LE2 Samplex

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College of Science

Physics 71

Set A

Second Long Exam

First Semester, AY 2015–2016

N

Naammee: : IInnssttrruuccttoorr::

S

Seeccttiioonn//CCllaasss s SScchheedduullee: : SSttuuddeennt t NNuummbbeerr::

C

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Instructions:

Instructions: ChoChoose the letteose the letter r of the best answeof the best answer r to each of to each of the follthe followowing queing questistionsons. . UseUse Mongol 2 pencil

Mongol 2 pencil only to shade your answer to the exam. To change your answer, erase neatly only to shade your answer to the exam. To change your answer, erase neatly your old answer and simply shade the new one.

your old answer and simply shade the new one. AnAnyy fforormm ofof chcheaeatitingng inin exexamamininatatioionsns oror ananyy act of

act of dishondishonesty in relation to studies, such as esty in relation to studies, such as plagiarplagiarism, shall be ism, shall be subjesubject to ct to discipdisciplinarylinary action.

action. FolFollowinlowing g instruinstructions is ctions is part of part of the examinatiothe examination.n.

1.

1. Parallel Universe. Parallel Universe. An object was displAn object was displaced by a position-aced by a position-dependependent force. dent force. In univIn universeerse I, the force is a piece-wise function of position, while in universe II, the force is a linear I, the force is a piece-wise function of position, while in universe II, the force is a linear funct

function of position. ion of position. Which is the correct relationshWhich is the correct relationship betweenip between

F

11 andand

F

22 so that the so that the netnet

work done in I is equal to that of II work done in I is equal to that of II??

A. A.

F

11

=

= F

F

22 B. B.

22F

F

11

=

= F

F

22 C. C.

F

11

=

= 22F

F

22 D. D.

22F

F

11

=

−

F

22

(3)

2.

2. Bayan o Sarili. Bayan o Sarili. Bayan and Sarili pushed a crate from the Bayan and Sarili pushed a crate from the

x

=

= 00

to to

x

=

= +3

+3..00

00 [m]

[m]ˆˆıı

along along the horizo

the horizontal frictionntal frictionless surface. less surface. From theFrom the

x

=

= 00

toto

x

=

= +2

+2..00

00 [m]

[m]ˆˆıı

, Bayan pushed it, Bayan pushed it with a constant force

with a constant force

+

+F

F

BB

ˆˆıı

. . Sarili replaced Bayan and applied a Sarili replaced Bayan and applied a constconstant force magnitudant force magnitudee

F

S S on the crate from on the crate from

x

x =

= +2

+2..00

00 [m]

[m]ˆˆıı

to to

x

x =

= +3

+3..00

00 [m]

[m]ˆˆıı

. . Sarili can chooSarili can choose to push the cratese to push the crate

with a force of either

with a force of either negative negative oror positive direction positive direction, with the corresponding, with the corresponding

∆

∆K

K

shown shown in the table:

in the table:

Table 1: Sarili’s push Table 1: Sarili’s push Direction of

Direction of F F S S ∆∆K K of the crate from of the crate from x x = 00 = to to x x = = +3+3..0000 [m][m]ˆˆıı

Negative

Negative x x--ddiirreeccttiioon n zzeerroo Positive

Positive x x-direction-direction +12+12..0[J]0[J]

What is the magnitude of

F

BB?? Mamili ka! Mamili ka!

A.

33..00

00 [N

[N]]

B.B.

44..00[N]

00[N]

C.C.

55..00[N]

00[N]

D.D.

66..00[N]

00[N]

3.

3. KnighKnight of the horse.t of the horse. A box is pulled at the A box is pulled at the constant ve- constant ve-locity

locity by a horse as shown in the ﬁgure. For by a horse as shown in the ﬁgure. For

90 90..00 [m

[min

ins]

s]

,, the horse provides a constant power rating of

the horse provides a constant power rating of

10 10..8[W]

8[W]

.. If the kinetic friction between the box and the ground is If the kinetic friction between the box and the ground is

11 11..8[N]

8[N]

, what is the, what is the speed speed of the box? of the box?

