301 (F98) Exam #1 Solution

301 (F98) Exam #1 Solution - 7########,##################-

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Unformatted text preview: 7########,##################- #######F#######d##################R##q##h#h###############J##j####j## ##j#(###R###|##`####`#P###x##2#8##(# ##H#####*## y##### ########`#m##########p#=##########################Name 1. [25 points total] Check the Fundamental Theorem for Gradients for the function: t = 3x3 + 6yz3 over the two paths sketched below from (0,0,0) to (1,1,1). Show your work.#A. Path #1: (0,0,0) (1,0,0) (1,1,0) (1,1,1)B. Path #2: (0,0,0) (1,1,1) along the curve z = x2, x = y 2. [20 points total] For the vector field: # show that the divergence theorem holds for the volume bounded by a sphere of radius a centered on the origin. #3. [25 points total] A cylindrical room is rotating fast enough that two blocks stacked against the wall do not drop. The mass of block A is 500 g and the mass of block B is 300 g. A. [7 pts] Draw separate free-body diagrams for blocks A and B and label the forces as instructed in class. B. [6 pts] Identify any Third Law companion forces on your diagrams above with tick marks as was done in class. C. [6 pts] Rank the magnitudes of all the horizontal forces that you identified above in order from largest to smallest. Explain your reasoning. D. [6 pts] Determine the magnitude (if possible) of each of the vertical forces on block A that you identified above. Show your work and explain your reasoning. (Use the approximation g 10 m/s2.) 4. [15 points total] Evaluate the integral: # where # and V is a sphere of radius 7 centered about the origin. 5. [15 points total] Which of the vector functions below could be a legitimate electrostatic field (Hint: electrostatic means that there are no time varying electric or magnetic fields present). Explain your reasoning.i. #ii. #Name Total Points Name Total Points Physics 317 (Fall 1996) First Exam (September 20, 1996)Name Total Points #v###v#######D###########6###########&##### ##################y%PostScript Hack by Mike Brors...
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301 (F98) Exam #1 Solution - 7########,##################-

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