05. Physics B 2009 Free Response (1)

8/18/2019 05. Physics B 2009 Free Response (1)

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Problem B-1

Problem B-2

Problem B-3

Problem B-4

Problem B-5Problem B-6

2009 AP Physics B

END

Problem B-7

Grade Distributions


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2009 Grade Distributions

14.9

5

18.6

4

27.2

3

18.3

2

20.9

1

62,702 Eams

!ean Grade " 2#$6

2009 AP Physics B

!enu


4/40

%n an e&eriment, students are to 'al'ulate t(e s&rin) 'onstant k o* a

+erti'al s&rin) in a small um&in) to t(at initiall rests on a table# .(en

t(e s&rin) in t(e to is 'om&ressed a distan'e x *rom its un'om&ressed

len)t( L0 and t(e to is released, t(e to& o* t(e to rises to a maimum

(ei)(t h abo+e t(e &oint o* maimum 'om&ression# /(e students re&eatt(e e&eriment se+eral times, measurin) h it( obe'ts o* +arious masses

ta&ed to t(e to& o* t(e to so t(at t(e 'ombined mass o* t(e to and added

obe'ts is m . /(e bottom o* t(e to and t(e s&rin) ea'( (a+e ne)li)ible

mass 'om&ared to t(e to& o* t(e to and t(e obe'ts ta&ed to it#

P(si's B-1 15 &oints

2009 P-B Eam


5/40

a 3 &oints

Deri+e an e&ression *or t(e (ei)(t h in

terms o* m, x , k , and *undamental

'onstants#

221m)(Ener)-#ons

m)2

(

2

=


1 &t# onser+ation o* Ener)

1 &t# orre't Ener) E&ression

1 &t# ol+in) *or (

2009 P-B Eam


6/40

.it( t(e s&rin) 'om&ressed a distan'e x " 0#020 m in ea'( trial, t(e

students obtained t(e *olloin) data *or di**erent +alues o* m#

b i# 2 &oints

.(at uantities s(ould be )ra&(ed so t(at t(e slo&e o* a best-*it strai)(t

line t(rou)( t(e data &oints 'an be used to 'al'ulate t(e s&rin) 'onstant k 8


(

1 +s#mor

m

1 +s#(Plot

2 &t# E&ression

(

1+s#m

m

1+s#( ⇔

2009 P-B Eam


7/40

.it( t(e s&rin) 'om&ressed a distan'e x " 0#020 m in ea'( trial, t(e

students obtained t(e *olloin) data *or di**erent +alues o* m#

b ii# 2 &oints

ill in one or bot( o* t(e blan 'olumns in t(e table it( 'al'ulated +alues

o* our uantities, in'ludin) units#

1:m )-1

50

33

25

20

17

1:( m-1

2#0

2#9

3#6

5#3

5#6


1 &t# illin) table it( 'orre't +alues#

1 &t# orre't ;nits#

2009 P-B Eam


8/40

' 4 &oints


9/40

d 2 &oints

;sin) our best-*it line,

'al'ulate t(e numeri'al +alueo* t(e s&rin) 'onstant#

0#5

0#4

0#3

0#2

0#1

0 10 20 30 40 50 60

(

1:m

(

∆

1 m

m

1

(lo&es

∆

∆

=

2

2

m020#0

m:s$#9)m0107#02 ⋅=

N:m524 =


1040

10#042#0

=

)m0107#030

32#0⋅

m)2

(

2

=

2

)(m2 =

2

)slo&e2 =

1 &t# al'ulatin) t(e lo&e

1 &t# orre't >alue *or &rin) onstant

2009 P-B Eam


10/40

e 2 &oints

Des'ribe a &ro'edure *or measurin) t(e (ei)(t h in t(ee&eriment, )i+en t(at t(e to is onl momentaril at t(at

maimum (ei)(t

;se a timer to measure t(e time t(e to is in t(e air#al'ulate t(e maimum (ei)(t rea'(ed usin) t(is time#


