A cyclist riding on a closed path....

In summary, the conversation discusses a closed loop in the shape of eight at a park with straight and circular sections. The total length of the loop is 280 m and a cyclist has run through it in a uniform motion in 46 seconds. The radius of the larger circle is 25 m and the radius of the smaller circle is 16.71 m. The angles a1 and a2 are 12 degrees 57 minutes and 8 degrees 39 minutes respectively, and the loop can be safely passed in the rain with speeds of 7.58 m/s and 9.26 m/s.
  • #1
Qwertz0099
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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.
 
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  • #2
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.
 
  • #3
CWatters said:
Not sure if yours or mine.
Not yours.
 
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Likes CWatters

Related to A cyclist riding on a closed path....

1. What is a closed path in cycling?

A closed path in cycling refers to a route or track that is completely enclosed and does not have any intersections or exits. This type of path is often used for races or training purposes.

2. Is riding on a closed path safe?

Riding on a closed path can generally be considered safe as there are no vehicles or pedestrians to contend with. However, it is still important to follow proper safety precautions and be aware of other riders on the path.

3. How is riding on a closed path different from riding on the road?

Riding on a closed path is different from riding on the road in several ways. Closed paths are typically smoother and have fewer obstacles, but they also lack the real-life conditions and challenges of riding on the road.

4. What are the benefits of riding on a closed path?

Riding on a closed path can provide a controlled environment for training and racing, as well as a safer option for cyclists who may not feel comfortable riding on the road. It also allows for uninterrupted riding without having to stop for traffic or signals.

5. Are there any rules or regulations for riding on a closed path?

Rules and regulations for riding on a closed path may vary depending on the specific location and event. It is important to always follow any posted rules and guidelines, as well as general cycling safety practices such as wearing a helmet and following traffic laws.

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