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Why?

Now here's the question that got me pondering

A cyclist rounds a bend, The surface of the road is horizontal. The cyclist is forced to lean at an angle of $20^\circ$ to the vertical to 'only just' take the bend successfully. The total sideways frictional force on the tyres is 360 N. The cycle has a mass of 20 kg. What is the mass of the cyclist? (Answer: 78.9 kg)

The trouble I'm having is that I don't understand why the cyclist has to lean to begin with, I tried drawing a free body diagram and equating the torques on the cyclist, but I get 80.9 kg as my answer instead. I also tried resolving the forces like shown here, which curiously also got me 80.9 kg.

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    $\begingroup$ Does this answer your question? How does tilting a bike make it turn sharper? $\endgroup$
    – AlphaLife
    Commented Sep 22, 2021 at 6:25
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    $\begingroup$ @AlphaLife yes, thank you $\endgroup$
    – joshua mason
    Commented Sep 22, 2021 at 7:14
  • $\begingroup$ Voting to reopen, because this is not a duplicate of physics.stackexchange.com/questions/419353/… (which I answered myself. That question is about why choosing to lean a bike to a particular angle can decrease the radius of the turn, by altering the weight location of the rider relative to the bike, which is a much more sophisticated question. This question asks why does the bike have to lean at all, when the rider mass is confined to be inline with the bike and why is there a unique solution for the lean of the bike rider combination. $\endgroup$
    – KDP
    Commented Apr 1 at 21:03
  • $\begingroup$ As explained in my other answer, a bike does not have to lean at all to negotiate a bend, if the rider is allowed to move his weight to the inside relative to the frame of the bike. That is why that question is different. $\endgroup$
    – KDP
    Commented Apr 1 at 21:05

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$g = 9.81\ \mathrm{m/s^2}$. You approximated $g = 10$ when converting masses to weights, so your answer for (mass of cyclist plus mass of bike) is $10/9.81$ of the total mass.

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  • $\begingroup$ Hmm it seems like it's the other way around, the answer used the approximation g=10, which does give the answer 78.9. Could you please show your working? $\endgroup$
    – joshua mason
    Commented Sep 22, 2021 at 7:13

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