2014 Academic Challenge

Transcription

1 2014 Academc Challenge PHYSICS TEST - REGIONAL Ths Test Conssts of 35 Questons Physcs Test Producton Team Len Storm, Eastern Illnos Unversty Author/Team Leader Doug Brandt, Eastern Illnos Unversty Author Kevn Ptts, Unversty of Illnos at Urbana-Champagn Revewer Mary Weaver, WYSE Coordnator of Test Producton GENERAL DIRECTIONS Please read the followng nstructons carefully. Ths s a tmed test; any nstructons from the test supervsor should be followed promptly. The test supervsor wll gve nstructons for fllng n any necessary nformaton on the answer sheet. Most Academc Challenge stes wll ask you to ndcate your answer to each queston by markng an oval that corresponds to the correct answer for that queston. Only one oval should be marked to answer each queston. Multple ovals wll automatcally be graded as an ncorrect answer. If you wsh to change an answer, erase your frst mark completely before markng your new choce. You are advsed to use your tme effectvely and to work as rapdly as you can wthout losng accuracy. Do not waste your tme on questons that seem too dffcult for you. Go on to the other questons, and then come back to the dffcult ones later f tme remans. *** TIME: 40 MINUTES *** DO NOT OPEN TEST BOOKLET UNTIL YOU ARE TOLD TO DO SO! 2012 Worldwde Youth n Scence and Engneerng WYSE, Worldwde Youth n Scence and Engneerng and the WYSE Desgn are servce marks of and ths work s the Copyrght 2012 of the Board of Trustees of the Unversty of Illnos at Urbana - Champagn. All rghts reserved.

2 Fundamental Constants Quantty Symbol Value Avogadro s number N A /mol Boltzmann s constant k J/K Electron charge magntude e C Permeablty of free space µ 0 4π 10 7 T m/a Permttvty of free space ε C 2 /(N m 2 ) Planck s constant h J s Electron mass m e kg Neutron mass m n kg Proton mass m p kg Speed of lght n vacuum c m/s Unversal gravtatonal constant G N m 2 /kg 2 Unversal gas constant R J/(mol K) Stefan-Boltzmann constant σ W/(m 2 K 4 ) Other nformaton: Acceleraton due to gravty at earth's surface: g = 9.80 m/s o C = K

3 WYSE Academc Challenge Physcs Test (Regonal) For a partcle, the tme rate of change of ts lnear momentum s equal to a. the net mpulse actng on the partcle. b. the net force actng on the partcle. c. the work done on the partcle. d. the tme rate at whch work s done on the partcle. e. none of the above. 2. A wooden board of unform thckness and densty s cut nto the shape (S) shown below. Pece S s then cut at ts center of mass to produce a rght pece (R) and a left, rectangular shaped pece (L). Whch of the followng s true. a. L must have greater mass. b. R must have greater mass. c. L and R must have equal mass. d. L and R must have equal surface areas. e. Both c and d are true. S L R 3. A small rock s released from rest from the top of a tall vertcal clff and falls freely. The rock falls a dstance of 19.6 m after 2.00 s have elapsed. How much farther does the rock drop n the next 1.00 s? a m b m c m d m e m 4. A motor boat crosses a rver wth ts bow to stern axs perpendcular to the rver flow. The boat travels at a constant speed of 12.0 km/hr as seen by an observer standng on one of the banks of the rver. If the water flows at a speed of 5.00 km/hr relatve to the same observer, what s the speed of the boat relatve to the water? bow stern bow to stern axs a km/hr b km/hr c km/hr d km/hr e km/hr 5. A 12.0 kg mass makes a head-on collson wth a 22.0 kg mass that s ntally at rest. As a result of the collson, the 22.0 kg mass acqures a speed of 15.0 m/s, and the 12.0 kg mass rebounds n the drecton opposte to ts ntal velocty, wth a speed of 4.00 m/s. The ntal speed of the 12.0 kg mass, pror to the collson, was: a m/s. b m/s. c m/s. d m/s. e m/s. 6. For the stuaton n problem 5, f the contact tme between the 12.0 kg mass and the 22.0 kg mass s s, what s the magntude of the average force actng on the 22.0 kg mass due to contact wth the 12.0 kg mass? a. 171 N b. 117 N c N d N e N

