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Physics C: Mechanics PHYSICS C
SECTION I, MECHANICS
Time—45 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 Questions 2—3 distance traveled versus time and the speed versus
time for an object uniformly accelerated from rest attime t= 0? (A) Distance W
W 0
(B) Distance W
t— (C) Distance W (D) Distance T
W (E) Distance K
N Speed Speed Sp ed F Speed Speed am a m 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. The ﬁnal speed of the ﬁrst 4kilogram mass is (A) 0 m/s
(B) 2 m/s
(C) 3 m/s
(D) 4 m/s
(E) 6m/s 3. The ﬁnal speed of the two 4kilogram masses that
stick together is (A) 0 m/s
(B) 2 m/s
(C) 3 m/s
(D) 4 m/s
(E) (Sm/s I 4. A particle of mass m moves along a straight
path with a speed 9 deﬁned by the function
u = in2 + c, where b and c areconstants
and r is time. What is the magnitude F of
the net force on the particle at time t = t1 ? (A) Mi2 + c
(B) 3mbt1 + 2c mbtl (D) mbrl + c
(E) Zmbti Physics c: Mechanics 5. An object released from rest at time t = 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 t = I second
to r = 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 I 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) Zlohr
(B) 1101“
(C) [in
(D) IO hr . (E) The point directly across from the starting point
cannot be reached under these conditions. N N
V
v1 2
W E W E
S S
Time tl Time 12 7. Vectors V, and V2 shown above have equal
magnitudes. The vectors represent the velocities
of an object at times t. and 11, respectively. The
average acceleration of the object between time
t. and t; was (A) zero (B) directed north (C) directed west (D) directed north of east
(E) directed north of west 8. A projectile of mass M1 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 Mz. If the kinetic energy of the projectile
after ﬁring is K, the gun will recoil with a kinetic
energy equal to (A) K M
(8) ﬁx M12 M22 K M1
(D) —“—M2 _ M] K MI (E) WK 9. 10. _..\‘: 61 ‘__’x

I A piece of wire of uniform cross section is bent in the shape shown above. What are the coordinates
(It, i) of the center of mass? 3" _.V_
(A) 15/14 6/7
(B) 6/7 6/7
(C) 15/14 3/7
(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 11. 12. Physics c: Mechanlca A particle moves along the xaxis with a non
constant acceleration described by a = 12!,
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 = 32 m
(E) x = 48 m
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 Phyclcc c: Meetnames l3. A ball is dropped from a height of 10 meters onto a
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 L4 5 (B) simple harmonic with a period of about 2.8 s (C) simple harmonic with an amplitude of 5 in (D) periodic with a period of about 2.8 s but not
simple harmonic (E) motion with constant momentum Questions 14 l 5 An object moving in a straight line has a velocity v in meters per second that varies with time t in seconds
according to the following function. v=4+0.5!2 14. The instantaneous acceleration of the object 15. at t = 2 sec0nds is (A) 2 m/s2
(B) 4 m/s2
(C) 5 m/sz
(D) 6 m/s2
(E) 3 m/s2 The displacement of the object between t = 0 and
r = 6 seconds is (A) 22 m
(B) 28 m
(C) 40 m
(D) 42 m
(E) 60 m 16. 17. A pendulum consists of a ball of mass m suspended
at the end of a massless cord of length L as shewn
above. The pendulum is drawn aside through an
angle of 60' with the vertical and released. At the
low point of its swing, the speed of the pendulum
ball is 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
time is equal to the (A) work done by the net force (F — W) (B) work done by F alone (C) work done by W alone (D) difference in the momentum of the rock before
and after this time (B) difference in the potential energy of the rock
before and after this time Physics c: Mechanlcs Questions 18—19 refer to the graph below of the displaoe 19. Which of the following graphs shows the kinetic
‘ment x versus time I 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 r '
x 0 x
18. Which of the following graphs shows the kinetic ¥x 0
energy K of the particle as a function of time t for
one cycle of motion?
(C) K (D) K (MK (B) K 0M1 OPALLT! 0 x o x
(C) K (D) K T (E) K
0 t 0 I
T
E ( _) K Physics C: Moehanlcs 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? M Anﬂlar Momentum
(A) Remains constant Remains constant
(B) Increases Increases
(C) Decreases Decreases Remains constant
Remains constant (D) Increases
(E) Decreases A newly discovered 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 w%&
(ma
©2m
(mJE
(E) R92 22. Two artiﬁcial satellites, l and 2, orbit the Earth in
circular orbits having radii R1 and R2, respec
tively, as shown above. If R; = 2R. , the accelera
tions 0: and a, of the two satellites are related by
which of the following? (A) a2 = 4a:
(B) a2 = 2m
(C) 02 = a]
(D) a2 = %
(E) a2 = 5’41 Phyelea c: Moehanlee 23. A bowling ball of mass M and radius R, whose Pm Q o
. —————  —f R
. . . . 2 2 l I l
moment of inertia about its center 15 3 MR , rolls \\ : ;
I /
without slipping along a level surface at speed 0. ' \\ x : I//
s. _._. ’
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
of length ll as shown above. The ball is released
(A) % i from rest from position P, where the string is hori it ascends an incline is g zontal. It swings through positiOn Q, where the
2 01 string is vertical, and then to position R, where the
(B) 5 E string is again horizontal. What are the directions of
the acceleration vectors of the ball at positions Q
(C) % 2;. and R ?
(D) l 0—2 Position Q Position R
10 g (A) Downward Downward
[,2 (B) Downward To the right
(E) :2— (C) Upward Downward
(D) Upward To the left (E) To the right To the left 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 Questions 2627 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 = 5 cos (3:)
y = 5 sin (3:) 26. What is the period of revolution of the particle?
1 ,
(A) g s (B) 38 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 approximawa 6,000 kilo—
meters. The acceleration of an astronaut in a
perfectly circular orbit 300 kilometers above the
Earth would be most nearly (A) Dm/s2
(B) 0.05 111152
(C) 5m/Sz
(D) 9 m/s2
(E) 1] t'n/s2 Phyelel c: Mechanics 20N
_ 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 2kilogram 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 to 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) ff
(B) g
(C) ",4;
(D) $
(E) § Physics c: Meehanlcs x—ﬁF—QAF 3]. 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) 7 (B) t
le—Q—i Irrl
o———>2F 0~——;——F (C)0'__Q__I (D)0‘_Q'__i D6032!" HE!" ‘ 30°I
(E) None of the above 32. A 10kilogram 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) = 6x2 — 4x + 3 The force on the particle at x = 3 meters is (A) 32N in +x direction
(B) 32N in x direction
(C) 45 N in +x direction
(D) 45 N in x direction
(E) 98 N in +x direction 33. 34. 35. 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) Sin/s
(B) 10 m/s
(C) 14.1m/s
(D) 20 m/s
(E) 28.3 m/s 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 A satellite moves in a stable circular orbit with
speed :20 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 t}
(A) 7° (13) ole (C) 00 (D) 290 w (E) 290 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. ...
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 Spring '05
 Goodlore
 Physics, mechanics

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