Lec 1, , Course Intro. PHYS-1401, General Physics I Spring Physics I Lab starts next week.

Transcription

1 Lec 1, , Course Intro Monday, January 14, :21 AM PHYS-1401, General Physics I Spring Physics I Lab starts next week. Science - Studying patterns in Nature Mathematics - Language and logic of science and patterns. Physics - Science of inanimate objects Measurement - Turning real-world observations into mathematical quantities. Basic types of quantities for Physics I Time, in seconds. Particular number of oscillations of Cesium Length, in meters. Distance light travels in a fixed time. Mass, in kilograms. Amount that makes Planck's constant known. Lec 1 Intro Page 1

2 Lec 2 - Conversions, Velocity Wednesday, January 16, :00 AM Unit Conversions 1. Factor-Label Method (aka "Multiply by 1", aka "Dimensional Analysis") 2. Substitution Method Useful for interpreting SI Prefixes What if we want to add an SI prefix? 3. Conversion by Ratios Lec 2 Conversions, Velocity Page 2

3 Kinematics Wednesday, January 16, :21 AM Kinematics is the description of motion using math. Time: Instants are particular times on a clock or calendar. Could be time since an experiment began. Intervals are the elapsed time between instants. For multi-stage processes, we may have Different subscripts represent different time intervals. We can drop the subscripts if we say what interval we're analyzing. During the first interval: During the second interval: Position: Mathematically describes where something is located. Delta of positions could mean several things: If the x's are two different objects, it's relative position If the x's are the same object at two times, it's displacement. Displacement is the straight-line distance between two points. For a journey with turns, the displacement is not the distance travelled. Distance traveled is at least as big as the displacement, but maybe Lec 2 Conversions, Velocity Page 3

4 Distance traveled is at least as big as the displacement, but maybe bigger. Distance traveled is always a positive value, called a Length. For a straight-line journey: Lec 2 Conversions, Velocity Page 4

5 Velocity and Speed Wednesday, January 16, :40 AM Velocity is the rate of motion of the position. It includes the direction of the motion. In 1-D, we use + or - to indicate the direction. It's part of the numerical value of the velocity. In 2-D, we use vectors. (Next week) Speed is the rate of distance travelled. Speed is always positive. The easiest way to calculate these are as averages: Note that these averages are calculated for intervals (or processes), not at instants. Fri: Instantaneous speed (at an instant) and velocity. Lec 2 Conversions, Velocity Page 5

6 Lec 2b Constant Velocity Friday, January 18, :54 AM 1-D Velocity can be + or -, while the speed is always positive. When the velocity is constant, the average is the velocity. Ex: I walk across a 10.0 m 4.0 m/s. How much time does it take? How do we deal with multi-stage situations? Ex: I walk across the 10.0 m 4.0 m/s, then walk 2.0 m/s. What are the overall average speed and velocity? The time, displacement, and distance columns added to form totals. The average velocity is in between the max and min, but not halfway in between. Same for speed. Lec 2b Constant Velocity Page 6

7 Similar example: I drive out to 15 m/s. How fast to I have to return for my average speed to be 30 m/s? What do we do about the distance? We could call it x, but then the times are ugly fractions. Instead, let's pick the distance to be 30x. Once we find the times for Part I and Total, we see there is time left for Part II. So it's impossible to fulfill the requirements. Lec 2b Constant Velocity Page 7

8 3-Person Race Friday, January 18, :32 AM Runners A, B, and C all race m, each with constant velocity. Runner A wins, in 15.0 s. Runner B was 20.0 m behind. Runner C loses 2nd place by 20.0 m, to win 3rd place. How far behind was C at the moment that A finished? More straightforward simultaneous equations method: See if you can solve for any variable numerically. If not, eliminate one variable. Pick the easiest equation and solve for the easiest variable. Lec 2b Constant Velocity Page 8

9 Pick the easiest equation and solve for the easiest variable. Use that to substitute into the other equation(s). Lec 2b Constant Velocity Page 9

10 Lec 3 - Const Accel Page 10 Lec 3 - Const Accel Friday, January 25, :56 AM (Substitute professor; I don't have the notes.)

