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University of the Philippines College of Science

Physics 71

Set A Second Long Exam First Semester, AY 2015–2016

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Second Long Exam

First Semester, AY 2015–2016

Physics 71

Instructions: Choose Choose the letter letter of the best answer answer to each of the follow following ing questi questions ons.. Use Mongol 2 pencil  only to shade your answer to the exam. To change your answer, erase neatly Any form orm of ch chea eati ting ng in exam examin inat atio ions ns or any any your old answer and simply shade the new one. Any act of dishonesty dishonesty in relation to studies, such as plagiarism, plagiarism, shall be subject subject to disciplinary disciplinary action. Followin Following g instructions instructions is part of the examination. examination.

1.   Parallel Universe. An object was displaced displaced by a position-depen position-dependent dent force. In universe universe I, the force is a piece-wise function of position, while in universe II, the force is a linear function function of position. Which is the correct relationship relationship between F 1 and  F 2  so that the net work done in I is equal to that of II?

A. F 1 =  F 2

C. F 1  = 2F 2

B. 2F 1 =  F 2

D. 2F 1 =

A– 2

−F 2

Second Long Exam

First Semester, AY 2015–2016

Physics 71

[m]ˆı  along 2.  Bayan o Sarili.  Bayan and Sarili pushed a crate from the  x = 0  to  x = +3.00 [m]ˆ [m]ˆı, Bayan pushed it the horizontal horizontal frictionless frictionless surface. From the x = 0 to x = +2.00 [m]ˆ with a constant force  +F Bˆı. Sarili replaced Bayan and applied a constant constant force magnitude magnitude F S  [m]ˆı to  x  = +3.00 [m]ˆ [m]ˆı. Sarili can choose choose to push the crate S  on the crate from  x  = +2.00 [m]ˆ with a force of either  negative or  positive direction, with the corresponding ∆K   shown in the table: Table 1: Sarili’s push   of the crate from  x  = 0 to  x  = +3.00 [m]ˆ ∆K  of [m]ˆı zero +12.0[J]

Direction of  F   F S  S   x Negative -direction Positive  x-direction

 F B ?  Mamili ka! What is the magnitude of  F 

[N] A. 3.00 [N]

B. 4.00[N]

C. 5.00[N]

D. 6.00[N]

Knight of the horse.  A box is pulled at the  constant ve3. Knight locity  by a horse as shown in the figure. For  90.0 [min [mins] s], the horse provides a constant power rating of  10.8[W]. If the kinetic friction between the box and the ground is 11.8[N], what is the  speed of the box?

× 10−1 [m/s] D. 1.02 × 10−2 [m/s]

A. 1.37[m/s] B. 6.10

C. 9.15

× 10−1 [m/s]

4.  TWork It Like Miley.  A block of weight w  slides down a rough inclined plane of angle θ. A constant constant frictio frictional nal force force f k  acts on the block so that it moves at a  constant velocity v down the incline. What is the  total work done on the block as it descends a height  h  down the incline?

A. W tot tot = 0 B. W tot tot = (w cos θ

C. W tot tot = (w cos θ

− f  )v D. W tot tot = (w cos θ − f  )h sec θ

− f  )h k

k k

A– 3

Second Long Exam

First Semester, AY 2015–2016

Physics 71

 ˆ  ˆ and 5.   That product.   What is the  scalar product  of vectors A and B, if  A = X ˆı  +  Y   B =  Y ˆı  X  ˆ?

−

A. X 2

− Y  2 B. X Y ˆı − Y X  ˆ

C. 2XY D. zero

6.  ArtWork.  A painting is moved from point A to point B at a distance of  10.0[m]. It is is  2 .00 [N] [N]. If the angle applied by an external constant force of  2 angle between between the extern external al force and the displacement is 60.0◦ , what is the  work done on the painting by an external force? A. 10.0[J]

B. 17.3[J]

C. 20.0[J]

D. 34.6[J]

For the next two items, consider a box of mass  15 [kg] [kg] , , that is attached to the spring with k   = 550[N/m] and  initially at rest at point P on a frictionless horizontal   surface.  It is then pushed by a constant force F.