A. A.

11..37[m

37[m//s]

s]

B. B.

66..10

10 _×

_×

10

10 −

−

11

_[m

_[m//s]

_s]

C. C.

99..15

15 _×

_×

10

10 −

−

11

[m

[m//s]

s]

D. D.

11..02

02 _×

_×

10

10 −

−

22

_[m

_[m//s]

_s]

4.

4. TWork It Like Miley. TWork It Like Miley. A block of weight A block of weight ww slides down a slides down a rough inclined plane of angle

rough inclined plane of angle

θθ

. . A constA constant fricant frictiotional fornal forcece f

f _k_k acts on the block so that it moves at a acts on the block so that it moves at a constant velocity constant velocity vv down the incline. What is the

down the incline. What is the total work done on the block total work done on the block as it descends a height

as it descends a height

h

down the incline? down the incline?

A.

W

tottot

=

= 00

B.

W

tottot

=

= ((w

w cos

cos θθ

−

f

kk

))h

h

C.

W

tottot

=

= ((w

w

cos

cos θθ

−

f

kk

))vv

D.

(4)

5.

5. That product. That product. What is the What is the scalar product scalar product of vectors of vectors AA andand BB, , if if AA

= X

=

X

ˆˆıı +

+ Y

Y

ˆ



andand B

B

=

= Y

Y ˆˆıı

₋

X



ˆˆ

?? A.

A.

X

22

₋

Y

2 2

B.

X

XY

Y ˆˆıı

₋

Y X

Y X ˆˆ



C. 2XY C. 2XY D. zero D. zero 6.

6. ArtWork. ArtWork. A painting is moved from point A to point B at a distance of A painting is moved from point A to point B at a distance of

10 10..0[m]

0[m]

. . IIt it iss applied by an external constant force of

applied by an external constant force of

2 2..00

00 [N

[N]]

. . If the If the angangle betwele between the en the exexternternal forceal force and the displacement is

and the displacement is

60 60..00

◦◦

, what is the, what is the work done on the painting by an external work done on the painting by an external force

force?? A.

A.

10 10..0[J]

0[J]

B.B.

17 17..3[J]

3[J]

C.C.

20 20..0[J]

0[J]

D.D.

34 34..6[J]

6[J]

For the next two items, consider a box of mass

15 15 [k

[kg]

g]

, , that is attached to the spring with

that is attached to the spring with

kk

= 550[N

= 550[N//m]

m]

and and initially at rest at point P on a frictionless horizontal initially at rest at point P on a frictionless horizontal surface.

surface. It is then pushed by a constant force It is then pushed by a constant force FF.. 7.

7. For starBOX lovers. For starBOX lovers. The speed of the box is The speed of the box is

1 1..55 [m

[m//s]

s]

after the spring is compressed by after the spring is compressed by some distance

some distance

x

. What is the. What is the work done by the constant force work done by the constant force FF if the work done by theif the work done by the spring on the box is

spring on the box is

₋

28 28 [J

[J]]

?? A.

A.

17[J]

B.B.

28[J]

C.C.

30[J]

D.D.

45 45 [J

[J]]

8.

8. For starBOX lovers 2.0. For starBOX lovers 2.0. Suppose the box reaches the Suppose the box reaches the maximum compression maximum compression of the of the spring, what is the

spring, what is the work done by the constant force work done by the constant force FF if the work done by the spring onif the work done by the spring on the box

the box at at maximmaximum compressioum compression n isis

₋

64[J]

?? A. zero

A. zero B.B.

32[J]

C.C.

64[J]

D.D.

12 1288 [J

[J]]

9.

