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 interac ve) 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, Accelera on b) 1-D Kinema cs with constant accelera on
Mechanics Lecture 1, Slide 8 Q: What are the benefits of par cipa ng ? A: You learn more
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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
Defini on:
Speed = |v(t)|
Mechanics Lecture 1, Slide 12 Displacement and Velocity in One Dimension
Are the plots shown at the le correctly related A) YES B) NO
Mechanics Lecture 1, Slide 13 Clicker Question The velocity vs. me plot of some object is shown to the right.
Which diagram below could be the Displacement vs. me 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 le , which is the correct plot of accelera on vs. me?
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, ini ally at rest, starts to roll down a ramp with constant accelera on. 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 C) 3 D) 4 E) 6
Mechanics Lecture 1, Slide 20 Checkpoint 2 Responses
3
4ft 1ft 9ft 16ft
Typical A answer A B C D E
If it moves 1 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 /s. Therefore if accelera on is constant, then velocity will have increased to 2 /s at 2 seconds. Therefore, in the me interval between 2 and 1 seconds, the ball would have moved 2 feet. Typical C answer Accelera on is 1 /s2 and the velocity at the end of the first interval is 2 /s so at the second interval the distance is 3 from the equa on 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 accelera on is constant, we can solve for accelera on using the formula x = v(ini al) * t + 0.5at2. Doing this we solve accelera on for 0.6096m/s2, a er ge ng this we can plug this in for total distance travelled and the answer comes out to 4 if calculated properly. Question asks for distance from t=1 s to t=2. Typical E answer The equa on 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 gravita onal 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