1. Mu of the Shoe Chapter 2, Activity 6

2. Friction What is friction? –A–An interaction between a moving object and its environment Produces heat and loss of energy Slows things down –W–Water  viscosity –A–Air  Air resistance

3. What is friction? –B–Between two surfaces, they may or may not be in motion relative to one another. If they are in motion relative to one another, it is kinetic friction. If the two objects do not move relative to one another, it is static friction

4. Braking friction

5. What do you think? Why do some sports require special shoes? –Shoe companies have done large amounts of research and development on the materials and design of shoes to enhance their performance. –Many of the design characteristics are to maximize the friction between the sole of the shoe and the surface it is intended to be used on.

6. Friction How does friction affect the motion of objects? –It can slow an object down like the friction between the tires and the road. –Friction is responsible for increasing the speed of an object like a car. –Friction is also responsible for objects being able to change direction.

7. Static Friction System F forward F friction F ground-on-crate F gravity F forward F friction F net = F forward – F friction Since the crate is not accelerating, F net = 0 F forward = F friction If the crate is not moving, then the pushing force will equal the frictional force F forward = F friction Static Friction: –The resistive force that keeps an object from moving.

8. Kinetic Friction System F forward F friction F ground-on-crate F gravity Kinetic Friction: –The resistive force that opposes the relative motion of two contacting surfaces that are moving past one another. F forward F friction F net = F forward – F friction F net If the crate is moving at a constant speed, then the pushing force will equal the frictional force F forward = F friction

9. Determining the Frictional Force The force of friction is proportional to the normal force and a proportionality constant (µ - pronounced mu) called the coefficient of friction. For static friction: –0 < F f, static < µ s F N For kinetic friction: –F f, kinetic = µ k F N Note: F N = the force normal (perpendicular) to the frictional force on the object. µ is dimensionless Note: F f, static > F f, kinetic (You have experienced this!)

10. The Normal Force The normal force is a force that opposes the Earth’s gravitational attraction and is perpendicular to the surface that an object rests or is moving on. –For a horizontal surface, F N = F g = mg. –In other words, the normal force equals the weight. FNFN FgFg

11. 1. The formula for friction is similar to those we have already used where there are three variables: F f = µF N –As just mentioned, for a horizontal surface, the normal force is the same as the weight of the object (F g = mg) m = mass in kilograms g = acceleration due to gravity (10 m/s 2 ) FfFf µ FNFN The Math of Friction

12. Determining the Mu of the Shoe 1. Determine the mass of the shoe in kg. 2. Determine the normal force, which will be the same as the gravitational force of the shoe (F g = mg), where g = 10 m/s 2. 3. Determine the tensional force in the spring scale while pulling the shoe at “constant speed.” Under these conditions, the tensional force will equal the frictional force. 4. Find µ : FTFT FfFf FgFg FNFN µ = F f /F N = F T /F g

13. Example 1: Determining Friction Assume that the man in the figure is pushing a 25 kg wooden crate across a wooden floor at a constant speed of 1 m/s. –How much force is exerted on the crate? System F forward FfFf FNFN FgFg

14. Diagram the Problem System F forward FfFf FNFN FgFg FfFf FNFN FgFg y-direction: Normal force equals gravitational force (F N = F g ) x-direction: F net = F forward - F f Since the crate is moving with constant speed, a = 0, F net = 0, and F forward = F f +y +x

15. State the Known and Unknowns What is known? oMass (m) = 25 kg oSpeed = 1 m/s oAcceleration (a) = 0 m/s 2 o  k = 0.2 (wood on wood - found in reference table) What is not known? oF forward = ?

16. Perform Calculations y-direction: oF g = F N = mg x-direction: a = 0 oF net = F forward – F f oF forward = F f oF forward =  k F N ; F forward =  k mg oF forward = (0.2)(25 kg)(9.8 m/s 2 ) oF forward = 49 N 0

17. Key Ideas Friction is an opposing force that exists between two bodies. Friction is proportional to the normal force and the coefficient of friction; static or kinetic. The force required to overcome static friction is greater than that required to overcome kinetic friction.