Unit 1. Newtonian Mechanics
VI. Oscillations and gravitation
1.
The period of orbit
T
is observed for eight of Jupiter’s satellites. Each satellite’s average distance from the center of Jupiter,
d
, is measured. A graph is produced with each satellite’s period
T
on the vertical axis. Which quantity should be graphed on the horizontal axis in order to most nearly produce a straight line graph?
d
d
3
d
1/2
d
3/2
d
2
2.
A satellite of mass m orbits the earth with tangential speed
v
at a distance
R
from the center of the earth. If a new satellite with mass 2
m
is launched to orbit at the same distance
R
, what will its tangential speed be?
v
/4
v
/2
v
2
v
4
v
Questions 3 & 4 refer to the following statement
A 0.50 kg mass attached to a spring undergoes simple harmonic motion according to the equation
x
(
t
) = 0.20cos(10
t
), where
x
represents displacement, in meters, from the mass’s central position and
t
represents time in seconds.
3.
What is the spring constant of the spring?
200 N/m
50 N/m
3.2 N/m
10 N/m
5.0 N/m
4.
What is the maximum speed of the mass?
10 m/s
0.20 m/s
0.50 m/s
2.0 m/s
5.0 m/s
5.
A simple pendulum is displaced an angle
θ
and released, as shown above. The restoring force
F
which acts along the arc of the bob’s displacement is
mg
sin
θ
. In order to treat this pendulum as a simple harmonic oscillator, which of the following approximations for the restoring force
F
must be valid?
F
=
mg
(
θ
2
/2)
F
= 0
F
=
mg
cos
θ
F
=
mg
F
=
mgθ
6.
A mass
m
attached to a spring of constant
k
oscillates with period
T
and amplitude
A
. Which of the following would double the period?
using a spring of constant
k
/4
using a mass
m
/4
using an amplitude
A
/4
using a spring of constant
k
/2
using a mass
m
/2
7.
An object is released from rest at position
x
=
A
. It oscillates about position
x
= 0 in simple harmonic motion with period
T
. After a time
T
/4, what is the position of the mass?
0
8.
An object is set into simple harmonic motion at position
x
= 0 with speed
v
. The central point of the harmonic motion is
x
= 0, and the amplitude of the motion is
A
. Let the oscillator’s total mechanical energy be
E
. At position
A
/2, what is the kinetic energy of the mass?
9.
The mass of Jupiter is 318 times the mass of the earth; the radius of Jupiter is 11 times earth’s radius. What is the gravitational field near the surface of Jupiter?
110 N/kg
2900 N/kg
2.6 N/kg
26 N/kg
290 N/kg
10.
The radius of mars is about 3400 km. At its surface, Mars’s gravitational acceleration is about 4.0 m/s
2
. Which of the following is a correct graph of Mars’s gravitational acceleration as a function of
d
, the distance from the planet’s surface, for the range
d
= 0 to 2000 m?
A
B
C
D