4 Physcs 2 7. If F denotes the th force actng on an object, and m s the mass of the object, whch of the followng s a statement of Newton s frst law of moton? (Assume all observatons of the object are made from an nertal frame of reference.) a. If F = 0, then the speed of the object wll decrease wth tme. b. If F = 0, then the velocty of the object must be 0. c. If F = 0, then the velocty of the object must be constant. d. The acceleraton of an object s gven by F / m. e. None of the above. 8. As a certan basketball travels from one bounce to another above a horzontal floor, the x and y components of dsplacement of ts center of mass are gven by: o ( 13.2 m/s) cos( 26.5 )t x = 0 + and ( ) ( ) ( ) o 1 y = m m/s sn 26.5 t 9.80 m/s 2 t 2, 2 where t s the tme n seconds from the frst bounce. What s the speed of the ball at the top most pont of ts path? a m/s b m/s c m/s d m/s e m/s 9. For the moton descrbed n problem 8, what s the tme between bounces? a s b s c s d s e s 10. Durng a certan trp, a car travels a total dstance of 126 km. The speed of the car s 32.0 km/hr for one part of the trp, and 68.0 km/hr for the remander of the trp. If t takes 3.00 hours to make the entre trp, the average speed durng the trp s: a km/hr. b km/hr. c km/hr. d. not determnable from the gven nformaton. e. none of the above. 11. Whch scentst frst devsed and dd experments nvolvng an apparatus whch used charged ol droplets to determne the elementary charge of an electron? a. Andre-Mare Ampère b. Félx Savart c. James Maxwell d. Charles Coulomb e. Robert Mllkan

5 12. A small block of mass kg s pushed up a frctonless nclne by a force of magntude 8.47 N actng at an angle of 11.2 o below the horzontal. After the block has been pushed a dstance of 1.85 m along the 43.3 o nclne, how much work has been done by the gven force? 1.85 m 43.3 o Physcs N 11.2 o a J b J c J d J e J 13. In problem 12, how much does the gravtatonal potental energy of the mass change as t moves 1.85 m along the nclne? (Assume the nclne s on the Earth.) a J b J c J d J e. Same answer as Agan usng the stuaton n problem 12, what s the magntude of the net force actng on the mass? a N b N c N d N e N 15. Assumng that a basketball s n free flght, when t s at the top of ts parabolc trajectory, the basketball: a. has a downward acceleraton and a downward velocty. b. has a horzontal velocty, but no acceleraton. c. has no acceleraton, but has both downward and horzontal components of velocty. d. has a downward acceleraton and both horzontal and downward components of velocty. e. has a downward acceleraton and a horzontal velocty. 16. An electrc cart has a battery capable of delverng 240. W h of energy. The cart and a sngle occupant/drver have a combned weght of 950. N. Startng wth fully charged battery, the cart s drven up a steady nclne at a slow, constant speed. If the cart eventually acheves an elevaton gan of 368 m before depletng the electrcal energy n the battery, what percentage of the battery s ntal energy was lost to frctonal forces and the lke? a. 59.5% b. 95.9% c. 14.9% d. 40.5% e. Cannot be determned snce the cart wll never reach an elevaton gan of 368 m. 17. A rgd box, havng a mass of 75.0 g, s attached to a unform rope, whch has a total mass of 18.0 g. The 10.0 cm 10.0 cm system s beng pulled by a force, F, as shown. If 75.0 gm frcton between box and the horzontal floor s neglgble, and the rope does not sag apprecably, what s the tenson n the rope at ts mdpont, 10.0 cm from each end? F a b F c F d F e F

6 Physcs A 28.9 g bullet, whch has a muzzle ext speed of 400. m/s, s fred straght downward from a vertcal clff and travels a dstance of 389 m before comng to rest nsde a thck block of wood. (Note that the 389 m ncludes the dstance traveled nsde the wood.) Ignorng ar frcton, f the bullet travels 23.7 cm nsde the block of wood before comng to rest, what s the magntude of the average force that the wood exerts on the bullet? a kn b kn c kn d kn e. 102 kn 19. A kg block s dropped onto a vertcally orented, massless sprng, whch has a sprng constant equal to 125 N/m. When the block makes contact wth the sprng, t becomes attached to t, and contnues to compress the sprng by m before momentarly stoppng. From ntal contact to maxmum compresson of the sprng, what s the combned work done on the block by the sprng force and the gravtatonal force actng on the block? a J b J c J d J e J 20. An automoble, havng a weght of N, accelerates unformly, and wthout slppng, from rest to 16.0 m/s n 7.20 seconds whle travelng along a horzontal stretch of road. Ignorng ar frcton, what average power was delvered to the wheels durng ths perod of tme? a. 251 kw b kw c. 279 kw d kw e. 558 kw 21. A pont object of mass 2.00 M s located on the y-axs at y = 4.00 cm. A second pont object of mass 1.00 M s located on the x-axs at x = 3.00 cm. What s the dstance from the orgn to the center of mass of ths two mass system? a cm b cm c cm d cm e cm 22. To smulate the hgh acceleratons experenced by astronauts durng lftoff, astronaut tranees are put nto a large centrfuge. If the tranee s to experence a centrpetal acceleraton of 12.0 tmes the acceleraton due to gravty at the Earth s surface, how many revolutons must the centrfuge rotate each second f the tranee s 18.0 m from the axs of rotaton? a b c d e Two dentcal, unform, frctonless cylnders, each havng weght W, are restng n statc equlbrum nsde a box, as shown. What magntude of force does the left wall of the box exert on the left cylnder? a W b W c W d W e W gravty 28.0 o

