Pre-Final Exam 151L

1. Pre-Final Exam 151L Created for BW Physics by Dick Heckathorn 12 December 2K + 9

2. 1. Clay Spheres Since computers fit data according to a mathematical formula without any thought process, the experimenter must often know something about the underlying science in order to choose the proper type of fitting equation. Based on what you know about clay spheres, volume, density, etc, what is the best fitting form for a graph of clay sphere mass vs. diameter?

3. a) Linear: y = mx + b b) Simple proportion: y = Ax c) 2nd Order polynomial: y = Ax^2 + Bx + C d) 3rd Order polynomial: y = Ax^3 + B x^2 + Cx + D e) Power function: y = A x^n

4. 2. Walking Professors Suppose you were tracking two professors walking in opposite directions at constant speeds. Assume that the origin is located midway between the two men's position and, as usual, take the positive x‑direction as being towards the right.

5. Sketch and label reasonable position‑time and velocity time graphs for the two white hat

6. Questions 3 ‑ 5: A low‑friction cart is given a push to the right so that it moves away from the motion detector and up an incline, reverses direction and returns to its initial position.

7. 3. Which of the following best represents the velocity‑time graph for the cart?

8. 4. Which of the following best represents the position‑time graph for the cart?

9. 5. Which of the following best represents the acceleration‑time graph for the cart?

10. Questions 6 ‑ 9 A low‑friction cart, in the above figure, is released so that it initially moves down the incline away from the motion detector, in the positive direction. In this case, the cart hits the bottom stopper but rebounds due to a built in spring bumper so that it moves up and down the incline several times. A portion of the cart's velocity‑time graph with several labeled points is shown below.

11. 6. Which point best indicates the point where the cart is just beginning to come in contact with the bottom stopper? a) A b) B c) C d) D e) E

12. 7. Which point best indicates the point where cart's spring bumper is at maximum compression? a) A b) B c) C d) D e) E

13. 8. Which point best indicates the point where the cart is at one of its momentary high points on the incline, that is, a point closest to the motion detector? a) A b) B c) C d) D e) E

14. 9. The cart is moving away from the detector a) between A and B only b) between B and C only c) between A and C d) between C and D only e) between D and E only

15. 10. Walking the Walk Sketch the Distance‑Time graph for a person walking the walk in the following manner. - Starting from x = 0, she walks away from the sonic ranger at 1.0 m/s for 3 seconds.

16. 10. Walking the Walk Sketch the Distance‑Time graph for a person walking the walk in the following manner. - She stops and waits for 4 seconds.

17. 10. Walking the Walk Sketch the Distance‑Time graph for a person walking the walk in the following manner. - She walks back to her starting point at a speed of 2.0 m/s.

18. 11. You attach a cart to a force probe and track its motion with a motion detector as you move the cart back and forth in random motion, as shown above. Sketch force vs. acceleration for a 2.0 kg cart assuming friction is negligible. slope = 2 kg (the mass)

19. Questions 12 ‑ 16 A lab group analyzed the motion of a plastic ball projectile and obtained the x and y velocity graphsfor the ball, as shown below. They fitted both velocity components to linear equations. The fitting equations are shown at the top of the graphs.

20. vv = 9.85t + 2.04 vx = 1.00t + 4.09

21. vv = 9.85t +2.04 vx = 1.00t + 4.09 12. What were the initial velocity components of the ball? That is, what were vxi and vyi. vxi = 4.09 m/s vyi = 2.04 m/s 13. What was initial speed of the ball? 4.57 m/s E 27.02o N 14. At approximately what time did the ball reach its peak height? t = 0.21 s

22. 15. In the absence of air resistance, the x‑velocity of the ball would be constant. Use the evidence of the x‑velocity graph to argue that air resistance is small, but detectable. Explain your reasoning. F = ma a = - 1.00 m/s2 16. Is there evidence that ay= g? Explain. Determine slope: 9.85 m/s2

