PHYS. 110
Exam ( 3 )
QATAR u NWE RsafY
_ ' Department of
Math ,S'tatics and Physics
14 Jun 2010 in Building 217 SD
Exam Duration: 2 hours (from 8: 00AM to 10: 00AM)
Student Name: . _ .
Question 1: Multiple Choice (24 points)
Circle your choice: '
1. Som
College of Arts & Sciences
Department of Mathematics, Statistics & Physics
Physics Program
Fall 2010
Instructor : Hemyan Ahmed Zayed AL-Kuwari
General Physics For Engineering I (PHYS191): L53 CRN: 11728
Final Examination
Exam Duration: 2 Hours
Sunday, 2nd
PHYS. 110
Exam ( 2 )
-.=I=I . 1:
QATAR umwzksva
Department of
Math ,Sratics and Physics
6 April 2010 in Building 217 SD
Exam Duration: 2 hours (from 9:00AM to 11:00AM)
Student Name: .
Question 1: Multiple Choice (13 points)
Circle your choice:
1. In a g
PHYS. 110
Exam (1)
] -. . L;-
IVERSE' Y
Department of Maia? Etatic Physics
25 March 2010 in Building 217 SD
Exam Duration: (from 9:00 to 10:00)
Student Name: .
Question 1 1 Multiple Choice
Circle your choice: (12 points)
1. Hair grows at a rate of about
LAB PHYS ll 1 Spring 2010 Dr Martha AlMuraikhi
Final Exam '
UNIVERSITY OF QATAR
FACULTY OF SCIENCE
Math ,Static & Physics Department 1 I 6 I 2010
*
Final Exam
Full Name of the Strident: . ' .
Note: any final result Without a unit is- not accepted
Ex
MATH 437-0101 MIDTERM PROBLEM SET
W. GOLDMAN
(1) Problems from 1 of do Carmo: 48, 1518.
(2) Find an example of a contravariant tensor whose alternation is
zero but is not symmetric.
(3) Interior products on a vector space
Let f : U > V be a linear map of
me we.
UNIVERSITY OF QATAR QATAR umvsssnv
FACULTY OF ART & SCIENCE
Physics Department 5 I 4 I 2010
*
Mid-term Exam
Full Name of the Student: .
Note: any nal result without a unit is not accepted
Experimental part:
1- Determination of. the Constant of
Md lat
Spring 2012 - Math 437 Section 0101
Final Exam May 2012
0 You may use your class notes and/or the class textbook during the test.
0 Electronic devices of any kind (including calculators, cell phones, etc.) are not
allowed.
0 Justify all answers car
' H5 Hath
Please write your name on this sheet and turn it in. Each problem is worth 25 points.
Math 437, Spring 2016, Final
Problem 1: (a) Dene f : 1R3 \ cfw_zaxis > R by f(a;,y, z) = %(log(:lc2 + y2)2 + z2. Show that
1 E R is a regular value of f and co
MOVIE!) V) g
Final MATH437
Problems
1.Describe polar coordinates in R2. Find area 2form in this coordinates.
Calculate angle coordinate (f) and angle 1form dd) in the complex coordinates
2,2
2.Dene closed and exact 1-forms in U C R2. Find condition for th
MATH 4370101 FINAL PROBLEM SET
W. GOLDMAN
(1) Let M be a smooth manifold and X a vector eld. Suppose
that ft is a family of diffeomorphisms of M for t E R such that
for each 1) E M and t E R,
$6429) = X(t (19)
and 50(1) 2 p. Use the uniqueness theorem for
Or to have mathematically well behaved quantities
This can be written as:
(11)
where , pronounced chi-squared, is a random variable in the sense that if we repeat the
measurement of and and calculate
every time, then obtained values will be randomly
distr
2. Zeros on the right, usually, are not significant for a non-decimal number but they are significant
for a decimal number:
Examples: 1200 has 2 significant figure (by the first part of this rule). 0.10 has also two significant
numbers (the second part of
3.
4.
5.
6.
7.
Fit linearly your data and get the slope and the intercept.
Using the Excel function linest, calculate the errors on the slope and intercept.
Does your data represent the model given by Eq.7? Look at the fit quality variable
.
Calculate the
lever arm is )
.
38.
The net total torque is then the same as found previously
In summary, the two conditions of equilibrium are as follow:
We will apply these conditions to the system in our experiment. Figure 4, representing the
setup of the experiment,
5 Data Analysis
5.1
Part I: Closed tube
1. Graph, using Excel, the data in table 1: Plot versus and draw the error bars. Do not
forget to put the titles and units on the axes.
2. Fit linearly your data and get the slope and the intercept.
3. Using the Exc
(question 6)
Our data is summarized in the following table:
Average
Time
0.124
0.1613
0.1983
0.238
0.2603
161.3
185.3
202.7
210.5
231.2
1. Putting the Data on X-axis:
The scale on the X-axis is defined such that (0.260 0.124)
corresponds to 14 cm .This is
Figure 7: first three resonances for an open tube. the maximum pressure amplitudes across the tube are shown.
Note that because the tube ends are in direct contact with the ambient air, the pressures at
those location are equal to the atmospheric pressure
Note that
takes only odd values. Equation 7 can be written as:
,
Which is, if we take
and
(8)
as the dependent and independent variables, the equation
of straight line with a slope equal
and zero intercept.
3 Equipment needed :
Function generator, tube, s
Measurement of Viscosity of a Liquid
Experiment (4)
1 Aim of the experiment
In this experiment you measure the viscosity coefficient of an engine oil.
2 Introduction
The viscosity coefficient quantifies the daily experimental fact that different fluids (i
(2)
where
and
are the position of the objects from the center of the see-saw.
and
are
also called lever arms. Therefore, in this case, it is the product
(force times lever arm) which
is of importance. Its called the torque of force .
Figure 2: static equi
1 Aim of the experiment
Measurement of the free fall acceleration due to earths gravity.
2 Theory
Near the earth surface the gravity force is constant. This means a free falling object will have a constant
acceleration . It can be shown that in such a sit
50
40
30
20
10
5 Data Analysis
1. Write down here the error on .
2. Plot, using Excel,
versus time (i.e. on the X-axis, and along the Y-axis) and draw
the error bars (on the same graph). Do not forget to put the titles and units on the
axes.
3. Fit linear
Then
The error on the slope is (see Eq. 17):
Thus
and
Note: The values of the errors
and
obtained here are not equal to the
51
ones obtained with Excel (
1.0468
65.45) . The reason is that Excel does not use the
error stated in the error bars (i.e.
) but
half of this and write the result as
. But in our labs we prefer to stick to the simpler
rule of quoting an error equal to one full unit of the smallest displayed digit).
Note: it should be stressed here that error estimated by the previous prescriptions
Now, if the errors are that important, how should we proceed to estimate them? Here we
distinguish two situations: Estimating the error on directly measured quantities and indirectly
measured quantities. We treat each in turn.
4 How do we Estimate the Err
Introduction
Phys-192 is a laboratory experimental course designed to accompany the theoretical lectures
given in the Phy-191 course. It therefore presents the student with unique opportunities to
have a firm grasp of the abstract concepts and laws he/she
Appendix C: Least-square fit
We will use the method of Least Square to fit our data to a straight line. The aim is to find the
line that represents best our measurements. For this we have to minimize the following
quantity:
(12)
where
and
are our measured
Figure 5: accuracy versus precision
9 Comparing Two Measurements15
If two quantities and
equal if their difference
are exactly known (i.e. no errors is attached to them) then they are
is equal to zero:
(9)
But if it happens that we know the two quantities