A cyclist riding on a closed path....

[Qwertz0099]

At the junction of paths in the park there is a closed loop in the shape of eight. Straight sections
intersect at right angles, and the circular sections follow in the tangent direction. Overall
the length of the loop is s=280 m and the cyclist has run through it in a uniform motion over time
t= 46 s . The radius of the larger circle is r2 = 25 m.
a) Specify the radius r1 smaller circular section.
b) Specify the magnitude of the angle a1 and angle a2, about which the cyclist is in the individual
curves deviated from the vertical direction.
c) Decide whether this way the loop can safely pass in the rain, when the factor
shear friction between the wheel and the wet asphalt surface is f= 0,35.
a) 3/4*2*π*r1 + 3/4*2*π*r2 + 2*r1 + 2*r2 =s → r1=(2*s/4+3*π)-r2=16,71 m
b) tg a = Fc/Fg=(m*(v^2/r))=((s/t)^2/g*r)=s^2/g*r*t^ → a1 = 12 degrees 57 minutes a2= 8 degrees 39 minutes
c) Ffric.≤Fc
m*g*f≤m*v^2/r
v≤√(g*f*r) → v1= 7,58 m/s v2= 9,26 m/s
→ the loop can be passed safely because v=s/t= 6,1m/s (v1, v2)>v

Thank you for your checking.

 

[CWatters]

I got similar answers to you.

I was a few mins different with my answers for b), probably rounding errors. Not sure if yours or mine.

 

[haruspex]

Not sure if yours or mine.

Not yours.