100 90 80 70 60 50 40 30 20 10 0

2. Recent exam scores are shown as a histogram ordered simply by student ID number. Exam Scores 100 90 80 70 60 50 40 30 20 10 0 Student ID number  What is the best approximation of the class average on this exam? A. 80 B. 60 C. 40 D. 20

3. The same scores are rearranged in ascending order below. Exam Scores 100 90 80 70 60 50 40 30 20 10 0 What is the best approximation of the class average on this exam? 100 90 80 70 60 50 40 30 20 10 0 avg = 85 A. 80 B. 60 C. 40 D. 20

4. velocity, v velocity, v A. B. time (seconds) time (seconds) C. D. velocity, v velocity, v time (seconds) time (seconds) Which of the graphs above could represent an object freely falling from rest?

5. vmax vmax 1 2 For the moving object graphed at left velocity, v A. vavg < vmax 1 2 time (seconds) vmax B. vavg = vmax 1 2 C. vavg > vmax 1 2 velocity, v vmin time (seconds) vmax vmax For the moving object graphed at left 1 2 velocity, v A. vavg < vmax 1 2 time (seconds) vmax B. vavg = vmax 1 2 C. vavg > vmax velocity, v 1 2 time (seconds)

6. Weight Support (floor)

7. Adding all these supporting forces together some pull left, some pull right, some pull forward, some pull back all tend to pull UP! (a tug-of-war balancing)

8. Styrofoam bridge weighted at center Pressure applied to rigid glass bar

9. x x x

11. W x F Natural length Springs may be compressed (shortening their “natural length”) until the “restoring force” it counters with in an attempt to regain its original shape exactly balances the applied force.

12. x Springs may be elongated (beyond their “natural length”) until the “restoring force” exactly balances the force pulling it open. Note:F x

15. Compound bows use systems of pulleys and cams to maintain a fairly constant resistance force over the full distance drawn. Otherwise, for a more conventional recurve or simple longbow Force to hold in place distance bow is drawn 

16. F x Force Displacement, x Also means:F = kx “spring constant” in units of N/m The restoring force grows so many Newtons for every meter stretched.

17. The weight of a 1250 kg car is evenly distributed over 4 coil springs with strength k = 32000 N/m. When carrying 5 passengers (each, on average 73.0 kg) how much lower does the car ride? The empty car already compresses each spring: ¼th total weight, empty car = 0.096 m = 9.6 cm With everyone on board: = 0.124 m = 12.4 cm It rides about 2.8 cm (a little more than 1 inch) lower.

19. snapped garage door spring sprung bicycle seat spring cracked suspension coil spring permanetly deformed Slinky!

20. plastic deformation elastic range failure Force proportionality limit Displacement, x

21. Work done against an elastic force ending with force= kx W = Favgd Force Fmax 2 = x 1 2 = k(x)2 starting with force 0 Displacement, x

22. F d The “full draw weight’ of this bow is 20 pounds (90 Newtons) at the 24 inches (0.60 meter) that this archer has drawn it. What is its effective spring constant? How much work was done in drawing the bow back? If all the energy goes into the 400 grain (26 gram) arrow’s kinetic energy, what speed will it leave the bow with?

23. Total Weight

24. A tennis ball rebounds straight up from the ground with speed 4.8 m/sec. How high will it climb? It will climb until its speed drops to zero! g = -9.8 m/sec2 final speed = 0 or and in that much time it will rise a distance since time up = time down the distance it falls from rest in 0.49 sec:

25. A tennis ball rebounds straight up from the ground with speed 4.8 m/sec. How high will it climb? It will climb until all its kinetic energy has transformed into gravitational potential energy! = = 1.176 meter

26. A skier starts from rest down a slope with a 33.33% grade (it drops a foot for every 3 horizontally). F h W 3h The icy surface is nearly frictionless. How fast is he traveling by the bottom of the 15-meter horizontal drop? The accelerating force down along the slope is in the same proportion to the weight W as the horizontal drop h is to the hypotenuse he rides: The long way: The slope is long So it takes him During which he builds to a final speed:

27. A skier starts from rest down a slope with a 33.33% grade (it drops a foot for every 3 horizontally). F h W 3h The icy surface is nearly frictionless. How fast is he traveling by the bottom of the 15-meter horizontal drop? The gravitational potential energy he has at the top of the slope will convert entirely to kinetic energy by the time he reaches the bottom. The short way: = 17.146 m/sec

28. D C 2h B 1.5h A h h ½h 3h 3h The bottom of the run faces a slope with twice the grade (steepness). Neglecting friction, the skier has just enough energy to coast how high?

29. We know rubber tires are easily deformed by the enormous weight of the car they support…but not permanently. They regain their round shape when removed. This “spring-like” resiliency explains the rebound of all sorts of balls.

30. Racquetball rebounding from concrete. Tennis ball rebounding from concrete.

31. Airtrack bumper carts:

32. Notice that if the spring bumbers reverberate (ring) this would have to represent some energy that did not get returned to forward motion! Unlike the stored potential of the compressed bumpers, this is not a “potential” energy that can ever be recovered as kinetic energy. This represents a fractional loss in kinetic energy! A purely ELASTIC COLLISION is defined as one which conserve kinetic energy.

33. Look how a racquetball still undulates after leaving the floor! These vibrations are a wasted form of energy!