pierh%qeoiw%srivizspyxmsr%iziv]%%2345%w3 · 4. a 6.1 kg object on the end of a massless connecting...
TRANSCRIPT
!" %R%SFNIGX%XVEZIPW%EPSRK%E%TEXL%EX%GSRWXERX%WTIIH"%%8LIVI%MW%E%GSRWXERX%RIX%JSVGI%EGXMRK%SR%XLI%SFNIGXXLEX$VIQEMRW$TIVTIRHMGYPEV$XS$XLI$HMVIGXMSR$SJ$XLI$QSXMSR2$$(IWGVMFI$XLI$TEXL$SJ$XLI$SFNIGX2
%" PMRIEV &" GMVGYPEV '" IPPMTXMGEP (" TEVEFSPMG
!" %R%SFNIGX%SJ%QEWW Q MW%SR%E%LSVM^SRXEP%VSXEXMRK%TPEXJSVQ"%%8LI%QEWW%MW%PSGEXIH%%9"!!%Q%%JVSQ%XLI
E\PI%ERH%QEOIW%SRI%VIZSPYXMSR%IZIV]%%2345%W3
E\PI
8LI$JVMGXMSR$JSVGI$RIIHIH$XS$OIIT$XLI$QEWW$JVSQ$WPMHMRK$MW$$45$27$$;LEX$MW$XLI
SFNIGX'W)QEWW#
%" #"$%&OK
&" #"$%OK
'" #"$%OK
(" #"$%OK
!" %R%SFNIGX%QSZIW%EX%E%GSRWXERX%WTIIH%EPSRK%E%GMVGYPEV%TEXL%EW%WLS[R"
! !
!
!
;LMGL%ZIGXSV%FIWX %VITVIWIRXW%XLI%GIRXVMTIXEP%EGGIPIVEXMSR%SJ%XLI%SFNIGX%EX%XLMW%TSMRX#
%" #
&" #
'" #
(" #
!"#"!
!" %$%"%!!$OK$TYGO$MW$EXXEGLIH$XS$E$%"3!%$OK$QEWW 1 F]$E$GSVH$XLEX$TEWWIW$XLVSYKL$E$LSPI$MR$E
JVMGXMSRPIWW+XEFPI.+EW+WLS[R1++8LI+TYGO+XVEZIPW+MR+E+GMVGYPEV+TEXL+SJ+VEHMYW+819:+Q1
1
TYGO
;LEX%MW%XLI%WTIIH%SJ%XLI%TYGO#
%" #"$%&Q(W&" #"$%&Q(W'" #"$%Q'W(" #"$%Q'W
!" %$GLMPH$MW$VMHMRK$SR$E$QIVV]3KS3VSYRH$[LMGL$MW$VSXEXMRK$EX$E$GSRWXERX$VEXI"$$;LMGL$SJ$XLI$JSPPS[MRK
HIWGVMFIW(XLI(GLMPH,W(WTIIH.(ZIPSGMX].(ERH(QEKRMXYHI(SJ(EGGIPIVEXMSR#
74))( :)03'-8= 1%+2-89())3*%'')0)6%8-32
%" GSRWXERX GSRWXERX GSRWXERX
&" GSRWXERX GLERKMRK GSRWXERX
'" GLERKMRK GSRWXERX GLERKMRK
(" GLERKMRK GLERKMRK GLERKMRK
!" %$%&&$2$GLMPH$XVEZIPW$MR$E$GMVGYPEV$TEXL$SR$E"JIVVMW"[LIIP+"";LMGL"JVII"FSH]%HMEKVEQ FIWX WLS[W%XLI
JSVGIW'[LMGL'GSYPH'EGX'SR'XLI'GLMPH'EW'WLI'TEWWIW'XLI'PS[IWX'TSMRX#
%"
*K!!!#$$!2
&"
*K!!!#$$!2
*2!!!#$$!2'"
*K!!!#$$!2
*2!!!#$$!2("
*K!!!#$$!2
*2!!!#$$!2
!"#"!
