L 91171 lllllllllllllllllll _j,.,, NZ~ SUPERVISOR'S NEW ZEALAND QUALIFICATIONS AUTHORITY MANA TOHU MATAURANGA 0 AOTEAROA Level 2 Physics, 2013 91171 Demonstrate understanding of mechanics 2.00 pm Wednesday 13 November 2013 Credits: Six Achievement Achievement with Merit Achievement with Excellence Demonstrate understanding of Demonstrate in-depth understanding of Demonstrate comprehensive mechanics. mechanics. understanding of mechanics. Check that the National Student Number (NSN) on your admission slip is the same as the number at the top of this page. You should attempt ALL the questions in this booklet. Make sure that you have Resource Sheet L2-PHYSR. In your answers use clear numerical working, words and/or diagrams as required. Numerical answers should be given with an appropriate Sl unit. If you need more space for any answer, use the page(s) provided at the back of this booklet and clearly number the question. Check that this booklet has pages 2-8 in the correct order and that none of these pages is blank. YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE EXAMINATION. High Excellence TOTAL 24 New Zealand Qualifications Authority, 2013. All rights reserved. No part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualifications Authority.
2 You are advised to spend 60 minutes answering the questions in this booklet. USE ONlY QUESTION ONE: MOTION Jason spends a day at an amusement park. He stands on a merry-go-round, which turns at a constant speed. The diagram below shows Jason standing on the merry-go-round, which is going around in a clockwise direction. (a) On the diagram above, draw an arrow on Jason to show the direction of his velocity at that point. (b) The radius of the merry-go-round is 4.0 m. The merry-go-round takes 15 s to do a complete circle. Jason has a mass of 65 kg. Calculate the centripetal force needed to keep Jason moving in a circle.?( I v: / t, v ~ ~- ~ir~ : Of;:~;- 1/= J 6 7 t; ~ -( '. """~ - - y; _..0 h\... -::- 4- :;-, 6 /ct 5,-... -. :: ~- ~?!~ (zs/} Physics 91171, 2013
3 (c) Jason then goes for a ride on a go-kart. Towards the end of the ride, he decelerates at 2.5 m s- 2 and comes to a stop in 4.2 seconds. By calculating Jason's initial velocity, determine the distance he travels while coming to a stop. rf :::_ v, _ r g {.?.-- l/,._--t ~ z_ ::::~ ~ - ~ ><...4.. -z ~- ~-~vr _ /Q;.,SY.,r{' f () X~ ' t _Z,..... ~.. d:::: z 7 J!? J /'VI c/. ~ --.::: ~ ~-. ~ z_ 2 ~_,.., ( 2-s/) (d) Jason sits on a slide, as shown in the diagram on the right. He is sliding down at constant speed. (i) State the size of the net force on Jason. (ii) On the diagram on the right, draw the remaining forces (as labelled vectors) acting on Jason. Fg has been drawn for you. (iii) Complete and label the vector addition diagram of the forces acting on Jason. (He continues to slide at constant speed.)!vel 4 Yt-c /K-.s(,./~1- ~c.-c ~ 0/V Physics 91171, 2013
