302 (S98) Exam #3

302 (S98) Exam #3 - 7#,# #E#;#x#\$#h#\$#h#:#:#:#:#<#= #= #=

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þ7########,############### ÷##EÚ#######;#######x##################\$##h##\$##h##:#####:#####:#####:##<##= ####= ####= #(##=2####=H####=^####=^#P##=®#x##:T#¶##>&# ##>F####@Ë#*##@õ#¨##:#########@Ë####>^#m##@Ë####@Ë####E±#=##@Ë####@Ë####@Ë####@Ë ####@Ë####@Ë####Name #1. [30 points] An object is dropped from rest. After falling a distance R, it enters a frictionless, semicircular groove of radius R (as shown to the right). Find the magnitude of the normal force exerted by the groove on the object as a function of f, where f is measured from the vertical.2. (GRE problem) Circle the letter corresponding to the best answer. This is all or nothing! [5 points] A rock is thrown vertically upward with initial speed vo. Assume a friction (resistance) force proportional to -v, where v is the velocity of the rock, and neglect the buoyant force exerted by the air. Which of the following is correct? A. The acceleration of the rock is always g. B. The acceleration of the rock is equal to g only at the top of the flight. C. The acceleration of the rock is always less than g. D. The speed of the rock upon return to its starting point is vo. E. The rock can attain a terminal speed greater than vo before it returns to its starting point.

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3. [20 points] In the presence of a resistive force of the form f = -mkv, we found the time of flight for a projectile on level ground to be:# to first order in the small expansion parameter k (where V=vosinq is the vertical component of the initial velocity of the projectile).A. [15 pts] Starting from the equation of motion, find an approximation to the range of the projectile to first order in k. Please show your work.B. [5 pts] For what values of k is this solution a good approximation to the range of the projectile? Express your answer in terms of givens in the problem: vo, q, m, g. Explain your reasoning.
4. [25 points] An object on a level surface is given an initial velocity vo > 0. Thereafter, it is acted on by a resistive force mbvn. In the text we learned that when n = 1, the stopping distance for the object was finite, but in class we learned that when n = 2, the stopping distance was infinite. For what value of n for 1 < n < 2 does the transition between a finite and an infinite stopping distance occur? Show your work.5. [25 points] Find the components of the acceleration vector # in plane polar coordinates (r,q). Show your work. (Hint: This was done in cylindrical coordinates as an example in the text. The answer is not very different in polar coordinates).Name Total Points Name Total Points Physics 301 (Fall 1997) Third Exam (October 31, 1997) #v#±##v#±#>#ü###±#######®#É###r#########®#É#bÿÿÿÿ##È###ÿ

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#ÿÿÿÿÿÿ##ÿÿ###È##########¡#À#y%PostScript Hack by Mike Brors 12/7/90/DisableNextSetRGBColor { userdict begin /setrgbcolor { pop pop pop userdict begin /setrgbcolor systemdict /setrgbcolor get def end } def end } bind def/bcarray where { pop bcarray 2 { /da 4 ps div def df setfont gsave cs wi 1 index 0 ne{exch da add exch}if grestore setcharwidth cs 0 0 smc da 0 smc da da smc 0 da smc c gray { gl} {1 setgray}ifelse da 2. div dup moveto show }bind put } if%% Used to snap to device pixels, 1/4th of the pixel in./stp { % x y pl x y % Snap To Pixel, pixel (auto stroke adjust) transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform} bind def/snapmoveto { % x y m -
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This document was uploaded on 10/29/2011 for the course PHSX 302 at MSU Bozeman.

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302 (S98) Exam #3 - 7#,# #E#;#x#\$#h#\$#h#:#:#:#:#<#= #= #=

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