Ch 1 Introduction and Mathematical Concepts.pdf

Ch 1 Introduction and Mathematical Concepts.pdf

(1) If A = sin 5 o and B = cos 5 o , then:

(1) the same direction as A and

(1) The unit for force is Newton (N) and it’s built

(1.10) The wavelength of the lines in the Balmer series

(1.11) The force between electrostatic charges is described

(1.4) The gas law for an ideal gas is PV = RT, P and T are measured variables, V is

(1.5) The fundamental frequency of vibration of a string is given by

(1.6) The linear expansion of a solid is described by ℓ = ℓo ( 1 +

(1.7) The velocity of outflow of an ideal fluid from a hole in the side of a tank is given

(1.8) A conical pendulum has a period given by where T and α are

(1.9) The discharge of a capacitor is described by

(10) An object falling near the surface of the earth has a constant acceleration of

(2) If A = sin 37 o and B = cos 37 o , then:

(2) magnitude mA .

(2) The unit for energy is Joule (J) and it’s built

(2.4) Choose the correct answer:

(2.5) You are performing an air track experiment. You determine that

(2.7) Your “special” digital watch (or Stopwatch) gives a time

(2.8) Compute the percent error of the approximate value

(3) The roots of the algebraic equation: x2 + 3x

(4) Compute:

(5) To convert from g/cm3 to kg/m3 , you must multiply by:

(6) The vector in the figure that could represent the vector A

(7) Three vectors A , B , and C have the following x and y components:

(8) You are traveling in your car at 82 km/h (23 m/s) when an emergency arises. If

(Hint: Review your lab manual “Introduction to Experimental

►A has and

● Equation of the graph.

● Evaluating the slope and intercept.

● Straight line graph.

● TAs, Lab Supervisors,... 32

● Two lab manuals (Uncertainty).

• At the risk of making data feel unwanted, we dare

• Graphically?

• In the “world of vectors”

• Length: Meter (m)

• Mass: Kilogram (kg)

• of A is written as A or A.

• Physics experiments involve the measurement of a variety of

• The ,

• The first step in ensuring accuracy and reproducibility is defining

• These measurements should be accurate and reproducible.

• Time: Second (s)

• Usually vectors are denoted by :

1.magnitudewithrsunit vectoareˆandˆ yx

1+1 does not necessarily

A B C

a protractor

A, B, ...etc A .

a. 1

a. 1 b. 2 c. 3 d. 4 e. 5

a. 1000 b. 0.01 c. 100 d. 0.001 e. 1000 00029

a. 3.3 × 10

a. 3.3 b. 5.0 c. 7.8 d. 14 e. 11

a. 4 ,

a. 8 b. 2 c. 6 d. 4 e. 10

a. A =

a. A+B=0 b. A

a. object falls 9.8 m during the first second of its motion.

a. the maximum value b. the average measured value

a. What are the “units” of k ?

A=Ax+Ay .

about....

Accuracy:

additional units, derived units, for other important

along the x axis, Ax and a vector

and are the scalar components of .x yA A A

and –B .

and basic trigonometric functions. 2

and your calculator will tell you 3.33333333.

and/or elastic band experiment, in the Introductory Lab Lint,

angle

Any vector A lying in the x-y plane

ao hhh += 13

are measured variables, ℓo is constant but unknown. Determine

Ax

Ax = A cos

Ax negative Ax positive

Ax negative Ax positive

Ay = A sin

Ay A

Ay negative Ay negative

Ay positive Ay positive

B from vector A. The vector –B is equal in

b. 2

b. object falls 9.8 m during each second of its motion.

b. What are the units of the number π.

−B=0 c. A2

−B2 =1 d. A2+B2 =1 e. none of these is correct

believe you have measured carefully to

billionths of the unit you are using.

brake with your foot) ?

but the direction of the

by , F and r are measured variables for

by –1, the magnitude of the

by definition the one that

by where v and P are measured variables. Determine d.

c. acceleration of the object increases by 9.8 m/s 2 during each second of its

c. Suppose your lab partner tells you to calculate the

c. the minimum measured value d. the “accurate” value

can be represented by a vector lying

completes the polygon . 19

components rather than the vector components.

consistency” in your lecture notes of chapter 1.)

coordinates (x,y).

d. speed of the object increases by 9.8 m/s during each second of its motion.

Deals with the

describe your method of solution in a few lines with schematic graphs.

direction . To subtract B and A , apply the rule

direction.

e. force of gravity on the object must be 9.8 SI units.