!" %$GEV$XVEZIPW$EX$E$YRMJSVQ$WTIIH$XLVSYKL$E$PIZIP$GMVGYPEV$GYVZI$MR$XLI$VSEH"$$;LMGL$SJ$XLI$JSPPS[MRK
GSVVIGXP](HIWGVMFIW(XLI(QEKRMXYHI(SJ(XLI(EGGIPIVEXMSR4(ZIPSGMX](ERH(JSVGI(EGXMRK(SR(XLI(GEV#
1%+2-89())3*%'')0)6%8-32
1%+2-89())3*:)03'-8=
1%+2-89())3**36')
%" GSRWXERX GSRWXERX GSRWXERX
&" GSRWXERX GLERKMRK GLERKMRK
'" GSRWXERX GLERKMRK GSRWXERX
(" GLERKMRK GLERKMRK GLERKMRK
!" %$WXYHIRX$TPSXW$E$KVETL$SJ$GIRXVMTIXEP$JSVGI$ *G !!ZIVWYW!XLI!WUYEVI!SJ!ZIPSGMX] Z! !!JSV!ER!SFNIGX
MR#YRMJSVQ#GMVGYPEV#QSXMSR-
Z!
;LEX%MW%XLI%WPSTI%SJ%XLMW%KVETL#
%"Q
V&"V
Q'"! !V
8!("8!
! !V
!" ;LMGL'SJ'XLI'JSPPS[MRK'HMEKVEQW'WLS[W'XLI'MRWXERXERISYW'ZIPSGMX]' Z 'ERH'GIRXVMTIXEP'JSVGI' *
JSV$ER$SFNIGX$MR$YRMJSVQ$GMVGYPEV$QSXMSR0
%"
'"
Z*
Z
*
&"
("
Z
*
Z
*
!"#"!
!"# %R&SFNIGX&XVEZIPW&[MXL&E&GSRWXERX&WTIIH&MR&E&GMVGYPEV&TEXL#&&8LI&RIX&JSVGI&SR&XLI&SFNIGX&MW
%" ^IVS"
&" XS[EVHW*XLI*GIRXVI"
'" E[E]&JVSQ&XLI&GIRXVI"
(" XERKIRX(XS(XLI(SFNIGX.W(TEXL"
!!" %$TL]WMGW$WXYHIRX$W[MRKW$E 3"4 OK TEMP$SJ$[EXIV$MR$E$ZIVXMGEP$GMVGPI$SJ$VEHMYW !"; Q"
Z
;LEX%MW%XLI%QMRMQYQ%WTIIH.%Z.%EX%XLI%XST%SJ%XLI%GMVGPI%MJ%XLI%[EXIV%MW%RSX%XS%WTMPP%JVSQ%XLI%TEMP#
%" #"$ Q W
&" #"$ Q W
'" #"$ Q W
(" #"$ Q W
!"# -R&E&TSTYPEV&EQYWIQIRX&TEVO&VMHI4&E&PEVKI&G]PMRHIV&MW&WIX&MR&VSXEXMSR#&&8LI&JPSSV&XLIR&HVSTW&E[E]
PIEZMRK(XLI(VMHIVW(WYWTIRHIH(EKEMRWX(XLI([EPP(MR(E(ZIVXMGEP(TSWMXMSR(EW(WLS[R3
6SXEXMRK(G]PMRHIV
;LMGL%SJ%XLI%JSPPS[MRK%MW%XLI%GSVVIGX%JVII0FSH]%HMEKVEQ%JSV%XLI%TIVWSR%EX%XLI%TSWMXMSR%WLS[R#
%" &" '" ("
!"#"!
!"#"!
!"# % !#% Q ''PSRK'TIRHYPYQ'VIEGLIW'E'WTIIH'SJ 6#7 Q W!!EX!XLI!FSXXSQ!SJ!MXW!W[MRK/
!"# OK
!"# Q
;LEX%MW%XLI%XIRWMSR%MR%XLI%WXVMRK%EX%XLMW%TSWMXMSR#
%" ##$2
&" #$%2
'" #$%2
(" #$%2
!"# %%%!%&''%OK%%GEV%VSYRHW%E%JPEX%GMVGYPEV%WIGXMSR%SJ%VSEH%EX &' Q W!!EW!WLS[R!MR!XLI!HMEKVEQ/
Z ! !" Q W
8LI$GSIJJMGMIRX$SJ$JVMGXMSR$FIX[IIR$XLI$GEV$XMVIW$ERH$XLI$VSEH$WYVJEGI$MW 23453$$;LEX$QMRMQYQ
JVMGXMSR(JSVGI(MW(VIUYMVIH(JSV(XLI(GEV(XS(JSPPS[(XLMW(GYVZI#
%" #"$ »!"! 2
&" #"$ »!"! 2
'" #"$ »!"! 2
(" #"$ »!"! 2
!"#"!