9. You had me at my best. You had me at my best. Which of the following Which of the following combination of spring’s constant and combination of spring’s constant and maximu

maximum m comprcompressionession is best suited for providing speed of is best suited for providing speed of

25 25..00 [m

[m//s]

s]

on on aa

77..20

20 [k

[kg]

g]

block in an

block in an horizontal, frictionless table horizontal, frictionless table?? A. A.

kk

= =

1..80

1

80 _×

_×

10

33

[N

[N//m]

m]

; ; x x ==

0 0..05

0500 [m

[m]]

B. B.

kk

= =

1..80

1

80 _×

_×

10

33

[N

[N//m]

m]

; ; x x ==

0 0..50

5000 [m

[m]]

C. C.

kk

= =

1..80

1

80 _×

_×

10

44

[N

[N//m]

m]

; ; x x ==

0 0..05

0500 [m

[m]]

D. D.

kk

= =

1..80

1

80 _×

_×

10

44

[N

[N//m]

m]

; ; x x ==

0 0..50

5000 [m

[m]]

(5)

10.

10. An Andd yyouou chchososee toto brbreaeakk mymy hheaeartrt.. CoConsnsididerer aa hehearartt mamadede ofof glglasasss compressed by a spring by distance

compressed by a spring by distance

d

with spring with spring



s constant of s constant of

k

.. If the glass and spring is placed above a horizontal frictionless If the glass and spring is placed above a horizontal frictionless table of height

table of height

h

, what is the, what is the speed of the glass speed of the glass when it reaches when it reaches elevation of elevation of

h/

h/33

?? A. A.

vv

=



kk

m

dd

22

₊

22

33 gh

gh

B. B.

vv

=



kk

m

dd

22

₊

44

33 gh

gh

C. C.

vv

=



kk

m

dd

22

₊

1

33 gh

gh

D. D.

vv

=



kk

m

dd

22

_{+ 2}

_{+ 2gh}

_gh

11.

11. Pyramid. Pyramid. As part of their routine, a cheerleader As part of their routine, a cheerleader is raised is raised from the ground to the top of from the ground to the top of their pyramid,

their pyramid,

10 10..0[m]

0[m]

above ground. What is the work done by gravity on the cheerleader above ground. What is the work done by gravity on the cheerleader if her mass is if her mass is

50..0[kg]

50 0[kg]

?? A. A.

+4

+4..90

90 _×

_×

10

33

[J]

B. B.

₋

44..90

90 _×

_×

10

33

[J]

C. C.

+5

+5..00

00 _×

_×

10

22

[J]

D. D.

₋

55..00

00 _×

_×

10

22

[J]

12.

12. Liberated. Liberated. Which of the following statements is Which of the following statements is TRUE TRUE when a when a non-conservative force non-conservative force acts on a system?

acts on a system? I.

I. The total mechaniThe total mechanical energy of the system is cal energy of the system is not conservnot conserved.ed. II.

II. The total work done on the particle is zero The total work done on the particle is zero when it returned to it’when it returned to it’s original positios original position.n. III.

III. The process is path independThe process is path independent.ent. A. I only

A. I only

B. I and II only B. I and II only

C. II and III only C. II and III only D. I, II, and III D. I, II, and III 13.

13. Bato-bato sa langit. Bato-bato sa langit. Stone A (mass Stone A (mass

m

AA) is thrown from point P at the top of the cliff,) is thrown from point P at the top of the cliff,

with an initial speed of

v

00AA at an angle at an angle

θ

AA above the horizontal above the horizontal. Also, from point P, stone. Also, from point P, stone

B (mass

m

BB) is thrown with an initial speed of ) is thrown with an initial speed of

v

00BB at an angle at an angle

θ

BB below the horizontal below the horizontal..

Neglecting air resistance, which of the following is

Neglecting air resistance, which of the following is ALWAYS TRUE ALWAYS TRUE about about

v

00AA and and

v

00BB if if

the two stones hit the ground with the same ﬁnal speed? the two stones hit the ground with the same ﬁnal speed?

A.

vv

00AA

=

= v

v

00BB

B.

vv

00AA

<

< vv

00BB

C.

vv

00AA

sin

sin θθ

AA

=

= v

v

00BB

sin

sin θθ

BB

D.

(6)

14.

