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PCS120 STATIC AND KINETIC FRICTION PRE-LAB QUESTIONS 1. A box is pulled at constant velocity along a horizontal plane. Use axes parallel and perpendicular to the horizontal plane and draw a diagram of the forces acting on the box. 2. Assume in question 1 the frictional force is reduced to zero but the non-zero active force is still parallel to the plane. How would the box move? • Sliding at constant velocity • Sliding at constant acceleration • Not sliding: remains in static equilibrium 3. A box is pulled at constant velocity upward along an inclined plane and parallel to it. Use axes parallel and perpendicular to the plane and draw a diagram of the forces acting on the box. 4. A box is placed on an inclined plane whose angle of inclination can be changed between 0 and 90 degrees. Show that the maximum angle for which the box will not slide down is θ max = arctan μ s ( ) ; or that μ s = tan θ max ( ) 5. The incline with the box in question 4 makes an angle just a little greater than θ max . Which is correct about the box: a. Still in static equilibrium b. Sliding at constant velocity c. Sliding at constant acceleration

PCS | 120 | Physics I | lecture notes | PCS120 STATIC AND KINETIC FRIC

PCS 120 - Physics I: Fall 2015 Kinematics in One Dimension Graphs of Motion and Math Description of Motion with Constant Acceleration Problem-Solving Strategies and Examples Tetyana Antimirova 1 Problem 2.19 3 rd edition of Knight A student standing on the ground throws a ball straight up. The ball leaves student’s hand with a speed of 20 m/s when the hand is 2.0 m above the ground. How long is the ball is in the air before it hits the ground? (The student move her hand out of the way) Understanding the Problem  Soluon: Once the ball leaves the student’s hand, the ball is in free fall and its acceleraon is equal to the free-fall acceleraon g that always acts vercally downward toward the center of the earth. According to the constant-acceleraon kinemac equaons of moon Substituting the known values 2 1 0 0 1 2 y y v t a t     2 2 1 1 2 m 0 m (15 m/s) (1/2)( 9.8 m/s ) t t      1 , t 1 3.2 s. t  Problem 2.30 A particle’s velocity is described by the function below. a) At what times does the particle reach its turning points? b) What is the particle’s acceleration at each of the turning points?   Solution

PCS | 120 | Physics I | lecture notes | PCS 120 - Physics I: Fall 2015

PCS130: Note 0, Pg 1 J. Yuan Welcome to PCS 130 Dr. Jian Yuan E-mail: jyuan@ryerson.ca Office: VIC 746 Phone: 416 979 5000 ext. 3812 Office Hours: Tuesday: 12:00 – 1:00 Thursday: 1:00 – 2:00 Alternative times can be arranged by appointment. Whenever you see me. Sections 11, 12, 13, 14, 15, 16, 17 PCS130: Note 0, Pg 2 J. Yuan Magnetism Syllabus Good Vibrations Seeing the light & going Nuclear D2L/Content/Module 1/Course Outline and Management Form PCS130: Note 0, Pg 3 J. Yuan Evaluation Scheme The minimum passing mark is 50%. No lab/tutorial exemptions. Lab/Tutorial - 2-hour lab/tutorial session in alternate weeks - Remember, lab/tutorial Starts on Jan. 23! • Check your schedule for the exact time/location • Detailed Lab info: http://www.physics.ryerson.ca/labs Partner!!! Module 1 Lab Quizzes: 5% Lab experiments/reports: 15% Tutorial work: 10% Web Assignments 10% Mid-term Exam: 20% Final Exam: 35%* Clicker Questions 5%* PCS130: Note 0, Pg 4 J. Yuan  “Physics For Scientists and Engineers”, 4th Ed., by Randall D. Knight  Mastering Physics access kit: http://www.pearsonmylabandmastering. com/northamerica/masteringphysics/ students/get-registered/index.html W17MJCARVALHO It’s open for enrollment now. Lecture Notes https://courses.ryerson.ca/d2l/le Study Materials i>Clicker Module 2 No REEF Polling! PCS130: Note 0, Pg 5 J. Yuan Lecture Style Students are strongly advised to attend every lecture and encouraged to participate actively. Posted Lecture Notes “SKELETON” Full Lecture Notes Only show in class PCS130: Note 0, Pg 6 J. Yuan ? PCS130: Note 0, Pg 7 J. Yuan Course information, supplementary materials and selected lecture notes will be posted at Brightspace ( https://my.ryerson.ca ). Web Instruction According to Policy 157 ( http://www.ryerson.ca/senate/policies/pol157.pdf ) Daily checks of your Ryerson email are recommended. The instructors will not respond to any other address. All email communications must contain an appropriate subject line, including the course code ( PCS130 ). The body of the email must contain your name , last four digits of the student number , and course code and section . The email must have text with complete sentences, correct spelling, and proper grammar. Turn on email forwarding of your regular email account if you do not want to check your Ryerson email account regularly. PCS130: Note 0, Pg 8 J. Yuan Missed Evaluations • A student who cannot be present for an evaluation because of illness must contact the First Year and Common Science Office (FYCSO) (VIC743) within a period of 3 days, as stated in Policy 134 – Undergraduate Consideration and Appeals (see http://www.ryerson.ca/senate/policies/pol134.pdf ). • The student must also submit to the FYCSO a Ryerson- approved medical form filled out by a doctor stating, among other things, that the student was too ill to attend on the day of the evaluation and giving the expected duration of the illness. Blank forms can be obtained from the Ryerson Web site http://www.ryerson.ca/senate/forms/medical.pdf .

