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StaticsEquilibrium of ParticlesFree-body diagramEquilibrium of Rigid Bodies
GravitationNewton’s Law of GravitationGravitational Field StrengthGravitational PotentialRealtionship bet g and GSatellite Motion in Cicular OrbitsEscape velocity
States of MatterSolid – Stress & StrainYoung’s ModulusFluids – Density and PressureArchimedes’ PrincipleBernoulli’s Principle
Temperature and HeatTemp and Thermal EqmThermometers and Temp ScaleThermal Expansion of Solids n LiquidsHeat
Gases and Kinetic TheoryGas Laws and Absolute TempKinetic Theory of Gases
Laws of ThermodynHeat Capacity of GasesWork and Internal EnergyFirst Law of ThermodynamicsSecond Law of Thermodynamics
RECOMMENDED TEXT:PHYSICS For Scientists & Engineers With Modern Physics by Giancoli, 4th Edition
REFERENCES:Fundamental of Physics by Halliday, Resnick, Walker;6th or 7th Ed., John Wiley &Sons, Inc.
The principles of physics are used in many practical applications, including construction. Communication between architects and engineers is essential if disaster is to be avoided.
1-2 Models, Theories, and LawsModels are very useful during the process of understanding phenomena. A model creates mental pictures; care must be taken to understand the limits of the model and not take it too seriously.
A theory is detailed and can give testable predictions.
A law is a brief description of how nature behaves in a broad set of circumstances.
A principle is similar to a law, but applies to a narrower range of phenomena.
1-3 Measurement and Uncertainty; Significant Figures
The number of significant figures is the number of reliably known digits in a number. It is usually possible to tell the number of significant figures by the way the number is written:
23.21 cm has four significant figures.
0.062 cm has two significant figures (the initial zeroes don’t count).
80 km is ambiguous—it could have one or two significant figures. If it has three, it should be written 80.0 km.
1-3 Measurement and Uncertainty; Significant Figures
When multiplying or dividing numbers, the result has as many significant figures as the number used in the calculation with the fewest significant figures.
Example: 11.3 cm x 6.8 cm = 77 cm.
When adding or subtracting, the answer is no more accurate than the leastaccurate number used.
The number of significant figures may be off by one; use the percentageuncertainty as a check.
1-3 Measurement and Uncertainty; Significant Figures
Calculators will not give you the right number of significant figures; they usually give too many but sometimes give too few(especially if there are trailing zeroes after a decimal point).
The top calculator shows the result of 2.0/3.0.
The bottom calculator shows the result of 2.5 x 3.2.
1-3 Measurement and Uncertainty; Significant Figures
Conceptual Example 1-1: Significant figures.
Using a protractor, you measure an angle to be 30°. (a) How many significant figures should you quote in this measurement? (b) Use a calculator to find the cosine of the angle you measured.
1-3 Measurement and Uncertainty; Significant Figures
Scientific notation is commonly used in physics; it allows the number of significant figures to be clearly shown.
For example, we cannot tell how many significant figures the number 36,900 has. However, if we write 3.69 x 104, we know it has three; if we write 3.690 x 104, it has four.
Much of physics involves approximations; these can affect the precision of a measurement also.
These are the standard SI prefixes for indicating powers of 10. Many are familiar; yotta, zetta, exa, hecto, deka, atto, zepto, and yocto are rarely used.
1-4 Units, Standards, and the SI SystemWe will be working in the SI system, in which the basic units are kilograms, meters, and seconds. Quantities not in the table are derived quantities, expressed in terms of the base units.
Other systems: cgs; units are centimeters, grams, and seconds.
British engineering system has force instead of mass as one of its basic quantities, which are feet, pounds, and seconds.
1-5 Converting UnitsExample 1-2: The 8000-m peaks.
The fourteen tallest peaks in the world are referred to as “eight-thousanders,”meaning their summits are over 8000 m above sea level. What is the elevation, in feet, of an elevation of 8000 m?
A quick way to estimate a calculated quantity is to round off all numbers to one significant figure and then calculate. Your result should at least be the right order of magnitude; this can be expressed by rounding it off to the nearest power of 10.
Diagrams are also very useful in making estimations.
1-6 Order of Magnitude: Rapid EstimatingExample 1-5: Volume of a lake.
Estimate how much water there is in a particular lake, which is roughly circular, about 1 km across, and you guess it has an average depth of about 10 m.
If you have ever been on the shore of a large lake, you may have noticed that you cannot see the beaches, piers, or rocks at water level across the lake on the opposite shore. The lake seems to bulge out between you and the opposite shore—a good clue that the Earth is round. Suppose you climb a stepladder and discover that when your eyes are 10 ft (3.0 m) above the water, you can just see the rocks at water level on the opposite shore. From a map, you estimate the distance to the opposite shore as d ≈ 6.1 km. Use h = 3.0 m to estimate the radius R of the Earth.
1-7 Dimensions and Dimensional AnalysisDimensions of a quantity are the base units that make it up; they are generally written using square brackets.
