Announcements
Review for Exam # 1
9 February 2012
• Homeworks 9 and 10 are due at 6 PM
today.
• Last class the following iClicker numbers
were not registered:
– 14A9E855
– 16BABA16
Pre-class Quiz
1. When is the equation x = (1/2) a t2 valid?
9
a) Constant a, v=0 and x=0 at t=0.
b) Constant acceleration with no initial
velocity.
c) Constant velocity.
d) It is always valid for 1D motion.
e) Any time the acceleration is constant.
40% correct, 42% chose b
Note on pre-class quizzes
• If you have specific questions that would be
difficult to answer in the lecture (such as what
happened to your quiz, lab, or clicker score)
send me an email directly.
• Put your name and CID in the email so I can
identify who you are.
• With the format of the comments on the preclass quizzes it is a 3 step process to respond to
you. It is much easier if you just email me
directly.
Pre-class quiz
2. A car is moving forwards at a constant
speed v and starts to slide at the position
shown. Which path will the car follow?
Explain your answer.
9
9
A
B
C
Practice Exam
1A. Two metal balls are the same size but one
weighs twice as much as the other. The balls
are dropped from a tall building at the same
instant of time. If we take air resistance into
account, which (if either) of the balls will reach
terminal velocity first?
9 1) the lighter one.
2) the heavier one.
3) same for both balls.
4) neither will reach terminal velocity.
79 % chose B
Solution
Practice Exam
• Both will feel the same retarding force at
the same velocity.
• The terminal velocity of the more massive
one will be higher, so it will take longer to
get there.
1B The velocity of a particle can be described in
a certain coordinate system as:
G
v = At iˆ − Bte−t / c ˆj + Dt 4 kˆ . Where A, B, C, and D are
constants. The units on the constant B must be
1) m
2) m/s
9 3) m/s2
4) m/s3
5) 1/s
6) None of the above choices are correct.
• If air drag were proportional to v then we
would have τ = m/b, which is larger for
greater m
Solution
Practice Exam
• The units of each term must be m/s.
• The term of interest is B t e-t/c j
• j is dimensionless, as is e-t/c.
• So B t has units of m/s. t has units of s, so
B must have units of m/s2 so that the s can
cancel to produce m/s.
Solution
Practice Exam
• The z-component of the velocity is Dt4
• The z-component of the acceleration is a z =
• So a z =
dv z d
= (Dt 4 ) = 4Dt 3
dt dt
1C The velocity of a particle can be described in a
certain coordinate system as:
G
v = At iˆ − Bte−t / c ˆj + Dt 4 kˆ . Where A, B, C, and D are
constants. The z component of the particle’s
acceleration is:
1) At
2) A
3) Bt
4) 4Dt4
9 5) 4Dt3
6) None of the above choices are correct.
dvz
dt
1D. A truck is climbing up a hill along a straight
road which is 10 degrees above the horizontal at
a constant 55 mile/hour. The acceleration of the
truck is:
1) Horizontal and nonzero
2) Vertical and nonzero
3) In the direction of the truck’s velocity
4) Opposite to the direction of the truck’s
velocity
9 5) Zero
6) None of the above choices are correct.
Solution
• The truck is moving in a straight line at a
constant speed. That is the definition of
zero acceleration.
Practice Exam
1E A small sphere is suspended from the ceiling by a string and set
swinging in a horizontal circular path with a constant speed. The
figure shows a “snap shot” image of one instant in time. At this
instant, the sphere is moving directly away from you in the view
shown in the figure. The net force at that instant on the sphere will
be in which of the directions represented by the arrows in the figure?
Ceiling
1
6
2
5
3
4
Solution
Practice Exam
• Since the ball is in a horizontal circular
path, the acceleration is toward the center
of the circle.
• That means that the net force must also
be toward the center of the circle.
2A A point particle in a certain
coordinate
G G
G
system has three forces ( A, B, and C ) acting
on it. These three forces hold the particle
G
stationary. If force A = 4iˆ + 4 ˆj − 3kˆ and
G
B = −2iˆ − 7 ˆj − 1kˆ, what is the magnitude of C?
