Answer Key 313xd

Concepts of Motion 1.1 Motion Diagrams 1.2 The Particle Model Exercises

l-5:

Draw a motion diagram for each motion described below.

. Use the particle model to represent the object as a particle. . Six to eight dots are appropriate for most motion diagrams. . Number the positions in order, as shown in Figure 1.4 in the text. . Be neat and accurate!

1. A car accelerates forward from

Slorts

a

a

olI o

a

a a

a stop sign.

lt eventually reaches

a

elevator starts from rest at the 1O0th'floor cif the Empire State Building and descends, with no stops, until coming to rest on the ground floor. (Draw this one vertically since the motion is vertical.)

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s*cr,.l

of45 mph.

a

5/

\ 3 \\---a'--'-

3

elyltpoii^S +

2. An

a steady speed

L

y

rpd

o.

Stcrts

lr

!c

J. tl .

5. 3. A skier startsJiom rest atthetop of a 30o snow-covered o

E= t! o

slope and steadily speeds bottom. (Orient your diagram as seen from the side.Label the 30' angle.)

foartffsOtes

to the

5taets

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Concepts of Motion

The space shuttle orbits the earth in a circular orbit, completing one revolution in 90 minutes.

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Bob throws a ball at an upward 45o angle from a third-story balcony. The ball lands on the ground below.

a

dd '1

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ho'i.o",1

ol spocing

5

tD. Exercises 6-9: For each motion diagram, write a short description of the motion of an object that will match the diagram, Your descriptions should name specific objects and be phrased similarly to the descriptions of Exercises I to 5. Note the axis labels on Exercises 8 and 9. 6.

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Stops O al -l .t5

8.

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i

ir Horizontill

: A cqr b"qle5 |o o stoo froa specJ of { o rt/x. .'

5all1 ln r^r.ches q rlciec b.lloo". fro- hcr Sccornd - floor winAow ln or. ot+ql;; |o hi+

(An" linoa,r -o{ior. of on slo,^,in5 lo,^.n 1o e slop.)

Cr, - bot frieind " ' (pro5ccti\c- wrotion)

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7.

oo

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Srans

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t! a

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wolks ste.o,dil., alonq o -qn pq+! +hd *rar.s t.o- ,if"tt^

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cHAPTER

I 1-3

1.3 Position and Time 10. The figure below shows the location of an object at three successive instants of time.

Blqtk

-

" '

RcJ $1.^c or

lr..' : .'

Gcce,n

.

J\

fr

a. Use a red pencil to draw and label on the figure the three position vectors V6,V1, and

0,

l,

and2.

f

at times

b. Use a blue or green pencil to draw a possible trajectory from 0 to I to 2. c. Use a black pencil to draw the displacement vector A/ from the initial to the final position. I I . In Exercise I 0, is the object's displacement equal to the distance the object travels? Explain.

No,the Aisplo.e*er,,+ is fhe bl"tk o'rrow ' a? ' The

dis*o''ce trqv..led

is

the.

, su,rn. of +hg lcr.,gths of lhc b\.^c or 5r"E", q,rro\^t!. 12. Redraw your motion diagrams from Exercises I displacement vectors Ar- on each diagram.

ot a ai

a? a;

to4in

the space be low. Then add and label the a

3

a;

a;

A

Ar

b

O.ill .rI 6..1,

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n

-'i Arl Ys

ail *,r .'l Arl

c !

-

c a

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o

,

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o:*u a;*

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Concepts of

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1.4 Velocity 13. The figure below shows the positions of a moving object in three successive frames of film. Draw and label the velocity vector ile for the motion from 0 to 1 and the vector i1 for the motion from I to 2.

Exercises 14-20: Draw a motion diagram for each motion described below. . Use the particle model. . Show and label thevelocity vectors. 1

4. A rocket-powered car on a test track accelerates from rest to

a high speed, then coasts at constant speed after running out of fuel. Draw a dashed line across your diagram to indicate the point at which the car runs out offuel.

iO t

I

3

tlr

ib=/-=-)l...-+l--+'--t' vi q ivor,

j

5

i e

tt"i*'Jit

15. Galileo drops a ball from the Leaning Tower of Pisa. Consider the ball's motion from the moment it leaves his hand until a microsecond before it hits the ground. Your diagram should be vertical.

1

b

a

A

Vj

G

-+

j'*:? vt ..r

vrl

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t6. An elevalor starts from rest at the ground floor. It accelerates upward for a short time, then tou., *irh constant speed, and finally brakes to a halt at tie tenth floor. Draw dashed lines across your diagram to indicate where the acceleration stops and where the braking begins. You'll need l0 or 12 poinrs indicate the motion

clearly.

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cHAPTER

I 1-5

t, t f ;l I'' q } { tt tI L T; ji - - -ltT - - ItoTt"g Dtsrvrs lys "

6lA

sllc

trI r*

- - ii'

accrlc"ation slops

lvs 3',i-lva ?t r, 17. A bowling ball being retumed from the pin area to the bowle, ,ru*rloii rolling at a constant speed. It then goes up a ramp and exits onto a level section at very low speed. You'll need 10 or 12 points to indicate the motion clearly.

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A track star runs once around a running track at constant speed. The track has straight sides and semicircular ends. Use a bird's-eye view looking down on the track. Use about 20 points for your motion diagram.

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19. A car is parked on a hill. The brakes fail, and the car rolls down the hill with an ever-increasing speed. At the bottom of the hill it runs into a thick hedge and gently comes to a halt. 1

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a

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v.,

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20. Andy is standing on the street. Bob is standing on the second-floor balcony of their apartment, about 30 feet back from the street. Andy throws a baseball to Bob. Consider the ball's motion from the moment it leaves Andy's hand until a microsecond before Bob catches it.

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Concepts of Motion

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cHAPTER

1 'l'7

1.5 Linear Acceleration you will "color code" the vectors' Draw Note: Beginning with this section, and for future motion diagrams, velocity vectors black and acceleration vectors red' in three successive frames of film' The obExercises 2l-24:The figures below show an object's position

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Usebrack

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- - - R EJ . Use the steps of Tactics Box 1.3 to find the change in velocity Ai. . Draw and label d next to dot 1 on the motion diagram' Use red' . Determine whether the object is speeding up, slowing down' or moving at a constant speed' write your

-

answer beside the diagram.

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21.

22.

-= -) ahY. aV r) (-i-

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up r

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ConceptsofMotion

2*29: Draw a complete motion diagram for each of the followi4g. IIlotk Draw and label the velocity vectors il. Use black Draw and label the acceleration vectors d. Use red. RcJ

Exercises

' .

25. Galileo drops a ball from the Leaning Tower of Pisa. Consider its motion from the moment it leaves his hand until a microsecond before it hits the ground.

vo

-r vl A

lJ lq

Y

l.r IA I

v-cl. IJ

ta

q

v

26. Trish is driving her car at a steady 30 mph when a small furry creature runs into the road in front of her. She hits the brakes and skids to a stop. Show her motion from 2 seconds before she starts braking

until

she comes to a complete stop.

.t

v&

a=o

A

v.|

t=o

o aQ

+o

vg

vb

v"

+;. qaa 4; c;

27. Aball rolls up a smooth board tilted at a 30o angle. Then it rolls back to its starting position.

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Concepts of Motion

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cHAPTER

I 1-9

rolls at a constant speed' then up a ramp' 28. A bowling ball being retumed from the pin area to the bowler and frnally exits onto a level section at very low speed'

Vg .l

a--o

i=o

t la

q

:

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only 80 m when Cynthia crosses 29. Twosprinters; Cynthia and Diane, start side by side' Diane has run the finish line of the 100 m dash. *

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Concepts of

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cHAPTER

I 1-11

1.6 Motion in One Dimension 1.7 Solving Problems in Physics 30. The four motion diagrams below show an initial point 0 and a final point l. A pictorial representation would define the five symbols i xs, x1,ysa>v1r, €uld a, for horizontal motion and equivalent symbols with y for vertical motion. Determine whether each of these quantities is positive, negative, or zero. Give your answer by writing +, -, or 0 in the table below.

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Stafls

0

0

Stans

A

B

C

D

xo or yo

o

o

+

or

+

o

X1

Vg, Of

X1

+

vgn

o

o

yljr or ylx

; ! q c o O N

o

l.

The three symbols

.tr,

combination is (x,

v'

".

v'

+

o +

and a*have eight possible combinations of sl'gns. For example, one

a, ) = (+,

-,

+).

List all eight combinations of signs for x, vx, ex.

r. 2. 3. 4

*++ +++-+ -++

o

+

qx or ay

3

llas initial velocitv

5. t-6. - +7. --+

1-12

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I . ConceptsofMotion

b. For each of the eight combinations of signs you identified in part a:

. . .

Draw a four-dot motion diagram of an object that has these signs for x,v*and ar. Draw the diagram above the axis whose number corresponds to part a. Use black and red for your i and a. vectors. Be sure to label the vectors.

ai

rf

-,

tn#

t.

8lc"k Rr.d

X

vx or +

+

+

,)

6q <;r

(-

2.

+

da -, -t

3.

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+

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+

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6.

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7.

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1-1 3

32. Sketch position-versus-time graphs for the following motions. Include a numerical scale on both axes with units that are reasonable for this motion. Some numerical information is given in the problem, but for other quantities make reasonable estimates. Note: A sketched graph simply means hand-drawn, rather than carefully measured and laid out with a ruler. But a sketch should still be neat and as accurate as is feasible by hand. It also should include labeled axes and, if appropriate, tick-marks and numerical scales along the axes. a. A student walks to the bus stop, waits for the bus, then rides to campus. Assume that all the motion is along a straight street.

xlln)

t(-i") b. A student walks slowly to the bus stop, realizes he forgot his paper that is due, and quickly walks home to get it. x I Y^n)

3oo

400 roo

t (u^in) c. The quarterback drops back 10 yards from the line of scrimmage, then throws a 20 yards to the tight end, who catches it and sprints 20 yards to the goal. Draw your graph for thefootball.Think carefully about what the slopes of the lines should be.

x (1d)

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Concepts of Motion

a very short "story" of what is happening. Be creative! Have characters and situations! Simply saying that'oa car moves 100 meters to the right" doesn't qualify as a story. Your stories should make specific reference to information you obtain from the graphs, such as distances moved or time elapsed.

33. Interpret the following position-versus-time graphs by writing

Aftcc drivina o" ihc i^Lrslo'{c f"r lO -,ir. o.t tdm"h. T sl"pxJ * a

a. Moving car r

lnii

rr.st qnor.

uh"n'I

qol L"Llc o',.{dt

lo l,.i"i ft-*.., slo*J for 3i -oh L., ; ;^;ti+,"" zonc off r sot r;;,:-. F,l""ttr, ;i' to;;u, ;t ;;- crit Zd'-i f.o- i"o.c. -Rftr.r i.""tt"i^" f"i to -,^ f nJized it"o.t T lq.+l *-" wcllc* ql hon'. so .I d,ro're.

roqJ lo',r,",

b^ck. wi*lrout it"ps er consic.^c*ro"' Jr,lo1S, o* r",phl

"S

Vt r'.rdr. a slo* di"r |o IOO- os \^lt

;:: i3 ^'i"Tt-.*':'":l r; i ll""i "+1 "s loo ,^^ lo li slcv, for io*-Js Sro*t

€nany shlps . Oh $o lUc'w b""^ htard. T,,.'q', o{osiva, *ov. }o ascgpe d.oth c\rr,rq{S. wt Ji.r.- }5 5OO- otd trt,lkc- o,.^.: * Ly o.rl l,o ses . S^fc o5ain, vs.- risc lo lhr surfq,cc, c. Two football players

Al {hc t
;-*ji'1.:1,:*\*j-i# Li-, in on'al[rnpt

b"t hissLJ lo |cc[lq q5 Frcd c 'sset +LL Sotd'lint. Brul"^s va,inlv *rits lo cctch *p. b.^t Frcd Sco cr,i. Foolisl^lv Br*}.ls .ottli"'uts qsrf F;LJ \'o.s alr*d'1 lo r.

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scored. G

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34. Can you give an interpretation to this position-versus-time graph?

If

so, then do so.

If not, why not?

is no scrnsi ble i'.tqr grefoli on t".o*s. th. Sraph ".q,4t."s thq oblcct to be 1'. !g 9\occs o*

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cHAPTER

1.8 Units and Significant Figures and show all steps in the conversion' 35. Convert the following to SI ug$$g!4IOf9-1he-!ine

a. e.r2 ps

x lo-t; : 1 I

rts

j..{a r l03

b.3.42kmx lO3rn I kwr

x

c. 44 cmlms

1

a*

t{,'l x lO"

lO3 -s , -T;-

lOI cvn

?

lvri n " J9! x F-,,^ * +=I,Os l.5tlcv"r .- lo-lm ,-- Y" mph * ryt .'# " I cr'n lboos = lin " I t"i

d. 80 km/h

e. 6o

f. 8 in

1". x lrS{cv'r * tOlcm lin

g.14

in2,

a,S{cm

x

\?*"-

h.25ocm3"t?rk

I in

' *3^tu,i) A

=

1.5x lO-{rr,3

picture may help'

use Table 1.5 to assess whether or not the following statements a, Joe is 180 cm talf

l90cvn = 18* lOcv'a t Rea sor.

a

5o *l

?:

"b[e 50*

Z-p;

= lOonnplt

No* Re.qsonob\e,

L O N

o

c, A skier reaches the bgttgm_of the hill goilg 25 m/s

iS ,. tg

t

?.5

Reo so",

'

are

reasonable'

ltx I in = Jl i"' = bf*

b. I rode my bike to campus at a speed of 50 m/s,

I € F.l

+

t?-^* 1.0*lo-3*,e { * ,O-t.. = I I cwr Cvr^

Note: Think carefully about g and h'

11

\-e\.

' 50 *Ph

ot\ e

(Dow^hill rqcers rqqc\" * 95 -ph)

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cHAPTER

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Concepts of Motion

d. I can throw a ball a distance of 2 km.

).km,., l. l

.

,

n.riles

Not Reqson ob\e

e. I can throw a ball at a speed of50 km/h.

sOP. t\' 3o^ph

[,$nro" Leo51e

Reosonqt\e.

' |hcorJ

pi

t.hcr5

-

qT r..l0Onph)

37. Justifytheassertionthatl m/s =2mph by exactly converting I m/sto English units. Bywhat percentage is this rough conversion in error?

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= l.

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= o.ll

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of

38. How many significant figures does each of the following numbers have? a.

6.21

3

o.J., 3

3 ".Jro a.Jro.o 5

e. 0.0621

3

f.

3-

0.620

e.0.62 h.

.62

i.

1.0621 5

r..

e--zr

r.

ilxro3 3

: J,rc' 3

] )

x

ro-3 3

39. Compute the following numbers, applying the significant figure standards adopted for this text. a,

33.3 x 25.4 =

b. 33.3 U.

- 25.4 =

33.3 + 45.1 =

d. 33.3

x 45.1 =

8.t'l b

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1,1 7, 38 " lO-' t,5o_a 103 (leodi'.3 one)

i

e. 2.345x3.321=

f.

G.32x1.23) -5.1 =

- ..^2

E. JJ.J

=

.h. VJJ.J tr;; =

t.l g g

l. x l0-' t,

t01'

(':*e"*

5,r1 103

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