Vectors
There is a great temptation to put vectors tail-to-tail when you go to add them.
May all the battles that you wage in your war against that temptation end with
your glorious triumph. Vectors add head-to-tail.
We are about to embark on the study of
Depicted below is a disk moving on a frictionless horizontal
surface. The diagram represents a single multiple-exposure
photograph of the disk. The light source is a strobe light
which flashes once every second (1.00 s). The photograph
has been annotated
(Demo) Suppose that both objects are spinning
at the same rate. In which case, if either is the
angular momentum greater?
a) The case in which the cylinders are close
to the axis of rotation.
b) The case in which the cylinders are far
from the axis of rot
A truck rear ends a car that is sitting at a traffic light. The
two stick together and slide into the intersection as one.
From the skid marks, a police officer determines the speed
of the pair at the instant after the collision. Then, she
applies conserv
A cannon with a lit fuse is sliding forward
on a flat horizontal frictionless surface.
The powder explodes, the ball exits the
cannon at a high speed and the cannon
itself comes to a complete rest. Is
mechanical energy conserved in this
process?
a) Yes
b)
A particle of mass m is launched from a height h
at a velocity of 15 m/s at an angle of 35 above
the horizontal over flat level ground. Where in
the trajectory of the particle is the potential
energy of the particle greatest?
a) At the first instant after
8/19/2007
st
1 Semester
SAC
Physics
Problems
SAC102
The set includes problems involving translational kinetic energy, the gravitational potential
energy of objects near the surface of the earth, and the principle of the conservation of
mechanical energy.
A physics professor wishes to demonstrate that applying
the same force to two different objects over the same
distance results in a bigger impulse to the more massive
object. He sets up two horizontal tracks with two identical
carts. A string extends hori
A piston is used to keep a gas compressed in a
cylinder such that the pressure of the gas is
greater than atmospheric pressure. The piston is
on top of the gas with the face of the piston facing
downward. A person is holding the piston down.
The person re
For motion along a line with forward
positive: Suppose the acceleration of an
object is a constant 2.00 m/s2. Further
assume that the object is released from rest
at time 0. How much does the velocity of
the object increase during the first second
of the
What is wrong with the part of the procedure,
shown below, used to solve this problem?
Two cars are headed toward each other. At time
zero they are 885 m apart. Car 1 is moving at a
steady 33.0 m/s (and continues to do so
throughout the period of observat
140
120
100
Position [m]
During which
time interval is
the car always
backing up?
a) 0-5s
b) 5-10s
c) 10-15s
d) None of
the above.
Position vs. Time
80
60
40
20
0
0
5
10
Tim e [s]
15
140
120
100
Position [m]
During which
time interval is
the car always
sp
Unit Vectors
What is probably the most common mistake involving unit vectors is simply leaving their
hats off. While leaving the hat off a unit vector is a nasty communication error in its own
right, it also leads one to worse mistakes such as treating ve
Integration
An integral is an infinite sum of infinitesimal terms.
An integral is an operator. I want to convey what I mean by the term operator by first
discussing an operator with which you are already familiar, namely the derivative operator. An
operat
Some Simple Algorithms1 for Calculating Derivatives
The Derivative of a Constant is Zero
Suppose we are told that
x = xo
where xo is a constant and x represents the position of an object on a straight line path, in
other words, the distance that the objec
A fully-loaded eighteen-wheel tractor-trailer rig
(a.k.a. a big truck) and a small passenger
vehicle experience a head-on collision with
each other. Which vehicle, if either, exerts a
greater force on the other vehicle, during the
collision?
a) The truck
(Demo) I launch one die forward and at the
instant of launch I drop another one from right
beside the first one.
Which die hits the floor first?
a) The launched die.
b) The dropped die.
c) Neither; both dice hit at the same time.
A boy throws a rock. It l
A professor simultaneously drops 2 metal
objects from a window of alumni hall. The
professor releases both objects from rest at
one and the same height (11m above the
ground). One object is a lot heavier than the
other. Air resistance is negligible. Which
Did you do the reading assignment?
a) Yes
b) No
c) Sort of.
A ship at sea is traveling with a compass
heading of 0 at (non-zero) speed vsw relative to
the water which itself is moving with speed vwg
at 15 east of south. In what
direction is the ship going
A disk is moving on the surface of the ice at an iceskating rink. An x-y coordinate system has been
defined for the surface of the ice. At time zero, the
disk is at the origin and moving with a velocity of
5 m/s at 70. The disk experiences a constant
acce
Is it possible to warm up an ice cube
without melting it?
a) Yes
b) No
Is it possible to heat up water vapor
beyond 100C?
a) Yes
b) No
If heat flows into liquid water, and
there is no other exchange of
energy between the liquid water and
the surroundings,
If 475 J of heat flows into a 225 gram
sample of water,
a) the heat of the sample decreases by
475 J.
b) the heat of the sample increases by
475 J.
c) None of the above.
Whenever heat flows into a substance,
the temperature of that substance
increases.
a)
The diagram shows an
object suspended vertically
by string 3 which is tied to
two other strings, string 1
and string 2. In which string
is the tension greatest?
2
1
3
m
a) String 1
b) String 2
c) String 3
d) Not enough information is given.
4
A bowling ba
Particles 1 and 2, having masses m1 = m and
m2 = 2m respectively, lie on the x axis at
(0, 0, 0) and (1.00 m, 0, 0) respectively. Where
is the center of mass?
a) Midway between the two particles.
b) Between the two particles, closer to
particle 1.
c) Betw
B
A
What is the direction of
?
a) Toward the right side of the page.
b) Toward the left side of the page.
c) Toward the top of the page.
d) Toward the bottom of the page.
e) Out of the page.
f) Into the page.
A small telescope is mounted on a ball and soc
What is the direction of the angular velocity of
the second hand of the clock on the wall in this
room?
a) Northward
b) Southward
c) Eastward
d) Westward
e) Upward
f) Downward
Axis of
Rotation
a
b
O
c
F
Which distance in the diagram above is the
moment ar
Did you do the reading assignment?
a) Yes
b) No
c) Sort of.
A person inverts a bicycle and gives the wheel
a spin. If I ask you how many revolutions it will
complete before it comes to rest, I am asking
you to find the value of:
a)
b)
c) I
d) None of th
Is it appropriate to say that a disk is spinning at
a rate of 15 m/s?
a) Yes.
b) No.
Is it possible for a particle to have a non-zero
acceleration while it is moving at a constant
speed?
a) Yes.
b) No.
A person ties a rock to the end of a piece of
string
Consider the two erasers on the whiteboard
tray. Are they exerting a gravitational force on
each other?
a)Yes.
b)No.
Consider the two erasers on the whiteboard
tray. Are they accelerating toward each other?
a)Yes.
b)No.
Consider the two erasers on the whi
Suppose you give a cart, that is at rest on a
horizontal frictionless track, a horizontal shove,
in the forward direction, with your hand. After
the cart leaves your hand:
a) The force of your hand on the cart is
forward.
b) The force of your hand on the