Encircle the correct answer:

encompasses a remarkable variety of phenomena:

equal 2.

equal since they

Every point is labeled with

exact).

extension x in meters. Use EXCEL program to find the slope

figures.

fixed and known q1, q2, and

fixed and known. Determine R.

for

for summing four

formula Why this formula “MUST” be

from other units: in this case kg. m/s 2.

from other units: in this case kg. m2/s 2 .

fundamental

Geometric construction

Goals of Chapter 1

h = Hypotenuse

h 0h

h0 = Length of side

ha = Length of side adjacent

has developed out of the efforts of men and

have equal length and

High Accuracy

High Accuracy

High Precision

High Precision

How close the

https://www.youtube.com/watch?v=89NdAq8rQYQ https://www.youtube.com/watch?v=41a3DR0sZ-c

https://www.youtube.com/watch?v=M6zams5GCoI

If m is a negative scalar quantity , the vector

If vector A is multiplied by a positive scalar

Imagine you need to work with force F or energy E.

in a cartesian coordinate system.

In all the following problems state the variables or combination of

in the linear region of Hooke’s Law │F│= k x.

In which graph of v versus t does the particle end up farthest from its starting

incorrect? (Hint: Review the meaning of “dimensional

information with the correct number of significant

intercept of the best fitting straight-line y = m x + b).

inverse-square law?

It is often easier to work with the scalar

kilogram (kg): unit of mass

known. Determine C.

located

Low Accuracy

Low Accuracy

Low Precision

Low Precision

lying along the y-axis , Ay , where

m2.67

mA is directed opposite A .

magnitude to vector B and points in the opposite

many more!

measure angles by using e.g.

measured value

measured variables, ℓ is fixed and known. Determine g.

meter (m): unit of length

motion.

Multiplication of a vector by a scalar

Need Help with EXCEL?

not report everything our calculator tells us.

of a vector A depend

of the hydrogen spectrum are given by

of vector addition to the combination of A

on the quadrant in

opposite the angle θ

others), are regarded as base SI units.

Parallelogram rule.

physical quantities such as force and energy.

Physics” the part of “Propagation of Error”.)

plot a graph for the load (hanged weight) F in Newtons vs. the

point ?

point in the same

Precision:

proportional to the magnitude of the vector.

q q

Q Q e−

Q: Is the following equation dimensionally correct?

Q: Is the following equation dimensionally correct?

Q: Is the following equation dimensionally correct?

Q: Is the following equation dimensionally correct?

quantities.

quantity m , the product mA is a vector that has:

R n

reaction time (i.e., the time interval between seeing the emergency and hitting the

reading in hours, minutes (and unseen seconds) as 08:36.

Repeated, independent measurements of a quantity will vary

report the measurement together with the absolute

represented by the distance r and the

S.I. base units.

second (s): unit of time

Signs of components

sin 0 , cos 1

sin 0 , cos 1

sin 0 0 , cos 0 1

sin 0 0 , cos 0 1

sin 1 , cos 0

sin 1 , cos 0

spread of results.

state how the unknown may be found (through the slope and/or

Such as : m , kg/m3 , ...etc. Typical examples are: temperature, speed, mass, density...

such as: m , m/s ,...etc.

Such as: velocity, force, displacement

t = 82.4 ± 0.3 s. What is its average velocity v?

The magnitude of the resultant of A , B , and C is :

the resultant R is the

The smallest readable division is only one minute. How to

the track cart travels a distance of x = 60.0 ± 0.3 cm in a time

the units in which the measurements are made.

the vector.

There are three

These vectors are all

This construction shows how to subtract vector

To differentiate between units and dimensions.

To express measurements and calculated

To know standards and units and be able to do

To practice vectors operations and break down

To refresh knowledge about coordinate systems

to the angle θ

to the true value.

to vector B,

triangle method.

uncertainty written in the form 00:00:00 ± 00:00:00?

unit conversions.

Using the data that you collected from your mass-spring

variables which should be plotted to check the suggested variation and

Vector addition

Vector addition using the

Vector addition using the

Vector Addition:

vector is reversed.

vector remains the same,

Vector Subtraction

vector that runs from the

vectors into x and y components.

vectors.The resultant R is

volume of a cone of radius r and height h using the

Wagih Ghobriel

When a vector is multiplied

When vector A is added

where f , ℓ , and T are measured variables. Determine m.

where Q and t are measured variables. R is fixed and

where λ and n are measured variables. Determine R.

which the vector is

with both

women

x component +6 −3 +2

your car is 4 m long, how many car lengths do you travel during the 0.7 s of

YouTube, UTM Library.

π = 3.1416 (consider this numerical value of

 By convention, the of a vector arrow is

 The of the arrow gives the direction of

 The units for length, mass, and time (as well as a few

 These units are used in combination to define

 Models

 Theories

 Because you are not given any numerical data it is just required to qualitatively

 Maxwell’s Equations → Telecommunications 3

 Newton’s Laws → Rocketry

What are the other four SI units? 6