!"# %%%!#&%OK%%QEWW%SR%XLI%IRH%SJ%E%WXVMRK%MW%VSXEXIH%MR%E%ZIVXMGEP%GMVGPI%SJ%VEHMYW%%9#:;%Q#
!"#$OK
V ! #$%&'Q
-J#XLI#WTIIH#SJ#XLI#QEWW#EX#XLI#XST#SJ#XLI#GMVGPI#MW##123#Q4W5#[LEX#MW#XLI#XIRWMSR#MR#XLI#WXVMRK#EX#XLMW
PSGEXMSR#
%" #"$%2
&" #$%2
'" #$%2
(" #$%2
!"# %%TIVWSR%MW%SR%E%LSVM^SRXEP%VSXEXMRK%TPEXJSVQ%EX%E%HMWXERGI%SJ%%7#8%Q%%JVSQ%MXW%GIRXVI#%%8LMW%TIVWSR
I\TIVMIRGIW)E)GIRXVMTIXEP)EGGIPIVEXMSR)SJ) /01)Q3W! !"";LEX"GIRXVMTIXEP"EGGIPIVEXMSR"MW"I\TIVMIRGIH"F]
ERSXLIV(TIVWSR([LS(MW(EX(E(HMWXERGI(SJ((012(Q((JVSQ(XLI(GIRXVI(SJ(XLI(TPEXJSVQ#
%" #"$%Q'W!
&" #"#$Q&W!
'" #"$ %Q'W!
(" #"$%Q'W!
!"# ,ERW()[LSWI)QEWW)MW))01)OK())VMHIW)SR)E)JIVVMW)[LIIP)MR)E)GMVGYPEV)TEXL)EX)GSRWXERX)WTIIH#));LIR)LI)MW
EX#XLI#XST#SJ#XLI#[LIIP+#XLI#WIEX#I\IVXW#ER#YT[EVH#JSVGI#SJ##345#2##SR#,ERW8
;LEX%MW%XLI%GIRXVMTIXEP%JSVGI%SR%,ERW%EX%XLI%XST%SJ%XLI%[LIIP#
%" #$%2
&" #$%&2
'" #$%&2
(" #$%&2
!"# %R&SFNIGX&MW&EXXEGLIH&XS&E&WXVMRK&XLEX&GER&[MXLWXERH&E&QE\MQYQ&XIRWMSR&JSVGI&SJ 9#: 2#&&8LI
SFNIGX'XVEZIPW'MR'E'GMVGYPEV'TEXL'SJ'VEHMYW' 45 64 Q'[MXL'E'TIVMSH'SJ'95: W5
QV !!"#!Q
;LEX%MW%XLI%QE\MQYQ%QEWW%SJ%XLI%SFNIGX#
%" #"$% OK
&" #"$% OK
'" #"$ OK
(" #"$ OK
!"# %%&'%OK%TMPSX%MR%E%WXYRX%TPERI%TIVJSVQW%E%ZIVXMGEP%PSST%[MXL%E%;<<%Q%VEHMYW#%%8LI%TPERI%VIEGLIW%E
WTIIH%SJ%()* Q W!EX!XLI!FSXXSQ!SJ!XLI!PSST,!!;LEX!MW!XLI!YT[EVH!JSVGI!SR!XLI!TMPSX!EX!XLI
FSXXSQ%SJ%XLI%PSST#
%" #$%&2
&" #$%&&$2
'" #$%&&$2
(" #$%&&$2
!"# 8LI'HMEKVEQ'WLS[W'E'1!'OK'GLMPH'VMHMRK'SR'E'*IVVMW'[LIIP'SJ'VEHMYW'9!'Q'ERH'TIVMSH'9;'W#
;LEX%JSVGI%+RSVQEP%JSVGI/%HSIW%XLI%WIEX%I\IVX%SR%XLI%GLMPH%EX%XLI%XST%ERH%FSXXSQ%SJ%XLI%VMHI#
V"!"$%"Q834 &38831
%" !"#2 !"#2
&" !"#$2 &'#$2
'" !"#$2 !"#$2
(" !"#$2 &'#$2
! "#!
!"# %%%"%!&&%OK%%GEV%MW%XVEZIPPMRK%EX !3 Q W!SR!E!LSVM^SRXEP!WYVJEGI!MR!E!GMVGYPEV!TEXL!SJ!VEHMYW!!23!Q5
;LEX%MW%XLI%RIX%JSVGI%EGXMRK%SR%XLMW%GEV#
%" #$2
&" #"# »"!"! 2
'" #"$ »!"! 2
(" #"$ »!"! 2
!!" %$$%&$OK$$WOEXIFSEVHIV$MW$QSZMRK$HS[R$E$VEQT$[MXL$E$$8"9$Q$$VEHMYW$SJ$GYVZEXYVI"$$%X$XLI$FSXXSQ$SJ
XLMW%VEQT%LI%VIEGLIW%E%WTIIH%SJ% /01 Q W!