PCS | 120 | Physics I | lecture notes | PCS130: Note 0  Pg 1 J. Yuan W

PCS 120 - Physics I: Fall 2015 Lectures 3, 4: Kinematics in One Dimension Graphs of Motion and Math Description of Motion with Constant Acceleration Tetyana Antimirova 1 • Kinemacs is the name for the mathemacal descripon of moon. • This chapter deals with moon along a straight line, i.e., runners, rockets, skiers. • The moon of an object is described by its posion , velocity, and acceleraon. • In one dimension, these quanes are represented by x , v x , and a x . • You learned to show these on moon diagrams in Chapter 1. Kinemacs (Chapter 2) • The distance an object travels is a scalar quanty, independent of direcon. • The displacement of an object is a vector quanty, equal to the ﬁnal posion minus the inial posion. • An object’s speed v is scalar quanty, independent of direcon. • Speed is how fast an object is going; it is always posive. • Velocity is a vector quanty that includes direcon. • The velocity vector is in the same direcon as the displacement • In one dimension the direcon of velocity is speciﬁed by the  or  sign. • In this chapter (2) we will limit the discussion to one- dimensional moon only Scalars and Vectors • Uniform moon is when equal displacements occur during any successive equal-me intervals. • Uniform moon is always along a straight line. • Why? • Something to think about later! Zero acceleraon Riding steadily over level ground is a good example of uniform moon. Uniform Moon Uniform Uniform Moon Moon • An object’s moon is uniform if and only if its posion- versus-me graph is a straight line. • The average velocity is the slope of the posion-versus-me graph. The instantaneous velocity is the same • The SI units of velocity are m/s. Uniform Uniform Moon Moon • An object’s moon is uniform if and only if its posion- versus-me graph is a straight line. • The average velocity is the slope of the posion-versus-me graph. The instantaneous velocity is the same • The SI units of velocity are m/s. • Somemes an object’s velocity is constant as it moves (as we saw above). • More oﬅen, an object’s velocity changes as it moves. • Acceleraon describes a change in velocity. • Consider an object whose velocity changes from to during the me interval ∆ t . • The quanty is the change in velocity. • The rate of change of velocity is called the average acceleraon: Acceleraon The Audi TT accelerates from 0 to 60 mph in 6 s. Taccs: Interpreng Posion-versus-Time Graphs

