Motion in two dimensions tutorial homework

N'lO'flON lN l.\4/O DIMLINSIOI{S Name Mech HW-- l 9

ll. Arr oll.icct rlr.ve:s clockrvise rvillt dccrctt.titt.g .t:ytt,e,r/ ar'rncl poilrts (i irnd l/ iu'r: shorvn bcloiv.

'loSt t'it'tr

an oval trac:k. 'l'he velocity vector.s at

Lt(;, rtH, allcl Ait

[)irection ol'cr

ii, ancl ri, (placed "tail-10-tai l")

b.

('ollf ihe: vectols il,; and i),, in the spacc at r.ight. and rlertcr-nlinel tltc chiutge in vclocity, veclor.. A;i

ll'Point l/ tvcre t'lttlseti to lie closcr til ptlint (r', {cscr.ibc ltxv Ail rvotrld cltaltqc.

[)csct'ibc ltOrv yott rvottliJ clcte rnrine: rhc accerlr:nrtion at poilrt C (lioth rnngniturlc ancl ctire.ction). In thc spacc ut risht. irirlicatc tltc direction of'f hc: acccle rution of'thc o[rjcct at proint (;. (\..otrr tlrawing neccl rirrly br: cplirlitativcly corrcct, )

tt. ('opv fi,, arrd,{, lplacccl "'titil-to-tiiir"') irr thc spai:c at right. f s the anglcr bctrvcen the'ac:celcration;urd thcr vcloci ry, trcutt,r tlttttt, lat.s tltrut, or etlttttllo g0o,l

c. (it:rteralizc ytlur results atrove ancl l'ronr ttrlorial to ansrver the lirl Irlrv i n g 11 ucsti r'rn :

lrrt'ttn tltl.iect,llloving alottg it curt'crcl tra.jccttl'y. horo,'clues the: angle between the accelerati'' ;tttcl thc'vcltlcitv conlparc to 90o il'thc olr.jecl nlovcs rvith (i)constant speed. (ii) ilcreasing spcecl, and (iii) dccl.casing spccrl,/

Mech Motion in two dimensiotts HW-20

2. Each diagram below shows the velocity and acceleration

Instant I hstant2

Acceleration

for an object at a certain instant in time.

Instant J lnstant 4

_->

Velocity

For each instant, state whether the object is .s:peecling nrctvirtg v,itlt cortsturtt .speed). Base your answers on problem l.

tt1t, slowinp down, or neitlter (e.g., what you have done in tutorial and

b. The diagram at right illustrates how the acceleration at as having two components: one parallel to the velocity perpendicular to the velocity (i,1.

instant I can be treated (Z ) and one

For each of the other instants, dralv a diagram

i

sirnilar to the one given for instant /. Label the parallel and perpendicular components of the acceleration relative to the velocity. If either component is zero. state so explicitly.

lnstant 2 Instant J Instant 4

c. For each of the instants l-4, contpare your descriptions of the motion in part a rvith the components of the acceleration in part b. Then answer the follolving:

i' Give a general rule that describes how the component of the acceleration pctrrtllel to the velocity affects the motion of an obiect.

ii. Give a general rule that describes how the component of the acceleration perpetrclic'ulor to the velocity affects the motion of an object.

Motion in two dimensiotts Name

3. An object moves clocklvise along the trajectory belorv (top vielv shown). The acceleration varies. but is ulw,ovs directed toward point K.

a. On the diagram belolv, indicate the direction of the acceleration at each of the points A-G.

Tbp viev,

For each of the points A-G, state whether the objectis speeding up, slowittg clown, or neither.

On thddiagram belorv, dralv a velocity vector for each of the points A-G. The relative nragnitudes of these vectors should be qualitatively correct.

Top viev,

Suppose that an object lvere to move at constant speed around an s-shaped curve as shown at right. The S-shaped curve is made of two half circles and a straight segrnent.

At each of the indicated points on the diagram. draw a vector to lepresent the acceleration of the ob.ject. If the magnitude of the acceleration is zero at any of these points. indicate so explicitly.

Tbp view

Ac t' e I e rat i o n v e c' tors .fbr c'ottstctttl speecl

Mech HW-21

b.

4.

Mcch Nlotion itt trtto dimensiotrs HW -22

5 A pr:nclulunr lrotr srvings lrack ancl lorth. At thc instant shrlwrt. thc bob is itt orrc ol'the luntarclttncl points. point A. '['he othc:r'turnarouncl point. ptlint IJ. iincl thc btlb's tra.iector,v (dashed) are shown.

a" (-hooser a pt'rint slightly al'ter point A, and lirbel it point ( . l)ralv a vector'lcl reprcscnt the velocity ol.the bob at point C'.

lr. Deterrnine: the c:hangc in vcrlocity vcctor Aii benvecn points A ancl C'.

c. Flolv rvoulcl yriu c:haruclc'rize thc dircction o{'Aii as pclirtt (- moves closer attcl closer tcr poirtt A;'

d. F:.irch trl'thl lollorving stutements is irtt'rtrrt,r't. Discuss thc flillvs in the'reasoning.

i. "The occelerotion of point A is zero. As point C becomes cioser ond closer to point A,the chonge rn velocity vector becomes smoller ond smcller. Eventuoily, it becomes zera."

ii. "At point A, the occelerotion mokes on angle with the tongent to the trolectory thot is greater thon 0o but less thon 90'since the ob3ect rs moving on o curve ond speeding up."

On thc cliagranr at right. drarv arrows ut points A ancl /l to irtclic:atc the dircction ol-tht: ircce f clatiorr irt those ltclints. (l'littt: Your Answcr shrlrrld br: consistcnt rvith vour ansrve r to parts c and cl. ) [:xpluin.