Tuesday, June 5, 2007
Graphical Analysis of Linear Motion
(a)+ Velocity Constant Velocity (b) + Velocity Changing Velocity
Acceleration due to Gravity
Drop two objects. Which object will reach the ground first ? (i.e. which will fall faster?)
In reality, both objects will reach the ground at the same time since all objects accelerate at the same rate.
The value of this acceleration is known as "g".
g = 9.80 m/s^2
In reality, both objects will reach the ground at the same time since all objects accelerate at the same rate.
The value of this acceleration is known as "g".
g = 9.80 m/s^2
Falling Objects
At a given location on the Earth and in the absence of air resistance, all objects fall with the same constant acceleration.
Monday, June 4, 2007
Example (average accleration)
A car accelertates along a straight road from rest to 75 m/s in 5.0 s. What is the magnitude of its average accelertaion?
Solution:
The car starts from rest, initial velocity = 0
final velocity = 75 m/s
time taken = 5 s
average acceleration = (75 -0) /5 = 15 m/s^2
Solution:
The car starts from rest, initial velocity = 0
final velocity = 75 m/s
time taken = 5 s
average acceleration = (75 -0) /5 = 15 m/s^2
Acceleration
An object whose velocity is changing is said to be accelerating.
Average Acceleration is defined as the change in velocity divided by the time taken to make this change:
Average Acceleration is defined as the change in velocity divided by the time taken to make this change:
Acceleration is a vector quantity.
See the Animation :
http://www.physicsclassroom.com/mmedia/kinema/acceln.html
Speed and Velocity
Speed: how fast an object is moving.
The Average Speed of an object is defined as the distance traveled along its path divided by the time it takes to travel this distance:
A person walked 70 m east and then 30 m west.
The total distance traveled was 70 m + 30 m = 100 m.
Suppose this walk took 70 s to complete.
The average speed was : distance /time = 100 m / 70 s
= 1.4 m/s.
= 1.4 m/s.
Velocity is used to signify both magnitude of how fast an object is moving and the direction in which it is moving.
Velocity is a vector.
Average Velocity is defined in terms of displacement.
A person walked 70 m east and then 30 m west. The displacement was 40 m.
Suppose this walk took 70 s to complete.
The average velocity was : displacement/time = 40 m/ 70 s = 0.57 m/s .
Instantaneous Speed - speed at any given instant in time.
Average Speed - average of all instantaneous speeds; found simply by a distance/time ratio.
Constant Speed & Changing Speed
Distance and Displacement
Distance: how much ground an object has covered during its motion.
Displacement : how far out of place an object is; it is the object's change in position.
Displacement is a quantity that has both magnitude and direction.
Such quantities are called vectors , and are represented in diagrams by arrow.
Displacement : how far out of place an object is; it is the object's change in position.
Displacement is a quantity that has both magnitude and direction.
Such quantities are called vectors , and are represented in diagrams by arrow.
Describing Motion: Kinematics in One Dimension (Chapter 2)
Describing Motion : Kinematics in One Dimension
Objectives
1. SI unit and its abbreviation associated with displacement, velocity, acceleration, and time.
2. the motion of an object relative to a particular frame of reference.
3. Differentiate between a vector quantity and a scalar quantity .
4. graphical analysis of Linear Motion .
5. the instantaneous acceleration at a point in time and the distance traveled in an interval of time.
Objectives
1. SI unit and its abbreviation associated with displacement, velocity, acceleration, and time.
2. the motion of an object relative to a particular frame of reference.
3. Differentiate between a vector quantity and a scalar quantity .
4. graphical analysis of Linear Motion .
5. the instantaneous acceleration at a point in time and the distance traveled in an interval of time.
Practice Questions
1. A kilogram is..........
(A) 10^3 grams.
(B) 10^3 grams.
(C) 10^6 grams.
(D) 10 grams.
2. A centimeter is...................
(A) 100 meters.
(B) 10 meters.
(C) 0.1 meters.
(D) 0.01 meters.
3. A megawatt is................
(A) 10^6 watts.
(B) 10^3 watts.
(C) 10^-3 watts.