7 Physcs A unform, horzontal plank, havng a weght of 254 N, s held n statc equlbrum by a frctonless pn at A and a cord ted at the plank s left end. The length of segment PA s 20.0 cm, and the length of AC s 70.0 cm. What s the tenson n the cord? P A C 58.0 o gravty a N b. 444 N c. 524 N d. 318 N e. 374 N 25. An object s dropped from rest. If a graph of the dstance the object has fallen, d, versus the square of the objects speed, v 2, s made as shown, what s the expected slope of the resultng lne, f ar frcton can be gnored? In the responses, u represents the correct SI unts of the slope. a u b u c u d u e. The result wll be a parabola, and thus the slope s not constant. d (m) Dstance Fallen vs. Speed 2 v 2 (m 2 /s 2 ) 26. A wheel, ntally rotatng at a rate of rad/s, rotates wth constant angular acceleraton, and reaches an angular speed of rad/s, 5.75 s later. What s the angular acceleraton of the wheel durng ths tme nterval? a rad/s 2 b rad/s 2 c rad/s 2 d rad/s 2 e rad/s A constant, horzontal force of 12.5 N acts upon a wheel of mass 16.0 kg and dameter m, causng t to accelerate on a horzontal surface, wthout slppng, at a rate of m/s 2. What s the magntude of frctonal force actng on the wheel? 12.5 N a N b N c N d N e N 28. For the same stuaton descrbed n problem 27, what s the angular acceleraton of the wheel? a rad/s b rad/s c rad/s d rad/s e rad/s 29. Assumng the ppes shown below are flled wth an ncompressble flud, what s the flow rate and drecton n the unlabeled ppe? a. 3 gal/mn n b. 4 gal/mn n c. 5 gal/mn out d. 4 gal/mn out e. 2 gal/mn out 5 gal/mn 3 gal/mn 6 gal/mn 4 gal/mn 8 gal/mn

8 Physcs If a 9.00 V battery wth neglgble nternal resstance were connected between ponts X and Y, (and thus n parallel wth the 6.00 Ω resstor), how much current would flow through the battery? a A b A c A d A e A 16.0 Ω 8.00 Ω 12.0 Ω X 4.00 Ω 6.00 Ω Y 31. A certan empty can has a total volume (ncludng wall and bottom thckness) of 1260 cm 3 and a mass of 152 g. Lead shot s added to the can untl the can floats n water wth 75.0% of the can s volume submerged. If the densty of lead s 11.4 g/cm 3, and that of water s 1.00 g/cm 3, how many grams of lead were added to the can? a g b g c. 945 g d g e. 793 g 32. A ray of lght travels from ar nto a transparent trangular prsm along the path shown n the dagram. If the ndex of refracton of the prsm s 1.32, and the value of α s 20.0 o, what wll be the value of β at the other prsm surface shown? a o b o c o d o e o o 25.0 α β 33. A sphere of radus m, surface temperature 29.0 o C, and emssvty s suspended nsde a large oven whose nsde walls are at a temperature of 129 o C. What s the net rate of radatve energy transfer to the sphere? a W b W c. 909 W d. 619 W e W 34. If a partcle wth a net charge equvalent to two electrons makes 6.00 rev n a magnetc feld of mt n a tme of 23.4 ms, what s the partcle s mass? a kg b kg c kg d kg e kg 35. A concave mrror has a radus of curvature equal to 48.0 cm. If t s postoned such that the uprght mage of a woman s eye s 2.80 tmes the sze of her actual eye, how far s her actual eye from the mrror? a cm b cm c cm d cm e cm