14. More Work. More Work. If you performed work If you performed work

W

in compressing a spring by a certain displacement in compressing a spring by a certain displacement from equilibrium

from equilibrium

x

, how much more work will you need to compress it further from, how much more work will you need to compress it further from

x

to to

22x

x

??

A.

W

B.B.

22W

W

C.C.

33W

W

D.D.

44W

W

F

For or the next two the next two itemitems, s, consconsider a ider a partparticle that is icle that is movmoving in ing in the x-dirthe x-directiection. on. The particThe particle isle is then acted on by a single conservative force with the following potential energy function. The then acted on by a single conservative force with the following potential energy function. The total mechanical energy of the particles is represented by the horizontal dashed line.

total mechanical energy of the particles is represented by the horizontal dashed line. 15.

15. True or False. True or False. If the particle is released from rest at A, If the particle is released from rest at A, which of the following statement/s is/are

which of the following statement/s is/are TRUE TRUE?? I. C, E and F are the stable equilibrium points. I. C, E and F are the stable equilibrium points.

II. It has the highest kinetic energy at point C and the II. It has the highest kinetic energy at point C and the

lowest kinetic energy at point A and G. lowest kinetic energy at point A and G. III. It has a positive acceleration at point B. III. It has a positive acceleration at point B.

A. II only A. II only

B. I and II only B. I and II only

C.

C. I and III onI and III onlyly D. II and III only D. II and III only 16.

16. May the FORCE be with you. May the FORCE be with you. Which of the following correctly describes the Which of the following correctly describes the force at force at point G point G?? A. A.

_| |

F

GG

||

=

||

F

E E

||

B. B.

_| |

F

GG

||

<

||

F

E E

||

C. C.

F

GG

>

> 0

0

D. D.

F

GG

<

< 0

0

17.

17. Impulsive-Compulsive. Impulsive-Compulsive. The forcThe force e veversursus time plots are shows time plots are shown in n in the ﬁguthe ﬁgure. re. The forThe forcece and the time in the plots are in Newtons and seconds, respectively. Which of the choices is and the time in the plots are in Newtons and seconds, respectively. Which of the choices is the correct ordering from the

(7)

A

A. . IIII, , II, , IIIII I BB. . IIIIII, , II, , III I CC. . IIIIII, , IIII, , I I DD. . IIII, , IIIIII, , II For the next two items, consider blocks A and B, each with masses

For the next two items, consider blocks A and B, each with masses

55..00

00 [k

[kg]

g]

and and

33..00

00 [k

[kg]

g]

respectively, arranged in a

respectively, arranged in a horizontal frictionless floor horizontal frictionless floor as shown in as shown in the figurthe figure. e. InitInitialliallyy, , thethe spring with

spring with

kk

=

= 55..00

00 _×

_×

10

44

[N

[N//m]

m]

is neither compressed nor stretched. is neither compressed nor stretched. Block B collides Block B collides elastically to block A

elastically to block A with an initial velocity of with an initial velocity of

₋

44..00[m

00[m//s]

s]ˆˆıı

.. 18.

18. One, two, three, Takbo! One, two, three, Takbo! What is the What is the ﬁnal ve- ﬁnal ve-locity of block A

locity of block A after after the collision?the collision? A. A.

₋

33..00[m

00[m//s]

s]ˆˆıı

B. B.

₋

22..00[m

00[m//s]

s]ˆˆıı

C. C.

+1

+1..00[m

00[m//s]

s]ˆˆıı

D. D.

+2

+2..00[m

00[m//s]

s]ˆˆıı

19.

19. Aray ko po, ang sakit. Aray ko po, ang sakit. What is the What is the maximum compress maximum compression of ion of the springthe spring after the colli- after the colli-sion?

sion? A.

A.

00..020

02000 [m]

[m]

B.B.

00..03

0300

00 [m

[m]]

C.C.

00..04

0400

00 [m]

[m]

D.D.

00..06

0600

00 [m]

[m]

20.