11 Lec 4 - Free Fall Friday, January 25, :56 AM Major example: Free Fall Object moving vertically under only gravity's influence. All objects accelerate 9.8 m/s^2 downward. Free fall starts **after** you launch or let go of the object. Free fall ends **before** the object lands or impacts. We use the regular constant-accel equations. Ex: Drop a ball. Where and what is it doing after 0.5 s? Lec 4 - Free Fall Page 11

12 Ex 2: Throw a ball 10 m/s. How long to get 3 m up? How fast is it going? Solving the quadratic is annoying, though. Is there another way? So, the v^2 equation is good: When solving for T is difficult When we don't know or care about T Lec 4 - Free Fall Page 12

13 Lec 5 - Review, Intro 2-D Monday, January 28, :54 AM If a car can slow to a stop in 50 m from 15 m/s, how much distance does it take to stop from 30 m/s? The ratio of stopping distances is the square of the ratio of speeds. Lec 5 - Review, Intro 2-D Page 13

14 2-Dimensional Kinematics Monday, January 28, :18 AM We are often concerned about the magnitude and direction of various quantities: Speed is the magnitude of velocity. Strength is the magnitude of a force. Distance (or length) is the magnitude of displacement. In 2-D, Direction is more complicated than just plus or minus. Even so, all of our kinematics acts just like the 1-D kinematics - mostly. Graphical Addition and Subtraction To get the components of Delta-v, we have to separately measure horizontally and vertically. Analytical Addition and Subtraction: Vector subtraction is the same as two separate "regular" subtractions. The coordinates are called components of the vector. Lec 5 - Review, Intro 2-D Page 14

15 Vector subtraction is the same as two separate "regular" subtractions. The coordinates are called components of the vector. Given 2 vectors, how can we add them to get the biggest result? Ex: A is 4 units and B is 3 units. The biggest possible A+B is literally 4+3 = 7 The smallest possible A+B is the difference 4-3 = 1 Any value in between is also possible. The magnitude of the result can only be positive. It is possible to "add" two vectors and get a zero result. They must be equal in magnitude. They must be opposite in direction. Lec 5 - Review, Intro 2-D Page 15

16 Vector Components Monday, January 28, :41 AM We need to be able to find the components given the magnitude and direction. Magnitude: Length of the vector. Direction: Angle from a reference. Conventional reference: x-axis When theta is measured from the x-axis, the x-component is the adjacent and comes from cos(). Once we know which component comes from cos(), the other comes from sin(). Lec 5 - Review, Intro 2-D Page 16

17 Lec 6 - Projectile Motion Wednesday, January 30, :55 AM Sideways motion of an object under only gravity's influence. Equations: Kinematics, keeping x and y separated. x-direction: Gravity has no effect. a_x = 0, v_x = constant. y-direction: Gravity causes accel. a_y = -g Ex: Let's say I slide an eraser off of a table. The table is 1.1 m tall, and the eraser lands 1.9 m from the base of the table. What is the impact velocity and speed? Lec 6 Projectile Motion Page 17

18 Let's see if we can get some general patterns. Assume horizontal launch, how are If I doubled the launch speed, what would happen to the range? Since v_x and Delta_x are both squared, they end up being proportional to each other. Lec 6 Projectile Motion Page 18

19 end up being proportional to each other. Lec 6 Projectile Motion Page 19

20 Diagonal launch Wednesday, January 30, :35 AM Special case: Landing at same height as launch. Next time: Range equation. Lec 6 Projectile Motion Page 20

21 Lec 6b More Projectile Motion Friday, February 1, :30 AM How far does the ball go? Lec 6b More Projectile Motion Page 21

22 If I can kick a soccer ball 50 m at the most, what is the launch speed? If a child can kick it half as fast, how far will it go? Halving the speed leads to quartering the distance. Lec 6b More Projectile Motion Page 22

23 Example Question Friday, February 1, :24 AM Summary: Launching to the top involves Lec 6b More Projectile Motion Page 23