2 &t# orre't, om&lete Pro'edure

2009 P-B Eam

!enu


11/40

/o small obe'ts, labeled 1 and 2 in t(e dia)ram abo+e, are sus&ended

in euilibrium *rom strin)s o* len)t( L# Ea'( obe't (as mass m and

'(ar)e ?Q . ssume t(at t(e strin)s (a+e ne)li)ible mass and are

insulatin) and ele'tri'all neutral# E&ress all al)ebrai' ansers interms o* m, L, Q, , and *undamental 'onstants#


2009 P-B Eam


12/40

a 3 &oints


13/40

b 2 &oints

Deri+e an e&ression *or t(e ele'tri' &otential at&oint , s(on in t(e dia)ram at t(e to& o* t(e

&a)e, (i'( is mida beteen t(e '(ar)ed

obe'ts#


22

11

r

r

>

r

A2> =

θ

sin=

A2

1 &t# (oin) ield ontributions#

1 &t# orre't E&ression

;sin) Gi+en Auantities

2009 P-B Eam

r

θsin=r


14/40

' 2 &oints


15/40

d 3 &oints

;sin) t(e 'onditions o* euilibrium, ritebut do not

sol+eto euations t(at 'ould, to)et(er, be sol+ed*or and t(e tension T in t(e le*t-(and strin)#

/

m)

E

θ

Esin/

m)'os/

2

2

r

A

2

2

sin=2

A

θ

=


1 &t# /C " E#

1 &t# / " m)#

1 &t# tatin) t(e /o Euations

;sin) Gi+en Auantities

m)'os/ =

2

2

sin=2

Asin/

θ

==

2009 P-B Eam

θsin=2r

r

!enu


16/40

metal rod o* mass 0#22 ) lies a'ross to &arallel 'ondu'tin)

rails t(at are a distan'e o* 0#52 m a&art on a tableto&, as s(on in

t(e to& +ie abo+e# 3#0Ω

resistor is 'onne'ted a'ross t(e le*tends o* t(e rails# /(e rod and rails (a+e ne)li)ible resistan'e but

si)ni*i'ant *ri'tion it( a 'oe**i'ient o* ineti' *ri'tion o* 0#20#

/(ere is a ma)neti' *ield o* 0#$0 / &er&endi'ular to t(e &lane o*

t(e tableto strin) &ulls t(e metal rod to t(e ri)(t it( a

'onstant s&eed o* 1#$ m:s#


2009 P-B Eam


17/40

a 3 &oints

al'ulate t(e ma)nitude o* t(e'urrent indu'ed in t(e loo& *ormed

b t(e rod, t(e rails, and t(e resistor#

% ε

=

Ω 0#3

m:s1#$m0#52/$0#0 25#0


B=+=

1 &t#


18/40

b 4 &oints

al'ulate t(e ma)nitude o* t(e

*or'e reuired to &ull t(e rod to t(eri)(t it( 'onstant s&eed#

m) * µ 2m:s9#$)0#2220#0 N0#43

B%=B = m0#520#25/$0#0 N0#10

B* N0#10N0#43 N0#53


1 &t# or'e o* ri'tion

1 &t# orre't !a)neti' or'e

1 &t# ddin) t(e /o or'es

1 &t# orre't anser

2009 P-B Eam

P( i B 3 15 i


19/40

' 3 &oints

al'ulate t(e ener) dissi&ated in

t(e resistor in 2#0 s#

PtE =

t %E2

s#023#00#25 2 Ω 0#3$


1 &t# Poer-Ener) elations(i&

1 &t# Ele'tri' Poer %2

1 &t# orre't ubstitution

2009 P-B Eam

P( i B 3 15 i t


20/40

d 2 &oints

al'ulate t(e or done b t(e

strin) &ullin) t(e rod in 2#0 s#

+td =

s2#0m:s$#1d =

m6#3d

d. =

m3#6N#540.

