PHYSICS Final Exam University of Wyoming 11 December 2013

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1 PHYSICS Final Exam Univesity of Wyoming 11 Decembe 013 This test is open-note and closed-book. Calculatos ae pemitted but computes ae not. No collaboation, consultation, o communication with othe people (othe than the administato) is allowed by any means, including but not limited to vebal, witten, o electonic methods. Shaing of mateials including calculatos is pohibited. Any notes used must be tuned in with this exam. If you have a question about the test, please aise you hand. Please do not open this test booklet until eveyone has eceived a booklet and the test administato has indicated fo you to begin. While you ae waiting, make sue that you name is witten clealy at the top of the fist page. Please wite diectly on the exam and attach othe sheets of wok if necessay. Multiple-choice poblems have only one coect answe. You may choose to cicle two answes on a multiplechoice poblem and, if one of them is coect, eceive half cedit. Cicle thee and if one is coect, 1/3 cedit, etc. Fo woked poblems, be complete and show all wok, beginning with diagams and fundamental, geneal equations used. Cicle you final answe fo each pat of each woked poblem.

Wothe K +U P F v Δt du Usping 1 kx Ugav mgy F K 1 mv W ΔK dx Kinematics! x x Δx vavg 1 t t1 Δ t Angula Motion dω α dθ ω I mi i i K ot 1 Iω d v v v Δv aavg 1 t t1 Δ t θ1 θ 0 + ω 0 t + 1 α t g 9.

2 dv a! v 4π R! x x + v t + 1 at a v1 v0 + a t v1 v0 + a(x1 x0 ) ad R T F ma w m g fs µs N fk µk N f k v f D v fsping kx dp mi xi Momentum/Impulse xcm F p mv J Δ(mv) FΔt mi Wok/Enegy ΔW W F s Fs cosθ K1 +U1 + Wothe K +U P F v Δt du Usping 1 kx Ugav mgy F K 1 mv W ΔK dx Kinematics! x x Δx vavg 1 t t1 Δ t Angula Motion dω α dθ ω I mi i i K ot 1 Iω d v v v Δv aavg 1 t t1 Δ t θ1 θ 0 + ω 0 t + 1 α t g 9.8 m/s 1 adian mile km 1 m in 3.8 ft ρwate 1000 kg/m3 ρice 90 kg/m3 ρai 1.0 kg/m3 G N-m/kg MSun kg MEath kg MMoon kg 1 AU m RSun m REath m RMoon m Moon distance m ω 1 ω 0 + α (θ1 θ 0 ) ω1 ω 0 +α t v ω π 360 atan α aad ω dl I I cm + Md τ F F sin φ τ τ I α W τ Δθ K tot 1 mvcm + 1 I cmω L p mv Iω ΔL τ Δt powe τω s θ! Fluids df da dv A1v1 A v dm ρ1 A1v1 ρ A v p p1 ρ g(y y1 ) p B ρvg p1 + ρ gy1 + 1 ρ v1 p + ρ gy + 1 ρ v Fluids 1 1 G N m/kg GM1M GM1M vescape Ug Fg GM1M GM1M Ug GM1 vescape vobit Fg Peiodic Motion G N m/kg GM1 k ω m Tobit GM1 f 1 T ω π f Simple pendulum Physical pendulum vλf Waves on a sting F µ f1 v L π π vobit GM1 Open pipe fn v B ρ nv, (n 1,, 3, ) L Closed pipe fn E 1 mv + 1 kx 1 ka I k b m 4m x Ae (b/ m)t cos(ω "t + φ ); ω " k π λ v ω k I fn nf1, (n 1,, 3, ) Sound pmax BkA Tobit π 3 π vobit GM1 Damped oscillations y(x, t) A cos(kx ω t) v vobit GM1 x A cos(ω t + φ ) mgd ω I g ω L Mechanical Waves 3 dm dv ρ1 A1v1 ρ A v A1v1 A v p1 + ρ gy1 + ρ v p + ρ gy + ρ v 1 Gavity Gavity B ρvg p p1 ρ g(y y1 ) df p da pmax p max ρv ρ B nv, (n 1, 3, 5, ) 4L I1 I 1 P 4π Pav 1 µ Fω A β (10 db)log fbeat fa fb I I0 fl v + vl fs v + vs

