Welcome to Kinematics! Classical Mechanics Mechanics Lecture 1, Slide 1 Modus Operandi SmartPhysics Protocol Online Prelectures (animated textbook, before lecture) Online Checkpoints (check knowledge, before lecture) Lectures (very interacCve) Online Homework (first deadline tomorrow, 80% credit for late online homework up to one week from tomorrow, 8am) Mechanics Lecture 1, Slide 2 Mechanics Lecture 1, Slide 3 Clicker Question 1 Do you have your i>clicker with you today? A) Yes B) No C) Maybe D) I like pudding Mechanics Lecture 1, Slide 4 Clicker Question 2 Which of the following best describes your high-school physics class? A) Great B) Pretty good C) So-so D) Not so good E) Awful Mechanics Lecture 1, Slide 5 Classical Mechanics Lecture 1 Today's Concepts: a) Displacement, Velocity, Acceleraon b) 1-D Kinemacs with constant acceleraon Mechanics Lecture 1, Slide 8 Q: What are the benefits of parCcipang ? A: You learn more 30 Viewer Non-Viewer 23 15 8 0 43.478347.826152.173956.521760.869665.217469.565273.91378.260982.608786.956591.304395.6522 100 Exam Score Students who… Exam 1 average Viewed pre-lectures 80% Blew through pre-lectures 73% Mechanics Lecture 1, Slide 7 Prelecture Example km 35 km Mechanics Lecture 1, Slide 9 Prelecture Example x(∆t) = x + v ∆t 0 avg · = 35 km + 65 km km 35 km 65 km in 1 hour Mechanics Lecture 1, Slide 10 Displacement and Velocity in One Dimension Displacement Time taken Mechanics Lecture 1, Slide 11 Displacement and Velocity in One Dimension The v(t) vs. t plot is just the slope of the x(t) vs. t plot Definion: Speed = |v(t)| Mechanics Lecture 1, Slide 12 Displacement and Velocity in One Dimension Are the plots shown at the leb correctly related A) YES B) NO Mechanics Lecture 1, Slide 13 Clicker Question The velocity vs. Cme plot of some object is shown to the right. Which diagram below could be the Displacement vs. Cme plot for the same object? A B C Mechanics Lecture 1, Slide 14 Acceleration Mechanics Lecture 1, Slide 15 Checkpoint 1 For the Displacement and Velocity curves shown on the leb, which is the correct plot of acceleraon vs. Cme? A B Mechanics Lecture 1, Slide 16 Clicker Question 4 Vote again A B A B Typical A answer Because a(t)= dv(t)/dt, according to the graph of velocity vs. time, acceleration vs. time graph should be the slope of the velocity vs. time graph. Thus, the answer should be the first graph. Typical B answer The velocity starts at a high positive value and then decreases to about zero before increasing again. Since the velocity graph curves first down then up, the acceleration decreases and then increases instead of just increasing for the entire time. Mechanics Lecture 1, Slide 17 Constant Acceleration constant a(t) = a Mechanics Lecture 1, Slide 18 Clicker Question 5 ? 4ft 1ft 9ft 16ft At t = 0 a ball, iniCally at rest, starts to roll down a ramp with constant acceleraon. Suppose it moves 1 ft between t = 0 sec and t = 1 sec. How far does it move between t = 1 sec and t = 2 sec? A) 1 B) 2 b C) 3 b D) 4 b E) 6 b Mechanics Lecture 1, Slide 20 Checkpoint 2 Responses 3 4ft 1ft 9ft 16ft Typical A answer A B C D E If it moves 1b in 1 sec, using x=xo+vt, v=1/1 or 1m/s. Using v=vo+at, a=1/1 or 1/s2. So in the interval of 1 second, the ball will move 1 foot. Typical B answer For the first second, the velocity is 1 b/s. Therefore if acceleraon is constant, then velocity will have increased to 2 b/s at 2 seconds. Therefore, in the Cme interval between 2 and 1 seconds, the ball would have moved 2 feet. Typical C answer Acceleraon is 1 b/s2 and the velocity at the end of the first interval is 2b/s so at the second interval the distance is 3 b from the equaon d= v + 1/2 at2 Mechanics Lecture 1, Slide 21 Checkpoint 2 Responses 3 4ft 1ft 9ft 16ft Typical D answer A B C D E Since acceleraon is constant, we can solve for acceleraon using the formula x = v(iniCal) * t + 0.5at2. Doing this we solve acceleraon for 0.6096m/s2, aer geng this we can plug this in for total distance travelled and the answer comes out to 4b if calculated properly. Question asks for distance from t=1 s to t=2. Typical E answer The equaon vf = vo + at will give us the final velocity and with that the final displacement. Given that vo = 1 foot/second, a = 4.9 (this is true due to the gravitaonal pull from the ramp assuming a 30° ramp) and t to be 1s. This calculates to the final answer being approximately 5.9 m. g≠9.8 ft/s2 — angle not necessarily 30° Mechanics Lecture 1, Slide 21.