20. Walang 4ever. Walang 4ever. Shown is the momentum vs. time ( Shown is the momentum vs. time (

p

₋

t

) graph of a block moving through) graph of a block moving through space. At which point is the

space. At which point is the magnitude of the average impulsive force maximum magnitude of the average impulsive force maximum??

21.

21. Yaya Bob. Yaya Bob. Bob A with mass Bob A with mass

m

, attached to a pendulum, attached to a pendulum of length

of length

L

, is released from a height, is released from a height

h

. . At iAt its lots lowewestst point, bob A collides with bob B with mass

point, bob A collides with bob B with mass

3 3m

m

, which is, which is initially at rest. What is the

initially at rest. What is the velocity velocity of the masses after of the masses after aa perfectly inelastic collision perfectly inelastic collision??

A. A.

√

22gh

gh

B. B.

√

22gh/

gh/22

C. C.

√

22gh/

gh/33

D. D.

√

22gh/

gh/44

(8)

F

For or the next 2 the next 2 quesquestiontion, , consconsider the ider the follfollowinowing g scenscenarioario. . The positiThe position on of of PPopoyopoy, , BashBasha a and and Trisha is described by the position vector

Trisha is described by the position vector R R_P_P

= (+1

= (+1..00[m

00[m//s]

s]

_··

t

t )

)ˆˆ



R R_B_B

=

= ((

₋

11..00[m

00[m//s]

s]

_··

t

)ˆ

)ˆıı

R R_T_T

= (+2

= (+2..00

00 [m] )

[m] )ˆˆıı + (2

+ (2..00[m

00[m//s]

s]

_··

t

t )

)ˆˆ



whe

wherre e t t is timeis time. . ThThe e masmass s of Pof Popoopoyy, , BasBasha and ha and TTririsha issha is

60 60..0[kg]

0[kg]

, ,

50 50..0[kg]

0[kg]

and and

40 40..0[kg]

0[kg]

respectively respectively 22.

22. dramatic silence scene. dramatic silence scene. What is the location ( What is the location (

X

CM CM

,, Y

Y

CM CM ) of the center of mass at) of the center of mass at

tt

=

11..00[s]

00[s]

?? A. A.

(0

(0..20

2000 [m

[m]],,

₋

00..93

9333 [m

[m])

])

B. B.

(0

(0..20

2000 [m

[m]],, 00..93

9333 [m]

[m]))

C. C.

(0

(0..93

9333 [m

[m]],, 00..20

2000 [m

[m])

])

D. D.

((

₋

00..93

9333 [m

[m]],, 00..20

2000 [m]

[m]))

23.

23. HabHabulan with Piolo Pascual love song ulan with Piolo Pascual love song scene.scene. What is the velocity of the center of mass? What is the velocity of the center of mass? A. A.

00..333[m

333[m//s]

s]ˆˆıı + 0

+ 0..933[m

933[m//s]ˆ

s]ˆ



B. B.

₋

00..333[m

333[m//s]

s]ˆˆıı + 0

+ 0..933[m

933[m//s]ˆ

s]ˆ



C. C.

00..200[m

200[m//s]

s]ˆˆıı + 0

+ 0..933[m

933[m//s]ˆ

s]ˆ



D. D.

₋

00..200[m

200[m//s]

s]ˆˆıı + 0

+ 0..93

9333 [m

[m//s]ˆ

s]ˆ



24.

24. Wala kayong pakialam. Wala kayong pakialam. Pastillas Girl, with mass Pastillas Girl, with mass

80 80..00 [k

[kg]

g]

was moving with velocity was moving with velocity

33 [m

[m//s]

s]ˆˆıı

whe when n she she sudsuddendenly ly exexploploded ded intinto o two Pabebtwo Pabebe e WWarriarriorsors, , PaPabebbebe e U U witwith h masmasss

50 50..0[kg]

0[kg]

and Pabebe K with mass and Pabebe K with mass

30 30 [k

[kg]

g]

. . If PabIf Pabebe U traebe U travevelsls

60 60..00

◦◦

above the horizon- above the horizon-tal, while Pabebe K travels

tal, while Pabebe K travels

45 45..00

◦◦

below the horizont below the horizontal, what al, what is theis the speed of Pabebe U speed of Pabebe U?? A.

