Download Final Exam from 2008

PH201
BASIC PHYSICS I
FALL 2008
EXAM IV – FINAL EXAM
All work on this exam must be your own. You may use a calculator and two 3"X5" cards of equations.
Clearly indicate your final answer for each question.
PART I: equilibrium and gravity
Section 1: Multiple choice. No partial credit will be given for this section. Circle only one answer for each
question. No justification required. (2 pts each)
1.
Given the graph on the right of the potential energy
of a particle as a function of its position, which of
the graphs below could possibly be the force on the
particle as a function of its position?
a)
i only.
b) ii only.
c)
iii only.
d) i or ii.
2.
Refer to the graph in question #1 of the potential energy of a particle as a function of its position. Of
all the positions graphed, where is the particle going the fastest?
a)
0.
b) 1.5 cm.
c)
4.25 cm.
d) 5 cm.
3.
A sign is hanging, held in equilibrum by three cables, as shown.
Consider the torques around the upper-right-hand corner of the sign.
The torque due to the horizontal cable is ____, and the torque due to
the vertical cable is ____. (Counterclockwise is taken as positive.)
a)
zero, negative
VOGEL
CORP
b) positive, negative
c)
negative, positive
d) negative, zero
4.
Consider the uniform ball shown on the right. All forces acting on the
ball are shown, each force acts either left or right, and each force acts
either at the center of the ball, at the edge of the ball, or halfway between
the center and the edge. In order for the ball to be in equilibrium, a fourth
force should be exerted
a)
at a point halfway between F and the center of the ball, pointing to
the right.
b) at a point halfway between F and the center of the ball, pointing to the left.
c)
at the center of the ball, pointing to the left
d) none of the above, the ball is already in equilibrium.
5.
Two planets have the same mass, but one has half the radius of the other (it is more dense). The escape
velocity on the smaller planet is ____ times the escape velocity on the larger planet.
a)
¼
b) ½
c)
2
d) 4
6.
A planet’s orbit around the sun is elliptical. The point in it’s orbit when it is closest to the sun
a)
is called the perihelion and is the point where the planet is moving fastest.
b) is called the perihelion and is the point where the planet is moving most slowly.
c)
is called the aphelion and is the point where the planet is moving fastest.
d) is called the aphelion and is the point where the planet is moving most slowly.
7.
A ladder is leaning up against a wall, in static equilibrium, as shown in the
drawing on the right. There is a horizontal frictional force between the ladder
and the ground. Taking counterclockwise as positive, the torque due to this
frictional force around the center of mass of the ladder is
a)
zero.
b) positive.
c)
negative.
d) answer depends on the coefficient of static friction.
8.
Kepler’s First law states that a planet’s orbit is elliptical, with the sun at one focus of the ellipse. What
is at the other focus?
a)
the planet.
b) another star.
c)
a different planet.
d) probably nothing.
9.
Consider a planet in a circular orbit around a star. If the planet were replaced by a more massive planet
in an orbit with the same radius, which of the following would be true:
a)
the period of the planet’s orbit would be shorter than before
b) the mechanical energy of the planet in orbit would be greater than before
c)
both (a) and (b)
d) neither (a) nor (b)
10. A red rocket of mass m is projected at the escape velocity from the surface of a planet of mass M and
radius R. A green rocket of mass 2m is projected at the escape velocity from the surface of a planet of
mass 2M and radius 2R. Compare the total mechanical energy of the two rockets:
a)
Egreen = 8 Ered.
b) Egreen = 4 Ered
c)
Egreen = 2 Ered.
d) all of the above, since Egreen = Ered =0
Section 2: Problems and questions. (20 pts each) Partial credit will be given for this section. Show all work
and justify all answers. Do three of the four problems. Do all parts of the problems you choose.
mass of the Moon = 7.36 × 1022 kg, radius of the moon = 1737.4 km, G=6.67X10-11 Nm2/kg2.
11. A ball is held 100km above the moon’s surface.
a)
Find the acceleration of gravity on the ball at that position.
b) If the ball is dropped from that height, how fast will it be going when it hits the moon’s surface?
Assume no dissipation.
12. A planet's moon travels in an approximately circular orbit of radius 5 X107 m with a period of 7 hours.
a)
Calculate the mass of the planet.
b) Find the speed of this moon in its orbit.
c)
State Keppler’s 2nd Law, also called the Law of Equal Areas. What does this law imply about the
speed of a satellite in an elliptical orbit?
13. A 50-g picture frame is hung from a wire, which is attached to two
other wires which are attached to the ceiling. The left wire has a
tension of 0.415 N and makes an angle of 40o with the ceiling.
a)
Find the tension in the right wire.
b) Find the angle the right wire makes with the ceiling.
14. Stuart the student is cleaning out his desk after finals. He opens the hinged
lid on his trash can by exerting a force that makes an angle of 80 o with
horizontal. He keeps the lid open at an angle of 40o with horizontal. The lid’s
mass is 50 g. Since the trash can lid is symmetric, this can be considered a 2D problem, and the center of mass of the lid is at its center.
a)
Write out an equation for equilibrium of torques acting on the lid, around
the hinge.
b) Find the magnitude of Stuart’s force on the lid.
c)
Find the vertical component of the force the hinge exerts on the lid.
PART II: Review
Section 1: Multiple choice. No partial credit will be given for this section. Circle only one answer for each
question. (1 pts each)
15. If the total momentum of a system is changing:
a)
particles of the system must be exerting forces on each other
b) the center of mass must have constant velocity
c)
a net external force must be acting on the system
d) none of the above, the total momentum cannot change
16. A ball is thrown straight up. Assuming no dissipation, during its motion after being thrown but before
hitting the ground, its acceleration is:
a)
downward at all times.
b) downward during ascent and upward during descent
c)
upward during ascent and downward during descent
d) upward at all times.
e)
downward at all times except at the very top, when it is zero
17. A ball strikes the floor at an angle and bounces back up at the same angle with the same speed. Let the
y-axis point up, and the x-axis point right in the figure:
The vector change in momentum of the ball is
a)
in the negative x direction.
b) in the positive x direction.
c)
in the negative y direction.
d) in the positive y direction.
e)
zero
18. A block is being pulled up a slope at constant speed by a force, F p, which is directed along the slope.
Which of the following is true (f = the frictional force, FN = the normal force, and Fg= the block’s
weight).
a)
| FN | = | Fg |.
b) | f | = | Fp |.
c)
Fg is a force exerted by the block on the slope.
d) more than one of the above is true.
e)
none of the above is true.
Section 2: Problems and questions. Do all of the following problems.
Partial credit will be given for this section. Show ALL WORK and JUSTIFY all answers. Be sure your
answers include UNITS where appropriate. (5 pts each)
19. A ball rolls horizontally off the edge a 0.9-meter-high table. It lands 50 cm away from the edge of the
table. How fast was it going when it left the table?
20. A crane operator lowers a 700 kg steel ball allowing it to speed up at a rate of 3.0 m/s2. What is the
tension in the cable holding the ball?
21. A 2.2-kg ball is moving horizontally at 24 m/s just before it is caught (brought to a stop). How much
work is done on the ball by the person catching it?
22. A hula-hoop has a mass of 27 g and a radius of 35 cm. Two small 5-g decorations are stuck to it, 90o
apart. How far from the center of the hula-hoop is the center of mass of the decorated hula-hoop?