# 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:

**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,

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

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.

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

## Related math problems and questions:

- The bridge

A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that - Accelerated motion - mechanics

The delivery truck with a total weight of 3.6 t accelerates from 76km/h to 130km/h in the 0.286 km long way. How much was the force needed to achieve this acceleration? - Overtaking

On the direct road, the passenger car overtakes the slower bus by starting to overtake 20 meters from the bus and after passing it ahead of it again 20 meters away. The car overtakes at a steady speed of 72 km/h, the bus goes at a steady speed of 54 km/h. - Two ships

The distance from A to B is 300km. At 7 am started from A to B a ferry with speed higher by 20 km/h than a ship that leaves at 8 o'clock from B to A. Both met at 10h 24min. Determine how far they will meet from A and when they reach the destination. - The tourist

The tourist came started from the hostel at an average speed of 5km/h. Half an hour later, the bicyclist started along the same route at a speed of 20km/h. How many minutes will a cyclist catch up and how many kilometers will he go? - Two people

Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa - Shortcut

The road from the cottage to the shop 6 km away leads either along a straight road that the bicycle can drive at a speed of 18 km/h or by "shortcut". It measures only 3.6 km. But the road from the cottage is all uphill - at a speed of 8 km/h, you can go h - Same force

The trunk of 5m length and 95 kilograms has a center of gravity 2m from the thicker end. The tribe is carried by two men, one at the thicker end. At what distance does the trunk carry a man from the other end to make the same force on it? - The car

The car weight 1280 kg, increased its speed from 7.3 m/s to 63 km/h on a track of 37.2 m. What force did the car engine have to exert? - The body

The body slides down an inclined plane forming an angle α = π / 4 = 45° under the action of a horizontal plane under the effect of friction forces with acceleration a = 2.4 m/s ^ 2. At what angle β must the plane be inclined so that the body slides on it - Two friends

Two friends on a bicycle rode against each other from two places 49 km apart. The first set off at 8.00 at a speed of 20km/h, the second 12 minutes later at a speed of 25km/h. What time do they meet? How many km will each of them travel since then? - Fighter

A military fighter flies at an altitude of 10 km. The ground position was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h. - Cyclist vs boat

The cyclist wants to ride a short distance by boat, but when he stops at the pier, the boat does not pick up passengers yet and is preparing to leave. The cyclist decides that the boat will catch up at the next stop. The stop is 12km far along the water a - Fly and cyclist

Two cyclists are at 20 km apart on a same line. They start at same time towards each other at a speed of 10 km/hr. A fly sitting on one of the cyclists handle start flying towards the other cyclists at a speed of 20 km/hr. It touches the handle and move b - Bomber

The aircraft flies at an altitude of 4100 m above the ground at speed 777 km/h. At what horizontal distance from the point B should be release any body from the aircraft body to fall into point B? (g = 9.81 m/s^{2}) - Two cyclists

Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start? - The cyclist

The cyclist drove from A to B, 60 km away. The first half drove at 30km/h, the second at 20km/h. How long did it take for him?