7.  For starBOX lovers.  The speed of the box is  1 .5 [m/s]  after the spring is compressed by some distance x . What is the  work done by the constant force F if the work done by the [J]? spring on the box is 28 [J]

−

A.  17[J]

B.  28[J]

C.  30[J]

[J] D.  45 [J]

8.   For starBOX lovers 2.0.   Suppose the box reaches the   maximum compression   of the spring, what is the  work done by the constant force F if the work done by the spring on the box at maximum maximum compression compression is 64[J]?

−

A. zero

B.  32[J]

C.  64[J]

 128 [J] [J] D.  128

9.  You had me at my best.  Which of the following  combination of spring’s constant and maximum maximum compression compression   is best suited for providing speed of  25.0 [m/s] on a 7.20 [kg] [kg] block in an  horizontal, frictionless table?

× 103 [N/m] ; x = 0.050 050 [m] [m] 500 [m] [m] B. k  =  1.80 × 103 [N/m] ; x =  0.500 050 [m] [m] C. k  =  1.80 × 104 [N/m] ; x =  0.050 500 [m] [m] D. k  =  1.80 × 104 [N/m] ; x =  0.500 A. k  =  1.80

A– 4

Second Long Exam

First Semester, AY 2015–2016

Physics 71

 And you ch chos osee to br brea eak k my heart eart.. Cons 10.  And Consid ider er a hear heartt made made of glas glasss  k . compressed by a spring by distance  d  with springs constant of  k If the glass and spring is placed above a horizontal frictionless table of height h, what is the  speed of the glass  when it reaches  h/3? elevation of  h/

A.

 k 2 v= d + gh  mk 43

B. v =

2

C.

d2 + gh m 3

 k  1 v= d + gh  mk 3

D. v =

2

m

d2 + 2gh

11.  Pyramid.   As part of their routine, a cheerleader  is raised  from the ground to the top of  their pyramid, 10.0[m] above ground. What is the work done by gravity on the cheerleader if her mass is 50.0[kg]?

× 103 [J] B. −4.90 × 103 [J]

× 102 [J] D. −5.00 × 102 [J]

A. +4.90

C. +5.00

12.  Liberated.  Which of the following statements is  TRUE  when a  non-conservative force acts on a system? I. The total mechanical mechanical energy of the system is not conserved. conserved. II. The total work done on the particle is zero when it returned to it’s it’s original position. position. III. The process is path independent. independent. A. I only

C. II and III only

B. I and II only

D. I, II, and III

13.  Bato-bato sa langit.  Stone   Stone A (mass mA ) is thrown from point P at the top of the cliff,  v0A  at an angle  θA  above the horizontal. Also, from point P, stone with an initial speed of  v  v 0B  at an angle  θ B  below the horizontal. B (mass  m B ) is thrown with an initial speed of  v Neglecting air resistance, which of the following is ALWAYS TRUE  about  v0A  and  v0B if  the two stones hit the ground with the same final speed? A. v0A =  v 0B

C. v0A sin θA = v 0B sin θB

B. v0A < v0B

D. v0A sin θA < v0B sin θB

A– 5

Second Long Exam

First Semester, AY 2015–2016

Physics 71

 W  in compressing a spring by a certain displacement 14.  More Work.  If you performed work  W  from equilibrium  x , how much more work will you need to compress it further from  x  to 2x? B. 2W 

A. W 

C. 3W 

D. 4W 

For the next two items, items, consider consider a particle particle that is moving moving in the x-directi x-direction. on. The particle particle is 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.