23. Questions 17 ‑ 19: Video Analysis of an Accelerating Fan Cart LoggerPro was used to track the motion of a 0.50 kg fan cart. The x‑position vs. time data was fitted to a quadratic function of the form y = At^2 + Bt +C. From the graph, the fitting parameters are: A = 0.5342, B = 0.2265, C = 0.07095

24. y = At2 + Bt +C df = 1/2at2 + vit + di A = 0.5342, B = 0.2265, C = 0.07095 17. Which of the following best represents the initial position and velocity of the fan cart? a) xi = 0.5342 m; vi = 0.2265 m/s b) xi = 0.2265 m; vi = 0.07095 m/s c) xi = 0.07095 m; vi = 0.5342 m/s d) xi = 0.2265 m; vi = 0.5342 m/s e) xi = 0.07095 m; vi = 0.2265 m/s

25. y = At2 + Bt +C df = 1/2at2 + vit + di A = 0.5342, B = 0.2265, C = 0.07095. 18. Which of the following best represents the velocity of the cart at time t = 1.0 s? a) v = 0.76 m/s b) v = 1.07 m/s c) v = 1.23 m/s d) v = 1.29 m/s e) v = 1.53 m/s

26. y = At2 + Bt +C df = 1/2at2 + vit + di A = 0.5342, B = 0.2265, C = 0.07095 19. Which of the following best represents the net force on the cart with a mass of 0.50 kg? a) F = 0.035 N b) F = 0.11 N c) F = 0.22 N d) F = 0.25 N e) F = 0.50 N a = 2A F = m a

27. Questions 20 ‑ 23: Harmonic Oscillator A lab group tracked the x‑position vs. time of a simple harmonic oscillator and obtained the position vs. time graph below.

28. 20. Which of the following most nearly represents the period of oscillation? a) Less than 1.5 s b) between 1.5 s and 1.6 s c) between 1.6 s and 1.8 s d) between 1.8 s and 2.0 s e) greater than 2.0 s

29. 21. Which of the following most nearly represents the amplitude? a) Less than 0.05 m b) between 0.05 m and 0.10 rn c) between 0. 10 m and 0. 15 m d) between 0.15 m and 0.25 rn e) greater than 0.25 m

30. 22. Which of the labeled points (A, B, C, or D) on the position‑time graph indicates a point where the acceleration was positive and a maximum? a) point A b) point B c) point C d) point D e) more than one of the above

31. 23. Which of the labeled points (A, B, C, or D) on the position‑time graph indicates a point where the velocity was positive and a maximum? a) point A b) point B c) point C d) point D e) more than one of the above

32. 24. A position vs. velocity graph (sometimes called a "phase- space" graph) of the oscillator's motion is shown at the right. Which one of the labeled points best indicates a point where the particle is at its maximum speed? a) point I only b) point II only c) point III only d) at more than one of the above points e) at none of the above points

33. 25. You investigated the motion of a spring oscillator using force and motion probes which were both "zeroed" at x = 0, the equilibrium position at the midpoint of the motion. Assume the object is set in motion. *Sketch a qualitative graph of the force vs. position for the oscillator. *Briefly explain how you can find the spring's force constant from this graph. F = -kx k = - F/x Find slope

34. 26. You studied the motion and the energies of a spring oscillator. On the graph at right, sketch and clearly label a) the potential energy b) the kinetic energy, and c) the total energy of the oscillator as functions of position. Assume that x = 0 is the equilibrium position. PE KE Total

35. 27. The figure at the right below represents a top view of a rubber stopper being whirled in a circle at a constant speed. Which of the arrows below best represents the direction of the net force on the stopper at the position indicated? e) None of the above. Since the speed is constant, the net force on the stopper is zero.

