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AP Physics C Chapter 11, 14 Test
1/17/2012
1. Of the satellites shown revolving around the planet in the
accompanying diagram, the one with the greatest speed is
a)
b)
c)
d)
e)
2.
Two planets, which we label A and B, orbit a star of mass
M. Planets A and B have masses mA and mB respectively,
and travel in circular orbits of radii rA and rB, respectively, about the star, with
orbital speeds vA and vB, (again) respectively. Planet B is twice as far from the star
as planet B (rB=2rA). From Newton’s Law of Universal Gravitation and the
expression for centripetal force, we can show that
a)
b)
c)
d)
e)
3.
1.9
1.9
3.6
3.6
3.6
x
x
x
x
x
10-57
10-54
10-53
10-47
10-41
N
N
N
N
N
A woman whose weight on earth is 500 N is lifted to a height of two earth radii
above the surface of the earth. Her weight
a)
b)
c)
d)
e)
5.
vA = vB
vA = (1/2) vB.
vA = 2 vB
vA = 2½ vB
We need to know the mass of the star before we can figure this one out.
What is the force of gravity between the proton and electron in a hydrogen atom,
given that G = 6.67 x 10-11 N-m2/kg2, mass of a proton = 1.67 x 10-27 kg, mass of an
electron = 9.1 x 10-31 kg, and average radius of the electron’s orbit in the hydrogen
atom = 0.0529 nm? (1 nm = 10-9 m)
a)
b)
c)
d)
e)
4.
1
2
3
4
5
decreases
decreases
decreases
decreases
decreases
to
to
to
to
to
one-half of the original amount.
one-quarter of the original amount.
one-fifth of the original amount.
one-third of the original amount.
one-ninth of the original amount.
Two planets have masses M and m, and the ratio M/m = 25. The distance between
the planets is R. The point P is between the planets as shown, and the distance
between M and P is x. At P the gravitational forces on an object due to M and m are
equal in magnitude. The value of x is
a)
b)
c)
d)
e)
5R/6
25R/36
R/25
6R/5
None of these is correct.
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AP Physics C Chapter 11, 14 Test
6.
Five homogeneous planets have relative masses and sizes as shown in the figure
(the radii of the larger ones are twice the radii of the smaller). A body of mass m
would weigh the least on which planet?
a)
b)
c)
d)
e)
7.
1
2
3
4
5
The mass of the earth is M, and its radius is R. If a projectile of mass m is
launched from the surface of the earth with escape speed, its total energy (K + U) is
a)
b)
c)
d)
e)
8.
1/17/2012
GMm/R
GMm/2R
zero
(1/2)mv2
2GMm/R
Again, let the mass of the earth be M and the radius of the earth be R. Suppose a
rocket is fired vertically from the surface of the earth with one-half the escape
speed. How far from the center of the earth will the rocket get before it falls back to
the earth?
a)
b)
c)
d)
e)
3R/2
4R/3
2R
3R
4R
9. The escape speed for a rocket at Earth's surface is ve . What would be the rocket's
escape speed from the surface of a planet with twice Earth's mass and the same
radius as Earth?
a) 2 ve
b)
2ve
c) ve
d)
ve
2
e) ve/2
10. A satellite is orbiting the earth (mass M) in a circular orbit of radius r from the
center of the planet. The total energy (kinetic + potential) of the satellite is
a)
b)
c)
d)
e)
zero
GMm/r
- GMm/r
- GMm/2r
None of these is correct
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AP Physics C Chapter 11, 14 Test
1/17/2012
11.
Test masses are used to measure the
gravitational field at various positions in and
near a solid sphere of uniform density. The
gravitational field will have its greatest value
at point(s)
a)
b)
c)
d)
e)
1
2
3
4
5
12. A tunnel passes all the way through a planet of uniform density, along a diameter
of the planet. Position r is measured from the center of the planet (r = 0) to an
infinite distance from the planet.
The radius of the surface of the
planet is R. There are two points,
one inside the planet and one outside
the planet, where the magnitude of
the gravitational field is one-half the
value that it has on the surface of the
planet. What is the value of r for
these two points?
a)
b)
c)
d)
e)
r = 0, 2R
r = R/2, R
r = R/2, 2½ R
r = R/4, 2½ R
None of these is correct.
13. Any body moving with simple harmonic motion is being acted on by a force that is
a)
b)
c)
d)
e)
Constant.
Proportional to a sine or cosine function of the displacement.
Proportional to the inverse square of the displacement.
Directly proportional to the displacement.
Proportional to the square of the displacement.
14. A particle moving with a simple harmonic motion has its maximum displacement of
+18 cm at time t = 0s. The frequency of the motion is 10 s-1 (10 Hz). At time t =
0.65 s, the position of the particle is
a)
b)
c)
d)
e)
+18 cm
Zero
– 13 cm
– 18 cm
+ 7.3 cm
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AP Physics C Chapter 11, 14 Test
1/17/2012
15. You want a mass that, when hung on the end of a spring, oscillates with a period of
1 s. If the spring has a constant of 10 N/m, the mass should be
a) 10 kg
b)
10 kg
c) 4π2(10) kg
d) 10/(4π2) kg
e) None of these is correct; the period depends on the length of the spring.
16. A particle is oscillating with simple harmonic motion. The frequency of the motion
is 10 Hz and the amplitude of the motion is 5.0 cm. As the particle passes through
its central equilibrium position, the acceleration of the particle is
a)
b)
c)
d)
e)
100 cm/s2
1.6 x 105 cm/s2
4 x 106 cm/s2
zero
3.2 x 106 cm/s2
17. A body of mass 5.0 kg moves in simple harmonic motion according to the equation
x  0.040 sin 30t   6 .
The units are SI. The period of this motion is

a)
b)
c)
d)
e)

