'll see how I forget this fact (I blame it on a poorly written question – that's my excuse anyway!).
*N.B. I have just picked up a new pair of glasses, and consequently previously flat surfaces such as my desk have now become curved, and gravity fails to act downwards. I expect this local anomoly to sort itself out over the weekend.
P.S. 17 February 2015. Sam now has the videos uploaded on physicslounge www.physicslounge.org