Classical Physics - pre Kinematics & Mechanics Energy & Light & Heat Electricity & Magnetism Wave Motion. Modern Physics - post 1900

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1 Scientific Method Observation or question Hypothesis - belief thru reason Procedure thru experiment Data, Calculations Analysis - conclusion to theory or law Prediction - check on theory for repeatability and accuracy Classical Physics - pre 1900 Kinematics & Mechanics Energy & Light & Heat Electricity & Magnetism Wave Motion Aug 19 2:11 PM Aug 19 2:14 PM Modern Physics - post 1900 Relativity & Atomic & Nuclear Quantum Mechanics Particle High Energy Fundamentals -- composed of matter occupy space exist in Aug 19 2:16 PM Aug 19 2:17 PM Units are your friend... Base Units vs. Derived Units we define a few fundamental units and see how other quantities happen MKS Aug 17 2:02 PM Aug 17 2:04 PM 1

2 e.g. length - 1/10000 of the distance between NP & equator # of λ from Kr distance light travels in a vacuum in 1/299,792,458 of a second mass - mass of Ir cylinder 39 mm high & d = 39 mm - Galileo used his pulse - duration of 9,192,631,770 periods of radiation transitions between the two hyperfine levels of the ground state of the Cs-133 atom velocity force Aug 17 2:05 PM Aug 19 2:25 PM Scientific Notation & Sig Figs giga micro 25,251 grams = Coversions 20.0 miles = 1.61 km = 1 mi Note: prefix chart is on the inside cover of your textbook note: conversion factors can be found on the inside cover of the text Aug 17 2:08 PM Aug 17 2:15 PM convert first and then calculate... find the volume of a cube with 1 cm sides Mathematical Models (graphs are your friend too!) linear (proportional) square inverse inverse square Aug 17 2:19 PM Aug 17 2:27 PM 2

3 Kinematics Motion Maps from the same root as "cinema" Aug 19 10:41 AM Aug 19 10:40 AM What motion does this represent? start here Aug 19 10:40 AM Aug 19 10:40 AM What motion does this represent? Graphically we can represent motion this way Aug 19 10:41 AM Aug 19 10:41 AM 3

4 What does the slope mean on the position graph? constant linear Velocity non constant curvy non linear position position Aug 23 2:11 PM Aug 17 7:39 AM position Aug 17 9:26 AM Aug 17 1:20 PM What is the velocity? position position velocity accel 9.81 m/s 2 Aug 17 1:20 PM Aug 17 1:26 PM 4

5 position position velocity velocity accel accel Aug 17 1:51 PM Aug 17 1:51 PM Derivation of Kinematics Equations Aug 17 2:00 PM Aug 22 8:48 AM 1. An antelope running with constant acceleration covers the distance between two points 60.0 meters apart in 6.00 seconds. Its speed as it passes the second point is 15 m/s. a. What is its speed at the first point? b. What is its acceleration? Aug 19 2:50 PM Aug 17 1:57 PM 5

6 2. If a flea can jump to a height of m, what is its initial speed as it leaves the ground? How long is it in the air? What does the sign of acceleration mean? in other words, what is + acceleration and what is - acceleration? Aug 17 1:57 PM Aug 23 1:52 PM position velocity accel + v + a +v - a 0 v + a 0 v - a - v + a -v - a motion Aug 17 2:07 PM Aug 23 2:03 PM the "first thumb rule" A brick is dropped from the roof of a building. The brick strikes the ground after 5.0 seconds. a. How tall is the building? b. What is the brick s velocity just before it reaches the ground? Aug 23 2:05 PM Aug 17 1:57 PM 6

