5. Test 2 Solutions

5. Test 2 Solutions - Problem 1(20 pts One mole of...

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Unformatted text preview: Problem 1 (20 pts) One mole of platinum (6 x 1023 atoms) has a mass of 195 grams (0.195 kg). The density of platinum metal 1: is 21.4 grams which is 21.4 x 103 —g cm3 ' m3 ' (a: 8pts) What is the diameter of a platinum atom inside a block of platinum metal? Show all steps in your work. W % f I;— ‘CIS—Icar ZB'QS'QhZ? 6-9230mcw 3 VOCJ-LM 3: WM 5 3-2.4—9‘22 .: f~§22~23u~e 03W“: 021-4 OQLOque 41w 2': 3/ /_52Q_23 :: 2. 4-?ng W 321‘ Set/(9 ‘Lk. (b: Spts) A thin bar of platinum hangs vertically. The bar is 2 m long with a cross section 1 mm by 1 mm, so the cross-sectional area is 1 x 10"6 1112. When a 10 kg mass is attached to the bottom of the bar, the bar stretches 1.2 mm (1.2 x 10—3 In). As measured by this experiment, what is Young’s modulus for platinum? Show all steps in your work. 'L/ ; ELL 3 (zones) (2) ASL/L (lake) (me—39 :: i-- 63 air N/hfi' (e: 4pts) Determine the effective stiffness of the spring-like interatomic force that acts between neighboring atoms in platinum. Show all steps in your work. is. 15.9.. at . ks ; v00 : Q-égeu)(2-4w—rsv) z” N/M— Problem 2 (27 pts) Suzie (mass = 66.5 kg) rides a roller-coaster and is heading along a section of the track whose radius of curvature is 7 m. As she goes over a rise, her speed is 6.2 m/s. (a: 3pts) On the diagram below, draw and label the following: o The force of the seat on Suzie o The gravitational force of the earth on Suzie ' -a o The direction of ($3 (b: llpts) What is the force of the seat on Suzie when she is at the top of this rise? You must start from the derivative form. of the momentum principle and Show all steps in your work. f...- E: f: Continued on next page Continued from previous page (C: 3pts) As Suzie goes through a clip on the ride, her speed is 17.7 m/s. On the diagram below, draw and label the following: i The force of the seat on Suzie o The gravitational force of the earth on Suzie o The direction of fig g{fir H; (d: lflpts) What is the force of the seat on Suzie when she is at the lowest point of the dip? You must start from the derivative form of the momentum principle and show all steps in your work. 19: so. an, 2— or" WU 1:, #59414!" F (a? r VIN E M .0 Jr. ‘3‘- m N Problem 3 (12 pts) A load of 190 kg is supported motionless above the ground by two ropes. Rope 1 exerts a force of (—300, 500, 0) N on the load. (a: Gpts) In the space below draw a diagTam showing all the forces acting on the load. Clearly label each force to identify it. /) ,7 8 /7 (11.03 E Sm—(€—) FE (b: Bpts) What is the force exerted by rape 2? You must start from the derivative form of the momentum principle and show all steps in your work. - .9 -*"> M’ - E’— (ata!o> r» (#306, 5790,69) +’<9/'190C7*99, "> + 2, fi 0 »l%2,0>+€ Problem 4 (35 pts) At a certain time a proton (charge +1.6 x 10—19 C) is at rest at location ( 5 x 10‘s, 2 x 10—5, 0) n1. An electron (charge —1.6><“19 C) is located at ( 3 x 10—5, 9 x 10‘s, 0) 1n and is moving with mo- ' mentum (4 x 10—27, #8 x 10-27, 0) kg - m/s (the speed is small compared to the speed of light). The proton and electron are in \) 2) outer space, far from any other objects. grflx electron (a: lpt) On the diagram, draw an arrow to represent the vector position of the electron relative to the proton. Label this arrow F. (b: lpt) On the diagram, draw an arrow to represent the unit vector associated with r and label this arrow 9. f“ N (c: lpt) On. the diagram, draw an arrow to represent the net force V proton acting on the electron and label this arrow find. ((1: 12pts) Choose the electron to be the system of interest. Calculate the net force (a vector) acting on the electron. Show all steps in your work. F) = (3M, ‘fv—é,o> -— we, 2-0—6, a) : <__.2_Q--g/ 79*6/ 63> M'- llfpl 1 {(294)14-(7w6f' L i-Z‘Eev-é’u" (3 : emf-ewefi : (e215: “2/”? awesé f : I _i33__F [VT—réa :(qecija-éo-ra (4-69-49 4kg); .Cfgz/o) (1282—6); P-(4-’5s"e—t<z)<-.7?«§‘/962/0) 3 (L129 @499 -L+~I%e—IS’/ o>/\/ Continued on next page. Continued from previous page. (e: 8pts) At a time 8 x 10—11 3 later, What is the new momentum of the electron? Start from the momentum principle and show all steps in your work. —'> F") p .2: Vb :. (42523;, -—°m--27/D> + 4‘0(.5Q,-26L __g.g4.e-7_g/ O > s (#076927, sages 2321/ 0> 113 nan/S (f: 3pts) At this later time, what is the new momentum of the proton? Start from the momentum principle and show all steps in your work. a" —v #2— ;: 49/ 0(0) + <.lt2.oe*f8/ HHS? 49/60 (994‘) Continued on next page. Continued from previous page. (g: 6pts) At this later time, what is the new position of the electron? Show all steps in your work. «I? A) .3, 1 E I; r1L + VME a : (gag, fiflwéio> +(Lf~o?6e—21/ —S/—?>3L{.e~2 3, 0) (Egan) 99—5t 3 (39-93, ‘ffi-élo> + <46S‘e’2/1rygée'z / ca) (go—(Q 369+, ?e~-e,o> + <§~64€-7/——7-4(e—1/0) ;<3-%ée—é/+%-2éQ—é/ «23> M— (h: 3pts) You had to make an approximation to update the position of the electron. What was that approximation, and why was it a reasonable one to make? ' V 1351/ 10 Problem 5 (6 pts) An alpha particle (a helium nucleus: two protons and two neutrons) passas near the nucleus of a gold atom, which is initially at rest. The alpha particle travels from location A to location B to location C along the path shown in the diagram below. The massive gold nucleus hardly moves and therefore can be considered to be at rest during this interaction. 2 .9 (a: 3pts) At each location marked by a letter draw an arrow representing the electric force exerted on the alpha particle by the gold nucleus. Label each of these fame arrows F. Make sure the direction of the arrow is correct, and the relative lengths of the arrows are correct (that is, larger magnitude is indicated by an arrow that is clearly longer). (13: 3pts) At each location marked by a letter draw an arrow representing the momentum of the alpha particle. Label each of these ownith air-Irma 13'. As above, make sure direction and relative magnitude are clear, and that your arrows are labeled. HINT: Think about what the Momentum Principle predicts in. this situation. Did you clearly label the vectors for parts (a) and (b) on the diagram above? 11 ...
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5. Test 2 Solutions - Problem 1(20 pts One mole of...

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