9#1. =


1 &t# orre't E&ression *or Distan'e

1 &t# orre't ubstitution *or or'e

2009 P-B Eam

P( i B 3 15 i t


21/40

e 2 &oints

om&are our ansers to &arts

' and d# Pro+ide a &(si'ale&lanation *or ( t(e are

eual or uneual#

nser ' does not in'lude or done b *ri'tion#

.or done b *ri'tion dissi&ates ener)#


1 &t# .or Done b ri'tion not %n'luded

1 &t# ri'tion Dissi&ates Ener)

2009 P-B Eam

9#1. d

0#3$E '

=

=

!enu

P( i B 4 10 i t


22/40

/(e 'linder 'ontains 2#2 ) o* ater +a&or initiall at a

+olume o* 2#0 m3 and an absolute &ressure o* 3#0 105 Pa#

/(is state is re&resented b &oint A in t(e P> dia)ram

belo# /(e molar mass o* ater is 1$ ), and t(e ater +a&or

'an be treated as an ideal )as#


2009 P-B Eam

P( i B 4 10 i t


23/40

a 3 &oints

al'ulate t(e tem&erature o*

t(e ater +a&or at &oint A#

n/P> =

n

P>/ =

H :mol$#31mol122

m#02Pa100#3 33

⋅

H 590

):mol10$1

)2#2n

3mol122


1 &t# %deal Gas =a

1 &t# orre't Number o* !oles


2009 P-B Eam

):mol10$1!

)2#2m

3.

.

=

=

P( si's B 4 10 &oints


24/40

b 1 &oint

al'ulate t(e tem&erature o* t(e ater +a&or at &oint C #

n P>/

=

H :mol$#31mol122m#52Pa100#4 33⋅

H 9$0


1 &t# orre't nser and ;nits

2009 P-B Eam

/(e absolute &ressure o* t(e

ater +a&or is in'reased at

'onstant +olume to 4#0 105 Pa

at &oint B, and t(en t(e +olume

o* t(e ater +a&or is in'reased

at 'onstant &ressure to 2#5 m3

at &oint C , as s(on in t(e P> dia)ram# mol122n =

P(si's B 4 10 &oints


25/40

' 3 &oints

Does t(e internal ener) o* t(eater +a&or *or t(e &ro'ess

AI BIC in'rease, de'rease, or

remain t(e same8

JJJJ%n'rease JJJJDe'rease JJJJemain t(e same

usti* our anser

%nternal ener) is &ro&ortional to tem&erature#


1 &t# ele'tin) %n'rease

2 &t# orre't usti*i'ation

2009 P-B Eam

H 9$0

H 590



26/40

d 3 &oints

al'ulate t(e or done on t(e

ater +a&or *or t(e &ro'ess

AI BIC #

/(e area under t(e 'ur+e re&resents t(e or

done on t(e ater#

>P. ∆

35m#500Pa100#4 100#2

5


1 &t# .or Euals rea ;nder ur+e

1 &t# orre't Numeri'al nser and ;nits

1 &t# Ne)ati+e i)n on nser

2009 P-B Eam

!enu



27/40

/(ree obe'ts o* identi'al mass atta'(ed to strin)s are

sus&ended in a lar)e tan o* liuid, as s(on abo+e#


2009 P-B Eam



28/40

a 3 &oints

!ust all t(ree strin)s (a+e t(e same tension8 JJJJ es JJJJ No

usti* our anser#

/(e tension in ea'( strin) de&ends on t(e ei)(t

and buoant *or'e on ea'( obe't#

/(e buoant *or'e on a submer)ed obe't de&ends

on t(e obe'tFs +olume#


1 &t# ele'tin) No


2009 P-B Eam



29/40

olume

1 &t# orre't nser

2009 P-B Eam



30/40

' 2 &oints

al'ulate t(e densit o* t(e liuid#

B =

>)

B

= =

23 m:s$#9m5-100#1

N12#0

=

3):m1200



1 &t# orre't nser

2009 P-B Eam

B

N12B =



31/40

d 2 &oints

ome o* t(e liuid is no drained *rom t(e tan untilonl (al* o* t(e +olume o* obe't is submer)ed#

