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Unformatted text preview: Physics C: Mechanics PHYSICS C
SECTION I, MECHANICS
Timei45 minutes
35 Questions Directions: Each of the questions or incomplete statements below is followed by five suggested answers or comple
tions. Select the one that is best in each case and then ﬁll in the corresponding oval on the answer sheet. 1. Which of the following pairs of graphs shows the
distance traveled versus time and the speed versus
time for an object uniformly accelerated from rest attime t: 0? (A) Distance F
l\— (B) Distance 6W
V (C) Distance W
l\_ (D) Distance V
V (E) Distance K—
W Speed Speed Speed Speed Speed 51 Questions 23 I Li I I A 4kilogram mass has a speed of 6 meters per second on a horizontal frictionless surface, as shown
above. The mass collides headon and elastically with
an identical 4kilogram mass initially at rest. The second
4kilogram mass then collides headon and sticks to a
third 4kilogram mass initially at rest, 2 Lo.) . The ﬁnal speed of the ﬁrst 4—kilogram mass is (A) 0 m/s
(B) Zm/s
(C) 3 m/s
(D) 4 m/s
(E) 6m/s . The ﬁnal speed of the two 4—kilogram masses that stick together is (A) 0 m/s
(B) 2 m/s
(C) 3 m/s
(D) 4 m/s
(E) 6 m/s . A particle of mass m moves along a straight path with a speed 0 deﬁned by the function
u = bl2 + c, where b and c are constants
and t is time. What is the magnitude F of
the net force on the particle at time t = t1 ? (A) [”12 ‘i' C
(B) 3mbt1 + 2c
(C) mbtl (D) mbtl + c
(E) 2mm] 80 ON TO THE NEXT PAGE Physics C: Mechanics 5. An object released from rest at time 1 = 0 slides down a frictionless incline a distance of 1 meter
during the ﬁrst second. The distance traveled by the
object during the time interval from I = 1 second
to t = 2 seconds is (A) 1m
(B) 2m
(C) 3m
(D) 4m
(E) 5m . Two people are in a boat that is capable of a
maximum speed of 5 kilometers per hour in still
water, and wish to cross a river 1 kilometer wide to
a point directly across from their starting point. If
the speed of the water in the river is 5 kilometers per
hour, how much time is required for the crossing? (A) ilﬁhr
(B) 11—01.:
(C) 1hr
(D) 10 hr (E) The point directly across from the starting point
cannot be reached under these conditions. 52 N N
V
v1 2
W E W E
S S
Time 11 Time t2 7. Vectors V1 and V2 shown above have equal magnitudes. The vectors represent the velocities
of an object at times t. and t2, respectively. The
average acceleration of the object between time ti and t2 was (A) zero (B) directed north (C) directed west (D) directed north of east
(E) directed north of west . A projectile of mass M I is ﬁred horizontally from a spring gun that is initially at rest on a frictionless
surface. The combined mass of the gun and projec
tile is M 2. If the kinetic energy of the projectile
after ﬁring is K, the gun will recoil with a kinetic
energy equal to (A) K M
(B) Hf" M.2 (C) WK (E) W 60 UN Tl] THE NEXT PAGE 9. 10. _,\< ——51
l
1 A piece of wire of uniform cross section is bent in the shape shown above. What are the coordinates
(Tc, i) of the center of mass? x J_
(A) 15/14 6/7
(E) 6/7 6/7
(C) 15/14 8/7
(D) 1 1
(E) 1 6/7 A projectile is ﬁred from the surface of the Earth
with a speed of 200 meters per second at an angle of
30° above the horizontal. If the ground is level, what
is the maximum height reached by the projectile? (A) 5 m
(B) 10 m
(C) 500 m
(D) 1,000 m (E) 2,000 m 53 11. 12. Physlcs c: Mechanics A particle moves along the xaxis with a non
constant acceleration described by a = 12t,
where a is in meters per second squared and t is in seconds. If the particle starts from rest so that
its speed 0 and position x are zero when r = 0,
where is it located when t = 2 seconds? (A) x = 12m
(B) x = 16m
(C) x = 24m
(D) x = 32m
(E) x =48m A ﬁgure skater is spinning on frictionless ice with her arms fully extended horizontally. She