V ! !"# Q
Z ! !" # Q W
;LEX%YT[EVH%JSVGI%EGXW%SR%XLI%WOEXIFSEVHIV%EX%XLI%FSXXSQ%SJ%XLI%VEQT#
%" #"$ »!"! 2
&" #"$ »!"! 2
'" #"$ »!"! 2
(" #"#»!"! 2
!"# %%WTEGI%WXEXMSR%LEW%ER%SYXIV%VEHMYW%SJ%%456%Q#%%8LI%WXEXMSR%VSXEXIW%WS%XLEX%XLI%SGGYTERXW%EX%<%EX
XLI$SYXIV$[EPP$I\TIVMIRGI$ER$EGGIPIVEXMSR$SJ 123 Q W! !"";LEX"EGGIPIVEXMSR"[MPP"XLI"SGGYTERXW"EX
="I\TIVMIRGI"EX"XLI""-.."Q""VEHMYW#
Z
%" #"$ Q W!
&" #"$ Q W!
'" #"$ Q W!
(" #$ Q W!
!"#"!
!"#"!
!"# %%FEPP%EXXEGLIH%XS%E%WXVMRK%MW%W[YRK%MR%E%LSVM^SRXEP%GMVGPI#
-
--
---
-:
:MI[%JVSQ%%FSZI
;LMGL%TEXL%[MPP%XLI%FEPP%JSPPS[%EX%XLI%MRWXERX%XLI%WXVMRK%FVIEOW#
%" -
&" --
'" ---
(" -:
!"# %%XIWX%XYFI%VSXEXIW%MR%E%GIRXVMJYKI%[MXL%E%TIVMSH%SJ 7#!8 »!"! " W "##8LI#FSXXSQ#SJ#XLI#XIWX#XYFI
XVEZIPW(MR(E(GMVGYPEV(TEXL(SJ(VEHMYW(23452 Q 3
7MHI%: MI[
!"#$! Q
8ST$:MI[
!"#$!Q
;LEX%MW%XLI%GIRXVMTIXEP%JSVGI%I\IVXIH%SR%E 2344 »!"! " OK#EQSIFE#EX#XLI#FSXXSQ#SJ#XLI#XYFI#
%" #"$% »!"! " 2
&" #"$% »!"! " 2
'" #"$$ »!"! " 2
(" #"$$»!"! 2
!"#$"!
!"# %R&SFNIGX&EXXEGLIH&XS&E&VSXEXMRK&XEFPI&MW&QSZMRK&MR&E&GMVGYPEV&TEXL&[MXL&E&GSRWXERX&WTIIH#
;LMGL%MW%XLI%GSVVIGX%JVII%FSH]%HMEKVEQ%JSV%XLI%SFNIGX#
%" &" '" ("
!"# %%%&'%OK%%WXYHIRX%MW%MR%E%GEV%XVEZIPPMRK%EX% !' Q W!!SR!E!LMPP!SJ!VEHMYW!!--.!Q0!!;LIR!XLI!GEV!MW!EX
XLI$XST$SJ$XLI$LMPP*$[LEX$YT[EVH$JSVGI$HSIW$XLI$WIEX$I\IVX$SR$XLI$WXYHIRX#
%" #$%&2
&" #$%&2
'" #$%&2
(" #$%&2
!"# %%%&!''%OK%%GEV%GER%XVEZIP%[MXLSYX%WPMTTMRK%EX%E%QE\MQYQ%WTIIH%SJ !" Q W!!MR!E!GMVGYPEV!TEXL
SJ#VEHMYW##*+#Q##SR#E#HV]#LSVM^SRXEP#WYVJEGI5##;LIR#MX#VEMRW7#XLI#GSIJJMGMIRX#SJ#JVMGXMSR#MW#VIHYGIH
XS#SRI#LEPJ#MXW#SVMKMREP#ZEPYI0##;LEX#MW#XLI#QE\MQYQ#WTIIH#YRHIV#XLMW#[IX#GSRHMXMSR#
%" #"$ Q W
&" #$ Q W
'" #$ Q W
(" #$ Q W
!"# %%FYW%SJ%[IMKLX *K !MW!QSZMRK!EX!E!GSRWXERX!WTIIH!SZIV!E!LMPP!ERH!HMT!XLEX!LEZI!XLI!WEQI!VEHMYW!SJ
GYVZEXYVI(Z
Z
;LIR%XLI%FYW%MW%TEWWMRK%SZIV%XLI%GVIWX%SJ%XLI%LMPP4%XLI%VSEH%I\IVXW%E%RSVQEP%JSVGI%SR%XLI%FYW%IUYEP%XS
XLVII%UYEVXIVW%SJ%XLI%FYW-W%[IMKLX% !! *K !"";LEX"MW"XLI"RSVQEP"JSVGI"XLI"VSEH"I\IVXW"SR"XLI"FYW"[LIR
XLI$FYW$MW$TEWWMRK$XLVSYKL$XLI$FSXXSQ$SJ$XLI$HMT#
%"!