(D) 10^-6 watts.
4. A nanosecond is...........
(A) 10^-3 seconds.
(B) 10^-6 seconds.
(C) 10^-9 seconds.
(D) 10^-12 seconds.
5. A kilometer is
(A) greater than a mile.
(B) less than a mile.
(C) about the size of a football field.
(D) less than a football field.
6. All of the following are base units of the SI system except:
(A) kilogram.
(B) kelvin.
(C) meter.
(D) pound.
7. The SI prefix for 10^-12 is
(A) tera-
(B) giga-
(C) nano-
(D) pico-
8. Convert 0.75 kilometers to meters.
(A)7500 m
(B) 750 m
(C) 75 m
(D) 7.5 m.
9. Convert 0.0215 m to mm.
(A) 0.215 mm
(B) 2.15 mm
(C) 21.5 mm
(D) 215 mm.
10. The number 9452 in scientific notation is
(A) 9.452 × 10^2
(B) 94.52 × 10^2
(C) 0.9452 × 10^4
(D) 9.452 × 10^3.
11. The number .0000475 in scientific notation is
(A) 4.75 × 10^-6
(B) 4.75 × 10^-5
(C) 4.75 × 10^-4
(D) 4.75 × 10^-3.
12.
A 10 L container has a volume expressed in m^3 of
(A) 0.1 m^3
(B) 0.01 m^3
(C) 0.001 m^3
(D) 0 .0001 m^3.
(A) 10^3 grams.
(B) 10^3 grams.
(C) 10^6 grams.
(D) 10 grams.
2. A centimeter is...................
(A) 100 meters.
(B) 10 meters.
(C) 0.1 meters.
(D) 0.01 meters.
3. A megawatt is................
(A) 10^6 watts.
(B) 10^3 watts.
(C) 10^-3 watts.
(D) 10^-6 watts.
4. A nanosecond is...........
(A) 10^-3 seconds.
(B) 10^-6 seconds.
(C) 10^-9 seconds.
(D) 10^-12 seconds.
5. A kilometer is
(A) greater than a mile.
(B) less than a mile.
(C) about the size of a football field.
(D) less than a football field.
6. All of the following are base units of the SI system except:
(A) kilogram.
(B) kelvin.
(C) meter.
(D) pound.
7. The SI prefix for 10^-12 is
(A) tera-
(B) giga-
(C) nano-
(D) pico-
8. Convert 0.75 kilometers to meters.
(A)7500 m
(B) 750 m
(C) 75 m
(D) 7.5 m.
9. Convert 0.0215 m to mm.
(A) 0.215 mm
(B) 2.15 mm
(C) 21.5 mm
(D) 215 mm.
10. The number 9452 in scientific notation is
(A) 9.452 × 10^2
(B) 94.52 × 10^2
(C) 0.9452 × 10^4
(D) 9.452 × 10^3.
11. The number .0000475 in scientific notation is
(A) 4.75 × 10^-6
(B) 4.75 × 10^-5
(C) 4.75 × 10^-4
(D) 4.75 × 10^-3.
12.
A 10 L container has a volume expressed in m^3 of
(A) 0.1 m^3
(B) 0.01 m^3
(C) 0.001 m^3
(D) 0 .0001 m^3.
REVIEW OF MATHEMATICS
SYMBOLS, SCIENTIFIC NOTATION, AND SIGNIFICANT FIGURES
It is important that you learn to use symbols, rather than numerical values, in doing calculations. Letters near the end of the alphabet, such as x, y and z, are used for unknown variables. Letters such as a, b, and c are often used for given constant quantities. Greek letters are used for angular variables. Subscripts are used to provide added information. For example, the position of an object at time t1 I label as x1, and its position at time t2 is x2. Commonly encountered symbols are listed below :
a = b means a is equal to b.
a ¹ b means a is not equal to b.
a > b means a is greater than b, and a ≥ b means a is greater
than or equal to b.
a >> b means a is much greater than b.
a < b means a is less than b, and a ≤ b means a is less than
or equal to b.
a << b means a is much less than b.
a µ b means a is proportional to b.
a @ b means a is approximately equal to b.
n! = 1 · 2 · 3 · 4 · · · n
y (x) means the quantity y depends on the value of x ; that is, y
is a function of x .