Tutorial 5 1. The figure shows four slits in a diffraction grating. A set of Huygens wavelets is spreading out from each slit. Four wave paths, numbered 1 to 4 are shown leaving the slits at angle θ 1 . The dashed lines are drawn perpendicular to the paths of the waves. a. How many extra wavelengths does wave 1 travel compared to wave 2? (1 mark) b. How many extra wavelengths does wave 2 travel compared to wave 3? (1 mark) c. As these four waves combine at some large distance from the grating, will they interference constructively, destructively, or in between? Explain. (2 marks) d. Suppose the wavelength of the light is doubled. (Imagining erasing every other wave front in the picture.) Would the interference at angle θ 1 then be constructive, destructive, or in between? Explain. Your explanation should be based on the figure, not on some equation. (3 marks) e. Suppose the slit spacing is doubled. (Imagining closing every other slit in the picture but keeping all the wavefronts.) Would the interference at angle θ 1 then be constructive, destructive, or in between? Explain. Again, base your explanation on the figure. (3 marks) 2. Laser light with a wavelength of 632.8 nm is directed through slit(s) and allowed to fall on a screen 2.60 m beyond. The figure below shows the pattern on the screen, with a centimeter ruler below it. a) Did the light pass through one slit, two slits or a diffraction grating? Briefly explain your reasons. b) If one slit, find its width. If two slits, find the distance between their centers. (a) One slit, as the central maximum is twice as wide as the other maxima. A diffraction grating pattern has much narrower and evenly spaced fringes. A two ‐ slit pattern has evenly spaced fringes (within a one ‐ slit diffraction envelope). (b) For precision, we measure from the second minimum on one side of the center to the second minimum on the other side: Students may measure different order maximum/minimum. As long as the final answer is close, still give them full credit. 3. Light of wavelength 600 nm passes through two slits separated by 0.20 mm and is observed on a screen 1.0 m behind the slits. The location of the central maximum is marked on the screen and labeled y = 0. (a) At what distance, on either side of y = 0, are the m = 1 bright fringes? (b) A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by 5.0 ×10 − 16 s in comparison to the wave going through the other slit. What fraction of the period of the light wave is this delay? (c) With the glass in place, what is the phase difference Δ ϕ 0 between the two waves as they leave the slits? (d) The glass causes the interference fringe pattern on the screen to shift sideways. Which way does the central maximum move (toward or away from the slit with the glass)? By how far does the central maximum move? Model: Two closely spaced slits produce a double-slit interference pattern. Visualize: Solve: (a) The 1 m  bright fringes are separated from the 0 m  central maximum by 9 (600 10 m)(1 0 m) 0 0030 m 3 0 mm 0 0002 m L y d             (b) The light’s frequency is 14 / 5.00 10 Hz. f c     Thus, the period is 15 1/ 2.00 10 s. T f     A delay of 16 15 1 4 5.0 10 s 0.50 10 s is . T      (c) The wave passing through the glass is delayed by 1 4 of a cycle. Consequently, the two waves are not in phase as they emerge from the slits. The slits are the sources of the waves, so there is now a phase difference 0   between the two sources. A delay of a full cycle ( ) t T  would have no effect at all on the interference because it corresponds to a phase difference 0 2 rad      Thus a delay of 1 4 of a cycle introduces a phase difference 0    1 1 4 2 (2 ) rad     (d) The text’s analysis of the double-slit interference experiment assumed that the waves emerging from the two slits were in phase, with 0 0    rad. Thus, there is a central maximum at a point on the screen exactly halfway between the two slits, where 0    rad and 0 m. r   Now that there is a phase difference between the sources, the central maximum—still defined as the point of constructive interference where 0    rad—will shift to one side. The wave leaving the slit with the glass was delayed by 1 4 of a period. If it travels a shorter distance to the screen, taking 1 4 of a period less than the wave coming from the other slit, it will make up for the previous delay and the two waves will arrive in phase for constructive interference. Thus, the central maximum will shift toward the slit with the glass. How far? A phase difference 0 2     would shift the fringe pattern by 3.0 mm, y   making the central maximum fall exactly where the 1 m  bright fringe had been previously. This is the point where (1) , r    exactly compensating for a phase shift of 2 π at the slits. Thus, a phase shift of 1 1 0 2 4 (2 )       will shift the fringe pattern by 1 4 (3 mm) 0.75 mm.  The net effect of placing the glass in the slit is that the central maximum (and the entire fringe pattern) will shift 0.75 mm toward the slit with the glass.

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