Review Exercise 1
Chapters 1 and 2
Section 1: Definitions
¢
The field of physics is usually
divided into the following two branches
Ø
_____________________ physics and
classical
Ø
______________________ physics.
modern
The former deals
with topics such as fluids, heat, and sound. The latter deals with things
such
topics as
relativity and cosmology.
¢ When scientists are trying to understand a set of phenomena, they often make a _________________. This is a kind of analogy of the
phenomena expressed in
terms of something
already known. It usually relatively simple.
model
¢
A ________________ is broader and
more detailed than the above. It can give testable predictions.
theory
¢
A _______________ is a concise and
general statement about how nature behaves (that energy is
conserved, for example).
Law
¢
The number of reliably known digits
in a number is called the number of
_______________________________
significant figures
¢ The phrase _____________________ often refers to the power of ten. This phrase also refers to a technique for rapidly obtaining an
approximate value for a quantity.
order of magnitude
¢
The field of mechanics is typically
divided into the following two parts. The first deals with a
The second deals with force and why objects move as they
do.
Ø
____________________________________
kinematics
Ø
____________________________________
dynamics
¢
The ______________________ of an
object refers to how far it has moved from its starting point.
displacement
¢ Distance travelled divided by total time is called ____________________ average speed
¢
Change in velocity divided by total
time is called _____________________
average acceleration
¢
A _____________________ is a
mathematical point with no spatial extent.
particle
¢ Given the quantity Dv/Dt, where the variables and symbol have the usual meaning as described in the text. If we take the limit of this quantity as
Dt
Þ
0
(meaning as given in the text) then we call
the result ____________________________.
instantaneous acceleration
Section 2: Units
¢
In the SI system, state the base
unit in each of the following
Ø
Time_________________
second
Ø
Mass_________________
kilogram
Ø
Length_______________
meter
Section
3: Measurements, Uncertainty, Significant Figures
¢
Given that 1 inch is 2.54
centimeters, express 1 foot in centimeters. Show your work.
1 foot =
12.0 inches, so (12 inches/foot)(1 foot)(2.54
centimeters/inch) = (2.54)(12.0) =
30.5 cm
¢
State how
many significant figures are in each of the following
Ø
0.0045 cm
_______________
2
0s are placeholders to show where the decimal
goes
Ø
1894.3 cm
_______________
5
¢
Express the following in scientific
notation
0.6324
___________________ 6.324 x 10-1
Section
4. Dimensions and Dimensional Analysis
¢ A student derived the following equations in which x refers to distance travelled, v the speed, a the acceleration in m/seconds2 and t the time in
seconds. The subscript 0 means a
quantity at time t = 0.
Could the equation possibly be
correct according to a dimensional check?
a. x = vot
+ 10at2
Yes. The quantity vot
has units of (m/s)(s) = m, and 2at2
has units of (m/s2)(s2)
= m. Thus, since each term has
units of meters,
this
equation can be correct.
b. v = y0t
+ yt
No. The quantity y0t as units of ms and the quantity yt has units
of ms. These do not equal m/s on the left
Section
5. Kinematics Equations for Constant Acceleration
¢ Suppose a ball is dropped from a tower that is 35 meters high. How far will it fall in 5 seconds? Take positive direction as down. Show all
calculations
y1
= v0t1 + (1/2)at12
= 0 +
(1/2)(9.80 m/s2)(5 s)2 = 122.5 m
The ball
hits the ground.
¢
Suppose a ball is thrown downward
from the above tower with a velocity of 2 m/s.
]
What would its position be (how far has it travelled) after 2 seconds?
y1
= v0t1 + (1/2)at12
as above but the initial velocity is no longer 0, it is 2 m/s
y1
= (2 m/s)(2 s) + (1/2)(9.80 m/s2)(2 s)2 = 23.6 m
]
What would its velocity be after 2 seconds?
v = v0
+ at = (2 m/s) + (9.80 m/s2)(2)
= 21.6 m/s
¢ Suppose a ball is thrown upward from a tower that is 40 meters high with an initial velocity of 20 m/s. Choose positive as up. How high does it go?
We are interested in the location of the ball when the velocity (not the acceleration) is = 0. This is the max height attained.
The following
calculations below are from the position thrown - no deductions if you
measure from the ground.
Positive direction is taken as up.
We use
the equation v2 = v02 + 2a(y - y0)
y0
= 40, v0 = 20, a = -9.80, v = 0
substituting these values into the above equation yields
0 = 202
+ 2(-9.80)(y - 40)
solving
for the variable of interest, y, yields
0 = 400
+ 19.60(y - 40) or
y =
384/19.60 = 19.59 or 19.6
¢
It was pointed out in the text that
the quadratic formula is very useful in solving a wide variety
y = y0
+ v0t + (1/2)at2
Use the quadratic
formula to solve for t in terms of the other quantities provided
Note. This formula is essential for chapter 3. For the purpose of this
review exercise, however, it is graded as an unannounced extra credit
problem.
The
quadratic equation or formula is usually written ax2 + bx + c = 0
where the values a, b, and c are constants. a is the coefficient of the
squared term containing the variable, b is the coefficient of the variable
to the first power and c is the constant.
The
solution is
x =
-b ± ((b2-4ac))1/2
2a
For
example, the equation of interest could be 4x + 9x2 = 10. We
first place it in the standard form
9x2 + 4x -10 = 0.
In this case a, b, and c are 9, 4, and -10 respectively.
In the
equation given above (y = y0 + v0t + (1/2)at2)
We first
place it in standard form as explained.
(1/2)at2
+ v0t + (y0 - y) = 0
t =
-b ± ((b2-4ac))1/2
where I have
replaced x with t
2a
The
coefficient of the squared term is (1/2)a, the coefficient of the single
power term is v0 and the constant is y0 - y
Just
substitute these into the given quadratic formula
Extra Credit
¢ For all of the courses I teach, I provide pictures and a brief biography of people that I consider giants in the field. List any 3 (last names only) that
are on my AP
physics home page. You must list 3 to get
any credit. I will count only the first 3 names listed if you list more than
3.
¢
I frequently repeat the following
quote from one of the giants whose picture and biography appears on my AP
Physics home page. His name is
____________________________
Richard Feynman
¢
____________________________ is
referred to as the Father of Science
Galileo
¢ The name of the physicist shown here is: ______________________________ Must list first and last names to get any credit. Richard Feynman
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