Example: Speed = distance/time
Dimensions of speed: [L/T]
Quantities that are being added or subtracted must have the same dimensions. In addition, a quantity calculated as the solution to a problem should have the correct dimensions.
1-7 Dimensions and Dimensional AnalysisDimensional analysis is the checking of dimensions of all quantities in an equation to ensure that those which are added, subtracted, or equated have the same dimensions.
Example: Is this the correct equation for velocity?
Summary of Chapter 1• Theories are created to explain observations, and then tested based on their predictions.
• A model is like an analogy; it is not intended to be a true picture, but to provide a familiar way of envisioning a quantity.
• A theory is much more well developed, and can make testable predictions; a law is a theory that can be explained simply, and that is widely applicable.
• Dimensional analysis is useful for checking calculations.
Summary of Chapter 1• Measurements can never be exact; there is always some uncertainty. It is important to write them, as well as other quantities, with the correct number of significant figures.
• The most common system of units in the world is the SI system.
• When converting units, check dimensions to see that the conversion has been done properly.
• Order-of-magnitude estimates can be very helpful.
Chapter 3Chapter 3
Vectors
3-1 Vectors and Scalars
A vector has magnitude as well as direction.
Some vector quantities: displacement, velocity, force, momentum
A scalar has only a magnitude.
Some scalar quantities: mass, time, temperature
3-2 Addition of Vectors—Graphical Methods
For vectors in one dimension, simple addition and subtraction are all that is needed.
You do need to be careful about the signs, as the figure indicates.
3-2 Addition of Vectors—Graphical MethodsIf the motion is in two dimensions, the situation is somewhat more complicated.
Here, the actual travel paths are at right angles to one another; we can find the displacement by using the Pythagorean Theorem.
3-2 Addition of Vectors—Graphical MethodsAdding the vectors in the opposite order gives the same result:
3-2 Addition of Vectors—Graphical MethodsEven if the vectors are not at right angles, they can be added graphically by using the tail-to-tip method.
3-2 Addition of Vectors—Graphical MethodsThe parallelogram method may also be used; here again the vectors must be tail-to-tip.
3-3 Subtraction of Vectors, and Multiplication of a Vector by a Scalar
In order to subtract vectors, we define the negative of a vector, which has the same magnitude but points in the oppositedirection.
Then we add the negative vector.
3-3 Subtraction of Vectors, and Multiplication of a Vector by a Scalar
A vector can be multiplied by a scalar c; the result is a vector cthat has the same direction but a magnitude cV. If c is negative, the resultant vector points in the opposite direction.
rV r
V
3-4 Adding Vectors by Components
Any vector can be expressed as the sum of two other vectors, which are called its components. Usually the other vectors are chosen so that they are perpendicular to each other.
3-4 Adding Vectors by Components
If the components are perpendicular, they can be found using trigonometric functions.
3-4 Adding Vectors by Components
The components are effectively one-dimensional, so they can be added arithmetically.
3-4 Adding Vectors by Components
Adding vectors:
1. Draw a diagram; add the vectors graphically.
2. Choose x and y axes.
3. Resolve each vector into x and y components.
4. Calculate each component using sines and cosines.
5. Add the components in each direction.
6. To find the length and direction of the vector, use:
and .
3-4 Adding Vectors by Components
Example 3-2: Mail carrier’s displacement.
A rural mail carrier leaves the post office and drives 22.0 km in a northerly direction. She then drives in a direction 60.0° south of east for 47.0 km. What is her displacement from the post office?
3-4 Adding Vectors by Components
Example 3-3: Three short trips.
An airplane trip involves three legs, with two stopovers. The first leg is due east for 620 km; the second leg is southeast (45°) for 440 km; and the third leg is at 53° south of west, for 550 km, as shown. What is the plane’s total displacement?
3-5 Unit VectorsUnit vectors have magnitude 1.
Using unit vectors, any vector can be written in terms of its components:
rV
3-6 Vector Kinematics
In two or three dimensions, the displacement is a vector:
3-6 Vector KinematicsAs Δt and Δr become smaller and smaller, the average velocity approaches the instantaneous velocity.
7-2 Scalar Product of Two VectorsDefinition of the scalar, or dot, product:
Therefore, we can write:
7-2 Scalar Product of Two VectorsExample 7-4: Using the dot product.
The force shown has magnitude FP = 20 N and makes an angle of 30° to the ground. Calculate the work done by this force, using the dot product, when the wagon is dragged 100 m along the ground.
11-2 Vector Cross Product; Torque as a Vector
The vector cross product is defined as:
The direction of the cross product is defined by a right-hand rule:
11-2 Vector Cross Product; Torque as a Vector
The cross product can also be written in determinant form:
11-2 Vector Cross Product; Torque as a Vector
Some properties of the cross product:
11-2 Vector Cross Product; Torque as a Vector
Torque can be defined as the vector product of the force and thevector from the point of action of the force to the axis of rotation:
11-2 Vector Cross Product; Torque as a Vector
For a particle, the torque can be defined around a point O:
Here, is the position vector from the particle relative to O.rr
Example 11-6: Torque vector.
Suppose the vector is in the xz plane, and is given by