then drops her arms to her sides. Which of the
following correctly describes her rotational kinetic
energy and angular momentum as her arms fall? Rotational Kinetic Angular
Energy Momentum
(A) Remains constant Remains constant
(B) Decreases Increases
(C) Decreases Decreases
(D) Increases Decreases
(E) Increases Remains constant [50 ON TO THE NEXT PAGE Physics C: Mechanics hard surface so that the collision at the surface may
be assumed elastic. Under such conditions the
motion of the ball is (A) simple harmonic with a period of about 1.4 s (B) simple harmonic with a period of about 2.8 s (C) simple harmonic with an amplitude of 5 m (D) periodic with a period of about 2.8 s but not
simple harmonic (E) motion with constant momentum 13. A ball is dropped from a height of 10 meters onto a T
L 16. A pendulum consists of a ball of mass m suspended
at the end of a massless cord of length L as shown
above. The pendulum is drawn aside through an Questions 1415 angle of 60° with the vertical and released. At the
 low point of its swing, the speed of the pendulum
An object moving in a straight line has a veloCity v ball is
in meters per second that varies with time t in seconds
according to the following function. (A) ‘ / gL
1: = 4 + 0.5 t2 (B) 2gL
1 14. The instantaneous acceleration of the object (C) 2 gL at t = 2 seconds is (D) gL (A) 2 m/s2 (B) 4 m/s2 (E) 2gL (C) 5 m/s: 8%) g 34:2 17. A rock is lifted for a certain time by a force F that is greater in magnitude than the rock’s weight W.
The change in kinetic energy of the rock during this 15. The displacement of the object between t = 0 and time is equal to the I = 6 seconds 15 (A) work done by the net force (F — W) (A) 22 m . (B) work done by F alone (B) 28 m (C) work done by W alone (C) 40 m (D) difference in the momentum of the rock before (D) 42 m and after this time (E) 60 m (E) difference in the potential energy of the rock before and after this time [100N111 lHE NEXT PAGE 54 Physics C: Mechanics Questions 1819 refer to the graph below of the displace 19. Which of the following graphs shows the kinetic
ment x versus time t for a particle in simple harmonic energy K of the particle as a function of its
motion. displacement x? x (A) K (B) K
0 T t
0 x 0 x
18. Which of the following graphs shows the kinetic energy K of the particle as a function of time t for
one cycle of motion? (C) K (D) K W n; M 60 UN ll] lHE NEXT PAGE :PW
EM
W 55 Physics C: Mechanics 20. A satellite travels around the Sun in an elliptical 21‘ orbit as shown above. As the satellite travels from
point X to point Y, which of the following is true
about its speed and angular momentum? SEeed Angular Momentum
(A) Remains constant Remains constant
(B) Increases Increases
(C) Decreases Decreases Remains constant
Remains constant (D) Increases
(E) Decreases A newly discrwered planet, “Cosmo,” has a mass
that is 4 times the mass of the Earth. The radius of
the Earth is Re. The gravitational ﬁeld strength at
the surface of Cosmo is equal to that at the surface
of the Earth if the radius of Cosmo is equal to m%&
(me
(C) 2R9 (D) \/ Re (E) Re2 56 22. Two artiﬁcial satellites, 1 and 2, orbit the Earth in circular orbits having radii R1 and R2, respec
tively, as shown above. If R2 = 2R1, the accelera—
tions :12 and al of the two satellites are related by
which of the following? (A) a; = 4a]
(B) (12 = 2611
(C) 02 = 61]
(ma=%
(E) a2 = % GO ON TO THE NEXT PAGE Physles C: Mechanics 23, A bowling ball of mass M and radius R, whose Pm 52 0_ ______ T R
l
moment of inertia about its center is % MR2, rolls \\ 1 I,
\ ' //
without slipping along a level surface at speed v. \ \ i // Q The maximum vertical height to which it can roll if 24. A ball of mass m is attached to the end of a string ‘1 ds an incline ’s .
