Phys 172 Exam 1, 2010 fall, Purdue University

Transcription

1 Phs 17 Eam 1, 010 all, Purdue Universit What to bring: 1. Your student ID we will check it!. Calculator: an calculator as long as it does not have internet/phone connection 3. Pencils Eam will take place in Elliot Hall o Music. When entering hall, please take a writing board (available at the entrance). Please prepare to be seated in eam ormation each other row and each other seat. Turn o our phone and keep it in our bag/pocket at all times Equation sheet is provided at the end o the eam. You can tear it o and use, ou do not have to return it. At the end o the eam please turn in our scantron sheet and paper eam to one o the TAs (don t orget to sign our paper eam at the right-top corner).

2 DO NOT OPEN YOUR EXAM UNTIL TOLD Practice Eam I, Phs 17, Spring 010 EXAM # Record our two-digit eam version number on scantron orm in the ield Test/Quiz number. Please do not omit leading zero.. Write our name in the top-right corner here and on the scantron orm 3. Record our PUID number in the respective ield on our scantron orm Do not use other paper. Write on the back o this test i needed. The page with major equations is provided with this eam (in the back) Circle our answers here and on scantron orm. At the end o the eam, ou will return scantron orm and this printout with circled answers to our TA.

3 Problems 1-3 For the net our problems consider vectors in the diagram shown below, in which each division is equal to 1 m. Problem 1 (5 pts) What are the components o the vector a? A) <8, -1> m B) <9, > m C) <-1, 8> m D) <3, 4> m E) <4, 3> m Problem (5 pts) What is the magnitude o the vector a? A) 8.06 m ( ) B) 9 m C) 8.1 m D) 8.3 m E) 5 m a c b d H a Problem 3 (5 pts) Which one o the ollowing statements is true about vectors a, b, c and d? A) a + b + c + d 0 B) a + b c d C) a + c b D) a c + b E) a b c

4 Problems 4-5 A tennis ball o mass 57 g is served in horizontal direction along -ais and initiall lies at speed 60 mph. z 60 mph Problem 4 (5 pts) What is the initial magnitude o its momentum? A) 340 kg. m/s miles meters B) 1.5 kg. m/s p mv 0.057kg hour mile seconds 3600 hour C) 1500 kg. m/s D) 3.4 kg. m/s E).1 kg. m/s Problem 5 (5 pts) What is the magnitude o the -component o this tennis ball ater 1 second? (gravitational orce on the ball is downwards in -z direction) A).1 kg. m/s B) 340 kg. m/s C) 1.5 kg. m/s, since there is no orce component in horizontal direction momentum component in this direction cannot changing (momentum principle) D) 3900 kg. m/s E).1

5 Problem 6 (5 pts) An electron was accelerated to rom a speed c, to c in 1 second (c m/s is the speed o light). What was the average orce applied to an electron during that second? Assume unidirectional motion. Mass o an electron is kg. A) N B) N C) N D) N E) N kg p i γmv kg m / s c 1 c 0 0 F p / t F kg m / s kg m / s 0 p kg m / s 0 ( )/1s N Problem 7 (5 pts) I an object moves at constant speed, ou can irreutabl conclude that: A) The object ma be interacting with other objects in the universe, but the net interaction is zero B) The object does not interact with anthing in the universe C) The net interaction with other objects in universe ma be not zero, but it is constant in time D) The object does not obe laws o phsics E) There is no gravit acting on that object

6 Problems 8-10 An object o mass kg moves at a constant speed 0.5 m/s along a path as shown. B v A Problem 8 (5 pts) What is the magnitude o the momentum change A to point B? A) 0 kg. m/s B) 1 kg. m/s C) 0.5 kg. m/s D) kg. m/s E) 1.41 kg. m/s Problem 9 (5 pts) Which vector best represents the direction o p when the object travels rom point p as the object travels rom point A to B? F G H A B p i E D C p Problem 10 (5 pts) What is the vector representing the direction o the average net orce applied to the object while it traveled rom A to B? F E G H D A C B - momentum principle - the orce is in the same direction as the change in momentum

7 Problems A 70 kg hocke laer sliding reel on his knees (no riction) on horizontal ic surace with velocit <-10,0,0> m/s. He then catches a 160g puck ling at speed <40,0,> m/s (z-ais is vertical) Problem 11 (5 pts) What is the momentum o the plaer beore he catches the puck? A) <-700,0,0> kg. m/s p mv 70kg 10,0,0 m / s B) <10,1400,140> kg. m/s C) <9,311,0> kg. m/s D) <43,4,0> kg. m/s E) <4.3,0.04,0> kg. m/s Problem 1 (5 pts) What is the velocit o the plaer ater he catches the puck? Note that the gu still slides along horizontal surace o the ice. A) <9.9, 0.046, > m/s B) <-9.9, 0.046, 0> m/s C) <-640, 3., 0.3> m/s D) <-9.58, 0.003, 0.001> m/s E) <-9.58, 0.003, 0> m/s pplaer + ppuck ptotal const ptotal, i 70kg 10,0,0 m / s kg 40,0, m / s 693.6,3.,0.3 kg m / s p (70kg kg) v, v, v p 693.6,3.,0.3 kg m / s v v v total, p p total, total, ( 700) / m / m total total z total, i ( 693.6kg m / s) /( 70kg kg) 9.89 ( 3.kg m / s) /( 70kg kg) 0.046m / s 70kg 10,0,0 m / s kg 40,0, m / s m / s ( 70kg kg) v, v, v ) (z-component must be still zero since the plaer cannot leave ice this component is not conserved in the sstem plaer-puck due to interaction with the Earth) Problem 13 (5 pts) What is the change in the momentum o the gu? A) <60, 5, 1> kg. m/s B) <600, 0, 0> kg. m/s C) <0.06, 1, 0> kg. m/s D) <7.7, 3.,0> kg. m/s E) <-50, 0, 0> kg. m/s Problem 14 (5 pts) What is the change in the momentum o the puck? A) <60, 5, 1> kg. m/s B) <600, 0, 0> kg. m/s C) <0.06, 1, 0> kg. m/s D) <-7.7, -3., -0.3> kg. m/s E) <-50, 0, 0> kg. m/s z