A.

22..17[m

17[m//s]

s]

B.B.

22..69[m

69[m//s]

s]

C.C.

33..51[m

51[m//s]

s]

D.D.

77..17[m

17[m//s]

s]

25.

25. Semantics. Semantics. Consider an isolated system comprised of two particles A and B. Let Consider an isolated system comprised of two particles A and B. Let FF_int,i_int,i and

and FF_ext,i_ext,i be the individual internal and external forces, respectively, and be the individual internal and external forces, respectively, and pp_A_A and and pp_B_B be the be the momenta of the particles A and B. Which of the following is

momenta of the particles A and B. Which of the following is TRUE TRUE about the system of about the system of particles?

particles? A. If

A. If



_iiFF_int,i_int,i

=

= 00

, then, then pp_A_A

+

pp_B_B

=

constant. constant. B. If

B. If



_iiFFint,iint,i

=

= 00

, then, then ppAA

=

ppBB

=

constant. constant.

C. If



_iiFF_ext,i_ext,i

=

= 00

, then, then pp_A_A

+

pp_B_B

=

constant. constant. D. If

(9)

26.

26. PAT. PAT. ThThee momommenentt ooff ininerertitiaa ababououtt ththee ededgege ooff aa solisolidd cylicylindenderr witwithh radradiusius

22..0[m]

0[m]

as shown in

20 20.. [kg

[kg

_··

m

22

]]

. What is the. What is the mass mass of the solid cylinder? of the solid cylinder? A. A.

00..74

74 [k

[kg]

g]

B. B.

11..1[kg]

1[kg]

C. C.

33..3[kg]

3[kg]

D. D.

66..4[kg]

4[kg]

27.

27. Tryanggulo. Tryanggulo. Objects with masses shown are glued to a light stick Objects with masses shown are glued to a light stick to form a right triangle. What is the

to form a right triangle. What is the moment of inertia about an moment of inertia about an axis

axis passing through one of the corners of the triangle? passing through one of the corners of the triangle? A. A.

11..50

50 [k

[kgg

_··

m

22

]]

B. B.

33..00

00 [k

[kgg

_··

m

22

]]

C. C.

55..00[kg

00[kg

_··

m

22

]]

D. D.

66..75[kg

75[kg

_··

m

22

]]

28.

28. Lazy Suzy. Lazy Suzy. An ant is located on the edge of a Lazy Susan (turntable) An ant is located on the edge of a Lazy Susan (turntable) with radius

with radius

R

and constant angular speed and constant angular speed

ω

. . ThThe ant goe ant got dizt dizzy anzy andd crawled halfway

crawled halfway thr througough h the radiuthe radius s of the of the turturntantableble. . By how muchBy how much did the ant

did the ant changed its changed its radial acceleratiradial accelerationon?? A

A. . ddoouubblleed d BB. . ssaamme e CC. . hhaallvveed d DD. . qquuaarrtteerreedd 29.

29. Ikot-ikot lang. Ikot-ikot lang. Sarah rides a gigantic spinning disk with an angular speed of Sarah rides a gigantic spinning disk with an angular speed of

20 20..0[rev

0[rev//s]

s]

.. If Sarah is

If Sarah is

0 0..10

1000 [m

[m]]

from the center of the disk, what is her from the center of the disk, what is her linear speed linear speed?? A.

A.

12 12..66 [m

[m//s]

s]

B.B.

66..28[m

28[m//s]

s]

C.C.

33..15[m

15[m//s]

s]

D.D.

22..00[m

00[m//s]

s]

30.

30. Wheel of fortune. Wheel of fortune. A wheel of fortune has an initial angular velocity of A wheel of fortune has an initial angular velocity of

+6

+6..35

35 [r

[rev

ev//s]

s]ˆˆ

k k _..

