Chapter 2.2 Announcements: Homework 2.2: (due Tuesday Feb. 12) Exercises: 21, 22, 24, 26, 27, 29, 31 Problems: 7, 11, 16 Homework rules: Show your work, use proper units You can collaborate, use tutors, but do your own work in the end. - In-class: 100% - Same day, late: 80% - Two days later: 50%

Chapter 2.2 Wheels Concepts Demos and Objects wheels pulling boxes burning wood by rubbing lighting a match rubbing hands ball bearings moving and spinning things static friction sliding friction sliding friction  thermal energy work, power, energy kinetic energy

i-clicker-1 You are in a tremendous hurry and you want your car to accelerate as quickly as possible. Will you accelerate faster if you “burn rubber” (skid your wheels), or if you just barely avoid skidding your wheels? Not enough information Related: What are the three advantages of anti-lock brakes? (later)

Observations About Wheels Without wheels, objects slide to a stop Friction is responsible for the stopping effect Friction seems to make energy disappear Wheels reduce friction enourmously Wheels can also propel vehicles, but how?

Friction Opposes the relative motion of two surfaces Consists of a matched pair of forces: Object one pushes on object two Object two pushes on object one Forces have equal magnitudes, opposite directions Comes in two types: static and sliding

Types of Friction Static Friction Sliding Friction Acts to prevent objects from starting to slide Forces can vary from zero to an upper limit Sliding Friction Acts to stop objects that are already sliding Forces have fixed magnitudes (for a given system)

Frictional Forces Increase when you: push the surfaces more tightly together roughen the surfaces Peak static force is greater than sliding force Surface features can interpenetrate better Friction force drops when sliding begins

Friction and Wear Static friction Sliding friction No work is done (no distance) No wear occurs Rolling is mostly static friction (microscopically like gears (sprockets)) Sliding friction Work is done (distance in the direction of force) Wear occurs Work is turned into thermal energy

The traffic light turns red, and now you need to stop as quickly as possible. What are the three advantages of anti-lock brakes? _______________________________________

Rollers Eliminate sliding friction at roadway Are inconvenient because they keep popping out from under the object

Wheels Eliminate sliding friction at roadway Wheel hubs still have sliding friction

Bearings Eliminate sliding friction in wheel hub Behave like automatically recycling rollers

Kinetic energy of objects The kinetic energy of an object with mass, m, moving with velocity, v is: The kinetic energy of an object with rotational mass, I, spinning with angular velocity, w is: Friction converts kinetic energy to thermal energy (objects heat up). Thermal energy is ‘disordered’ energy.

i-clicker-2 A cannon ball of mass 1 kg moves at 100 m/s. A truck of mass 10,000 kg moves at 1 m/s. A tire with rotational mass 2 kg‧m2 spins at 100 rad/s. Which has more kinetic energy? A. The tire B. The truck C. The cannon ball D. Same E. Need more information i-clicker-2

Is it true that you use up the same amount of energy when going up a hill faster, vs. slower? If so, why does it feel so different?  More power output when you go faster. Power

How long will it take him to climb a 500 m (1640 ft) high mountain? The units of power are joule/sec (J/s) = Watt (W) James Watt (1736-1819); Scottish inventor and engineer whose improvements to the steam engine were fundamental to the changes wrought by the Industrial Revolution. (from Wikipedia) (1 horsepower = 746 W) An elite athlete (mass 70 kg) has a power output of 450 W (at the aerobic threshold). How long will it take him to climb a 500 m (1640 ft) high mountain? (Power output for a good athlete is 200 – 300 W)