ffi
A 45 kg child on a water slide passespoint A at 8.3m/s.
hu=o*
tl^,A--?\ rrr
VR= 7.3-/s
ffi =-\5 Kc5
Wt=
11ru
I
_{_
As the child descendsfrom A to B, 3600J of heat energyis createdbecauseof friction. What
is his speedat B?
i tqsqtq.aw,.S*(qsr
i@
u)(x.s%a-
3 Poi"t B
Poi"t A
' PEo+ KEA = KFg*
lsr5
Hea\ Energy
r.ngh^** r-r-.t^" = 5*u6f,*
mMto\
\?.l-ls
Hcol EnenSrT
Enerqy:5",vaQ
a *$ r ., r^t
\I J(*Sh
.
-ge c ^\ F ^er,1
y)'_
Jl/
= \3
)-. n Uf*f. with massof 5.00tffutm.hed to a horizontalspringwith springconstantk =4.00
x 102N/m. Thesurfacetheblockrestsuponis frictionless.If the blockis pulledout to x1=
0.05m and released
Find the speedof the block at the equilibrium point
otr
r Lelt
-
FKx'=
f.F
'5 l"
| o.osq
(**l
1:6.u{idl5
=-::o[
\<Ee
v=
\ooN/^ (o.OS^\q
VA
8fftv
-\
v: o.qql-/s
0.0250mVf .1
Findthespeedwhenx=
P E e,;=K E S + p E .
,X*^rt= /'.*,uf*#f xf
i
t
[
Qi.",\
tn ,\' ro \
fK'1ry':\q
\
\
\
rYr
\+ = C,31-/5
-,tO6"1,"(o.c35t'
-- 1.?O',-(o,os)a
t"1
Rene,whose massis 85 kg, skis down the hill, passlngZ with a kinetic energyof 9,700J.
If friction is ignored, to what maximum height, h, can Rene ski?
KE;= PE+
Ke i = ,-,"gh
t1 = ,
l'. t-r
rn3
h-- \l,L^
= h
Q,tooT
_ I
-h
SsrsGSA-e\
A 20 kg block is placed at the top of a l0 m long inclined plane. The block starts from rest
and slides without friction down the length of the incline.
Vi=o-ls
h;:5""
d = lOrn
T
T
5 .0m
a. Determine the gravitational potential energyof the block at the top of the incline.
pE;=mth
PEi--lora(R.tr*lsi(S*)
?E': qt I S
b. Determinethe kinetic energyof the block just asit reachesthe botrom of the incline.
P Ei-KE+
9T t 5: KEt
no frictioo
s
4. A 0.150kg puck on a frictionlesssurfaceis pressedagainstaspringwith a springconstantof
2.00N/m.Thepressurecauses
the springto compress
0.30m. What velocitywill the puck
attainwhenreleased?
fn =o, \ 5 K 3
K = ? x'/rn
PEe,=l KEE
A X = O. 3 rn
/x-x
{jl Lrl
)=
X".r,.*t
|.-*-']
\.\'/s = \{
5. As a 62 kg skierdescends
from A to B her velocityincreasesfrom 8.5m/s to 23.3mls.
FrictionbetweenA andB generates
8,700J of heat energy. Through what vertical height, h,
did the skierdescend? Vp,__g.5_lS
=
PEitKE;
KEe+ t\eal Enertly
rnghi * f rr'tv;t= }*-,vqat \\ec.tEnegy
*gh I a 5*vqa+H*\ EnerX!- 5 r,-vi)
h i = i *uqe+Heo\Enerc5!5*v;J
rnq
I'
r';r=13.31r/s h r
a
= b (r,ag\(as.3*;ff*
r,rooT-\(r,,
hi(b.5)
G, q (q.El-/si
h;= 38.3r^^
6. A 250 kg roller coastercar travelspast points A and B with speedsshown in the diagram
below. What is the work done bv friction?
+-v.
