May all the forces be with you!

The title of this blog is taken from Book 3: Predicting Motion from my S207: The Physical World OU course book. It made me chuckle.

At the moment, I’m studying forces and pressure, and the line above was in reference to the fact that we don’t implode under the weight of the atmosphere. Normal atmospheric pressure is about 1.013 x 105 Pa, which exerts a force equal in magnitude to the combined weight of 163 people, each of mass 63.5 kg, on a patch of Earth one metre square. That is a LOT of weight.

How are we not crushed? Well, the pressure inside our bodies is approximately equal to the pressure outside, so all the forces just about balance. Which means we are in perfect balance with our normal environments. Simple!

Fictitious forces

So, forces. Everyone knows what a force is, right? The equation is F = ma (force = mass x acceleration). There is frictional force, centripetal force, weight, and the linear restoring force… but what isn’t there?

Fictitious forces are not real forces at all; they are associated with real phenomena that arise when we use non-inertial frames of reference (i.e. frames of reference that move around). Newton’s laws of motion can only be applied in inertial frames of reference. They start to collapse in the face of excitement…

Gravity: No, gravity is not a force. Gravity is a downward acceleration that is, on Earth at least, approximately equal to 9.81 m s-2. That means that any object falling under gravity (assuming that there is no friction or air resistance) falls at a speed which increases at the rate of 9.81 metres per second, every second.

Gravity does, however, give rise to a force: weight. Our everyday use of the word ‘weight’ is not, technically, correct. We use it to mean ‘mass’, which is constant wherever you may be. Weight is a force arising from gravity, described by the equation W = mg (weight = mass x gravity) and it varies depending upon its environment. For example, you weigh more here than you would on the Moon.

Under gravity, objects exert a force (weight) upon the rigid surface on which they rest. The rigid surface exerts a force right back at it, called the normal reaction force. These two forces balance, meaning that the object stays where it’s put, unless it is acted upon by an unbalanced force, such as a good hard kick.

The Coriolis force: This is a weather phenomenon that is actually pretty cool. In the Northern Hemisphere, moving air masses tend to wander off to the right, as if they were being pushed there by a force.

Arising from the Earth’s rotation, this result is not due to an unseen force at all, but is due to the fact that the motion of the air masses is being observed from the non-inertial frame of the spinning Earth.

The air masses are moving in a straight line, as all things are wont to do under their own steam; it is the rotation of the Earth that makes the air appear to veer off to the right in the North. The effect is real enough; the force is an illusion.

Centrifugal force: Everyone who has ever travelled in a fast-moving car, or been on a roller coaster, knows exactly what centrifugal force is. It pushes you out to the side when you go round a sharp bend at speed.

Except it doesn’t. From the frame of reference of the car’s interior, you’re pushed by an outwardly directed ‘centrifugal force’, but this, too, is an illusion. Think outside the box. Or outside the car, if you like.

Unless acted upon by an unbalanced force, all objects in motion will tend to travel in a straight line – even you. Within a car, you will tend to travel in a straight line, regardless of what the car is doing. It is only when your forward motion connects with the side of the car as it’s making the turn that your motion deviates from the straight and narrow. So although it feels as though an unseen force is throwing you to one side, it isn’t. In fact, you are travelling in a straight line until you are no longer able to because the car door is in the way.

Acceleration in a straight line: Another car example. Cars are great for describing and examining forces in physics. When a car accelerates, you get pressed back into the seat by the force of… what? Well, nothing. In an inertial frame of reference, e.g. the one attached to the road, there is no physical force moving you backwards.

The non-inertial reference frame attached to the moving car does have a backward fictitious force though. In fact, the real force is the forward force produced by the car’s engine. When the car accelerates, you carry on moving at the pace you were moving at before, until the solid seat requires you to move along with it.

Put your mind outside the car and observe from there: you’re not subject to any forces that the car is not subject to.

Treating the fictitious forces as real forces within their non-inertial frames of reference allows us to apply Newton’s laws them, which can be kind of useful. It’s important though to remember that they are not real forces. They are nature’s illusions.

S207: the story so far

So far, S207 is fabulous, but very challenging. The maths is extremely tricky for those without a background in maths, so I’m finding it hard going. Challenging is good: it makes it all the more rewarding when I realise I understand something fully. TMA01 netted me 78 per cent, which I’m pretty happy with – plus my tutor’s comments were really helpful. Bring on TMA02!

Things I am struggling with so far:

  • Simple harmonic motion: not so simple
  • Interpreting graphs. I don’t know why; it’s a mental stumbling block

Everything else, I’m taking my time with. The more I do, the more it makes sense. And every now and then I come back to something I was struggling with, and suddenly it makes perfect sense. Which is nice…

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