!*K
&"!
!*K
'"!
!*K
("!
!*K
!"##"!
!"# 8LI'HMEKVEQ'WLS[W'ER'SFNIGX'SJ'QEWW'!#"'OK'XVEZIPPMRK'MR'E'GMVGYPEV'TEXL'SJ'VEHMYW'<#='Q'[LMPI
WYWTIRHIH'F]'E'TMIGI'SJ'WXVMRK'SJ'PIRKXL'456'Q5'';LEX'MW'XLI'GIRXVMTIXEP'JSVGI'SR'XLI'QEWW#
%" #$%2
&" #$%2
'" #$%2
(" #$%2
!"!
!"#$Q
956phpk - 2 - May 1, 1996
1. The diagram shows a toy plane flying in a circle of radius 1.20 m, supported by a string which makesan angle of 28° with the vertical. The tension in the string is 1.80 N.
28°
1.20 m
a) What is the mass of the plane? (3 marks)
F T = 1.80 N
F c
F g
28°
Fg = FT cos 28°
= 1.59 N ← 2 marks
m = 1.599.8
= 0.16 kg ← 1 mark
956phpk - 3 - May 1, 1996
b) How long does the plane take to complete one orbit? (4 marks)
FC = FT sin 28°
= 0.845 N ←2 marks
m4π2rT2 = 0.845
T = 0.16 × 4π2 ×1.200.845
= 3.00 s ←2 marks
966phpk - 4 - September 18, 1996
2. A 35 kg child rides a ferris wheel of radius 12 m. The child moves in a vertical circle at aconstant speed and completes one rotation every 9.0 s.
12 m
a) As the child travels over the top, what is the magnitude of the force that the seat exerts on thechild? (5 marks)
FN
Fg
Fnet = Fg − FN
Fc = Fg − FN ← 2 marks
FN = Fg − Fc
= mg − m4π 2rT 2
= 35( ) 9.8( ) −35( ) 4π 2( ) 12( )
9.0( )2 ← 2 marks
= 343 − 205
FN = 138 N ← 1 mark
b) How does the magnitude of the child’s acceleration at the top of the ride compare to heracceleration at the bottom?
The child’s acceleration at the top is: (circle one) (1 mark)
i) less than at the bottom.ii) greater than at the bottom.iii) the same as at the bottom.
Explain your choice using principles of physics. (3 marks)
Since this child is moving in uniform circular motion her net force must be a constant centripetalforce. The magnitude of the acceleration must therefore be constant.
978phpk - 5 - October 27, 1997
3. A 3.5 kg object is suspended by a string and moves in a horizontal circle of radius 0.60 m. Thetension in the string is 36 N.
string
r = 0.60 m
3.5 kg
18°
a) What is the magnitude of the net force on the object? (3 marks)
FT
Fg
18°FT Fg
Fnet
sin18° = FnetFT
Fnet = FT sin18°
= 36( )sin18°
Fnet = 11 N ← 3 marks
b) What is the period of revolution of the object? (4 marks)
Fnet =m4π2rT 2
← 2 marks
T 2 = m4π2rFnet
← 1 mark
=3.5( ) 4π2( ) 0.60( )
11
T = 2.7 s ← 1 mark
986phk - 6 - July 24, 1998
4. A 6.1 kg object on the end of a massless connecting rod moves in uniform circular motion ina vertical circle with radius 1.2 m . The period of revolution is 0.80 s .