∑i xi = x1 + x2 + x3 + · · · + xn .
It is important that you learn to use symbols, rather than numerical values, in doing calculations. Letters near the end of the alphabet, such as x, y and z, are used for unknown variables. Letters such as a, b, and c are often used for given constant quantities. Greek letters are used for angular variables. Subscripts are used to provide added information. For example, the position of an object at time t1 I label as x1, and its position at time t2 is x2. Commonly encountered symbols are listed below :
a = b means a is equal to b.
a ¹ b means a is not equal to b.
a > b means a is greater than b, and a ≥ b means a is greater
than or equal to b.
a >> b means a is much greater than b.
a < b means a is less than b, and a ≤ b means a is less than
or equal to b.
a << b means a is much less than b.
a µ b means a is proportional to b.
a @ b means a is approximately equal to b.
n! = 1 · 2 · 3 · 4 · · · n
y (x) means the quantity y depends on the value of x ; that is, y
is a function of x .
∑i xi = x1 + x2 + x3 + · · · + xn .
1.1 UNIT AND STANDARDS MEASUREMENT
UNIT
LENGTH
The distance traveled by light in a vacuum during time interval of 1/299792458 second
Meter (m)
MASS
The mass of a specific platinum –iridium alloy cylinder kept at the International Bureau of Weights and Measure at Sevres , France.
Kilogram(kg)
TIME
9 192 631 770 times the period of oscillation of radiation from the cesium atom.
Second(s)
TEMPERATURE
1/273.15 of the thermodynamic temperature for the triple point of water
Kelvin(K)
ELECTRIC CURRENT
The value of the full current which flowa in two straight and parallel conductors of infinite length neglecting the area with a force magnitude 2 X 10 -7 Newtons permeter length acts upon those two wires
1 Ampere (A)
LENGTH
The distance traveled by light in a vacuum during time interval of 1/299792458 second
Meter (m)
MASS
The mass of a specific platinum –iridium alloy cylinder kept at the International Bureau of Weights and Measure at Sevres , France.
Kilogram(kg)
TIME
9 192 631 770 times the period of oscillation of radiation from the cesium atom.
Second(s)
TEMPERATURE
1/273.15 of the thermodynamic temperature for the triple point of water
Kelvin(K)
ELECTRIC CURRENT
The value of the full current which flowa in two straight and parallel conductors of infinite length neglecting the area with a force magnitude 2 X 10 -7 Newtons permeter length acts upon those two wires
1 Ampere (A)
Sunday, June 3, 2007
1.4 ESTIMATION & ORDER OF MAGNITUDES
Estimation
· All measurement are estimations only
· Measurement is comparative value between object that to be measured and a standard scale or the theoretical value.
· Should be determined by accurate measurement
Order of magnitude
We frequently use prefixes to obtain units of more convenient size. Here are examples of commonly encountered prefixes :
1 nanometer = 1 nm = 10-9 m (a little bigger than an atom diameter)
1 micrometer = 1 μm = 10-6 m ( a human blood cell is about 7μm)
1 milimeter = 1mm = 10-3 m ( a pencil lead is about 0.5 mm in
diameter)
1 centimeter = 1 cm = 10-2 m (the diameter of a ballpoint pen)
1 kilometer = 1 km = 10 3 m (about 0.6 m)
1 microgram = 1 μg = 10-6 g = 10-9 kg (mass of a small dust particle)
1 miligram = 1 mg = 10-3 g = 10-6 kg (a raindrop is about 2 mg)
1 gram = 1 g = 10-3 kg = 10-3 kg (the mass penny is about 2.5g)
1 nanosecond = 1 ns = 10-9 s (time for light to travel 30 cm)
1 microsecond = 1 μs = 10-6 s (time for a rifle bullet to travel about 1mm)
1 millisecond = 1 ms = 10-3 s (about 14 ms between human heart beats)
· All measurement are estimations only
· Measurement is comparative value between object that to be measured and a standard scale or the theoretical value.
