Wednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu1PHYS 1441 – Section 004Lecture #3Wednesday, Jan. 28, 2004Dr. Jaehoon Yu• Chapter two: Motion in one dimension– Fundamentals– Velocity and Speed (Average and instantaneous)– Acceleration (Average and instantaneous)– One dimensional motion at constant acceleration• Free FallToday’s homework is homework #2, due 1pm, next Wednesday!!Wednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu2Announcements• Reading Assignments: Sections 2.6 – 2.8, follow through the examples• Homework Registration: 58/61 (56 of you submitted it)–You mustmust download, print, solve and submit electronically your homework to obtain 100% credit for homework #1– Homework #1 due 1pm, Today– Roster will close 6pm, Today• E-mail distribution list (phys1441-004-spring04)– 33 of you subscribed as of 9am this morning– Send an e-mail to [email protected]• “subscribe phys1441-004-spring04 fn ln” • Without a subject. Put the above in the body ONLY!––3 points3 pointsextra credit if done by 6pm Wednesday, Jan. 28––1 point1 pointextra credit if done by 6pm Monday, Feb. 2• Lab begins next Monday, Feb. 2 Î Pick up the information sheet if haven’t already• Utilize the Physics Clinic– When: MWF: 12-7pm, T,Th: 12-7:30pm– Where: SH114 this week, SH010 from next week onwardWednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu3Survey Results• Class composition– Mixture of many disciplines, biology and architecture are majority– Excellent opportunity to work together with people in other discipline Î Learn from each other• Previous physics experience– 33 yes, 11 no• 14 mechanics• 12 electromagnetism• Math: most of you had sufficient math training for this course• Why take this course?– Mandatory: 42– Like physics: 7Wednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu4Wednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu5Some Fundamentals• Kinematics: Description of Motion without understanding the cause of the motion• Dynamics: Description of motion accompanied with understanding the cause of the motion• Vector and Scalar quantities:– Scalar: Physical quantities that require magnitude but no direction • Speed, length, mass, etc– Vector: Physical quantities that require both magnitude and direction• Velocity, Acceleration, Force, Momentum• It does not make sense to say “I ran with velocity of 10miles/hour.”• Objects can be treated as point-like if their sizes are smaller than the scale in the problem– Earth can be treated as a point like object (or a particle)in celestial problems– Any other examples?Wednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu6Some More Fundamentals• Motions:Can be described as long as the position is known at any time (or position is expressed as a function of time)– Translation: Linear motion along a line– Rotation: Circular or elliptical motion– Vibration: Oscillation• Dimensions– 0 dimension: A point– 1 dimension: Linear drag of a point, resulting in a line ÎMotion in one-dimension is a motion on a line– 2 dimension: Linear drag of a line resulting in a surface– 3 dimension: Perpendicular Linear drag of a surface, resulting in a stereo objectWednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu7Displacement, Velocity and SpeedOne dimensional displacement is defined as: Displacement is the difference between initial and final potions of motion and is a vector quantityixxx f−≡∆Average velocity is defined as: Displacement per unit time in the period throughout the motionffixixxvtt−≡−Average speed is defined as: Interval Time TotalTraveled Distance Total≡vCan someone tell me what the difference between speed and velocity is?xt∆=∆Wednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu8Difference between Speed and Velocity• Let’s take a simple one dimensional translation that has many steps:Let’s call this line as X-axisLet’s have a couple of motions in a total time interval of 20 sec.+10m+15m-15m-5m -10m+5mTotal Displacement:x∆Total Distance Traveled:D=Average Velocity:ffixixxvtt−≡−Average Speed:Total Distance TraveledTotal Time Intervalv ≡xt∆=∆020=0( / )ms=f ixx≡−iixx=−0( )m=10 15 5 15 10 5 60( )m+++ + +=6020=3( / )ms=Wednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu9Example 2.121f ixxxxx∆≡−= −• Displacement: • Average Velocity: ffixixxvtt−≡−• Average Speed: Total Distance TraveledTotal Time Intervalv ≡The position of a runner as a function of time is plotted as moving along the x axis of a coordinate system. During a 3.00-s time interval, the runner’s position changes from x1=50.0m to x2=30.5 m, as shown in the figure. What was the runner’s average velocity? What was the average speed?30.5 50.0=− 19.5( )m=−2121xxxtt t−∆==−∆19.56.50( / )3.00ms−==−50.0 30.5 19.56.50( / )3.00 3.00ms−+===+Wednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu10Instantaneous Velocity and Speed• Can average quantities tell you the detailed story of the whole motion?dtdxtxvx =∆∆=→lim0Δt*Magnitude of Vectors are Expressed in absolute values•Instantaneous speed is the size (magnitude) of the velocity vector:dtdxtxvx =∆∆=→lim0Δt• Instantaneous velocity is defined as:– What does this mean?• Displacement in an infinitesimal time interval• Mathematically: Slope of the position variation as a function of timeWednesday, Jan. 28, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu11Position vs Time Plottimet1t2t3t=0Positionx=0x112 31. Running at a constant velocity (go from x=0 to x=x1in t1, Displacement is + x1in t1time interval)2. Velocity is 0 (go from x1to x1no matter how much time changes)3. Running at a constant velocity but in the reverse direction as 1. (go from x1to x=0 in t3-t2time interval, Displacement is - x1in t3-t2time interval)It is useful to understand motions to draw them on position vs time plots.Does this motion physically make
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