PHYS 172: Modern Mechanics. Summer r p. Lecture 9 Motion Along a Curve Read Ch 5

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1 PHYS 172: Moden Mechanics Summe 2010 Δ sys = F net Δt ΔE = W + Q sys su su ΔL sys = τ net Δt Lectue 9 Motion Along a Cuve Read Ch 5

3 Statics Static means that something doesn t change in time. What do we exect fo ou measues of inteactions in a statics oblem?

4 Clicke Question Which of the following statements is tue? A) If = 0 d then = 0 dt = 0 d 0 d dt = 0 dt = 0 d 0 0 dt d = 0 dt B) If then C) If then D) If then E) If then may o may not be zeo

5 Motion Along a Cuve An object is following the cuved tajectoy shown below. The object is at constant t seed. Let s look at what kind of foce is necessay to get the Let s look at what kind of foce is necessay to get the object to move like this!

6 Motion Along a Cuve An object is following the cuved tajectoy shown below. The object is at constant t seed. Let s look at what kind of foce is necessay to get the Let s look at what kind of foce is necessay to get the object to move like this!

7 Peendicula and Paallel Comonents seed = constant Δ Δ Peendicula foces change the diection of momentum, but not magnitude.

8 Motion Along a Cuve An object is following the cuved tajectoy shown below. The object is seeding u. Let s look at what kind of foce is necessay to get the Let s look at what kind of foce is necessay to get the object to move like this!

9 Paallel and Peendicula Comonents Δ i Δ Δ Δ sys = Fnet Δt F aticle must be aallel with the F F g net f The net foce on the change in momentum.

10 Motion Along a Cuve Δ Δ Δ Δ Δ In comaison with the motion at a constant seed, hee we have a aallel comonent of the change in momentum and thus a aallel comonent to the net foce. Since the only thing that has changed fom the evious examle is that the object is seeding u, we conclude that the aallel comonent of the net foce is esonsible fo the change in magnitude of the momentum.

11 Detailed Fomulae = ˆ d d = ˆ + dt dt dˆ d t change in diection of momentum change in magnitude of momentum dˆ dt = v R nˆ R = adius of kissing cicle

12 Paallel and Peendicula Comonents dˆ v = nˆ = F dt R d ˆ dt = F fo magnitudes only: v R = F Often called the centietal foce

13 Centietal Foce The centietal foce is simly a new name fo foces aleady esent. It is not an additional (new) foce! Rathe it is the label given to the foce o Rathe it is the label given to the foce o the sum of foces that cause the cicula motion

14 Unifom Cicula Motion v v R = F

15 CLICKER QUESTION In Lab #5 you ll ty to secify an initial seed v such that the caft will move in a cicula obit about the Eath. R = 6.4e7 m M E = 6e24 kg M C = 15e3 kg G = 6.67x10-11 Nm 2 /kg 2 g=9.8 m/s 2 Fist, what is the magnitude of the gavitational ti foce on the caft? v= v =? Caft A N F = F ˆ B N C. 147,000 N D e10 N E. Need moe infomation. ( ) CE CE CE R Eath MEMC F CE = G = N 2 CE

16 CLICKER QUESTION In Lab #5 you ll ty to secify an initial seed v such that the caft will move in a cicula obit about the Eath. You just calculated that the Eath exets a foce of magnitude N on the caft. What seed does the caft need to go in a cicula obit? R = 6.4e7 m m E = 6e24 kg E m C = 15e3 kg v = v =? Eath G = -6.67x10-11 Nm 2 /kg 2 Caft R A. 17, ms B m/s v C m/s Fgav, CE = F = R D m/s E. Need moe infomation. v RF gav, CE m = = m s

17 Clicke Question: Tazan Tazan swings on a vine to coss a ive. At the bottom of his swing what is the diection? a) d) b) e) has no magnitude c)

18 Clicke Question: Tazan Assume Tazan has some momentum to the ight. What is the net foce on Tazan? = 0 2 F net F net =< 0, mg, 0 > ml F net =< 0, mg, 0 > 2 mv F net = mg 2 L F net =< 0,, 0 ml A) = 0 D) B) E) C) >

19 Clicke Question: Tazan What is the foce that Tazan exets on the vine? 2 F Tazan F Tazan =< 0, mg, 0 2mL A) =< 0, mg, 0 > D)F > 2 ml B) =< 0, mg, 0 > E) F Tazan 2 ml C) F Tazan =< 0, mg, 0 > F Tazan =< 0,0, 0 >

20 Clicke Question The vine snas and sends Tazan in to the ive, what should Tazan do if he wants to make it acoss the ive? A) Ty a longe vine B) Ty a shote vine C) This was clealy a fluke ty again with the same length

21 Clicke Question Tazan successfully swings acoss the ive. As he aoaches the othe side what should haen to the magnitude of his momentum? A) Inceases B) Deceases C) Stays the same

PHYS 172: Modern Mechanics. Summer Lecture 4 The Momentum Principle & Predicting Motion Read

PHYS 172: Modern Mechanics. Summer Lecture 4 The Momentum Principle & Predicting Motion Read PHYS 172: Moden Mechanics Summe 2010 Δp sys = F net Δt ΔE = W + Q sys su su ΔL sys = τ net Δt Lectue 4 The Momentum Pinciple & Pedicting Motion Read 2.6-2.9 READING QUESTION #1 Reading Question Which of