8 PHYS 17 - Spring 010 Hand-Graded part o Practice Eam 1: Name (Print): Signature: PUID: Mark our recitation time with an X :30 10:30 11:30 1:30 1:30 :30 3:30 4:30 Tu W Th F When ou use a undamental principle ou must eplain clearl what phsical sstem ou are appling it to and which objects in the sstem s surroundings are interacting signiicantl with it. Problem 1 (0 points) You see our 10 kg bag sitting at rest on the loor at the airport baggage claim, and ou rush over to grab it. You jerk the bag o the ground b pulling on it with a constant orce o 130 N, at an angle o 70 above horizontal, or 0.1 seconds. The orce o our pull is in the - plane (where the -ais is parallel with the ground, and the -ais points straight up in the air). We want to know the velocit o the bag at the end o this 0.1 second period o tugging, and also the total distance through which the bag moved Deine the sstem ou re using in this problem. Sstem bag. You can chose a dierent sstem but ou will have to stick to that sstem in the ollowing questions. 1.. List the eternal objects that interact signiicantl with the sstem. Make a careull labeled diagram showing their interaction with the sstem. List an object that doesn t interact signiicantl with the sstem. Signiicant interaction: Earth, person Insigniicant: Sun, Jupiter etc. See diagram on the net page. Note: the diagram depends on the choice o the sstem. I ou chose dierent sstem ou should stick to it and use it in the diagram

9 F person z bag θ70 F Earth 1.3. Use the momentum principle to ind the velocit o the bag at the end o the 0.1 second period o time. Show all steps, include units, and circle the inal answer. (Note: You re not being asked or the speed o the bo.) Momentum principle: p Fnet t, or p pi Fnet t Force: Fnet Fperson + FEarth FEarth 0, mg,0 0, 98,0 N Fperson Fperson cos θ, Fperson sin θ, ,1, 0 N Fnet Fperson + FEarth Fper son cos θ, Fperson sin θ mg,0 N From the momentum principle ind the momentum ater 0.1s: p pi Fnet t p 0 F cos θ, F sin θ mg,0 t per son person m p 4.45,.4, 0 kg s Knowing momentum we can ind the velocit: p γ mv mv (use nonrelativistic approimation, v << c) And the answer is: v p m 0.45, 0.4, 0 m s

10 1.4. Through what total distance did the bag move during the 0.1 second period o time? Show all steps, include units, and circle the inal answer. Start rom the position update (which is another orm o deinition o average velocit): r v t ave Under constant orce, the average velocit is: 1 vave ( v ) 0., 0.1, 0 + vi m s Where initial velocit was 0. Thereore: r v t 0.0, 0.01, 0 m ave And the distance is: d r r m ( ) ( )

11 Problem (10 points) As ou are walking down a hallwa in the Phsics building ou overhear two students discussing a Phs 17 problem in which two boes are being moved across a loading dock. The smaller o the two boes is on top o the larger one. As a worker pushes on the larger bo, both boes move together with increasing speed across the level, polished concrete loor. One student sas The worker must be eerting a orce on the top bo, otherwise its motion would not be changing and it would be let behind as the bottom bo moves. The other student responds No, the worker isn t eerting an signiicant orce on the top bo because he isn t in contact with it. The motion o the top bo does change though, so, it must be interacting signiicantl with some other object in its surroundings. Starting rom undamental principles, how do ou eplain the changing motion o the top bo in this situation? What objects in its surroundings is the top bo interacting signiicantl with? The second student is correct. The worker is not interacting signiicantl with the top bo because he is not in contact with it. The top bo is interacting signiicantl with the Earth and with the bottom bo*. It is interacting gravitationall with the Earth and it is interacting with the bottom bo b contact. The vertical components o the orces eerted on the top bo b the Earth and b the bottom bo are equal in magnitude but opposite in sign so the cancel. Appling the momentum principle to the sstem consisting o the top bo alone, we see that this eplains wh the vertical component o the momentum o the top bo remains zero. There is a horizontal component o static-riction orce eerted on the top bo b the bottom one. This is the net orce on the sstem consisting o the top bo alone and, so, appling the momentum principle to that sstem eplains wh the horizontal component o the momentum o the top bo increases. * Note: The top bo is also in contact with the air (atmosphere). Because the net (buoant) orce eerted on the bo b the air in negligible in this case, we did not mention it.

12 v avg r r ri t t t p γ mv p F t net Equation list or eam I, PHYS 17, spring 010 i r dr v lim t 0 t dt γ 1 v 1 c p p + F t i net dp d p dpˆ dp v pˆ + p p F dt dt dt dt R r r + v t t ( ) i avg i vi + v r ri + t ti v p / m dp dt F net p 1+ mc ( ) p + p 0 sstem surrounding dp dp F dt dt F k s spring S FT A L Y L ks A Y L kint eratomic Yd m m F G rˆ 1 1 grav on b1 1 elec on b1 1 r 4πε 1 0 r 1 F 1 q q rˆ p h k m ( ) ( t) Acos( ωt ) t k m s ω π T ω 1 T Constants: 11 N m 1 9 N m G kg 4πε 0 C h kg. m /s c m/s g 9.8 N/kg N A mol -1 Geometr: π 3.14 Circle: circumerence πr, area πr Sphere: area 4πr, volume (4/3)πr 3