3 Name: MULTIPLE CHOICE: Questions 1-11 ae 5 points each. 1. To double the total enegy of a mass-sping system oscillating in simple hamonic motion, the amplitude must incease by a facto of a. 16 b. 4 c. d. e. 4 f. E 1 ka!. A peson swings on a swing. When the peson sits still, the swing oscillates back and foth at its natual fequency. If, instead, the peson stands on the swing, the natual fequency of the swing is a. geate. b. smalle. c. the same. Mass moves close to the pivot, inceasing the fequency. 3. Two identical symmetic pulses of opposite amplitude tavel along a stetched sting and intefee destuctively. Which of the following is/ae tue? a. When the two pulses intefee, the enegy of the pulses is momentaily zeo. b. Thee is an instant at which the sting is completely staight. c. Thee is a point on the sting that does not move up o down. d. Thee ae seveal points on the sting that do not move up o down. When two equal but opposite pulse ovelap, they cancel each othe out exactly. PHYS 110 Final Exam 1 of 7

4 Name: 4. Pof. Kabappel is deliveing a physics lectue. Lisa is sitting 3m away in the font ow, and Bat is sitting 30m away in the back ow. How does the intensity of Pof. Kabappel s voice sound to Lisa as compaed to Bat? a. 1/100 the intensity. b. 1/10 the intensity. c. The same intensity. d. 3 times the intensity. e. 10 times the intensity. f. 30 times the intensity. g. 100 times the intensity. h times the intensity. i times the intensity. Intensity 1/ 5. A hollow ball and a solid ball of the same mass and adius initially have the same total kinetic enegy when they stat olling up the same amp of constant angle above the hoizontal. Which of the following is tue? a. They both go the same height up the amp befoe coming to a stop. b. They both have the same moment of inetia. c. They both stated with the same tanslational speed. d. They both each the top of thei maximum height at the same time. e. They both stated with the same angula speed. When they stop, all the kinetic enegy (both tanslation and otational) ae conveted into gavitational potential enegy. 6. On a day when thee is no wind, you ae moving towad a stationay souce of sound waves. Compaed to what you would hea if you wee not moving, the sound that you hea has a. the same fequency and the same wavelength. b. the same fequency and a shote wavelength. c. the same fequency and a longe wavelength. d. a lowe fequency and the same wavelength. e. a lowe fequency and a shote wavelength. f. a lowe fequency and a longe wavelength. g. a highe fequency and the same wavelength. h. a highe fequency and a shote wavelength. i. a highe fequency and a longe wavelength. Wavelength doesn t change if the souce doesn t move. Howeve, the time between aivals of wave cests is compessed as you move towad the souce. PHYS 110 Final Exam of 7

5 7. A unifom solid sphee olls without slipping along a level suface. What faction of its total kinetic enegy is otational, and what faction is tanslational? a. 1/3 otational and /3 tanslational. b. /3 otational and 1/3 tanslational. c. 1/5 otational and 4/5 tanslational. d. 4/5 otational and 1/5 tanslational. e. /5 otational and 3/5 tanslational. f. 3/5 otational and /5 tanslational. g. /7 otational and 5/7 tanslational. h. 5/7 otational and /7 tanslational. i. 1/ otational and 1/ tanslational. E tans ½mv E ot ½Iω ½(/5)m ω (1/5) mv E tot (1/+1/5) mv (7/10) mv E tans /E tot (1/)/(7/10) 5/7 E ot /E tot (1/5)/(7/10) /7 8. A fish bites at a baited hook and swims downwad, pulling the fishing line and float down with it. As the fish pulls the float deepe below the suface, how does the inwad pessue on the float change? a. The pessue inceases. b. The pessue does not change. c. The pessue deceases. Pessue inceases with depth: p p 0 + ρgd 9. In the scenaio of the pevious question, how does the upwad foce of buoyancy acting on the submeged float change as the fish pulls the float deepe unde wate? a. The buoyancy foce inceases. b. The buoyancy foce does not change. c. The buoyancy foce deceases. Buoyancy depends only on mass of wate displaced. Wate is incompessible. 10. Wate flows though a pipe with a naowing adius, as shown in the diagam. Whee is the pessue of the wate the geatest? a. At point A. b. At point B. c. It is the same at A and B. Speed is highe at B, so accoding to A Benoulli s law, the pessue is lowe at B. B PHYS 110 Final Exam 3 of 7

6 11. The Kuipe Belt Object known as Pluto is about 1/5 the mass of Eath s Moon and aveages about 40 times fathe fom the Sun than Eath s Moon. Compaed to the aveage gavitational pull Eath s Moon exets on the sun, how stong is the gavitational pull that Pluto exets on the sun? a. 5/40 the gavitational pull of Eath s Moon. b. 1/(5 40) the gavitational pull of Eath s Moon. c. 5/40 the gavitational pull of Eath s Moon. d. 1/(5 40 ) the gavitational pull of Eath s Moon. e. 1/(5 40 ) the gavitational pull of Eath s Moon. f. 40/5 the gavitational pull of Eath s Moon. g. 1/(5 40) the gavitational pull of Eath s Moon. h. 5 /40 the gavitational pull of Eath s Moon. i. 5 /40 the gavitational pull of Eath s Moon. k. 40 /5 the gavitational pull of Eath s Moon. F Gm 1 m / m 1 is the mass of the sun, m is the mass of the Moon o Pluto, is the distance. Pluto s mass is 1/5 that of the moon, so that deceases the foce by a facto of 5. Pluto is 40 times futhe away, so that deceases the foce by a facto of 40. PHYS 110 Final Exam 4 of 7

