2. Nothing’s moving, but not from lack of trying! 1 6 3 1. Stranded motorist pushes on car. 2. Car pushes back on her. How do we know? 5. With feet dug in, she pushes back into the sand. 6. The sand pushes back on her. This is what balances 2. 3. Because it is mired in sand, the car’s tires have a mound of sand to push up against. 2 4. Sand pushes back on car. How do we know? 4 5 What needs to be changed to get out?

3. How do you walk? What are the forces involved that allow you to walk? As bracing yourself to push a car showed, you push back against the ground below you to propel yourself forward. Imagine trying to walk across a surface without friction!

4. Smooth plastic surface Micro-polished glass

5. 500  m 50  m A smoothly varnished surface.

6. Polished carbon steel surfaces

7. Since even the smoothest of surfaces are microscopically rough, friction results from the sliding up and over of craggy surfaces, and even the chipping and breaking of jagged peaks. There are TWO TYPES of friction. Static Friction Acts to prevent objects from starting to slide Forces can range from zero to an upper limit Sliding Friction Acts to stop objects that are already sliding Forces of sliding friction have a fixed value that depends on the particular surfaces involved.

8. force the sliding surfaces together more tightly (increase an object’s weight). Frictional forces increase when you: The peak static force is always greater than sliding force Surface features interpenetrate more deeply when stationary objects settle. Friction force drops when sliding begins Cold welds are broken and moving objects ride across the craggy surfaces higher.

9. W f The force of friction, f, is directly proportional to the total force (usually W for objects sliding horizontally) that presses the sliding surfaces together: We write: f =  W where  is known as the “coefficient of friction”

10. Typical coefficients of friction maximum Materialstatic sliding Rubber on dry concrete 0.90 0.80 Steel against steel 0.74 0.57 Glass across glass 0.94 0.40 Wood on wood 0.58 0.40 Wood on leather 0.50 0.40 Copper on steel 0.53 0.36 Rubber on wet concrete 0.30 0.25 Steel on ice 0.10 0.06 Waxed skis on snow 0.10 0.05 Steel across teflon 0.04 0.04 Synovial joints (hip, elbow) 0.01 0.01 What happens when objects slide to rest? Where does the lost kinetic energy go? It generates heat, an additional form of energy.

11. Rotation Velocity Wheels can circumvent friction by using the fact that objects can roll without sliding

12. If friction prevents slipping at this point, the foot planted at bottom stays stationary as the entire assembly tips forward, rotating about its axis.

13. Notice while the planted foot stays put, the axle moves forward at half the speed that the top edge of our wheel does! v = 0 v 2v2v Remember:pathlength out a distance r from the center of a rotation: s = r  and the tangential speed at that point: v = r 

15. Each time this tethered ball comes around, a wack of the paddle gives it a boost of speed speed  v. But this  v is directly related to an angular velocity,  (in radians/sec)  v = r  r For an individual mass m rotating in an orbit of radius r rotational kinetic energy m

16. d F We’ve noted that an unbalanced force acting continuously over a distance d delivers kinetic energy to the object being pushed: work donekinetic energy

17. d Often the distance over which the forces act in a collision becomes difficult to measure directly.

18. Particularly for sudden, jarring “impulses” where the contact forces act for only brief instances. Impulse is a physics term describing how sudden the application of force during such collisions is. Analogous to our definition of work, consider: Force  time over which it acts v = v 0 + at Recall: producing a change in “momentum”

19. Momentum is inertia of motion Easy to start Hard to start While inertia depends on mass Momentum depends on both mass and velocity Easy to stop Hard to stop v v v v m m m m momentum = mass  velocity “Quantity of motion”

20. To change velocity  Force To change momentum  Impulse Ft (mv)Ft (mv) Ft (mv)Ft (mv) Ft (mv)Ft (mv) short “twang”  small momentum long “twang”  larger momentum Ft (mv)Ft (mv) Small force  may not break! Short time  large force