94785 - Problem 1 (20 Points) A proton moving in the a:...

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Unformatted text preview: Problem 1 (20 Points) A proton moving in the a: direction is speeded up by a constant electric force in the av direction, of magnitude 3.4 X 10”12 N. When the proton passes the location a: : 5 In, its speed is 2.95 x 108 m/s. (a 3pts) What is the rest energy of this proton? {r 3 “<22 = (M V’lo'a7)[3./0’)z I ’I S" ' I0-IOJ' (b 3pts) What is the total energy of this proton at this point? Z l— (-2): 10 ’I RIO" " ‘3' (c 3pts) What is the kinetic energy of the proton at this point? a 'L .. .. K— (w)ch - Er Er ’0 : 3.284040—15/40' 1 6n 7? r Ia'm'J' (d llpts) When the proton passes the location m = 9 In, What is its kinetic energy? If you could not do part a, call the answer to part a ”Ka” and express your answer to part b in terms of Ka. AK: FAX (S’t = o\?7.lo"°+ 3-‘I'mwi‘l'gl [ID I b\‘l\"ow J Problem 2 (15 Points) A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of dmm (inside the orbit of Mercury)7 at Which point its speed is m. Its farthest distance from the Sun is dmax (outside the orbit of Pluto). You can assume that the mass of the sun M sun is much greater then the mass of the comet Mamet What is its speed when it is farthest from the Sun in terms of the given variables? qu'kw‘. comet 4: Sun 1 V‘ , dam L AEthnfio it Vt: dated NU [SW—:0 Kr'Ki 4’ New: 0 K; 2: iii-"HQ 4K; I - z '_ _ . .f 2%)," \v + Gtgflféms + iJV-L Problem 3 (15 Points) Here are graphs of kinetic energy and gravitational potential energy for two stars that interact with each other. Each graph represents a difierent possible situation for a system consisting of two stars. Eu 6 rgy En ergy En e rgy KM (a 5pts) In each graph, label which curve represents kinetic energy and which curve represents potential energy and explain/ justify your choice. O 0 (b 5pts) Which graph represents a bound state, 1, 2, or 3? How do you know? a ’ 4‘ D (c 5pts) On each graph, draw a curve representing the sum of kinetic energy plus potential energy. Problem 4 (20 Points) By ”weight” we usually mean the gravitational force exerted on an object by the Earth. However, when you sit in a chair your own perception of your own ” weigh ” is based on the contact force the chair exerts upward on your rear end rather than on the gravitational force. How fast must a roller coaster car go through a circular dip for you to feel three times as ” heavy” as usual, due to the upward force of the seat on your bottom being three times as large as usual? (The center of the car moves along a circular arc of radius Include a carefully labeled force diagram. Rea; "r 5 M3 Problem 5 (15 Points) A professor of mass M swings from a vine of length R. When the vine makes and angle of G) : 30° from the vertical the professor is moving With speed V. What is the tangential component of the rate of change of momentum at this instant? l Problem 6 (15 Points) A block of mass M is attached to the end of a vertical spring whose relaxed length is LO‘ When the block oscillates up and down in the lab room, it takes T seconds to make a round trip. (a 5pts) What is the stifiness of the spring? 3 [if 50:27fft’gg: if“ r2 Mufti: = M (g?) (b lOpts) Air resistance eventually damps out the oscillation and the block hangs motionless from the spring. How long is the spring now? Justify your analysis by starting from a fundamental physics principle. No credit will be given Without this justification. '2 F5 E: O ‘, @ VMa {swusfa HLrLol—‘MJ'L 0 Lo lLvalz, L '2. %..Q%LD :: j Lb L t Lo ...
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This note was uploaded on 09/23/2009 for the course PHYSICS 2211 taught by Professor Uzer during the Fall '08 term at Georgia Tech.

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94785 - Problem 1 (20 Points) A proton moving in the a:...

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