4 QUESTION TWO: FORCES AND MOTION The diagram below represents a see-saw on a pivot at its centre with Jane and her dad sitting on opposite sides such that the see-saw is in equilibrium. The mass ofthe see-saw itself is 60 kg. (a) On the diagram below, draw labelled vectors to show all the forces acting on the see-saw. 3.0m <1 " ""'...!> (b) Jane and her dad move to opposite ends of the see-saw. The diagram below shows what happens when Jane sits at one end of the see-saw while her dad sits at the other end. Jane's mass Jane's dad's mass mass of see-saw length of see-saw = 30 kg = 72kg 60kg 3.0m Calculate the size of the support force from the ground at the end where Jane's dad sits. Round your answer to the correct number of significant figures. tt/w = -. Cu<:.-~ 7 lk.ry :<. 1- g' r-r ~ x /. ) ~ f S'Pfl'./~u :\ /.);,., -=: 10.5 5. ~!Vi"" f.5vp~vf f~.-u.xl rr-- ~ 5'?/flr'J- hr~,'\ j, ~ :::: -6 / '7. 4- JV f""...?vffk(} /tr-_a - -~/ l6 /V_ ~I 0/V ~j11f-0-pi5. (z..sf) Physics 91171, 2013
5 Hillary attempts to throw a basketball into a hoop. (c) Explain the effect ofthe force(s) acting on the ball, once it has left Hilary's hand until it reaches maximum height. You may ignore the effects of air resistance.. ~... k~((f. {;f."cl'~:n~/ VC:(.{:~:- /!y... 0-,_//. r.vt?/... C::.ht!'::y: < _ft-..1- ~ /I/ ; 'h ~~ A~.. ftz-::1/r.f-'~q:c-:0... J.-e-!~?..I.IJ... _ 0(._(::... I _.k tf:'<... 'J t~~b ~t l velc.'{. 1-h.. r.-~.11.. ))'!;~ rt/f.d.~..f.~':!:~:~-:-t.'~~-'. ~{f--v-;, J'::?I-Y?f(;. c/-? 'l ~~: ~4 J '. tp/- ~..,#~7~1 h 7 -.. /1-v ~ -- - " I...;d~.- - /lp / } "I I-'V:II/ V.)'O'!.t vvr.4?;-/,{ 1./ (d) On another occasion, Hillary stands 3.0 metres from the hoop. She throws a ball with an initial velocity of 6.5 m s- 1 at an angle of 60 to the horizontal. The hoop is 1.35 m above the bottom of the ball when it is thrown initially. Carry out calculations to determine whether or not the ball will go through the hoop. Begin your answer by calculating the horizontal and vertical components of the initial velocity ofthe ball. Vr ~'7 {P~( b{): vl'/'6' fi.v. J 1... fl................_............. _6. r)\ ~s 6~ -=))1...... VII ::- ).. 6. ~-.X)Jh 60 ;.- V.................... \/....? ~M_.f~ 1 Vv. :::?~. b 2 q ~6. - I vr:yf,,~.,. I foy Itt h~!l..!?.y:-:. lt.-~ 1 ~. If: -!:?~;// /4 "hj!-i.tl 4..!"'!( t:/lt~... )--t.d'vv-~ /-.:../ '1y k.vn-y ~/W 5-Pff'-J ~ s.(!""ftl ~ryaiy. ~.?~~J.4.. /. 3S~.. dt, -~ ~. VH ~ d v..=- 1/j f T :/z. ~ t-.7-? pp_: >- ~s-r-s->~ t r;iv.=?~ -~.-z._ctxt.~ :~ G-z; /'.- (. J:.,_-! o- t; 2 J ~~ ~ ~.. > f.s.. d.v :: (..? 2 u_ ct ;v~_. _........ t ~ u. _ q_ -.. [/:e... v::-",_ ~ t.;t/..&..'ll.hf....!...-?_.. Itt h--tt. II,j. vvrft.lrj ;,..pf...?.-(~ ::.L...0.~.. (z ~f)_........... ~1/... h./&...... Jr.~ f.. ~.'..3... -~'jlr!rrr1 E~ fp /'v-r~; h /Ct A.!--tp. Physics 91 171, 2013
