Download Gravity and SHM Review Questions

Gravity and SHM Review Questions
1. The mass of Planet X is one-tenth that of the Earth, and its diameter is one-half that of the Earth. The
acceleration due to gravity at the surface of Planet X is most nearly
(A) 2m/s2
(B) 4m/s2
(C) 5m/s2
(D) 7 m/s2
(E) 10 m/s2
2. A satellite travels around the Sun in an elliptical 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?
Speed
Angular Momentum
(A) Remains constant
Remains constant
(B) Increases
Increases
(C) Decreases
Decreases
(D) Increases
Remains constant
(E) Decreases
Remains constant
3. 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
(A) ½Re
(B) Re
(C) 2Re
(D) R e
(E) Re2
4. Two artificial satellites, 1 and 2, orbit the Earth in circular orbits having radii R1 and R2, respectively, as
shown above. If R2 = 2R1, the accelerations a2 and a1 of the two satellites are related by which of the
following?
(A) a2 = 4a1
(B) a2 = 2a1
(C) a2 = a1
(D) a2 = a1/2
(E) a2 = a1/4
5. A satellite moves in a stable circular orbit with speed vo 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)
v0
2
(B)
v0
2
(C) vo
(D)
2v 0
(E) 2vo
6. When an object is moved from rest at point A to rest at point B in a gravitational field, the net work
done by the field depends on the mass of the object and
(A) the positions of A and B only
(B) the path taken between A and B only
(C) both the positions of A and B and the path taken between them
(D)
the velocity of the object as it moves between A and B
(E) the nature of the external force moving the object from A to B
7. A newly discovered planet has twice the mass of the Earth, but the acceleration due to gravity on the
new planet's surface is exactly the same as the acceleration due to gravity on the Earth's surface. The
radius of the new planet in terms of the radius R of Earth is
2
(A) ½R
(B)
R
(C) 2 R
(D) 2R
(E) 4R
2
8. A small mass is released from rest at a very great distance from a larger stationary mass. Which of the
following graphs best represents the gravitational potential energy U of the system of the two masses as
a function of time t?
(A)
U
(B)
U
(C)
O
O
t
t
(D)
U
O
U
(E)
O
U
O
t
t
t
9. A simple pendulum of length l. whose bob has mass m, oscillates with a period T. If the bob is replaced
by one of mass 4m, the period of oscillation is
(A)
1
T
4
(B)
1
T
2
(C) T
(D) 2T
(E)4T
Questions 10-11
A 0. l -kilogram block is attached to an initially unstretched spring of force constant k = 40 newtons per
meter as shown above. The block is released from rest at time t = 0.
10.
What is the amplitude of the resulting simple harmonic motion of the block?
(A)
11.
1
m
40
(B)
1
m
20
(C)
1
m
4
(D)
1
m
2
(E) 1m
At what time after release will the block first return to its initial position?
(A)
π
40
s
(B)
π
20
s
(C)
π
10
s
(D)
π
5
s
(E)
π
4
s
12.
A particle moves in simple harmonic motion represented by the graph above. Which of the following
represents the velocity of the particle as a function of time?
(A) v(t) = 4 cos πt
(B) v(t)= πCosπt
2
(C) v(t) = -π cosπt
(D) v(t) =-4 sinπt
(E) v(t) = - 4πsinπt
13.
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 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
Questions 14-15 refer to the graph below of the displacement x versus time t for a particle in simple
harmonic motion.
14.
Which of the following graphs shows the kinetic energy K of the particle as a function of time t for
one cycle of motion?
15.
Which of the following graphs shows the kinetic energy K of the particle as a function of its
displacement x ?
16.
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)
17.
d
g
(B)
g
d
(C)
d
mg
(D)
m2 g
d
(E)
m
g
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
1. A satellite of mass m is in an elliptical orbit around the Earth (Figure on Left), which has mass Me and
radius Re. The orbit varies from closest approach of a at point A to maximum distance of b from the center
of the Earth at point B. At point A, the speed of the satellite is vo. Assume that the gravitational potential
energy Ug = 0 when masses are an infinite distance apart. As the satellite passes point A, a rocket engine on
the satellite is fired so that its orbit is changed to a circular orbit of radius a about the center of the Earth
(Figure on Right). Express your answers in terms of a, b, m, Me, Re, vo, and G.
a. Determine the speed of the satellite for this circular orbit.
b. Determine the work done by the rocket engine to effect this change. (See your solutions to
“Kepler’s Law Worksheet” Problem #4)