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Friction & Circular Motion Static and Moving Friction Centripetal and Centrifugal Forces. Friction was introduced in last lecture, expand Nature of Friction, its origins Static Friction Friction in Motion Circular motion using centripetal force ‘Equivalence’ with gravity

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Friction & Circular Motion

Static and Moving Friction

Centripetal and Centrifugal Forces

  • Friction was introduced in last lecture, expand

    • Nature of Friction, its origins

    • Static Friction

    • Friction in Motion

  • Circular motion using centripetal force

    • ‘Equivalence’ with gravity

    • Linear analogues


  • Aim of the lecture

    • Concepts in Friction

      • Depends on surfaces

      • Depends on contact Forces

      • Depends on motion

      • Air resistance

    • Circular Motion

      • Centrifugal and Centripetal Forces

  •   Main learning outcomes

    • familiarity with

      • forces needed to sustain motion

      • static and moving friction, coefficients

      • Forces needed for circular motion

      • Centrifugal and Centripetal force

Lecture 4


  • Newton’s First Law

  • Reminder: It appears that:

    • A force is needed to keep an object moving at constant speed.

    • An object is in its “natural state” when at rest.

  • These are wrong

    • friction creates this illusion.

  • ” Where does friction come from?

  • The illustration shows two surfaces in contact – at the microscopic level Surfaces are NOT ‘flat’.

    • ‘locked’ together

      • to make them slide will require force

        • to ‘break the locking’

      • even when already moving

        • to keep ‘breaking the locking’


Friction Law

  • How hard it is to break the ‘locking’ will depend on:

    • nature of the surfaces

      • smoother, less locking

      • rougher, more locking

      • (also other effects ‘sticky’ surfaces like rubber)

    • How hard the surfaces are pressed together

    • because the ‘true’ contact area depends on force:


  • Where:

  • F is the force need to overcome friction

  • R is the force between the surfaces

  • m is a constant which depends on the surfaces in contact

Note:

This does NOT depend on the area in contact!

If the force BETWEEN the surfaces, R, is the same, then the area does not matter.


  • Why is the area not important?

  • Friction force depends on

    • Force per unit area

    • Total area

  • Double area, with same TOTAL force, means

    • force per unit area is halved

  • So (total area) × (force per unit area) is not changed

Total force needed = const × (F/A) × A


  • m is called the coefficient of friction

    • depends on BOTH surfaces

      • low for ice on metal

      • High for rubber on concrete

  • NOTE:

    • rolling friction is a different thing

      • high m for rubber tyre on concrete

        • Stops tyre sliding

        • Helps with braking

      • Does NOT resist the wheel rotating

        • because there is no sliding of wheel past concrete for rotation


  • It is easier to keep something sliding than to start it moving

  • There are two coefficients of friction

    • One for static friction, ms

      • force needed to start a static object moving

    • One for dynamic friction mr

      • force needed to keep moving at constant speed

ms > mr

Easier to keep sliding than

to get moving



Often it is gravity that is creating the force

  • The force due to gravity is the weight of the top object

  • This is a ‘Reaction force’, hence use of ‘R’ in formula

R = Force = mg


Brass-Steel ‘sticky’.ms = 0.51

W = 10kg x 9.81 ms-1 = 98N

So F = ms x R = 98N x 0.51 = 50N

This is the force it takes to get a

10kg steel block sliding over

a brass surface.

STEEL

10kg

BRASS


The reaction force between ‘sticky’.

the surfaces is given by

R = mg cos(q)

The force down the slope is

F = mg sin(q)

If F > msR block will slide

mgsin(q) > msmgcos(q)

ie if tan(q) > ms

q


  • Note that there are other forms of friction ‘sticky’.

    • Rolling

    • Pulley

    • Air resistance

  • These do not all behave the ‘same way’ as simple sliding

    • eg for many situations the force due to air resistance is

  • F = k v2

  • Where v is the velocity and k a constant which depends on

    • Air density

    • Shape of object moving through air.

kplane < kbus

(at same altitude offlight)

Supersonic plane


Circular Motion ‘sticky’.

It takes a force to

change the direction

of a moving object

motion

force

New motion




The force needed to make a circle is: ‘sticky’.

Where

m is the mass of the circling body

v is its speed

r is the radius of the circle

the force is called the centripetal force

r

F

v


If the body is made to circle by ‘sticky’.a string, then the string will feela force pulling it into tension.

This is the centrifugal force.

Of course these two different namesare really describing the same force.

But from different perspectives

  • Centripetal

    • Force applied to make circular motion

  • Centrifugal

    • Force ‘felt’ by object being made to circle


Riders feel the ‘sticky’.centrifugal forceholding them inthe car.

The rail applies

a centripetal force

to make the carcircle.

Riders ALSO

feel gravity,

but it is not enoughto make them fallout of the car


It is common to use ‘sticky’.w instead of v, where

w = v/2pr

This is the angular speed

- number of radians per second

Then the centripetal force is:

F = w2r


With F = ‘sticky’.mR (concrete-rubber m = 1.0) and F = mv2/r

can answer question:

How fast can you drive your Ferarri round a corner?

Answer: Depends on the speed limit

Answer: I cant afford a Ferarri

Answer: I cant afford a Ferarri, but in theory:


Consider a real car (Lotus Elise) ‘sticky’.

v

r

Centripetal force

  • Force needed to make the car turn in circle

    • Fcircle = mv2/r

  • Force provided by friction between wheel and road

    • Ffriction = mR where R = mg

  • If Fcircle is greater than Ffriction then friction will not be enough

    • and Elise will slip (but designed with oversteer so will slip rear end first – chance to recover)

Condition is mv2/r = mmg => v = √(mgr)


Answer: v = √( ‘sticky’.mgr) (BUT remember m is much smaller in the wet!)


  • Finally, when cornering: ‘sticky’.

  • remember that F = mR

  • R can be bigger if the car has proper aerodynamics

    • The reason cars have ‘wings’ on them is to force the car down increasing R to a bigger value than mg, [it flies into the ground]

  • In formulae 1, the cars are designed so R is very large,

    • the cars stick like limpets round the corners,

    • but only if they go fast, so R is larger than mg!


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