PHY131H1F - Class 4. Clicker Question

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1 PHY131H1F - Class 4 Today: Vector Math Velocity and Acceleration in 2- dimensions Relative Velocity Constant Acceleration in x and y Projectile Motion Motion on a Circular Path Clicker Question A large, light beach ball is falling towards the beach on a windless day. The force of gravity on the ball, F g, is greater than the upward drag force from the air, F D. Which of the following directions is closest to the direction of the net force F net = F g + F D on the ball? A.North B.East C.South D.West E.The net force makes an angle of 90 with respect to all four of these directions. F D F g East 1

2 The Pointing Game There are three pairs of orthogonal directions in this room. Within a pair, each direction is anti-parallel to the other. Each pair is perpendicular to the other two pairs. Point with me: North - West - Up South East - Down Class 4 Preclass Quiz on MasteringPhysics This was due this morning at 8:00am 92% answered correctly: In the study of physics, a scalar is specified with a single number, but a vector is specified using both a magnitude and direction. Harlow note (based on student comments): A scalar can have dimensions, or be dimensionless. ie: m = 5 kg. is a scalar with dimensions of mass [M]. But π = 3.14 is a dimensionless scalar (it is a ratio). Most vectors have dimensions, but unit-vectors do not. 2

3 Class 4 Preclass Quiz on MasteringPhysics 88% answered correctly: The speed of the mouse relative to the floor is the vector sum of the mouse speed relative to the belt and the belt speed relative to the floor (5 m/s) 88% answered correctly: Both bullets hit the ground simultaneously! 84% answered correctly: When an object moves in a circular path at a constant speed, the velocity and acceleration vectors are perpendicular. Student comments from Class 4 Preclass Quiz Was the mouse on the conveyor belt or was it on the edge of the belt before it saw the cheese? Harlow answer: It was on the belt. The belt was the mouse s universe at that time it didn t care that the factory floor was moving at a different velocity. I understand that in theory, both bullets should reach the earth at the same time. However, doesn't the curvature of the earth become a factor when firing a bullet over longer distances? If so, would that not alter the height at which the bullet being fired actually hits the ground? Harlow answer: YES! That s a really good point! In fact, due to the curvature of the earth, the fired bullet would take slightly longer to hit the ground, because it would fall a further distance. 3

4 Student comments from Class 4 Preclass Quiz I did this quiz without doing the assigned readings. I don't even know what the assigned readings are, but I will find out now and read it all posthaste. Harlow comment: Okay. Thank you for your honesty. Keep in mind that you have defeated the entire purpose of the preclass quiz by doing this, though. Relative velocity seems like witchcraft. Please explain this sorcery. I just wonder what the rules are for this feedback section in order to get the mark. Surely profanity is off the table, but what about emoticons? Well, here goes nothing :P Student comments from Class 4 Preclass Quiz Confused why the section name includes 3-d motion, when there isn't 3-d motion Harlow answer: 3-d motion exists. Most motion for this course does happen in 2-D, which is a lot easier to draw. But you should be aware that we live in a 3-D universe so, in general, everything happens in 3-d. I like many people find frames of reference to be very confusing. I watched the youtube video Frames of Reference (1960) which helped me a lot with my understanding. Surprisingly, this film was created in UofT many years ago. Harlow note: little known fact: Patterson Hume, one of the two guys in that famous Frames of Reference video was my grandmother s first cousin. (The taller one with straight hair.) I have hung out with him on many family gatherings and he was a super-cool guy. 4

5 Student comments from Class 4 Preclass Quiz Q: What do you get when you cross a mosquito with a mountain climber? A: You can t cross a vector and a scalar! what is the prime of velocity, v'? (isn't that acceleration?) Harlow answer: No, no! This prime has nothing to do with derivatives! It s just a label to distinguish it from v. circular motion makes me dizzy Last day I asked at the end of class: Can you add a scalar to a vector? ANSWER: No. A 2-D vector is represented by a pair of numbers (ie x- and y- components, or magnitude and direction), and you can t add a scalar number to this. Can you multiply a vector by a scalar? ANSWER: YES! When you multiply a vector by a scalar, you can either: Multiply both the x and y components by this scalar, or Multiply the magnitude by the scalar, and keep the direction unchanged (but you flip direction 180 for a negative scalar) 5

6 Vectors There are two kinds of Physical quantities we will deal with: Scalar (Only has a size) Quantity that can be described with only one number. Examples: time, speed (just a magnitude say 5 m/s ) Vector: (Has size and a direction) Quantity that is described with two numbers: Magnitude Direction Examples: Position, velocity (magnitude say 5 m/s and direction say north ) 6

7 Distance vs Displacement Example From High Park, you ride your bike 6 km East on Bloor St, then 5 km North on Yonge St to the corner of Yonge and Eglinton. a. What is the distance traveled? b. What is your displacement? Clicker Question: Which figure shows A A A?

