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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

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**Lecture 4 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

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**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’

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**Friction 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:

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**F = m R Where: F is the force need to overcome friction**

For objects sliding over each other Can be described by simple equation: F = m R 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.

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**F = m R 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

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**F = m R 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

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F = m R 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

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**[ 1.0 is the biggest normal value. If >1.0, then ‘sticky’.**

Approximate coefficients of friction Materials Dry & clean Aluminum Steel 0.61 Copper 0.53 Brass 0.51 Cast iron 1.05 Zinc 0.85 Concrete (wet) Rubber careful driving in wet! 0.3 Concrete (dry) 1.0 Glass 0.68 0.94 Teflon Non-stick! Static friction, [ 1.0 is the biggest normal value. If >1.0, then ‘sticky’.

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**F = m R 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

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Brass-Steel 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

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**The reaction force between**

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

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**(at same altitude of flight)**

Note that there are other forms of friction 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 of flight) Supersonic plane

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**It takes a force to change the direction of a moving object motion**

Circular Motion It takes a force to change the direction of a moving object motion force New motion

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**If a constant force is always applied perpendicular to the motion then**

the object will go in a Circle Its speed will not change Just the direction alters

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**The force of gravity does this, keeping planets in orbits**

The force of the sun is always towards the sun Which is perpendicular to the direction the plants travel (not quite a circle – but don’t consider that here)

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**r F v The force needed to make a circle is: 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

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If the body is made to circle by a string, then the string will feel a force pulling it into tension. This is the centrifugal force. Of course these two different names are 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

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**Riders feel the centrifugal force holding them in the car.**

The rail applies a centripetal force to make the car circle. Riders ALSO feel gravity, but it is not enough to make them fall out of the car

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**It is common to use 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

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**Answer: Depends on the speed limit **

With F = 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, but in theory: Answer: I cant afford a Ferarri

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**Consider a real car (Lotus Elise)**

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)

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**Answer: v = √(mgr) (BUT remember m is much smaller in the wet!)**

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**Finally, when cornering:**

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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Circular Motion Lecturer: Professor Stephen T. Thornton

Circular Motion Lecturer: Professor Stephen T. Thornton

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