15.  True or False.  If the particle is released from rest at A, which of the following statement/s is/are TRUE? I. C, E and F are the stable equilibrium points. II. It has the highest kinetic energy at point C and the lowest kinetic energy at point A and G. III. It has a positive acceleration at point B. A. II only

C. I and III only only

B. I and II only

D. II and III only

16.  May the FORCE be with you.  Which of the following correctly describes the  force at point G? C. F G >  0

A. F G  = F E  E 

 | | | | B. |F  |  < |F  | G

D. F G <  0

E  E 

17.  Impulsive-Compulsive. The force force versu versuss time plots are shown shown in the figure. figure. The force force and the time in the plots are in Newtons and seconds, respectively. Which of the choices is the correct ordering from the  smallest to largest impulse?

A– 6

Second Long Exam

First Semester, AY 2015–2016

A. II, I, III

B. III, I, II

C. III, II, I

Physics 71

D. II, III, I

[kg] and  3.00 [kg] [kg] For the next two items, consider blocks A and B, each with masses 5.00 [kg] respectively, arranged in a horizontal frictionless floor  as shown in the figure. figure. Initiall Initiallyy, the spring with k = 5.00 104 [N/m]   is neither compressed nor stretched.   Block B collides elastically to block A with an initial velocity of  4.00[m/s]ˆ s]ˆı.

 ×

−

18.  One, two, three, Takbo!  What is the  final velocity of block A  after the collision?

s]ˆı  −3.00[m/s]ˆ s]ˆı B. −2.00[m/s]ˆ

A.

s]ˆı C. +1.00[m/s]ˆ s]ˆı D. +2.00[m/s]ˆ

19.  Aray ko po, ang sakit.  What is the  maximum compression compression of the spring after the collision? A. 0.0200 0200 [m]

B. 0.0300 0300 [m] [m]

C. 0.0400 0400 [m]

D. 0.0600 0600 [m]

20.  Walang 4ever.  Shown is the momentum vs. time ( p  t) graph of a block moving through space. At which point is the  magnitude of the average impulsive force maximum?

−

21.  Yaya Bob.  Bob A with mass  m , attached to a pendulum of length L, is released from a height h. At its its lowe lowest st point, bob A collides with bob B with mass  3m, which is initially at rest. What is the velocity  of the masses after a  perfectly inelastic collision?

√ 2gh √  B. 2gh/ 2

A.

√ 2gh/3 √  D. 2gh/ 4 C.

A– 7

Second Long Exam

First Semester, AY 2015–2016

Physics 71

For the next 2 question question,, consider consider the followin following g scenario scenario.. The position position of Popoy, opoy, Basha Basha and  Trisha is described by the position vector 

RP  = (+1.00[m/s]  t  )ˆ  ) ˆ RB

· = (−1.00[m/s] · t  )ˆı

RT  = (+2.00 [m] )ˆ )ˆı + (2.00[m/s]  t  )ˆ  ) ˆ

·

wher where t is time. time. The The mass mass of Popo Popoyy, Basha Basha and Trisha risha is 60.0[kg] , 50.0[kg] and  40.0[kg] respectively

22.  dramatic silence scene.  What is the location (X CM  CM  , Y CM  CM  ) of the center of mass at t = 1.00[s]?

200 [m] [m], A. (0.200

−0.933 933 [m]) [m])

933 [m] [m], 0.200 200 [m]) [m]) C. (0.933

200 [m] [m], 0.933 933 [m]) [m]) B. (0.200

933 [m] [m], 0.200 200 [m]) [m]) D. ( 0.933

−

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

s]ˆı + 0.933[m/s]ˆ A. 0.333[m/s]ˆ   B.

s]ˆı + 0.933[m/s]ˆ C. 0.200[m/s]ˆ  

s]ˆı + 0.933[m/s]ˆ    −0.333[m/s]ˆ

s]ˆı + 0.933 933 [m/s]ˆ    −0.200[m/s]ˆ

D.

