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1 Friction

2 Friction Friction causes objects to slow down. Friction creates heat. Friction degrades an object s energy

3 Friction is: Friction: A force that resists the relative motion or tendency to such motion of two bodies in contact. Source: Dictionary.com Or why this won t work very well

4 Places where friction is good The soles of shoes Car tires The feet of table legs Rock climbing holds Brakes etc

5 Places where friction is bad In engines In transmissions On the bottoms of skis and snowboards (To a point) When you are trying to move a box by pushing it along the floor etc

6 What causes friction?

7 Source of Friction At the microscopic level even the smoothest of surfaces is dotted with little mountain peaks. The tips of the peaks are the only parts that touch the other material. Only a very small portion of the apparent surface area is in contact with the other surface Picture of extremely smooth mica with a scanned probe microscope This causes extremely high pressures to form on the parts that touch. This causes the two surfaces to become welded almost at the points of contact

8 Friction Surface imperfections and micro-welds.

9 Source of friction (continued) The true surface contact area is proportional to the normal force because the peaks will deform plastically when force is applied increasing the contact area Plastic deformation: to change shape permanently without fracturing Other lesser reasons for friction Surface adhesion between pure metals Ploughing of one surface by the other harder one Elastic deformation

10 Experiment: Does the friction force depend on surface area? We stick a 1kg mass on a piece of plexiglass on top of the clean surface and, using a Newton meter, pull the weight across the table with the string provided at constant speed. We put the same weight on a different piece of plexiglass with drastically different surface area and repeat What do you notice?

11 Friction doesn t depend on apparent surface area (much) You may have noticed a small dependence. This is partially due to the greater weight of the larger piece of plexiglass, and also partially due to the fact that there is a dependence of friction on surface area, just one that is small enough to be ignored under most circumstances. Why is the friction force approximately independent of surface area? Because as discussed previously the materials plastically deform at the peaks depending on the pressure increasing real surface area. RSA = real surface area, F = Normal Force, SA = Surface area, F/SA = P Pressure, C = constant depending on the materials RSA = SA x P x C = SA x F/SA x C = F x C

12 Static Friction

13 Static Friction Normal force Friction, Resistance Applied Force Objects at rest. Applied force is insufficient to move object. Weight = mg

14 Finally something useful.. The only formula you need for friction forces: Friction Force = coefficient of kinetic friction x norrnal force or F f = µf n

15 Newton s Second and Third Laws Newton s Second Law: If there is an unbalanced force on an object it will accelerate according to F Unbalanced = m a Newton s Third Law: If you exert a force on an object it exerts an equal and opposite force on you

16 Block at Rest on a Table

17 Normal Force From Newton s third law we know that if gravity or some other force pushes an object (like a block) into a second object (like a table) that second object will be exerting an equal force back on the first. Normal force is the force the table exerts back on the block Normal force is always exerted perpendicular to the surface Friction Force is always parallel to the surface So if the table is horizontal and gravity is the only force on the block F n = -F g

18 Normal force on a hill Normal force is exerted perpendicular to the surface in accordance with Newton s Third law No unbalanced force so the block is stationary or at least not accelerating

19 Static Friction The relationship is µ s = force of friction/normal force. Where µ is called the coefficient of static friction. It has no units and varies between 0 and 2 in general. We usually rearrange the equation: f = µ s N (Mu)

20 Example of Static Friction What is the coefficient of static friction between a tabletop and a 2 kg block of wood if a 2 N force is required to start the block moving? Identify knowns and unknown: m = 2 kg, applied force = 2 N, v = 0, µ s =?

21 Appropriate equation: f = µ N. What is N? On a level surface the normal force upward is equal to the weight of the object downward, i.e. N = W = mg. So, f = µ mg or µ = f/mg = 2 N/(2 kg *9.8m/s 2 ) µ = 0.102

22 Kinetic Friction

23 Kinetic Friction The word kinetic stems from the Greek word, kinema meaning motion, so kinetic friction deals with the friction present when motion is occurring. The resistance is less because the microscopic impediments are being sheared off and no time for micro-welds to form.

24 Kinetic Friction Constant Less than static friction. This is the key to non-skid brakes. Force Frictional Applied Force, N

25 Why? The slightly larger value for static friction results from irregularities and contaminants on the surfaces and is less accurate in general than the coefficient of kinetic friction Between (very) carefully cleaned surfaces the difference between the two coefficients disappears

26 Compare skidding with no skidding. A car moving at 25 m/s slams on its brakes. The coefficient of static friction with the road is 1.2 and the kinetic coefficient is How far does the car slide? Knowns: v o = 25 m/s, v = 0 m/s, µ s = 0.4. Unknown: x =? Equations: v 2 =v o2 +2 ax, F = ma, N = mg, f =µn.

27 Solve for x: x = -v o2 /2a = -v o2 /2(-F/m) =-v o2 /2(-µN/m) =-v o2 /2(-µmg/m) = v 2 o2 /2 /2µg =(25 m/s) 2 /(2*0.85*9.8 m/s 2 ) =37.5 m

28 Now, solve the same problem using non-skid brakes so the wheels keep turning while the car slows down. In this case we use the state coefficient of friction x = v o2 /2µg =(25 m/s) 2 /(2*1.2*9.8 m/s 2 ) =26.6m Imagine if the pavement wear wet and the coefficient of kinetic friction was The stopping distance would be nearly 75 m!

29 Frictional force and normal force. Frictional force is proportional to the normal force, f α N. On a level surface N = W, but what if someone is lifting up on the object? Won t that reduce the normal force?

30 Free Body Diagram N + T = W, so N = W T. If T pulls at some angle, then just decompose into components. Normal, N Lift from person,t Weight, W

31 Example: A person pulls on a 300 N crate with a rope that makes a 37 0 angle to the ground. If the coefficient of static friction is 0.6, how much tension must the person exert to get the crate moving? Knowns: W = 300 N, θ = 37 o, µ = 0.6. Unknown: T =? Equations: f = µn. All forces balance when at rest.

32 Horizontal Tension = T cos θ Vertical Tension = T sin θ Net vertical force = N + Tsin θ W = 0, so N = W - Tsin θ. Net horizontal force = Tcos θ f = 0 Tcos θ = f = µn = µ(w - Tsin θ), so

33 Tcos θ = µ(w - Tsin θ) Tcos θ + µ Tsin θ = µw T(cos θ + µ sin θ) = µw T = µw/(cos θ + µ sin θ) T = 0.6*300N/(cos *sin30 0 ) T = 180N/( ) T = 180 N/(1.166) T = 154 N

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