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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:

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Centripetal force the road1

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


Centripetal acceleration recap

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


Over the top 1

Consider a car with mass circle has a constantly changing velocity, it is therefore experiencing acceleration and hence a force towards the centre of rotation.m and speed v moving over the top of a hill...

Over the top 1

S

mg

r


Over the top 2

  • 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 / rv0 = (gr)½

  • Any faster and the car will leave the ground

  • Over the top 2


    Around a roundabout 1

    On a opposite direction to the weight (mg). It is the resultant between these two forces which keep the car moving in a circlelevel 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


    Around a roundabout 2

    • To avoid skidding or slipping, the force of friction opposite direction to the weight (mg). It is the resultant between these two forces which keep the car moving in a circleF0 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

  • At the point of slipping:

    • F0 = mv02 / r mg = mv02 / r

    •  v0 = (gr)½

  • Around a Roundabout 2


    Banked tracks 1

    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


    Banked tracks 2

  • and the vertical components balance the weight

    • (N1 + N2) cos = mg

  • Banked Tracks 2


    Banked tracks 3

    • Rearranging friction alone. Banked corners allows greater speeds before friction is overcome

      • 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 

  • Banked Tracks 3


    Problems 1

    • 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


    Problems 2

    • A car is racing on a track banked at 25 curvature of 15m at a speed of 10 ° 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


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