[kg]   was moving with velocity 24.  Wala kayong pakialam.   Pastillas Girl, with mass 80.0 [kg] 3 [m/s]ˆ s]ˆı   when when she sudden suddenly ly explo exploded ded into into two Pabebe Pabebe Warriors arriors,, Pabeb Pabebee U with with mass mass 50.0[kg]  and Pabebe K with mass  30 [kg] [kg]. If Pabebe Pabebe U trave travels ls 60.0◦  above the horizontal, while Pabebe K travels  45.0◦  below the horizontal, horizontal, what is the  speed of Pabebe U ? A. 2.17[m/s]

B. 2.69[m/s]

C. 3.51[m/s]

D. 7.17[m/s]

25.  Semantics.  Consider an isolated system comprised of two particles A and B. Let Fint,i and Fext,i  be the individual internal and external forces, respectively, and pA  and pB  be the momenta of the particles A and B. Which of the following is  TRUE  about the system of  particles? A. If  B. If  C. If  D. If 

   

i

Fint,i = 0, then pA + pB =  constant.

i

Fint,i = 0, then pA = pB =  constant.

i

Fext,i = 0, then pA + pB =  constant.

i

Fext,i = 0, then pA = pB =  constant.

A– 8

Second Long Exam

First Semester, AY 2015–2016

Physics 71

26.  PAT. The The mom moment ent of iner inerti tiaa abou aboutt the the edge edge of a solid with radius radius 2.0[m] solid cylinde cylinderr with as shown in  20. [kg  m2 ]. What is the  mass of the solid cylinder? [kg] A. 0.74 [kg]

·

B. 1.1[kg] C. 3.3[kg] D. 6.4[kg]

27.   Tryanggulo.  Objects with masses shown are glued to a light stick  to form a right triangle. What is the  moment of inertia about an axis  passing through one of the corners of the triangle?

[kg  m2 ] A. 1.50 [kg

C. 5.00[kg  m2]

· [kg · m2 ] B. 3.00 [kg

· D. 6.75[kg · m2]

28.  Lazy Suzy.  An ant is located on the edge of a Lazy Susan (turntable) with radius R   and constant angular speed ω . The The ant got got dizzy dizzy and and crawled halfway  throug  through h the radius radius of the turnta turntable ble.. By how much acceleration? did the ant  changed its radial acceleration A. doubled

B. same

C. halved

D. quartered

 20.0[rev/s]. 29.  Ikot-ikot lang.  Sarah rides a gigantic spinning disk with an angular speed of  20 100 [m] [m]  from the center of the disk, what is her  linear speed? If Sarah is 0.100 A. 12.6 [m/s]

B. 6.28[m/s]

C. 3.15[m/s]

D. 2.00[m/s]

ˆ. [rev/s]k  30.  Wheel of fortune.   A wheel of fortune has an initial angular velocity of  +6.35 [rev It has a constant angular acceleration so that it can rotate 14 .2  revolutions before it stops. Assuming the wheel lies in the x-y plane, what is its  angular acceleration? ˆ  −8.92 [rad [rad/s2]k  ˆ 226 [rad [rad/s2]k  B. −0.226

ˆ [rad/s2 ]k  C. +8.92 [rad

A.

ˆ [rad/s2]k  D. +0.226 [rad

A– 9

Second Long Exam

First Semester, AY 2015–2016

Physics 71

31.  Karwahe ni Luna.  A carriage carriage is pulled pulled by a horse at a constant acceleration acceleration of  1  1.0 [m/s2 ]. The radius of the wheels on the carriage is 0.50[m]. After 5.0[s], what is its   angular displacement if it is initially at rest? A. 50. [rad]

[rad] B.  25 [rad]

C. 10. [rad]

[rad]] D. 5.0 [rad

32.   Amazing Race.  A solid ball and a (solid or hollow) cylinder roll down an inclined plane without without slipping. slipping. If the ball and the cylinder cylinder have have equal mass and radius and came from the same altitude of the inclined plane, which reaches  the bottom first? A. The ball reaches the bottom first. B. The cylinder reaches the bottom first. C. They arrive at the bottom at the same time. D. It depends on whether the cylinder cylinder is solid or hollow. hollow. 33.  Bear this Cross.  A metal rod lies in the  xy -plane -plane and it is hinged hinged at the origin. origin. A force    is applied to the rod at  ( x, y ) = ( 2.0[m], 3.0[m]). What F = 3.0 [N] [N]ˆı  4.0[N]ˆ What is the the torque in the rod?

