Angled cyclist turn

The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?

Correct answer:

A =  13.5567 °

Step-by-step explanation:

r=20 m v=25 km/h m/s=25:3.6  m/s=6.94444 m/s g=10 m/s2  Fo + Fg = F Fg = m   g Fo = m v2 / r  tan A = Fg Fo  tan A =  m g m v2 / r  tan A =  r g v2  A1=arctan(r gv2)=arctan(20 106.94442)0.2366 rad  A=A1  °=A1 π180   °=0.2366 π180   °=13.557  °=13.5567=13°3324"



Did you find an error or inaccuracy? Feel free to write us. Thank you!



Showing 1 comment:
Matematik
A cyclist has to bend slightly towards the center of the circular track in order to make a safe turn without slipping.

Let m be the mass of the cyclist along with the bicycle and v, the velocity. When the cyclist negotiates the curve, he bends inwards from the vertical, by an angle θ. Let R be the reaction of the ground on the cyclist. The reaction R may be resolved into two components:

(i) the component R sin θ, acting towards the center of the curve providing necessary centripetal force for circular motion and
(ii) the component R cos θ, balancing the weight of the cyclist along with the bicycle.

Thus for less bending of the cyclist (i.e for θ to be small), the velocity v should be smaller and radius r should be larger. let h be the elevation of the outer edge of the road above the inner
edge and l be the width of the road then,





Tips for related online calculators
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Do you want to convert mass units?
Do you want to convert velocity (speed) units?
See also our right triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: