Problem1
The earthrotatesonceper day aboutan axis passingthroughthenorth and southpoles,an axis
that is perpendicularto the planeof the equalor.A.ssumingthe earthis a spherewith a radiusof
6.38 x 10' m, determinethe speedandcenhipetalacceleralionofa personsituatedat the equator.
f = 6.3gx lDbrn
7=
V
td"y -- tt",\oos
-- ).'rrc = Ar (to.n^ looq)
86,Hoos
T
a.
Q=
1= Uer!:t
(o.ax"tout)
lnl nfe
a : 3.3?xlD1/s\
Problem2
pump.
Eachofthe spaceshuttle'smainenginesis fed liquid hydrogenby a high-pressure
point
of
the
blades
traces
out a
on one
Turbinebladesinsidethe pump rotateat 617rcv/s.A
circle with a radiusof0.020 m asthe bladerotales.(a) What is the magnitudeof the centripetal
accelerationthat the blademust sustainat the point? (b) Expressthis accelerationasa multiple of
s : 9.80r/s2.
=)),b)du-ltu*^-$rfuA
-T = ,/aq^"-1,
:
.x9' dl-o,",iJ)a q,r,'^\ b+ "-
ot 6t'/,-/5,
|.t AnlD-'s
':---
q= v7r
^
L\=
| ].-ot,/-\
L
v = AtTt
*
,' t,/
I
?n*n
T*
4 r, (0.03'o'",)l
( l.uan lo 3s)a
q = l " o r J O sr v l / 5 \
Problem3
A 2100kg demolitionball swmgsat the end of a i 5 m cable on the arc of a vertical.circle. At the
lowestpoint of the swing,the ball is movins at 7.6 m/s. Determine the tension in the cable.
T
4
l5 r"r
I t"
tFt=^v%
iI
t
\,bnlS
I F,=rnqy o,=v\r
|ag
T-
ut/" --+ T= rng+nva/,
mg = r,.,
-l- = ,"' ( q-,
"%)
-l-=(rroore)r.so"7r'*
(r;?id- -]
f
= a,grfDqN
Problem 4
A child is twirling a 0.0120kg ball on a stringin a horizontalcirclewhoseradiusis 0.100m. The
ball travelsoncearoundthe circle in 0.500s. (a) Determinethe centripetalforce acting on the
ball. (b) Ifthe speedof the ball is doubled,doesthe centripetalforce double?If not, by u,trat
factor doesthe centrioetalforce increase?
\/' - - -=
Xtr=r-oq= ^u7,
ro= o.ole'orS
r = o ' l D ot ' r
(1
a!
rn
t-
f
(") ! F-
I
--T-
a.
l-1 r- f
r.r(2.irr/r)'=
a_rF=
7-= o "5oos
/'TT
t
\
1 i ( o"rDor.) ( D"Drror?)
F= D"l3gN
( D . 5 o o F r) a
( b) 2;'*
(-'l .-
/ <-r r-
At=frN'/,
/l
, ,,r\
t2-, l-^u )t
Problem 5
A block is hungby a string from the insideroofofa van. Whenthe van goesstraightaheadat a
speedof 28 m/s, the block hangsvertically down. But whenthe van maintainsthis samespeed
aroundan unbakedcurve (radius= 150m), the block swingstowardthe outsideof the curve.
Thenthe stringmakesan angle0 with the vertical. Find e.
l a)e
_i
x +) -l .,.r,"U
Jz^rdA\r".b
-J
Oo{*or\ytv
L
rrrg
X F, --D4* Q" =v7r
X trr =rnv%.
Fr: tQa, = O
'T
vatO-.3
T=9
@o
t -uJ,wn9
=0
-/
-rt
_.2
^"/t- t'
'/
(y
-tao/ ) a,*g = ^y,
r,gbto=n\7r-
,Dtg"* qr
-t
n )l
0 =tro;'('2,) =F^' I (7.t(xr4.
r/s')
s') (too*) l
O= 43"
Problem6
A motorcyclgis haveling up one sideofa hill anddown the other side.The crestis a circular arc
with a radiusof 45.0 m. Determinethe maximum speedthat the cycle canhavewhile moving
over the crest without losing contact-
FN
Jt
q=vt/r
c>l/W down aa J
fng(?
= iley
tr l-..7
r.rt - Fn = n'o%
r-
du
Problem7 )
f-x -
tr\|-nvr
X rtArtr frr, $fr.rDdofu
&t
t4"'! ".,*^LuU
Ct
y = At,omf
A curve ofradius 120 m is banked at an angle of 180.At what speedcan it be negotiated under
icy conditionswherefriction is negligible?
,a-e-o
$t"yu
n
S'tl
\
rn3
F)4.
(l
fAt',t-
F^ orD = rn?
,N
X q = ,tro^ o,^=YYc
o
(--
D
tI
e_J
I
T
xFr=t\ Ry
v
Fn*re
Vt-
n .tr, )
l--
a)'/,
-,.
( :g
ttag/
mq
_---a-
r,aa6
r.glanO
iv =r"" fiAl
tI tt
,
),a,uoo = rl\v7
/l
.b
l-N,i"rO=E9
I