=4-50 url's
PE6+ KEp = \(Eg + Fric-troy1
nnghl+
.R
5*uRt = Er^VBr t Fric\ion
rnqhq + *"t(uot-vJ\=
F.iclio.,
18"0ur
lsorS(r.tn,rl(\t.,\ + i I r sor",1(\, b^- rs\ = Fricticr''
\ 755\ 5=
Fric*ron
*u'g
= 15'0rnis
A 0.10kg ball droppedverticallyfrom a heightof 1.00m abovethe floorbouncesbackto a
energylost by theball asit bouncesis
heightof 0.80m. Themechanical
n-
\rFi =PE* + l -nec ay LoS :
fngh' = n^3\ +Ene gy [-oss
nn3(h,-he\ - EnersY Loss
O , \ q( q,8\n/s{( t*
-O.? *\ = E ncrqiT L o 5 5
C.\qbas = E^e.ov Lo!'s
The diagram below shows a O.l kg apple att?6hedto a branch of a rree 2 m abovea spring on
the ground below.
P Eg,i =P E e$
n"gh i= ! r f , * e o
Apple
f
-?r^gh
xF i -
g = ?(o,t\ccr\(9.8,1n"\(a'
\
W
3m
( = 3qA...tNl,^^
The apple falls and hits the spring, compressingit 0.I m from its rest position. If all of the
gravitational potentiai energyof the apple on the tree is transferred to the spring when it is
compressed,what is the spring constant of this spring?
A I kg rock is droppedfrom a cliff 90 m high. After falling 20 m, the kinetic energyof the
rock is approximately
P E g , i= KE+tFE" rg
nn3h; = \( L€ +-yr^Bhs
Fr.gh, - mqh+
nn3(hi-h+)= KE€
rK3(l,8\mrsi
-- K{1+
lqo:
_roA =
l Y ( ,J
KE+
h; -_?o"..,
ht = lO *
I0. A I kg ball is dropped from the top of a building. Just before striking the ground, the ball's
speedis 12m/s. What was the ball's gravitational potential energyrelative to the ground at
the instant it was dropped?
PE, = KEt
\
'-- Ei
f
\
= 3r.nrl4o
PEi = | (rK")[r]^/s)r
P E , ' = t eT
Ii. A 3.0kg mass-isattachedto a spring having a spring constantf 30 N/m. The massis pulled
0.20 m from the spring's equilibrium position and released.What is the maximum kinetic
energyachievedby the mass-springsystem?
K=3C)"/n^
r n :3p3
AX -- O.Orr.,
T\l-
rEq.; -
\.
c'
\xLp
t K* ' = K E +
rF+
* (eo'A(o,?,-1t:
O.G S=KE+
12.A 0.250-kgblockis placedon a light verticalspring(k =5.00' 103N/m) andpushed
the spring0.100m. After the block is released,
it leavesthe spring
downwards,compressing
andcontinuesto travelupwards.What heightabovethe point of release
will the blockreach
if air resistanceis negligible?
K = 5OON/r'-'
A X= C . l nr
Fr=LC]*
PE",i=PEg
\11
-aKx"-nn3n
rn=O.e5K1
rt .,2
|
,_^ = h
3rttt
5Oo \r/rn (O
\
, tJ
t(o.asror)S.Btgs\
13.An athleteon a trampolineleapsstraightup into the air with aninitial speedof 9.0m/s.Find
(a) the maximumheightreachedby the ath-leterelativeto the trampolineand (b) the speed
of the athletewhensheis halfwayup to hermaximumheight.
h'6 = J,OS.^r.,
\i= 1*ls
G,)
b ) K E(= KE r+? L e
*fl',n = i"r,nr'"dg\+
KE;= PE3,f
t1-n',t'"y'qh9
.\jn-=h+
a3
* ' v , a- 3\ i= : \ + a
-A-')'
J(l,8\*ls\
*,\ * --h4
\ r [r (l'"1r;'-1l\"61.r.r:s
-.-\
t o.7 h/s=\4