.ould t(e tension in t(e strin) to (i'( obe't is

atta'(ed in'rease, de'rease, or remain t(e same8

JJJJ %n'rease JJJJ De'rease JJJJ emain t(e same

usti* our anser#

=ess liuid is dis&la'ed t(ere*ore t(e buoant *or'e is less

Bm)/


1 &t# ele'tin) %n'rease


2009 P-B Eam

!enu



32/40

%n a 'lassroom demonstration, a beam o* 'o(erent li)(t o*

a+elen)t( 550 nm is in'ident &er&endi'ularl onto a &air o* slits#

Ea'( slit (as a idt( w o* 1#2 10 6 m, and t(e distan'e d beteen

t(e 'enters o* t(e slits is 1#$ 10 6 m# /(e 'lass obser+es li)(t and

dar *rin)es on a s'reen t(at is a distan'e L o* 2#2 m *rom t(e slits#


2009 P-B Eam



33/40

a 2 &oints

al'ulate t(e*reuen' o* t(e li)(t#

λ

* '

λ

'*

m10550

m:s103#0

9

$

KL105#514

=


1 &t# &eed-reuen'-.a+elen)t(

1 &t# orre't anser

2009 P-B Eam

m:s100#3'

m105509

9



34/40

b 3 &onts

al'ulate t(e distan'e beteen

to ada'ent dar *rin)es ont(e s'reen#

d=m

λ

1m

d

=

λ

=

m10#$1

m10505m#22

5

9

=

m067#0


1 &t# %nter*eren'e &osition

1 &t# %nter*eren'e e&aration


2009 P-B Eam

λ

" 550 nm L " 2#2 m

d " 1#$ 10 6 m



35/40

/(e entire a&&aratus is no immersed in a trans&arent *luid(a+in) inde o* re*ra'tion 1#4#

' 2 &oints

.(at is t(e *reuen' o* t(e li)(t in t(e trans&arent *luid8

KL105#5* 14=


2 &t# reuen' Does Not (an)e

2009 P-B Eam



36/40

d 3 &oints

Does t(e distan'e beteen t(e dar *rin)es in'rease, de'rease, or

remain t(e same8

JJJJJ %n'rease JJJJJ De'rease JJJJJ emain t(e same

E&lain our reasonin)#

d

=

λ

=

is &ro&ortional to t(e a+elen)t( nad

t(e a+elen)t( de'reases in t(e *luid#


1 &t# ele'tin) De'rease

2 &t# orre't easonin)

2009 P-B Eam

!enu



37/40

&(oton o* a+elen)t( 250 nm ee'ts an ele'tron *rom a metal#

/(e ee'ted ele'tron (as a de Bro)lie a+elen)t( o* 0#$5 nm#

a 3 &oints

al'ulate t(e ineti' ener) o* t(e ele'tron#

2

m+H

2

=

m+

(=

λ

m

(

+

2

m

(m

2

λ

=

2

2

m2(H λ

2931

234

m10#$50)1011#92

s1063#6

⋅

=

103#3 19=



o* a+elen)t( *or >elo'it

1 &t# orre't ubstitution o* Plan'Fs onstant

1 &t# orre't ubstitution o* Ele'tron !ass

2009 P-B Eam



38/40

b 3 &oints

ssumin) t(at t(e ineti' ener) *ound in a is t(e maimum ineti'

ener) t(at it 'ould (a+e, 'al'ulate t(e or *un'tion o* t(e metal#

&(oton o* a+elen)t( 250 nm ee'ts an ele'tron *rom a metal#

/(e ee'ted ele'tron (as a de Bro)lie a+elen)t( o* 0#$5 nm#

φ

(* H

H (* H ('

λ

103#3m10502

m:s103#0s1063#6 199

$34

=

107#419

=

&

1 &t# P(otoele'tri' E**e't

1 &t# orre't ubstitution o* P(oton .a+elen)t(

1 &t# orre't ubstitution o* ('

1 &t# orre't ;nits in Parts a and b2009 P-B Eam



39/40

' 3 &oints

/(e in'ident &(oton as 'reated (en an atom underent an ele'troni'

transition#


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05. Physics B 2009 Free Response (1)