6 QUESTION THREE: MOMENTUM AND ENERGY Each bumper car has a rubber bumper all round it. (a) The mass of a bumper car is 240 kg. Jason has a mass of 65 kg and is travelling at a speed of 2.4 m s- 1 Calculate the size of the momentum of Jason and his bumper car.. p.-: F'-" v_ (b).. (?. =:.. (~. ft(j ~). _t...&j~~ ) f(_ 2:_../.r"":) :.:.. -....... - ' -= _,;,:. "'~cv">-~-~ -' =7 ;o :::?_ 30 1~-;-~l._ - : (z >fl The bumper cars are designed to minimise injury. Discuss the reasons for the bumper cars having rubber bumpers all round them. Assume cars with and without bumpers have the same mass. Assume change in velocity is the same with and without bumpers.. If..<: --~-1&-. )z~r"'~--rr.. -~--.r:~j.u. ;{.,_...w-_.~ r--"ll::!: 'h~ic... /:4 n?-4. t?l /t~jvv -y. ---... ~.r. (0AI'. (f'::./.p.sf.!?::,tr.c.:)).. 04'0-t.Y.. t?.-y.~ru_. /y?:f:j:~r-4l7j_. t/v:./ ~,!P.r..;f!"A'. ~-~t~.v( et.. ~lrh.. ~ IJ:?.c-vv.,J.c. A ~?<;roy; lh_ u r - v.~,...~~ wr/1 fx-. ~..ft/1;r:.~.. '0-..t./lf:..t/1!'::!. - ~,,/f,t~!jt. P!J',n/,h~ -. ;}k::r"'~ k1,'yv~ 'Vr-1 _.. t,&.,.. /.~:; +!. "D'... ~{!' "- i]. ~ 0---0. Y.J/...r /.":.. "<"'"' _...! -- I!P Physics 91171, 2013
:c) 7 Jason collides head-on with Janet who is in another bumper car. The bumpers don't work properly and after collision both cars lock together. The mass of each bumper car is 240 kg. Jason has a mass of 65 kg and Janet has a mass of 58 kg. They are travelling towards each other in opposite directions, Jason with a speed of2.4 m s- 1 to the right and Janet with a speed of 2. 7 m s- 1 to the left. 2.4 m s- 1 ----1~ Jason (65 kg) Janet (58 kg) (d) Calculate their combined velocity after collision. Include a direction with your answer.. frrnm.. =:. --~tp.>.)s?. f.t:-~_~ -... - -- -flr~~~-- : _ f1-0:t?.~-~~j : ~ -?:.:.". ~- ~ ---- - -- ~ / "? z i -I I 1/. - /,) /~j_y'-a,s IJ' _(14-/~If},)-- '" -Jir.p lz!~l =:: j2j0pv> -!: j?r~a -- -- - - - - -- _. ~.?.? ~ -~J~~ : f _ ~_ f:(!~ :.b.~ r-..s :~ '--- - -- r..,.:: "'"~v. -- --.... --- -- -= ~ /!?-... 6_~!1(:~->- -/ ~ ~~?AJ -- _ :-: _-~??.-. -~ 1r~-- --~ - - -:.??:.~ 6/or.-~~~ - ~--- k ~ 4.6!- -- --------- -.. --- -- -- - J /, ""'t "' _, 72. 6 j"'ff "'--.J- ' : {2-(,t. v i- b.~-;- '24-v.i-- -;-y-) x V.:=/ v :::. 0. 7-v -~ ~,...} 1. = 0. I 2--,., > { 2->r) ;-r; 4 The rubber bumper in Jason's bumper car has a spring constant of 78 000 N m- 1 On one occasion he collides with the wall, causing a compression of 15 em. (i) Calculate the elastic potential energy stored in the rubber bumper. E ~~A _,?&.... fof'. ~......... ~ _!Jz_ x_ 7 ~oovjvy'-1-, "'_f!!i ~t [;~0 ; _0.-/~""'} ::: ~ 7 7..;-.J = / Er :.- 8' StJ (z.sl) (ii) Determine the impulse if the collision lasted for 0.80 s. Include a unit with your answer. p f. :. f. fj _t 6p.. =- (7 ~q_vr;;;;v..., -' ~{): 1~-rv)_Q_. r-.?..?.. 9 r ~ 1 ~?.!:. ~AJ~,- ~...!Jr -= t/? uo h;:r "'" -, (-;..s.?j Physics 9117 1, 2013
8 QUESTION NUMBER Extra paper i ~ required. Write the question rmmber(s) if applicab!e. A SSESSOR'S Physics 91171,2013