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## PowerPoint Slideshow about 'Centripetal Force & the Road' - sunila

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Learning Objectives### Centripetal Force & The Road

Book Reference : Pages 26-27

- To show that the centripetal force is provided by real world forces such as tension, gravity & friction
- To consider three particular cases of motion:
- Over the top of a hill or humped back bridge
- Around flat curves (roundabouts)
- Around banked curves

During the last lesson we saw that an object moving in a circle has a constantly changing velocity, it is therefore experiencing acceleration and hence a force towards the centre of rotation.### Centripetal Acceleration : Recap

We called this the centripetal force: The force required to keep the object moving in a circle. In reality this force is provided by another force, e.g. The tension in a string, friction or the force of gravity.

At the top of the hill, the support force S, is in the opposite direction to the weight (mg). It is the resultant between these two forces which keep the car moving in a circle### Over the top 2

- mg – S = mv2 / r
- If the speed of the car increases, there will eventually be a speed v0 where the car will leave the ground (the support force S is 0)
- mg = mv02 / rv0 = (gr)½
- Any faster and the car will leave the ground

On a level road, when a car travels around a roundabout the centripetal force required to keep the car moving in a circle is provided by the friction between the road surface and tyres### Around a Roundabout 1

Force of Friction F

F = mv2 / r

friction

velocity

To avoid skidding or slipping, the force of friction F0 must be less than the point where friction is overcome which occurs at speed v0### Around a Roundabout 2

- Friction is proportional to weight and can be given by the coefficient of friction ():
- F mg F = mg
- At the point of slipping:
- F0 = mv02 / r mg = mv02 / r
- v0 = (gr)½

For high speed travel, race tracks etc have banked corners. In this way a component of the car’s weight is helping friction keep the car moving in a circle### Banked Tracks 1

N1

N2

Towards centre of rotation

mg

Without any banking the centripetal force is provided by friction alone. Banked corners allows greater speeds before friction is overcome### Banked Tracks 2

- The centripetal force is provided by the horizontal components of the support forces
- (N1 + N2) sin = mv2 / r
- and the vertical components balance the weight
- (N1 + N2) cos = mg

Rearranging### Banked Tracks 3

- sin = mv2 / (N1 + N2) r
- cos = mg / (N1 + N2)
- and since tan = sin /cos
- tan = mv2 / (N1 + N2) r x (N1 + N2) / mg
- tan = mv2/ mgr v2 = gr tan
- Thus there is no sideways frictional force if the speed v is such that v2 = gr tan

A car with mass 1200kg passes over a bridge with a radius of curvature of 15m at a speed of 10 ms-1. Calculate:### Problems 1

- The centripetal acceleration of the car on the bridge
- The support force on the car when it is at the top
- The maximum speed without skidding for a car with mass 750kg on a roundabout of radius 20m is 9ms-1. Calculate:
- The centripetal acceleration of the car on the roundabout
- The centripetal force at this speed

A car is racing on a track banked at 25° to the horizontal on a bend with radius of curvature of 350m### Problems 2

- Show that the maximum speed at which the car can take the bend without sideways friction is 40ms-1
- Explain what will happen if the car takes the bend at ever increasing speeds

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