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Unformatted text preview: PHYS 172: Modern Mechanics Fall 2010 Lecture 2  Momentum & Relativity Read: 1.71.11 Announcement Prof Carlson's Ofﬁce Hours: Tuesdays and Thursdays, 34pm in Room 279 QUESTIONS? Email Prof. Andrew Hirsch [email protected] Today • General Course Information • Newton's First Law of Motion • Vectors • Velocity • Principle of Relativity • Special Relativity Syllabus & General Information: This is a 4 credit hour course. The rule of thumb at this University is that you should spend twice as many hours (on average) studying for this course outside of class as you do in class. That is, eight hours a week spent reading, doing the homework, recitation, and laboratory assignments, and studying for the quizzes and exams would be a typical investment of time for most students in this course. QUESTIONS? Email Prof. Andrew Hirsch [email protected] Syllabus & General Information: Evening Exams (3) Final Exam Labs Homework (WebAssign) Clicker questions Recitation TOTAL 30% 20% 15% 15% 5 15% 100% We will use an absolute grading scale with values as given on the syllabus. 89% or better to get an A. QUESTIONS? Email Prof. Andrew Hirsch [email protected] Syllabus & General Information:
Reminders: For help with homework problems, go to the Physics Learning Center in Room 12 (PHYS Bldg) during the assigned hours. Schedule can be found on the home page. It is staffed by trained teaching assistants assigned to this course. Use it! 1. Extensions can be granted for Homework assignments, if you have a good reason and don’t abuse the privilege. Download form under “HW Extension request” from the course web site. 2. To request an Excused Grade for a quiz or an exam due to a valid reason (illness, etc), download “Absentee Report” from the course web site. Do this in advance if at all possible. Advance notification is required for Evening Exams and the Final. See the Syllabus for more details. QUESTIONS? Email Prof. Andrew Hirsch [email protected] Syllabus & General Information: Academic Honesty You are encouraged to work on homework together – discussing ideas and concepts reinforces the material for everyone involved in the conversation. Just be sure that what you turn in is your own work that you fully understand. The following are examples of cheating: • Any effort to represent somebody else’s work as your own, or allowing your work to be represented as somebody else’s • Having somebody else solve assigned problems for you • Entering iClicker responses for anybody else • Being in possession of more than one iClicker in lecture Read the syllabus. QUESTIONS? Email Prof. Andrew Hirsch [email protected] Indicators of interaction
Change of velocity Change of identity Change of shape Change of temperature Lack of change when change is expected H2 + O2 → H2O bending a wire heating pot of water on a hot stove balloon floating in sky Uniform motion: velocity is constant Newton’s first law of motion
≡ uniform (constant) velocity An object moves in a straight line and at constant speed except to the extent that it interacts with other objects
The stronger the interaction, the faster the change in velocity • (Object at rest is a case of uniform velocity) Does this match what you see in the REAL WORLD?? Vectors have Magnitude and Direction
In three dimensions and Cartesian coordinates: Vectors Unit vectors in the direction of the axes: coolest trick in the book! General unit vector: HOME READING: OPERATIONS WITH VECTORS Vectors vector magnitudes scalar multiplication Clicker Question
Are these two vectors the same vector? A) YES B) NO Velocity has Magnitude and Direction
Magnitude of Velocity = Speed (a scalar) 100 m in 10 s Average speed: If we know speed we can predict future: If we know speed we can reconstruct past: Velocity has Magnitude and Direction Velocity is a Vector
z y x 100 m in 10 s Definition: average velocity Example y
9 8m 7 6 5 4 3 2 2 1 1 2 3 4 5 6 7m x Instantaneous vs. average velocity
The trajectory of a ball through air:
Instantaneous velocity at point B It is tangent to trajectory at point B It's the SLOPE! The average velocity will depend on the choice of Instantaneous velocity: derivative and Δt Acceleration = Change in Velocity
d v = a dt
Express v as =  v v vˆ
 v vˆ d v  ˆ   v dt Now use the chain rule to take the derivative:
d v d = dt dt = a Rate of change of direction = d  v v+ ˆ dt Rate of change of magnitude of velocity (speed) is parallel to the velocity. Predicting new position The position update formula Interactions: changing velocity
Newton’s first law of motion is qualitative: An object moves in a straight line and at constant speed except to the extent that it interacts with other objects Interactions can change velocity! ? What factors make it difficult to change an object velocity? Mass! Introduce new parameter that involves product of mass and velocity: momentum The stronger the interaction, the larger the change in momentum The simplest way:
MOMENTUM (Legal Disclaimer: there's more to momentum for objects near the speed of light! Void in NH.) Average rate of change of momentum The stronger the interaction, the faster is the change in the momentum Average rate of change of momentum: Units: Instantaneous rate of change of momentum: The principle of relativity
Physical laws work in the same way for observers in uniform motion as for observer at rest Inertial reference frame Inertial frame moves at constant velocity. Physical laws work in the same way in any inertial frame Are you in an inertial reference frame right now? Special theory of relativity
Inertial frame moves at constant velocity. Speed of light = constant in all inertial reference frames! SPACE AND TIME WARP TO ENSURE THIS STAYS TRUE Time dilation: time runs slower in moving reference frames Length contraction: object length becomes shorter in moving reference frame Momentum – The Whole Story
Definition of momentum:
(Lorentz factor) For v << c, γ≈1, approximation:
p= v, m/s 0 300 30,000 3×107 1 γ YOU ARE HERE
p= 1.0000000000005 1.000000005 1.005 0.9999c 70.7 No mass can reach speed of light! What We Did Today • General Course Information • Newton's First Law of Motion • Vectors • Velocity • Principle of Relativity • Special Relativity ...
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This note was uploaded on 09/29/2010 for the course PHYS 17200 taught by Professor Gaboracsathy during the Spring '09 term at Purdue.
 Spring '09
 GABORACSATHY

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