7 FREE RESPONSE: Questions 1-14 ae 15 points each. Show all you wok and clealy indicate you answe fo each section. 1. You discove a new exoplanet obiting a sta that is times the mass of the Sun, o kg. It completes one obital peiod in 10 days, o s. Assuming the obit is pefectly cicula, what is the adius of its obit in AU? (1 AU m) v cic (GM/) 1/ T π/v cic π/(gm/) 1/ π 3/ /(GM) 1/ 3 /GM (T/π) [GM(T/π) ] 1/3 [(6.67e-11 N m /kg )(1.50e30 kg)(8.64e5 s/π) ] 1/3 [(1.00e0 N m /kg)(1.89e10 s )] 1/3 (1.89e30 m 3 ) 1/3 1.4e10 m * (1 AU/1.50e11 m) AU. PHYS 110 Final Exam 5 of 7

13. A stetchy cod of mass 10.0 g and unstetched length.00 m is tied to an immovable wall at one end. The othe end is daped ove a pulley 1.00 m fom the wall, and then a 0.00 kg mass is attached.

8 13. A stetchy cod of mass 10.0 g and unstetched length.00 m is tied to an immovable wall at one end. The othe end is daped ove a pulley 1.00 m fom the wall, and then a 0.00 kg mass is attached. The cod has an elastic coefficient of k5.00 kg/s. a. [5 pts] What is µ (mass pe length) of the stetched cod? b. [5 pts] If the length of ope between the wall and the pulley is plucked like a guita sting, how long will it take fo the wave pulse to tavel fom the wall to the pulley? c. [5 pts] On the diagam, daw the appeaance of the sting if it is vibating in the thid hamonic ( nd ovetone). 1/3 m 1/3 m 1/3 m λ /3 m a) The sting stetches like an ideal sping: F -kx. F weight of the 0.00 kg mass mg (0.00 kg)(9.8 m/s ) 1.96 N k 5.00 kg/s x F/k (1.96 N)/(5.00 kg/s ) 0.39 m New length oiginal length + x.00 m m.39 m. Mass pe length mass / total length (0.010 kg)/(.39 m) kg/m b) Need to know the speed of the wave: v (F/µ) 1/ (1.96 N/ kg/m) 1/ v 1.7 m/s. Distance between the wall and the pulley 1.00 m. t d/v (1 m)/(1.7 m/s) s. c) See diagam above. PHYS 110 Final Exam 6 of 7

9 14. Doi, whose mass is 65 kg, climbs into an empty oak bael of mass 60 kg. The bael is sealed watetight and sent floating down a ive. The bael has an inteio volume of 0.10 m 3, oak has a density of 770 kg/m 3, and ive wate has a density of 1000 kg/m 3. Will the bael sink o float? If it floats, what pecentage of the volume of the entie bael will be above the wate? If it sinks, what minimum foce must be applied to a ope attached to the bael in ode to aise it to the suface? Whethe the bael will sink o float depends on how its total density compaes to the density of wate. The total mass is m Doi +m bael 65 kg + 60 kg 15 kg. The total volume is V inteio +Vbael. V inteio 0.10 m 3 V bael m bael /ρ bael 60 kg / 770 kg/m m 3 V total 0.10 m m m 3 Theefoe, the total density is ρ m/v 15 kg/0.198 m kg/m 3. Since this is less than 1000 kg/m 3, the bael will float. The floating bael has two foces acting on it: the buoyant foce pushing up, and the weight foce pulling it down. These foces ae equal and opposite. The buoyant foce is B ρ wate V disp g whee V disp is the volume displaced by the bael+doi. The weight foce is w mg ρ total V total g. Setting these equal, ρ wate V disp g ρ total V total g ρ wate V disp ρ total V total. The faction of the bael undewate is V disp /V total ρ total /ρ wate Theefoe, the faction of the bael above the wate is 1 - V disp /V total 0.369, o 36.9%. PHYS 110 Final Exam 7 of 7

PHYSICS Final Exam University of Wyoming 11 December 2013

PHYSICS Final Exam University of Wyoming 11 December 2013 PHYSICS 110-0 Final Exam Univesity of Wyoming 11 Decembe 013 This test is open-note and closed-book. Calculatos ae pemitted but computes ae not. No collaboation, consultation, o communication with othe