Centripetal Force & the Road - PowerPoint PPT Presentation

1 / 12

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:

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Centripetal Force & the Road

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

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

• 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

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

• At the point of slipping:

• 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

• and the vertical components balance the weight

• (N1 + N2) cos = mg

• Banked Tracks 2

• Rearranging

• 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

• 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