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Centripetal Force & the RoadPowerPoint Presentation

Centripetal Force & the Road

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Centripetal Force & the Road

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Centripetal Force & the Road

Learning Objectives

Book Reference : Pages 26-27

Centripetal Force & The Road

- 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.

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.

Centripetal Acceleration : Recap

Consider a car with mass m and speed v moving over the top of a hill...

Over the top 1

S

mg

r

- 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
- mg – S = mv2 / r

- mg = mv02 / rv0 = (gr)½

Over the top 2

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
- Friction is proportional to weight and can be given by the coefficient of friction ():
- F mg F = mg

- F0 = mv02 / r mg = mv02 / r
- v0 = (gr)½

Around a Roundabout 2

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
- The centripetal force is provided by the horizontal components of the support forces
- (N1 + N2) sin = mv2 / r

- (N1 + N2) cos = mg

Banked Tracks 2

- Rearranging
- sin = mv2 / (N1 + N2) r
- cos = mg / (N1 + N2)

- sin = mv2 / (N1 + N2) r
- and since tan = sin /cos
- tan = mv2 / (N1 + N2) r x (N1 + N2) / mg
- tan = mv2/ mgr v2 = gr tan

Banked Tracks 3

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

Problems 1

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

Problems 2