(all forces are given in Newtons)
• That direction is 5.
Practice Exam
Practice Exam
2B. A ball is dropped from at platform 75 m
high. How fast will it be traveling when it
reaches the ground? (ignore air
resistance).
2C. A ball of mass 12 kg is attached to a
string and set spinning in a circular path
on a flat frictionless horizontal table. The
radius of the circular path is 0.5 meters. If
the string will break at a tension of 1500 N,
what is the maximum speed that the
particle can move in this circular path?
Practice Exam
Practice Exam
2D. A 40 kg box is placed on a rough slope (25
degrees above the horizontal). Someone
pushes directly horizontally on the box with a
force of 400 N. The box does not move. What
is the magnitude of the normal force on the box
due to the slope?
F
2E. You are standing on the shore of the Panama
Canal. A cruise ship (in the canal) is passing
you at 10 m/s. You see your Aunt Ruth walking
up a stairway on the cruise ship in the general
direction the ship is moving. The stairway
makes an angle of 35 degrees with the
horizontal. You have previously measured that
your Aunt Ruth walks stairs at a speed of 2 m/s.
If you trace the path of your Aunt Ruth, she
would appear to you to be moving at what angle
(in degrees) relative to the horizontal?
Practice Exam
Practice Exam
• Our hero “Physics Man” has just foiled the latest
scheme hatched by his evil, but clueless arch
enemy “Bad-Physics Man”. We join our hero
standing on the top of a building (height H) and
just having spotted “Bad-Physics Man” (BPM)
running from the building at ground level. We
see that he (BPM) is traveling directly away from
the building with a constant velocity v. As fate
would have it, there is a fishing net on the roof of
this building. This is, of course, a special “point
particle” net with no air resistance.
3A. “Physics Man” throws this net directly
out from the building along the path of
BPM, with an initial velocity of Vnet (the
initial velocity is all in the horizontal
direction). How long does this net take to
reach the ground? The answer should be
in terms of the variables given above (H, v,
Vnet) and fundamental constants. Explain
your reasoning.
Practice Exam
Practice Exam
3B. At the instant the net is thrown, BPM is
x1 meters from the building. How far will
he be from the building when the net
lands? The answer should be in terms of
the variables given above (H, v, Vnet, x1)
and fundamental constants. Explain your
reasoning.
3C. What must the initial velocity of the net
(Vnet ) be in order to catch BPM? Assume
here that H = 30 m, v = 10 m/s, and x1 =
15 m. The answer should be numerical.
Explain your reasoning.
Practice Exam
4. Two masses (M and m) are
attached together with a length of
idealized string and hung over an
ideal pulley (it has no mass and
no friction) as shown in the figure.
The larger mass is a distance h
above the floor and the smaller
mass is resting on the floor. The
string is taught. They are
released from that position,
initially at rest.
Practice Exam
4A. What is the acceleration of the larger
mass (M). Give the answer as a
magnitude and direction in terms of the
given variables and fundamental
constants. Explain your reasoning.
M
m
Practice Exam
4B. How fast is the smaller mass moving
when it is at the same height as the larger
mass? Answer should be in terms of
given variables and fundamental
constants. Explain your reasoning.
Practice Exam
4C. If M = 10 kg, m = 7.5 kg and h = 0.75
meters, how long does it take the 10 kg
mass to get to the floor? Explain your
reasoning.
Practice Exam
Practice Exam
5. One small compact block (mass ms) is placed
on top of a large flat object (mass mL). The
large flat object is resting on a frictionless
surface as shown. There is friction between the
block and object (μs and μk), but none between
the flat object and the lower surface.
5A. A force F is applied to the smaller block
as shown. If F = 20 N, mS = 5 kg, mL = 9
kg, μs = 0.3 and μk = 0.2, what are the
accelerations of the two objects (aS and
aL)? Explain your reasoning.
Friction
F
mS
No Friction
mL
Practice Exam
5B. If mS is initially 1.0 m from the edge of
mL, will mS ever slide off the edge of mL?
If so, how long will it take? Explain your
reasoning.