· Should be determined by accurate measurement
Order of magnitude
We frequently use prefixes to obtain units of more convenient size. Here are examples of commonly encountered prefixes :
1 nanometer = 1 nm = 10-9 m (a little bigger than an atom diameter)
1 micrometer = 1 μm = 10-6 m ( a human blood cell is about 7μm)
1 milimeter = 1mm = 10-3 m ( a pencil lead is about 0.5 mm in
diameter)
1 centimeter = 1 cm = 10-2 m (the diameter of a ballpoint pen)
1 kilometer = 1 km = 10 3 m (about 0.6 m)
1 microgram = 1 μg = 10-6 g = 10-9 kg (mass of a small dust particle)
1 miligram = 1 mg = 10-3 g = 10-6 kg (a raindrop is about 2 mg)
1 gram = 1 g = 10-3 kg = 10-3 kg (the mass penny is about 2.5g)
1 nanosecond = 1 ns = 10-9 s (time for light to travel 30 cm)
1 microsecond = 1 μs = 10-6 s (time for a rifle bullet to travel about 1mm)
1 millisecond = 1 ms = 10-3 s (about 14 ms between human heart beats)
1.2 UNIT CONVERSION
We sometimes encounter data given in units other than those used in the SI system.
In this case we must convert the units to the SI system using known conversion factors.
1 mile = 1610 ml and 1 hour = 60 min = 3600 s
Wherever “mile” appears, write 1610 m, and where “hour” appears, write
3600 s.
Thus, 30 mi/h = 30 1610 m = 13.4 m/s
3600 s
Length
1 inch (in) = 2.54 cm
1 foot (ft) = 0.3048 m
1 mile (mi) = 5280 ft = 1.609 km
1 m = 3.281 ft
1 km = 0.6214 mi
1 angstrom (A) = 10-10 m
1 light year = 9.461 ´ 1015 m
1 astronomical unit (AU) = 1.496 ´ 1011 m
1 parsec (pc) = 3.09 ´ 1016 m
Mass
1 slug = 14.59 kg
1 kg = 1000 g = 6.852 ´ 10-2 slug
1 atomic mass unit (amu) = 1.6605 ´ 10-27 kg
(1 kg has a weight of 2.205 lb where the acceleration due to gravity is 32.174 ft/s2)
Time
1 day = 24 h = 1.44 ´ 103 min = 8.64 ´ 104 s
1 year = (yr) = 365.24 days = 3.156 ´ 107 s
1 h = 60 min = 3600s
Speed
1 mi/h = 1.609 km/h = 1.467 ft/s = 0.4470 m/s
1 km/h = 0.6214 mi/h = 0.2778 m/s = 0.9113 ft/s
Volume
1 liter (L) = 10-3 m3 = 1000 cm3 = 0.3531 ft3
1 ft3 = 0.02832 m3 = 7.481 U.S gallons (gal)
1 U.S gal = 3.785 ´ 10-3 m3 = 0.1337 ft3
Force
1 pound (lb) = 4.448 newtons (N)
1 N = 105 dynes (dyn) = 0.2248 lb
Work and Energy
1 joule (J) = 0.7376 ft · lb = 107 ergs
1 kilogram-calorie (kcal) = 4186 J
1 Btu (60°F) = 1055 J
1 kilowatt-hour (kWh) = 3.600 ´ 106 J
1 electron volt (eV) = 1.602 ´ 10-19 J
Angle
1 radian (rad) = 57.30°
1° = 0.01745 rad
Pressure
1 pascal (Pa) = 1 N/m2 = 1.450 ´ 10-4 lb/in2
1 lb/in2 = 6.895 ´ 103 Pa
1 atmosphere (atm) = 1.013 ´ 105 Pa = 1.013 bar = 14.70 lb/in2 = 760 torr
Power
1 horsepower (hp) = 550 ft · lb/s = 745.7 W
1 watt (W) = 0.7376 ft · lb/s
In this case we must convert the units to the SI system using known conversion factors.
