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?


A =  13.557 °


r=20 m v=25 km/h=25/3.6 m/s=6.94444 m/s g=10 m/s2  Fo+Fg=F Fg=m g Fo=mv2/r  tanA=FoFg tanA=mv2/rm g tanA=v2r g  A1=arctan(v2r g)=arctan(6.9444220 10)0.2366 rad  A=A1 =A1 180π  =13.55675  =13.557=133324"r=20 \ \text{m} \ \\ v=25 \ km/h=25 / 3.6 \ m/s=6.94444 \ m/s \ \\ g=10 \ \text{m/s}^2 \ \\ \ \\ F_o + F_g=F \ \\ F_g=m \cdot \ g \ \\ F_o=m v^2 / r \ \\ \ \\ \tan A=\dfrac{ F_o }{ F_g } \ \\ \tan A=\dfrac{ m v^2 / r }{ m \cdot \ g } \ \\ \tan A=\dfrac{ v^2 }{ r \cdot \ g } \ \\ \ \\ A_{1}=\arctan(\dfrac{ v^2 }{ r \cdot \ g } )=\arctan(\dfrac{ 6.9444^2 }{ 20 \cdot \ 10 } ) \doteq 0.2366 \ \text{rad} \ \\ \ \\ A=A_{1} \rightarrow \ ^\circ =A_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =13.55675 \ \ ^\circ =13.557 ^\circ =13^\circ 33'24"

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 1 comment:
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 to related online calculators
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have 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.

Next similar math problems:

  1. Cyclists and walkers
    time_1 A group of tourists started at 8:00 at speed 4 km/h walk. At half-past ten, another group started on a bike and caught up with a group of tourists at 10:50. What was the average speed of cyclists?
  2. Water current
    river John swims upstream. After a while, he passes the bottle, from that moment he floats for 20 minutes in the same direction. He then turns around and swims back, and from the first meeting with the bottle, he sails 2 kilometers before he reaches the bottle.
  3. Filament of bulb
    bulb _1 The filament of bulb has a 1 ohm resistivity and is connected to a voltage 220 V. How much electric charge will pass through the fiber when the electric current passes for 10 seconds?
  4. Aircraft angines
    aircraft-02 The two engines of the aircraft are enough to supply the fuel for five hours of operation. However, one of the engines has a malfunction and thus consumes one-third more fuel. How long can the plane be in the air before it runs out of fuel? After an hour
  5. RPM
    motor_rpm An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
  6. Resistance of the resistor
    Elektrárna_1 The resistor terminals have a voltage of 20 V and a current of 5 mA is passed through. What is the resistance of the resistor?
  7. Coil as a girl
    tlmivka_TL1.JPG The electrical resistance of the copper wire coil is 2.0 ohms. What current runs through the coil when the voltage between the terminals is 3.0 V?
  8. Gravitation
    vodorovny_vrh From the top of the 80m high tower, the body is thrown horizontally with an initial speed of 15 m/s. At what time and at what distance from the foot of the tower does the body hit the horizontal surface of the Earth? (use g = 10 ms-2)
  9. Where and when
    cars The truck left Kremnica at 11:00 h at a speed of 60km/h. At 12:30 h, the passenger car started at an average speed of 80km/h. How many kilometers from Kremnica will the passenger car reach truck, and when?
  10. Car loop
    preteky The toy car runs at an average speed of 2 m/s. In a minute, it will pass the entire circuit five times. How long is the loop?
  11. Resistance
    bulb_1 Determine the resistance of the bulb with current 200 mA and is in regular lamp (230V).
  12. Cheetah vs antelope
    motion2 When the cheetah began chasing the antelope, the distance between them was 120 meters. Although the antelope was running at 72km/h, the cheetah caught up with it in 12 seconds. What speed was the cheetah running?
  13. Transformer
    trafo Solve the textbook problems - transformer: a) N1 = 40, N2 = 80, U2 = 80 V, U1 =? b) N1 = 400, U1 = 200 V, U2 = 50 V, N2 =?
  14. Fog
    fog The car started in fog at speed 30 km/h. After a 12-minute drive, the fog dissipated and the driver drove next 12 minutes distance 17 km. On the last 17 km long again the driving conditions deteriorated and the driver drove the speed of 51 km/h. a) Calcu
  15. Voltmeter range
    predradnik We have a voltmeter which in the original set measures voltage to 10V. Calculate the size of the ballast resistor for this voltmeter, if we want to measure the voltage up to 50V. Voltmeter's internal resistance is 2 kiloohm/Volt.
  16. The tourist
    tourist The tourist traveled 78km in 3 hours. Part of the journey went on foot at 6km/h, the rest of the trip by bus at 30km/h. How long did he walk?
  17. Between two bus stops
    bus27 Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that whether he was running to one or the other stop, he would have arrived at the bus stop. The average bus speed is 60 km/h. What is the average