1 3306“ 1 0f length 52 as shown above. The ball is released (A) l E from rest from position P, where the string is hori
5 g zontal. It swings through position Q, where the
2 v2 string is vertical, and then to position R, where the
(B) 3 g string is again horizontal. What are the directions of
2 the acceleration vectors of the ball at positions Q
(C) % v? and R '2
(D) 7 ”2 W W
10 g (A) Downward Downward
1,2 (B) Downward To the right
(E) E ' (C) Upward Downward
(D) Upward To the left
(E) To the right To the left GO ON Tﬂ THE NEXT PAGE 57 Physics C: Mechanics 25. A mass m moves on a curved path from point X to point Y. Which of
the following diagrams indicates a possible combination of the net force F on the mass, and the velocity v and acceleration a of the mass at the loca
tion shown? (A) y (B) y [30 ON TO THE NEXT PAGE 58 Questions 26—27 A particle moves in a circle in such a way that the x
and ycoordinates of its motion are given in meters as
functions of time t in seconds by: x
.V 5 cos (3:)
5 sin (32‘) 26. What is the period of revolution of the particle? (A) %s (B) 35 (E) 67: s 27. Which of the following is true of the speed of the
particle? (A) It is always equal to 5 m/s. (B) It is always equal to 15 m/s. (C) It oscillates between 0 and 5 m/s.
(D) It oscillates between 0 and 15 m/s.
(E) It oscillates between 5 and 15 m/s. 28. The radius of the Earth is approximately 6,000 kilo
meters. The acceleration of an astronaut in a
perfectly circular orbit 300 kilometers above the
Earth would be most nearly (A) ()m/s2
(B) 0.05 m/32
(C) sin/s2
(D) 9m/s2
(E) 11 m/s2 59 Physics C: Mechanlcs 20N
— 3kg 2kg 29. Two blocks are pushed along a horizontal friction 30. less surface by a force of 20 newtons to the right, as
shown above. The force that the Zkilogram block
exerts on the 3kilogram block is (A) 8 newtons to the left
(B) 8 newtons to the right
(C) 10 newtons to the left
(D) 12 newtons to the right
(E) 20 newtons t0 the left When a mass m is hung on a certain ideal spring,
the spring stretches a distance d. If the mass is then
set oscillating on the spring, the period of oscillation
is proportional to (A) f
(B) 5
(C) mi;
(D) %
(E) g 60 UN 11] THE NEXT PAGE Physlcs C: Mechanics Xswma
___1F 31. In which of the following diagrams is the torque
about point 0 equal in magnitude to the torque
about point X in the diagram above? (All forces lie
in the plane of the paper.) (A) (B) Q
sw—i hﬂ
0*——7? 0—?“ “yew—4 J—wa
i‘étPZF 2135i” 30°I (D) (E) None of the above 32. A lOkilogram body is constrained to move along
the x—axis. The potential energy U of the body in
joules is given as a function of its position x in
meters by U(x)= 6x24x +3 The force on the particle at x = 3 meters is (A) 32N in
(B) 32 N in
(C) 45 N in
(D) 45 N in
(E) 98 N in +x direction
ex direction
+x direction
ﬁx direction
+x direction 33. A rock is dropped from the top of a 45meter tower,
and at the same time a ball is thrown from the top
of the tower in a horizontal direction Air resistance
is negligible. The ball and the rock hit the level
ground a distance of 30 meters apart. The horizontal
velocity of the ball thrown was most nearly (A) Sm/s
(B) 10 m/s
(C) 14.1 m/s
(D) 20 m/s
(E) 28.3 m/s 34. Two objects of equal mass hang from independent
springs of unequal spring constant and oscillate up
and down. The spring of greater spring constant
must have the (A) smaller amplitude of oscillation
(B) larger amplitude of oscillation
(C) shorter period of oscillation
(D) longer period of oscillation (E) lower frequency of oscillation 35. A satellite moves in a stable circular orbit with
speed so at a distance R from the center of a
planet. For this satellite to move in a stable circular
orbit a distance 2R from the center of the planet,
the speed of the satellite must be (A) % ﬂ).
2 (C) 00 (D) M (E) 200 (B) END OF SECTION I, MECHANICS IF YOU FINISH BEFORE TIME IS CALLED, YOU MAY CHECK YOUR WORK
ON SECTION I, MECHANICS, ONLY.
DO NOT TURN TO ANY OTHER TEST MATERIALS. 60 ...
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