1/30 s
π/15 s
π/6 s
15/π s
30 s
18. A body of mass 5.0 kg moves in simple harmonic motion according to the equation
x  0.040 sin 30t   6 .
The units are SI. The maximum speed of this body is approximately

a)
b)
c)
d)
e)

0.013 m/s
0.40 m/s
0.60 m/s
1.2 m/s
30 m/s
19.
A particle moves in one dimension with simple harmonic motion according to
the equation
d 2 x / dt 2  4 2 x
where the units are SI. Its period is
a)
b)
c)
d)
e)
4 2 s
2 s
1s
1/(2) s
1/(4 2) s
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AP Physics C Chapter 11, 14 Test
1/17/2012
20. A 1.0 kg mass oscillates along the x axis with simple harmonic motion. Its position
as a function of time is given by
x  2 cost / 6   / 3
where the units are SI. When t = 2 s, the kinetic energy of the mass is
a)
b)
c)
d)
e)
2/24 J
2/72 J
2/9 J
2/9 J
2/4 J
21. A 0.5 kg mass is suspended from a massless spring that has a force constant of 79
N/m. The mass is displaced 0.1 m down from its equilibrium position and
released. If the downward direction is negative, the displacement of the mass as a
function of time is given by
y  0.1cos158t   
b) y  0.2 cos158t   
c) y  0.1cos12.6t   
d) y  0.2 cos12.6t   
e) y  0.1 cos2t   
a)
22. To double the period of a pendulum, the length
a)
b)
c)
d)
e)
Must be increased by a factor of 2.
Must be decreased by a factor of 2.
Must be increased by a factor of 2½.
Must be increased by a factor of 4.
Need not be affected.
23.
A simple pendulum has a period of 2 s for small amplitude oscillations. The
length of the pendulum is most nearly
a)
b)
c)
d)
e)
1/6 m
1/4 m
1/2 m
1m
2m
24. Which of the following equations could represent the angle θ that the pendulum of
#22 makes with the vertical as a function of time t ?
a) θ = θmax sin
b)
c)
d)
e)
θ
θ
θ
θ
=
=
=
=

2
t
θmax sin πt
θmax, sin 2πt
θmax sin 4πt
θmax sin 8πt
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AP Physics C Chapter 11, 14 Test
1/17/2012
25. A mass M suspended by a spring with force constant k has a period T when set into
oscillation on Earth. Its period on Mars, whose mass is about 1/9 and radius 1/2
that of Earth, is most nearly
a)
b)
c)
d)
e)
1/3 T
2/3 T
T
3/2 T
3T
26. A 1.0 kg mass is attached to the end of a vertical ideal spring with a force constant
of 400 N/m. The mass is set in simple harmonic motion with an amplitude of 10
cm. The speed of the 1.0 kg mass at the equilibrium position is
a)
b)
c)
d)
e)
2 m/s
4 m/s
20 m/s
40 m/s
200 m/s
27.
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)
d
g
b)
g
d
c)
d)
e)
d
mg
m2 g
d
m
g
28. A frictionless pendulum of length 3 m swings with an amplitude of 10°. At its
maximum displacement, the potential energy of the pendulum is 10 J. What is the
kinetic energy of the pendulum when its potential energy is 5 J ?
a)
b)
c)
d)
e)
3.3 J
5J
6.7 J
10 J
15 J
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AP Physics C Chapter 11, 14 Test
1/17/2012
29. Which of the following statements concerning the motion of a simple pendulum is
incorrect?
a) The kinetic energy is a minimum when the displacement is a maximum.
b) The acceleration is a maximum when the displacement is a maximum.
c) The period is changed if the mass of the bob is doubled and the length of the
pendulum is halved.
d) The time interval between conditions of maximum potential energy is one period.
e) The velocity is a maximum when the acceleration is a minimum.
30. A uniform disk (Icm = ½MR2) of mass M and radius R is
suspended from a point on its rim. If it oscillates as a
physical pendulum its period is
a)
2 3R / 2 g
b)
2 3R / g
c)
2 g / R
d)
2 g / 2 R
e)
2 g / 3R
31. The graph shows the square of
the period versus the length of a
simple pendulum on a certain
planet. The acceleration due to
gravity on that planet is
approximately
a)
b)
c)
d)
e)
0.100 m/s2
10.0 m/s2
3.95 m/s2
395 m/s2
0.628 m/s2
32.
What is the length L of a simple pendulum with the
same period as a physical pendulum consisting of a hoop
suspended at its rim?
1
R
2
b) L  1 / R
c) L  2R
d) L  R
e) L  2 R
a)
L
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AP Physics C Chapter 11, 14 Test
1/17/2012
32.
In the laboratory, a stick 1 m
long is pivoted at various points to
illustrate the motion of a physical
pendulum. A plot of the period versus
the distance of the pivot point from
the center of mass is shown. The data
presented demonstrate which of the
following?
a) The motion of the pendulum is
circular about the center of mass.
b) The center of mass is at 0.4 m.
c) The graph is meaningless in this form.
d) There is a minimum period in the
neighborhood of 1.5 seconds at a
pivotal distance of approximately 0.4
m from the center of mass.
e) The graph should be drawn as a straight line from A to C; point D is obviously
wrong.
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