It has a constant angular acceleration so that it can rotate

14 14..22

revolutions before it stops. revolutions before it stops. Assuming the wheel lies in the x-y plane, what is its

Assuming the wheel lies in the x-y plane, what is its angular acceleration angular acceleration?? A. A.

₋

88..92

92 [r

[rad

ad//ss

22

]]ˆˆ

k k B. B.

₋

00..22

2266 [ra

[rad

d//ss

22

]]ˆˆ

k k C. C.

+8

+8..92

92 [r

[rad

ad//ss

22

]]ˆˆ

k k D. D.

+0

+0..226

226 [ra

[rad

d//ss

22

]]ˆˆ

k k

(10)

31.

31. Karwahe ni Luna. Karwahe ni Luna. A A carriagcarriage is e is pullepulled by a d by a horse at a constant accelerathorse at a constant acceleration of ion of

1 1..00 [m

[m//ss

22

]]

.. The radius of the wheels on the carriage is

The radius of the wheels on the carriage is

00..50[m]

50[m]

. A. Afftteerr

55..0[s]

0[s]

, what is its, what is its angular angular displacement

displacement if it is initially at rest? if it is initially at rest? A.

A.

50 50.. [rad]

[rad]

B.B.

25 25 [ra

[rad]

d]

C.C.

10 10.. [rad]

[rad]

D.D.

55..00 [r

[rad

ad]]

32.

32. Amazing Race. Amazing Race. A solid ball and a (solid or hollow) cylinder roll down an inclined plane A solid ball and a (solid or hollow) cylinder roll down an inclined plane witho

without slippinut slipping. g. If the ball and the If the ball and the cylincylinder havder have equal mass and radius and came frome equal mass and radius and came from the same altitude of the inclined plane, which reaches

the same altitude of the inclined plane, which reaches the bottom first the bottom first?? A. The ball reaches the bottom first.

A. The ball reaches the bottom first. B. The cylinder reaches the bottom first. B. The cylinder reaches the bottom first.

C. They arrive at the bottom at the same time. C. They arrive at the bottom at the same time. D.

D. It depends on whether the It depends on whether the cylincylinder is der is solid or hollowsolid or hollow.. 33.

33. Bear this Cross. Bear this Cross. A metal rod lies in the A metal rod lies in the

xy

-pl-plane and it is ane and it is hinhinged at the origiged at the origin. n. A forceA force F

F

=

= 33..00 [N

[N]]ˆˆıı

₋

4 4..0[N]ˆ

0[N]ˆ



is applied to the rod at is applied to the rod at

(

(x,

x, yy)

) =

= ((

₋

22..0[m]

0[m],, 33..0[m])

0[m])

. . WhWhat is tat is thehe torque

torque in the rod? in the rod? A. A.

+1

+1..00 [N

[N

_··

m]

m]ˆˆ

k k B. B.

₋

11..00 [N

[N

_··

m]

m]ˆˆ

k k C. C.

₋

18[N

_··

m](ˆıı

m](ˆ

₋

ˆ



))

D. D.

₋

18[N

_··

m]

34.

34. Nakakahilong body. Nakakahilong body. The angThe angulaular r mommomententum of um of a a spispinnnning boding body y is conseis conservrved. ed. Let theLet the ex

exteternrnalal foforcrceses acactitingng onon ththee bobodydy bebe

−

F

→

11

,,

→

F

→

−

22

,,

·· ·· ··

,,

−

→

F

ii

·· ·· ·· −

F

−→

F

→

N N and and their their correspcorrespondiondingng torqutorqueses

with respect to the body’s center of mass are

−

→

τ

11

,,

−

→

τ

22

,,

·· ·· ··

,,

−

→

τ

ii

· · ·· ·· −

−→

τ

→

N N . Which of the following. Which of the following

conclusion is

conclusion is ALWAYS CORRECT ALWAYS CORRECT?? A.

A.

−

→

F

ii

=

= 00

for all for all

i

B.