7 A hot air balloonist, rising vertically with a constant velocity of magnitude 8.00 m/s, releases a sandbag at an instant when the balloon is 20.0 m above the ground. a. Find the height above the ground and the velocity of the sandbag at the following s after its release: s and 2.00 seconds. b. How long after its release does the bag strike the ground? c. What is its velocity just before it reaches the ground? 2-24 A jet plane is crusing at 250 m/s when suddenly the pilot turns the engines up to full throttle. After traveling an additional 2.0 km the jet is moving with a speed of 300 m/s. a) What is the jets acceleration (assume a = constant)? b) Is this a reasonable answer? Justify Aug 17 1:59 PM Aug 17 1:59 PM 2-27 You're driving down the highway late one night at 20 m/s when a deer steps onto the road 35 m in front of you. Your reaction before stepping on the brakes is 0.50 s and the maximum acceleration of the car is -10 m/s 2. a) How much distance is between you and the deer when you come to a stop? b) What is the maximum speed you could have and still not hit the deer? 2-30 Ball bearings can be made by letting spherical drops of molten metal fall inside a tall tower -- called a shot tower -- and solidify as they fall. a) If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be? b) What is the bearings impact velocity? Aug 22 10:28 AM Aug 22 9:09 AM 2-34 In an action movie, the villain is rescued from the ocean by grabbing onto the ladder hanging from a helicopter. He is so intent on gripping the ladder that he lets go of the briefcase full of money when he is 130 m above the water. If the briefcase hits the water 6.0 s later, how fast was the helicopter rising? 2-42 Two stones are released from the edge of a cliff, one a short after the other. a) As they fall, the first is always going faster than the second. Does the difference between their speeds get larger, get smaller or stay the same? Justify your answer. b) Does their separation increase, decrease or stay the same? Justify. c) Will the interval between the instants at which they hit the ground be small then, equal to, or larger than the interval between the instants of their release? Justify Aug 22 10:33 AM Aug 22 10:35 AM 7

8 2-59 A juggler throws a ball straight up into the air with a speed of 10 m/s. With what speed would she need to throw a second ball half a second later, starting from the same position, in order to hit the first ball at the top of its trajectory? 2-67 A "rocket car" is launched along a long straight track at t = 0s. It moves with constant acceleration a 1 = 2.0 m/s 2. At t = 2.0 s, a second car is launched with constant acceleration a 2 = 8.0 m/s 2. a) At what does the second car catch up with the first? b) How far down the track do they meet? Aug 22 10:37 AM Aug 22 10:39 AM Do problems Page 64: 19, 32a, 33, 46, 54, 62, 70, 76 Preview Chapter 3.1 & 3.3 for next class Vectors a scalar has only magnitude a vector has magnitude and direction Aug 23 2:11 PM Aug 25 2:24 PM Displacement -- a vector quantity B Vector addition method 1: tip to tail A + B + C + D A D C A B remember vectors only have a magnitude and a direction -- no fixed starting point answer is called the resultant Aug 25 2:24 PM Aug 25 2:22 PM 8

9 Vector addition? A + B + C + D = B + D + A + C A C D Can you add two vectors with different magnitudes and get a resultant of zero? three vectors? B Aug 25 2:28 PM Aug 25 2:29 PM Notation: boldface indicates a vector quantity italics or plain type indicates a scalar A A How to draw a vector draw the length proportional to the magnitude of the vector direction is measured from +x axis Aug 25 2:32 PM Aug 25 2:59 PM Try a practical application of vector addition... Start in Strausberg, South Dakota, follow the directions you and your partner are given. Where do you end up? vector addition: method 2: Vector Components A θ Aug 25 3:02 PM Aug 25 3:03 PM 9

10 back to South Dakota 230 km 30 o N of E 260 km 32 o W of S 80 km 38 o E of N 84 km 32 o N of E 220 km 46 o W of N 180 km 56 o S of W Aug 25 3:20 PM Sep 3 10:46 AM Find standard angles 230 km 30 o N of E --> 30 o 260 km 32 o W of S --> 238 o 80 km 38 o E of N --> 52 o 84 km 32 o N of E --> 32 o 220 km 46 o W of N --> 136 o 180 km 56 o S of W --> 236 o find the x components - -add them together 230 km cos 30 o 260 km cos 238 o 80 km cos 52 o 84 km cos 32 o 220 km cos 136 o 180 km cos 236 o km km Sep 3 10:48 AM Sep 3 10:50 AM find the y components - add them together 230 km sin 30 o 260 km sin 238 o 80 km sin 52 o 84 km sin 32 o 220 km sin 136 o 180 km sin 236 o 5.66 km km Scale your results & find your final destination Porcupine 5.66km = cm Strasbourg km =-3.85cm Sep 3 10:51 AM Sep 3 10:53 AM 10

11 unit vectors Aug 25 3:03 PM Aug 30 8:15 AM Multiplication of Vectors -- Multiplication by a Scalar stretches or shrinks or reverses direction of original vector answer is a vector Aug 30 8:25 AM Aug 29 1:12 PM Multiplication of Vectors -- Scalar Multiplication - Dot Product (How much of B is in A's direction.) Answer is a scalar Aug 29 1:13 PM Aug 30 8:37 AM 11

