Chapter4 - Chapter 4 Demos:

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PHYS276, S09 Chapter 4 1 Chapter 4 Demos: http://www.physics.umd.edu/deptinfo/facilities/lecdem/lecdem.htm C2-21: balls dropped and shot C2-25: funnel cart D1-33: rotating mass on string Thanks to Prof LaPorta and “Peer Instruction” by Eric Mazur
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Exam 1 PHYS276, S09 Chapter 4 2 First exam is Wednesday (3 March). The exam will cover the material including that in the HW due on 1 Mar (hopefully up to and including chapter 4.4) You may bring one 4”x6” index card to the exam. Please start preparing it now so you don’t need to do this the night before the exam. Please note the following additions to the web site • a link to exams (and their solutions) from previous semesters • a list of additional problems you may wish to use to practice for the exam It generally takes me about 1 week to grade the exams.
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goal PHYS276, S09 Chapter 4 3 We spent chapter 2 understand this motion: Let’s use our understanding of constant acceleration and our new 3D tools to study the effect of gravity on 2 D motion. Our goal is to understand the following motion: (projectile) And also this motion: (circular)
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PHYS276, S09 Chapter 4 4 2D motion vectors The definitions of position, displacement, velocity, acceleration vectors (average and instantaneous) are just vector extensions of the 1D definitions f i D p p p D v t v a t = Δ = = Δ Δ = Δ Note that, of these, only position depends on the location of the origin of the coordinate system
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PHYS276, S09 Chapter 4 5 Displacement, etc In all that we do, we will make use of the independence of the coordinates 1 2D motion can be broken into 2 separate 1 D motions We will usually be breaking 2D problems into 2 separate 1D problems, and 3-D problems into 3 separate 1D problems
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PHYS276, S09 Chapter 4 6 Average D = ( D x , D y ) D x = x f x i D y = y f y i v x = x f x i Δ t v y = y f y i Δ t a x = v x , f v x , i Δ t a y = v y , f v y , i Δ t
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PHYS276, S09 Chapter 4 7 Instantaneous v x = dx dt : v y = dy dt : v=v x ˆ i + v y ˆ j a x = dv x dt : a y = dv y dt : a=a x ˆ i + a y ˆ j
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PHYS276, S09 Chapter 4 8 Motion with constant velocity What is his displacement? velocity? Where will he be at t=10 s? Moves from point A to B in 5 seconds at constant speed. NOTE THE AXES! D = (0.5 m ,1.0 m ) v = (0.1 m / s ,0.2 m / s )
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Chapter 4 9 Equations A person starts at: p 0 = (0 m ,0 m ) He moves with a velocity v = (0.1 m / s ,0.2 m / s ) Where is he after 10 seconds? (2 questions: what is his x position after 10 s? what is his y position after 10 s?) p f = p 0 + vt p f = ( x f , y f ) = (0 m ,0 m ) + (0.1 m s ,0.2 m s ) i 10 s p f = ( x f = 0 m + 0.1 m s 10 s , y f = 0 m + 0.2 m s 10 s ) p f = (1 m ,2 m ) Can you rewrite this in ihat, jhat notation? Our old 1D equations of motion work equally well for 2 and 3 D, used for each
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Chapter4 - Chapter 4 Demos:

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