−

−

ˆ A. +1.0 [N  m]k 

 −18[N · m](ˆı −  ˆ) D. −18[N · m] C.

· ˆ B. −1.0 [N · m]k 

34.  Nakakahilong body. The angula angularr moment momentum um of a spinn spinning ing body body is conserv conserved. ed. Let the , F i F N  exte extern rnal al forc forces es acti acting ng on the the body body be F 1, F 2, corresponding ng torques torques N  and their correspondi with respect to the body’s center of mass are τ 1 , τ 2 , , τ i τ N  N . Which of the following conclusion is  ALWAYS CORRECT ?

−→ −→ · · · −→ · · · −→ → − −→ · · · −→ · · · −→

 −→ →τ  = 0 for all i B. −  =1 −→F  = 0 → − C. Each F   are maybe nonzero, but −τ   are maybe nonzero, but  =1 −→τ  = 0 D. Each → A. F i = 0 for all i i

N  i N  i

i

i

i

i

35.  Ayaw ko nang mangarap. A  solid uniform sphere  with radius R  is spinning about a frictionless axle through its center. Its surface is applied applied by a frictional frictional force f  so  so that its has an angular acceleration magnitude  α 0 . If the  radius of the sphere were reduced half  of its size  while applying the same f  and maintaining its mass, what is its  new angular acceleration magnitude? A. 4α0

B. 2α0

C. α0

A – 10

D. α0/2

Second Long Exam

First Semester, AY 2015–2016

Physics 71

36.   Transformer.  Iko-tron is a robot that can transform from a disk of radius R  to a rod of  length  4 R. In an outer space battle, Iko-tron spins in his disk form with an angular speed  ωdisk . He then transforms himself into a rod (see the extraordinary figure below), giving of  ω him a new angular speed of  ω  ωrod . What is the  ratio of  ω  ωdisk  to that of  ω  ωrod ?

A. 1:4

B. 1:6

C. 2:3

37.  Super Stick.   A uniform stick with length 3.00[m] and [kg] is moving and rotating about its center of  mass 5 .00 [kg] mass (CM) as shown in the figure. If the stick and point O both lie in the same xy -plane, what is the  total angular momentum  of the stick at point O at the instant shown?

 −76.7[kg · m2/s] k ˆ ˆ B. −95.4[kg · m2/s] k 

A.

ˆ C. +76.7[kg  m2 /s] k 

· ˆ D. +95.4[kg · m2 /s] k 

38.  Nahuhulog ka na ba?   A block with mass  m  rests on a frictionless, horizontal horizontal surface. A cord attached to the block passes over over a pulley whose radius is  R , to a hanging block with mass  2m. The system begins to accelerate with magnitude a   after having been released released from from rest. What What is the magnitude of the net torque on the pulley? A. 2mg

 | − ma|R B. |2mg − 2ma|R

C. 2mg

 |

D. maR

A – 11

− 3ma|R

D. 8:3

Second Long Exam

First Semester, AY 2015–2016

Physics 71

[kg]  and radius  0 .55 [m] [m]  rolls without slipping on 39. Ang  K E rot rot .  A solid sphere of mass  25 [kg] a horizo horizonta ntall surfac surface. e. If its translat translation ional al kineti kineticc energ energy y as it moves moves is 50. [J], what is its rotational kinetic energy? A. 10. [J]

B. 20. [J]

C. 30. [J]

D. 40. [J]

40.   Yow-yow.   A solid sphere yoyo has mass M   and radius R. What hat is the the  velocity of its center of mass  after falling a height  h  from a stationary hand? A.

 10 7

gh

B.

 4 3

gh

C.

A – 12

 10 9

gh

D.

 5 3

gh