12 Does a. b =b. a? Can a scalar product ever be negative? If so, what does it mean? If a. b = 0, does it follow that a and b are perpendicular to each other? Aug 29 1:19 PM Aug 30 8:44 AM Multiplication of Vectors -- Vector Multiplication - Cross Product answer is a vector area of parallelogram formed by A and B Aug 29 1:18 PM Aug 30 8:56 AM Does axb = bxa? B = 6i + j - 2k D = -i + 3j Find B. D What is the angle between B and D? Aug 29 1:20 PM Aug 29 1:24 PM 12

C = 2i -j F = i + 2j - 3k Find C. F What is the angle between C and F? Lab reports Setting up a lab report folder on googledocs Aug 29 1:26 PM Aug 29 1:27 PM Dropping vs Launching (thank you Mr.

13 C = 2i -j F = i + 2j - 3k Find C. F What is the angle between C and F? Lab reports Setting up a lab report folder on googledocs Aug 29 1:26 PM Aug 29 1:27 PM Dropping vs Launching (thank you Mr. Galileo for this insight) a projectile may be treated as if it were two simultaneous INDEPENDENT motions: a horizontal flight (constant velocity) and a vertical free fall Aug 29 1:36 PM Aug 29 1:41 PM Projectile: an object moving in 2 dimensions (x and y) under only the influence of gravity. s = x i + y j v = v ix i + v iy j v = v i cosθ i + v i sinθ j a = a ix i + a iy j a = 0 i -g j Lab: 2 Dimensional Motion Video Analysis Purpose: To study the independence of vertical and horizontal motion in projectiles. Data: Collect information about the horizontal and vertical positions of a projectile with respect to. Calculation/Analysis: Graph: (1) X horizontal vs (2) Y vertical vs (3) Y vertical vs 2 Conclusion: 1. Comment on velocity and acceleration for horizontal motion. 2. Comment on velocity and acceleration for vertical motion. 3. Write the mathematical model for a. X horizontal vs b. Y vertical vs 2 4. What are the sources of error? (Consider with respect to the precision and accuracy of your results.) 5. Calculate the 5% rule for the X horizontal vs data. 6. Calculate the % error for the vertical acceleration using 9.8 m/s 2 for the theoretical acceleration. Aug 29 1:41 PM Aug 29 1:45 PM 13

14 2D motion notes Motion on a Ramp Use ruler button to set scale on video. Carefully mark ball the better you do here the better your results will be. On graphs (3) Autoscale from 0 Make a calculated column for squared Include best fit curves θ Sep 1 7:47 AM Sep 8 1:45 PM A skier is on a slope which makes an angle of 38 o with the horizontal. If gravity is the only source of acceleration, how far will he travel before reaching 20 m/s? How long will this take? Kinematics: Projectile Equations motions in the x and y directions are INDEPENDENT x = x i + v ix t x = x i + v i cosθt v x = v ix y = y i + v iy t - ½gt 2 y = y i + v i sinθt - ½gt 2 v y 2 = v iy 2-2g(y-y i ) (vsinθ) 2 = (v i sinθ) 2-2g(y-y i ) Sep 8 1:47 PM Aug 29 1:41 PM A person in the gondola of a balloon throws a ball at a 40.0 o to the horizontal at 10.0 m/s. If the ball is launched at a height of 100 m, where will it land? Ignore air resistance. A baseball recoiling from a bat soars into the air at an angle of 40.0 o above the ground traveling at 45.7 m/s. Assuming it is caught at the same height it was hit, calculate the theoretical range of the ball, ignoring air resistance. Sep 7 3:16 PM Sep 7 3:17 PM 14

15 Derivation of Time of Flight [t f] and Range [R] Equations A baseball recoiling from a bat soars into the air at an angle of 40.0 o above the ground traveling at 45.7 m/s. Assuming it is caught at the same height it was hit, calculate the theoretical range of the ball, ignoring air resistance. Sep 8 1:40 PM Sep 8 1:42 PM Sep 8 2:07 PM 15

Chapter 3 Kinematics in Two Dimensions; Vectors

Chapter 3 Kinematics in Two Dimensions; Vectors Vectors and Scalars Addition of Vectors Graphical Methods (One and Two- Dimension) Multiplication of a Vector by a Scalar Subtraction of Vectors Graphical