1.2 m
6.1 kg
constant v
connecting rod
a) Draw and label a free body diagram for the object at the bottom of the circular path. (2 marks)
Fg
T
2 marks←
b) Calculate the tension in the connecting rod at this position. (5 marks)
Fnet = ma
T − Fg = m 4π2
T 2r
T − mg = m 4π2
T 2r
← 2 marks
T − 6.1 kg ⋅9.8 m s2 = 6.1 kg ⋅ 4π2 ⋅1.2 m0.80 s( )2
T − 60 N = 452 N
← 2 marks
T = 510 N ← 1 mark
0206phk - 7 - July 23, 2002
5. A space station of radius 90 m is rotating to simulate a gravitational field.
v90 m
a) What is the period of the space station’s rotation so that a 70 kg astronaut will experiencea normal force by the outer wall equal to 60% of his weight on the surface of the earth?
(5 marks)
Fnet = mac
0.60 mg = m 4π2
T 2 R
T 2 = 4π2 90( )0.60 9.8( )
T = 25 s
← 1 mark
⎫
⎬⎪⎪
⎭⎪⎪
← 3 marks
← 1 mark
b) What would be the effect experienced by the astronaut if the space station rotated faster sothat the period of rotation was decreased? Explain your predicted effect. (4 marks)
The period is decreased and therefore the centripetal force increases ( Fc ∝ 1T 2 ). Since the
centripetal force is only provided by the normal force, the normal force on the astronaut
increases ( FN is perceived as weight.)
- 8 -
6. A 85 kg acrobat supported by a 6.0 m rope swings along a circular path from rest at position X as shown below. The rope hangs from the end of a uniform boom of mass 54 kg. Find the tensionforce as the acrobat passes the lowest point, position Y. (9 marks)
6.0 mHinge
Cable
32
320
°X
6.0 m
Y
2.0 m
( )( )marks2
sm8.100.68.92gh2v
mv21mgh
COE
2
���
���
�
===
=
T
Fg
Fc
( )marks3
N25000.68.108.985
rvgmT
rmvmgFFT
FBD
FBD
22
2
cg
���
���
�
=��⌅
���⇤
�+=��
⌅
���⇤
�+=
+=+=
( )( ) ( )( ) ( )( )( )( )( ) ( )( )( ) ( )( )( )
marksT
TWT
cable
cableboomrope
ccwcw
30.432sin0.38.9540.62500
0.432sin0.30.60
0
��
���
=+
=+
t=t ��
} markNTcable 11082.7 3·=
7. A racetrack surface has the shape of an inverted cone on which cars race in horizontal circles. For a steady speed of 29 m/s, to what distance d should a driver take her car, if she wishes to stay on a circular path without friction? (9 marks)
420420
d
- 9 -
Fc
FN
Fg
( )( )
marks2m130d
d95
dr48sin
marks2m95r
298.9r48tan
marks3vrg
rmvmg
FF
48cosF48sinF
marks2F48cosF
F48sinF
0
20
22C
g0
N
0N
C0
N
g0
N
��
���
=
==
��
���
=
=
���
���
�
===
��
���
=
=
006phk - 10 - July 20, 2000
8. A mass is suspended by a string attached to a spring scale that initially reads 14 N as shown inDiagram 1.
Rope
Spring scale
Q
F = 14 N
The mass is pulled to the side and then released as shown in Diagram 2.
F = ?
Rope
Spring scale
Q
As the mass passes point Q, how will the reading on the spring scale compare to the previousvalue of 14 N? Using principles of physics, explain your answer. (4 marks)
The reading will be greater than 14 N. by mv2
r
← 1 mark
Initially, the net force is zero, so the spring scale reads the weight of the mass. Whenmoving, there is a net (centripetal) force provided by the spring scale (tension in the rope)which exceeds the weight (force of gravity) of the mass so that the mass goes in a verticalcircle. ← 3 marks
0306phk - 11 - July 17, 2003
FRc µ
ÊËÁ
ˆ¯˜
1
9. During a roller coaster ride, the riders move through two loops, the second being one-half theradius of the first. The riders, however, travel at the same speed at the top of each of these twoloops.
v
FN
FN
12 R
R v
Using principles of physics, explain why the riders would experience a greater normal force atthe top of the second smaller loop than at the top of the first larger loop. (4 marks)
The centripetal force is the sum of the normal force and the force of gravity on the riders
(1 mark). Since the radius decreases while the velocity does not change in the smaller loop
the centripetal force must increase (2 marks). The normal force must increase to
provide a greater centripetal force as force of gravity remains constant (1 mark).