1 mile = 1610 ml and 1 hour = 60 min = 3600 s
Wherever “mile” appears, write 1610 m, and where “hour” appears, write
3600 s.
Thus, 30 mi/h = 30 1610 m = 13.4 m/s
3600 s
Length
1 inch (in) = 2.54 cm
1 foot (ft) = 0.3048 m
1 mile (mi) = 5280 ft = 1.609 km
1 m = 3.281 ft
1 km = 0.6214 mi
1 angstrom (A) = 10-10 m
1 light year = 9.461 ´ 1015 m
1 astronomical unit (AU) = 1.496 ´ 1011 m
1 parsec (pc) = 3.09 ´ 1016 m
Mass
1 slug = 14.59 kg
1 kg = 1000 g = 6.852 ´ 10-2 slug
1 atomic mass unit (amu) = 1.6605 ´ 10-27 kg
(1 kg has a weight of 2.205 lb where the acceleration due to gravity is 32.174 ft/s2)
Time
1 day = 24 h = 1.44 ´ 103 min = 8.64 ´ 104 s
1 year = (yr) = 365.24 days = 3.156 ´ 107 s
1 h = 60 min = 3600s
Speed
1 mi/h = 1.609 km/h = 1.467 ft/s = 0.4470 m/s
1 km/h = 0.6214 mi/h = 0.2778 m/s = 0.9113 ft/s
Volume
1 liter (L) = 10-3 m3 = 1000 cm3 = 0.3531 ft3
1 ft3 = 0.02832 m3 = 7.481 U.S gallons (gal)
1 U.S gal = 3.785 ´ 10-3 m3 = 0.1337 ft3
Force
1 pound (lb) = 4.448 newtons (N)
1 N = 105 dynes (dyn) = 0.2248 lb
Work and Energy
1 joule (J) = 0.7376 ft · lb = 107 ergs
1 kilogram-calorie (kcal) = 4186 J
1 Btu (60°F) = 1055 J
1 kilowatt-hour (kWh) = 3.600 ´ 106 J
1 electron volt (eV) = 1.602 ´ 10-19 J
Angle
1 radian (rad) = 57.30°
1° = 0.01745 rad
Pressure
1 pascal (Pa) = 1 N/m2 = 1.450 ´ 10-4 lb/in2
1 lb/in2 = 6.895 ´ 103 Pa
1 atmosphere (atm) = 1.013 ´ 105 Pa = 1.013 bar = 14.70 lb/in2 = 760 torr
Power
1 horsepower (hp) = 550 ft · lb/s = 745.7 W
1 watt (W) = 0.7376 ft · lb/s
Introduction (Chapter 1)
Objectives
1. Distinguish between a scientific model and a scientific theory.
2. why experiments are important
3. Explain why uncertainty is present in all measurements
4. Calculate the percent uncertainty in a measurement.
5. State the SI units of mass, length, and time.
6. State the metric (SI) prefixes (multipliers)
7. Distinguish between basic quantities and derived quantities as well as basic units and derived units.
8. a number in power of ten notation .
9. an order‑of‑magnitude estimate
1. Distinguish between a scientific model and a scientific theory.
2. why experiments are important
3. Explain why uncertainty is present in all measurements
4. Calculate the percent uncertainty in a measurement.
5. State the SI units of mass, length, and time.
6. State the metric (SI) prefixes (multipliers)
7. Distinguish between basic quantities and derived quantities as well as basic units and derived units.
8. a number in power of ten notation .
9. an order‑of‑magnitude estimate
Giancoli (Physics with Applications)
Introduction
Physics is the most basic of the sciences.
It deals with behavior and structure of matter.
The field of Physics is usually divided into the areas of motion, fluids, heat, sound, light, electricity and magnetism, and the modern topics of relativity, atomic structure, condensed-matter physics, nuclear physics, elementary particles, and astrophysics.
Physics is the most basic of the sciences.
It deals with behavior and structure of matter.
The field of Physics is usually divided into the areas of motion, fluids, heat, sound, light, electricity and magnetism, and the modern topics of relativity, atomic structure, condensed-matter physics, nuclear physics, elementary particles, and astrophysics.
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