8 Vector Components Components add and subtract like scalars! 8

9 Announcements The first term test will be on Tuesday Oct. 6, from 6:00pm to 7:30pm. Test 1 will cover chapters 1-4 of Wolfson, plus what was done in lectures and Practicals. You must bring a calculator and one 8.5x11 aid sheet which you prepare, double-sided If you have a conflict at that time with an academic activity (test, lecture, tutorial, lab), you must register to write at the Alternate Sitting of this test by going to portal and filling out the online form no later than Sep. 29 by 4:00pm. (The Alternative Sitting is on Tuesday Oct. 6, from 4:30pm to 6:00pm.) 9

10 Where to get good help for free Your classmates: form a study group Your two graduate student TAs. Learn their address, office hours, and office location. Me. After class, office hours are T10, R2, F11, and my office is MP121-B. The Physics Drop-In Centre in MP125, back corner MTWR 12-3, F11-2 Academic Success Centre in Koffler 1 st floor, inside the Career Centre Student Comments from Class 4 Preclass Quiz For the "cheat sheet" can we write some info too or is it strictly equations? Harlow answer: You can write whatever you would like. I will be providing helpful numbers such as conversion factors on the front page, so you shouldn t need those. You will need to write whatever equations might be useful for chapters 1-4 questions. Is there going to be anything about the labs asked on the test/exam? Harlow answer: Yes! The material in Practicals is also testable. Are we allowed to use graphing/programming calculators on the tests and exams? Harlow answer: Yes! 10

11 Student comments from Class 4 Preclass Quiz Will these type of questions be asked on the exam? if not, what is the purpose? "How much would it cost to cover the entire land area of Canada with five dollar bills? Harlow answer: Yes, there will be an estimation question on test 1, and possibly on the final exam. It will be multiple choice, where the five choices all differ by at least a factor of 10. You will be able to figure it all out using numbers and simple equations which will be in the possibly useful information on the front page of the test. Are there assigned or recommended questions that we should try out? Harlow answer: Yes, suggested end-of-chapter items from Wolfson chapters 1-4 have been posted on the portal page for this course under Extra Study Materials Projectile Motion 11

12 Projectile Motion Projectile motion is made up of two independent motions: uniform motion at constant velocity in the horizontal direction and free-fall motion in the vertical direction. The kinematic equations that describe these two motions are: 12

13 Clicker Question B A C A tennis ball is launched at an angle, and flies through the air in a parabolic path, as shown, A B C. At point B A. the velocity is horizontal, and the speed is maximum. B. the velocity is horizontal, and the speed is minimum. C. the velocity is horizontal, but the speed is neither a maximum nor a minimum. D. the velocity is not horizontal, but the speed is minimum. E. the velocity is not horizontal, and the speed is neither a maximum or minimum. Monkey and Hunter Demonstration (and clicker question) The classic problem: A monkey hanging from the branch of a tree is spotted by a hunter. The monkey sees that the barrel of the gun is pointed directly at him. At the exact instant the gun is fired, the monkey lets go of the branch. Will the bullet (A) go above the monkey, (B) go below the monkey, or (C) hit the monkey? Our demonstration uses a pressurized tennis ball launcher. The laser is aimed directly at the monkey, which is supported by an electromagnet. As the tennis ball leaves the launcher, it breaks a connection that releases the magnet. 13

14 Joke: Why Did the Chicken Cross the Road? Aristotle (330 BC): Because it is the nature of chickens to cross roads. Newton (1687): Because there is no external net force causing the chicken s velocity across the road to change. Einstein (1905): Is the chicken crossing the road, or is the road moving under the chicken? [image downloaded 9/30/2013 from ] Relative Motion 14

15 Relative Motion If we know an object s velocity measured in one reference frame, S, we can transform it into the velocity that would be measured by an experimenter in a different reference frame, S, using the Galilean transformation of velocity. Or, in terms of components, Example: You are running on flat ground at 7 m/s when you throw a ball to a friend in front of you. In your own reference frame, you launch the ball at an angle of 45 above the horizontal at a speed of 12 m/s. What is the ball s initial velocity relative to the ground? 15

16 Clicker Question You are on an Eastbound subway train going at 20 m/s. You notice the Westbound train on the other track. Relative to the ground, that Westbound train has a speed of 20 m/s. What is the velocity of the Westbound train as measured by you? A. 40 m/s, West B. 20 m/s, West C. zero D. 20 m/s, East E. 40 m/s, East [image from ] 16

17 Analyzing the acceleration vector An object s acceleration can be decomposed into components parallel and perpendicular to the velocity. a is the piece of the acceleration that causes the object to change speed a is the piece of the acceleration that causes the object to change direction An object changing direction always has a component of acceleration perpendicular to the direction of motion. Uniform Circular Motion Acceleration Speed is constant. v = 2πr T where T = Period [s] 17

18 Centripetal Acceleration Centripetal Acceleration 18

19 Before Class 5 on Monday Please read Chapter 4, sections 4.1 through 4.4 of Wolfson. Problem Set 1 is based on Wolfson Chapters 1 and 2: it is due this Friday by 11:59pm. Something to think about: A paperback novel has a mass of 0.3 kg and slides at a constant velocity. A chemistry textbook has a mass of 3.0 kg, and slides at the same constant velocity. How does the net force on the textbook compare to the net force on the novel? 19