36. 28. A centripetal force of 4.0 Newtons is required to keep a rubber stopper moving in a circle of radius r at a constant speed. What force would be required if the radius were doubled to 2r with no change in the speed? a) 1.0 N b) 2.0 N c) 4.0 N, no change. d) 8.0 N e) 16.0 N

37. 29. In the centripetal force experiment, you twirled a rubber stopper at various speeds and radii. Assuming the mass and radius are kept constant, which of the graphs below best represents the expected variation of needed centripetal force with the stopper speed

38. 30. Suppose a lab group plots their measured centripetal force vs. the velocity of their rubber stopper. What sort of fitting function form is most appropriate? a) Linear: y = mx + b b) Simple proportion: y = Ax c) 2nd Order polynomial: y = AX^2 + Bx + C d) Power function: y = A x^n e) Natural Exponent: y = A*exp(‑C*x) +B

39. 31. The four factors might reasonably be expected to have some effect on the period of a simple pendulum. Based on your experiments, including the Interactive Physics simulation of a pendulum, which two factors are the most important? I the length of the string II air resistance III the amplitude of oscillation IV the acceleration of gravity a) III and IV b) I and IV c) II and III d) I and e) III and IV

40. 32. Elastic One‑Dimensional Collisions Suppose cart‑1 coming from the left collides elastically with cart‑2, initially at rest. Under what circumstances would you expect cart‑1 to come to a complete stop? When the masses of the cart are the same.

41. 33. Elastic One‑Dimensional Collisions In an elastic collision, the total kinetic energy remains constant before, during, and after the collision. True or False? If circled "False," briefly explain your reasoning. a) True b) False Some of the total energy is stored in the system then released during the collision.

42. 34. One Dimensional "Explosion“ In a one‑dimensional explosion, Newton's 3rd Law (action and reaction) implies that the two carts always (circle all that apply) a) experience the same force in opposite directions b) experience the same acceleration in opposite directions c) gain the same momentum in opposite directions d) gain the same kinetic energy e) gain the same velocity in opposite directions

43. 35. One Dimensional "Explosion" The two low‑friction carts of unequal mass are placed together, initially at rest, for a one‑dimensional spring explosion. (M1= 1.50 kg & M2 = 0.50 kg). The carts were tracked with a video analysis program. The velocity vs. time graph of Cart#1 (left hand side cart) is shown below. On the same graph, sketch and label a velocity‑time graph for Cart#2. As usual, take motion to the right as the positive direction.

44. 36. One Dimensional Elastic Collisions Cart #l initially moving towards the right collides elastically at time t' with Cart #2 which was initially at rest. The distance vs. time graph for the two carts is shown at the right. Based on the graph, which of the following is most accurate? a) m1 = m2 b) m1 < m2 c) m1 > m2

45. 37. Impulse Impulse is the area (integral) under the curve of what kind of graph? a) Force‑Distance b) Force‑Time c) Force‑Acceleration d) Distance‑Time e) Velocity‑Time

46. 38. Work Work is the area (integral) under the curve of what kind of graph? a) Force‑Distance b) Force‑Time c) Force‑Acceleration d) Distance‑Time e) Velocity‑Time

47. Questions 39 ‑ 40: The Redstone rocket launched the U.S.'s first astronaut (Alan Shepard) into space. With video analysis, the rocket was tracked until it left the movie frame (at t = 8 s). From time 0 to = 2 seconds the rocket had not left the launch pad. The rocket's y‑velocity VS. time was plotted.

48. 39. What was the net force on the rocket between t ~ 2 and 8 seconds? The rocket mass is shown in the first movie frame. m = 3.0 x 104 kg Fnet = 6.75 x 104 N

49. 40. What was the thrust force generated by the rocket engines during this time? slope = 2.25 m/s2 FT = Fa + Fg FT = 3.62 x 105 N

50. 41. A student heats two samples of water for the same time with an immersion heater. Both samples are initially at room temperature. The first sample has a mass of 0.200 kg and the data is shown at the right. Sketch a qualitatively correct heating curve for the heating curve for the second sample which consists of half as much water (0.100 kg).