−

→

τ

ii

=

= 00

for all for all

i

C. Each

−

→

F

ii are maybe nonzero, but are maybe nonzero, but



_iiN N ₌₁₌₁

−

→

F

ii

=

= 00

D. Each

−

→

τ

ii are maybe nonzero, but are maybe nonzero, but



_iiN N ₌₁₌₁

−

→

τ

ii

=

= 00

35.

35. Ayaw ko nang mangarap. Ayaw ko nang mangarap. AA solid uniform sphere solid uniform sphere with radius with radius

R

is spinning about a is spinning about a frictionless axle through its center

frictionless axle through its center. . Its surface is applieIts surface is applied by a d by a frictiofrictional forcenal force

f

so that its so that its has an angular acceleration magnitude

has an angular acceleration magnitude

α

00. If the. If the radius of the sphere were reduced half radius of the sphere were reduced half

of its size

of its size while applying the same while applying the same

f

and maintaining its mass, what is its and maintaining its mass, what is its new angular new angular acceleration magnitude

acceleration magnitude?? A.

(11)

36.

36. Transformer. Transformer. Iko-tron is a robot that can transform from a disk of radius Iko-tron is a robot that can transform from a disk of radius

R

to a rod of to a rod of length

length

4 4R

R

. In an outer space battle, Iko-tron spins in his disk form with an angular speed. In an outer space battle, Iko-tron spins in his disk form with an angular speed of

of

ω

diskdisk. He then transforms himself into a rod (see the extraordinary ﬁgure below), giving. He then transforms himself into a rod (see the extraordinary ﬁgure below), giving

him a new angular speed of

ω

rodrod. What is the ratio of . What is the ratio of

ω

diskdisk to that of to that of

ω

rodrod??

A

A. . 11::4 4 BB. . 11::6 6 CC. . 22::3 3 DD. . 88::33

37.

37. Super Stick. Super Stick. A uniform stick with length A uniform stick with length

33..00[m]

00[m]

andand mass

mass

5 5..00

00 [k

[kg]

g]

is moving and rotating about its center of is moving and rotating about its center of mass (CM) as shown in the ﬁgure. If the stick and point mass (CM) as shown in the ﬁgure. If the stick and point O both lie in the same

O both lie in the same

xy

-plane, what is the-plane, what is the total an- total an-gular momentum

gular momentum of the stick at point O at the instant of the stick at point O at the instant shown? shown? A. A.

₋

76 76..7[kg

7[kg

_··

m

22

//s]

s] ˆˆ

k k B. B.

₋

95 95..4[kg

4[kg

_··

m

22

//s]

s] ˆˆ

k k C. C.

+76

+76..7[kg

7[kg

_··

m

22

//s]

s] ˆˆ

k k D. D.

+95

+95..4[kg

4[kg

_··

m

22

//s]

s] ˆˆ

k k 38.

38. Nahuhulog ka na ba? Nahuhulog ka na ba? A block with mass A block with mass

m

rests on a friction- rests on a friction-less, horizon

less, horizontal surface. tal surface. A cord attached to the block passes ovA cord attached to the block passes overer a pulley whose radius is

a pulley whose radius is

R

, to a hanging block with mass, to a hanging block with mass

2 2m

m

. The. The system begins to accelerate with magnitude

system begins to accelerate with magnitude

a

after having been after having been rele

released froased from rest. m rest. WhaWhat is t is thethe magnitude of the net torque magnitude of the net torque onon the pulley? the pulley? A. A.

_| |

22mg

mg

₋

ma

_||

R

B. B.

_| |

22mg

mg

₋

2 2ma

ma

_||

R

C. C.

_| |

22mg

mg

₋

3 3ma

ma

_||

R

D. D.

maR

(12)

39.

39. AngAng

K

K E

E

rotrot.. A solid sphere of mass A solid sphere of mass

25 [k

25 [kg]

g]

and radius and radius

0 0..55

55 [m

[m]]

rolls without slipping on rolls without slipping on

a

a horhorizoizontantal l sursurfacface. e. If If its transits translatlationional al kinkinetietic c eneenergrgy y as as it movit moves es isis