24 Home Run Example Friday, February 1, :41 AM Lec 6b More Projectile Motion Page 24

25 Lec 7 Examples Friday, February 1, :41 AM Home Run Example (Solving it) Simultaneous Equation Strategies: Look for ways to add or subtract equations to cancel things out. Eliminate a variable. Look for the easiest equation and solve for the easiest variable. Avoid eliminating a variable that is squared in the other equation. If possible, avoid eliminating the variable that you need. Above, can use tan(theta) if theta was unknown. Lec 7 Examples Page 25

26 If possible, avoid eliminating the variable that you need. Above, can use tan(theta) if theta was unknown. Convert numerically: Lec 7 Examples Page 26

27 Field Goal Attempt Monday, February 4, :39 AM involves only one unknown, so we can solve it immediately. No simultaneous equations needed. We were still given 4 chunks of info, but the work was easier. Lec 7 Examples Page 27

28 Lec 8 More Examples Wednesday, February 6, :56 AM 1-D Kinematics (constant v, constant a) Vectors (components, basic trig, adding) 2-D Motion, Projectile Motion Lec 8 More Examples Page 28

29 Ex: Launching to a Ceiling vs. to a Roof Wednesday, February 6, :17 AM What if we throw the projectile onto a 3.0 m roof? Lec 8 More Examples Page 29

30 Lec 8 More Examples Page 30

31 Solving for the angle Wednesday, February 6, :41 AM Lec 8 More Examples Page 31

32 Lec 8b More Vectors Friday, February 8, :00 AM HW2 - due Sunday night. Exam 1 - Next Friday (Chap 1-3) Resultant and Equilibrium Resultant is the total of a few vectors. Equilibrium is a special situation in which the total vector sum is zero. For F2, the direction is given in a non-standard way. Another Example: A velocity is 20 m/s in a direction 25 degrees East of South. Lec 8b More Vectors Page 32

33 Angle was measured from -y, so the y component gets the negative cosine. Once we know the components of a vector, how do we find the magnitude and direction? Sometimes atan() gives the exact wrong direction. If so, add 180. Lec 8b More Vectors Page 33

34 Finding a vector to form equilibrium Friday, February 8, :37 AM The only for two vectors to add up to zero is if they are equal and opposite. Lec 8b More Vectors Page 34

35 Components in weird directions Friday, February 8, :42 AM How much of gravity is perpendicular to the ramp, and how much is parallel to the ramp? Lec 8b More Vectors Page 35

36 Lec 9 Kinematics Review Monday, February 11, :55 AM Angle of final location? Forces also add like vectors. Lec 9 Review Page 36

37 Kinematics Example Monday, February 11, :25 AM Two people start 240 m apart and move toward each other. Person A walks at 2 m/s. Person B rides a bike at 6 m/s. Where and when do they cross paths? 80 seconds later? 120 seconds later? 30 seconds later? 40 seconds later? 60 seconds later? x_ab is the relative position of A, with respect to B. v_ab is the relative velocity of A, with respect to B. Lec 9 Review Page 37

38 Reading Position Equations Monday, February 11, :42 AM Is this object moving at t=0? Yes, v=-4, so it's moving in the - direction. Is it speeding up at t=0? No, it's slowing because v and a are opposite. Will the object ever be speeding up? Lec 9 Review Page 38

39 Lec 9b - Review II Wednesday, February 13, :56 AM Exam 1 Fri 2/15 - Covers Chap Practice in Spring 2018 subfolder of Course Web Folder This week's prelab practice is important. Projectile Motion Review Three Special Cases: Horizontal Launch Launch to the peak Launch and landing level with each other Lec 9b - Review II Page 39

40 Looked at Spring 2018 Practice Exam 1, #20. Lec 9b - Review II Page 40

41 Wednesday, February 13, :36 AM How can an object have velocity but zero acceleration? (Constant velocity motion, such as a rolling car without friction.) How can an object have acceleration but zero velocity? (Peak of free fall, with v_x = 0.) When a dropped object hits the ground, what is the final velocity? (Not zero. This is the "impact velocity".) We're probably analyzing the free fall. After the object touches, it comes to rest, but that's another process. In the process of bouncing, the ball compresses by 5 cm. What is the average acceleration during the bounce? Lec 9b - Review II Page 41

42 Bring a non-internet calculator and a pencil. Lec 9b - Review II Page 42