Banked Tracks for Turning Isaac Physics

Here is my working

Thank you! I've managed to get the answer now - but I have a couple of qs.
1) Shouldn't frictional force always oppose and act in the opposite direction of another force - in this question which force is it opposing as there are none that are pointing up the slope.
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2) Why does the centripetal force point horizontally - I thought it always points towards the centre of the rotation.

I am not sure why you have such thinking.
Go back to your textbook definition of friction and then read the question that you have asked to see if it makes sense. If it does, let me know how it makes sense.



I am not sure what you mean by centre of rotation.

With q1) I misunderstood the definition - Friction always acts in the direction opposite to that of the direction of the object in motion. My misunderstanding was that it acts in the direction opposite another force - which it doesn't, it only opposes the direction of motion, which in this case is the car 'leaving' the track.

With q2) I have drawn a diagram that labels my current thinking. The green centripetal force is in the correct direction, whereas the red centripetal force is incorrect and was what I thought the direction of the centripetal force was (as it's pointing towards the 'centre of rotation'). After research, I realised the centripetal force was always acting against the axis of rotation, so doesn't always point towards the 'centre of rotation', which is why the correct direction for the centripetal force is horizontal.

I'll try to change my terminology because I think it's causing confusion - my mistake for calling it rotation not motion.

Well from what I've been taught, the centripetal force always points towards the centre of whatever circular motion it's travelling in - I don't see why it wouldn't in this scenario.

I guess in a 'banked turn' it confused me into thinking the centripetal force points towards the 'centre', when really it points towards the 'axis'.