PHYS 151 Dr. Richard A Lindgren University of Virginia USA

Course Lecture Notes http://people.virginia.edu/~ral5q/PHYS_151_2012_Hue Textbook: Physics for Scientist and Engineers Fourth Edition Author Giancoli

Physics for Scientists & Engineers, with Modern Physics, 4th edition Lecture PowerPoints Chapter 1 Physics for Scientists & Engineers, with Modern Physics, 4th edition Giancoli

Final Grade Determination Attendance 5% Homework 25% Quiz 1 20% Quiz 2 20% Final 30%

Syllabus First Week Tuesday Wednesday Thursday Friday 1. Measurement and Estimating 2. Projectile Motion Wednesday 3. Kinematic in 2D Thursday 3. Kinematics in 2D 4. Newtons Laws Friday

Syllabus Second Week Monday Tuesday Wednesday Thursday Friday 5. Friction, Drag forces, and Circular motion Tuesday Quiz 1 Wednesday 6. Gravitation Thursday 7. Work and Energy Friday 8. Conservation of Energy

Syllabus Third Week Monday Tuesday Wednesday Thursday Friday 8. Conservation of energy Tuesday Quiz 2 9. Conservation of Momentum Wednesday Thursday 10. Rotational Motion Friday 11. Angular Motion

Syllabus Fourth Week Monday Tuesday Wednesday 11. Angular Momentum Tuesday 12. Static Equilibrium, Elasticity and Fracture Wednesday 12. Static Equilibrium, Elasticity and Fracture Review Thursday Final Exam Friday Grade Determination

Assignment 1 Chp 1 1-33,1-52 Chp 2 2-58, 2-72 Chp 3 3-22, 3-80 Due Monday 10:00

Chapter 1 The Nature of Science Models, Theories, Laws and Principles Units, and unit conversions Measurement, Accuracy, Precision, and significant figures Dimensional analysis Estimating and Approximations Matter and Interactions Principles – predict the future Short Math Review Vectors and Calculus

The system of units we will use is the Standard International (SI) system; the units of the fundamental quantities are: Length – meter Mass – kilogram Time – second

Fundamental Physical Quantities and Their Units Unit prefixes for powers of 10, used in the SI system:

Accuracy and Significant Figures The number of significant figures represents the accuracy with which a number is known. Terminal zeroes after a decimal point are significant figures: 2.00 has 3 significant figures 2 has 1 significant figure. Important for webassign in getting the correct answer For the homework problems (2%).

Accuracy and Significant Figures If numbers are written in scientific notation, it is clear how many significant figures there are: 6. × 1024 has one 6.1 × 1024 has two 6.14 × 1024 has three …and so on. Calculators typically show many more digits than are significant. It is important to know which are accurate and which are meaningless.

Scientific Notation Example Scientific notation: use powers of 10 for numbers that are not between 1 and 10 (or, often, between 0.1 and 100): When multiplying numbers together, you add the exponents algebraically. When dividing numbers, you subtract the exponents algebraically. Example

1-4 Dimensional Analysis The dimension of a quantity is the particular combination that characterizes it (the brackets indicate that we are talking about dimensions): [v] = [L]/[T] Note that we are not specifying units here – velocity could be measured in meters per second, miles per hour, inches per year, or whatever. Force=ma [F]=[M][L]/[T2]

Estimates or Guesstimates– How a Little Reasoning Goes a Long Way Estimates are very helpful in understanding what the solution to a particular problem might be. Generally an order of magnitude is enough – is it 10, 100, or 1000? Final quantity is only as accurate as the least well estimated quantity in it

Guesstimates How many golf balls would it take to circle the equator ? N= Circumference of Earth/ Diameter of Golf Ball Diameter of the golf ball is about 2 inches or 4 cm. How to estimate the circumference of the earth? US is 3000 miles wide because it takes a jet at 500 mph to fly from NY to LA in 6 hours It is also 3 times zones wide and there are 24 time zones across the world and therefore the circumference is 3000 x 24/3=24,000 miles or 40,000 km

Principles or Laws Mathematics Predict the future Conservation of Energy Conservation of Momentum Newton's Laws Principle of Relativity Laws of physics work the same for an observer in uniform motion as for an observer at rest. Mathematics Predict the future

In this course we will mostly work with the following forces Friction Gravity Contact forces Spring forces Buoyant forces ………. Also keep in mind that we assume in many instances when we have contact interactions, we assume also that we are dealing with rigid bodies. In actual fact a body is never purely rigid.

Rigid Body is made up of Matter Matter is made up of atoms which is made up of electrons orbiting the nucleus. This gives us our solids, liquids and gases. For example the surface of a solid might look something like this.

Solids STM images of a surface through silicon Atoms are arranged in a crystalline array or 3D solid Note defects in the lower image

Ordinary matter on earth is made up of tiny Atoms

Other Interactions (Action at a distance) Also called fundamental interactions. Strong - inside the nucleus of the atom Electromagnetic - between charged particles Electric Magnetic Weak - involves the neutrino Strength : Strong > electromagnetic > weak > gravitational

Math Review Short Math Review Algebra - Trigonometry and geometry Solving simultaneous equations Cramers Rule Quadratic equation Trigonometry and geometry sin, cos, and tan, Pythagorean Theorem, straight line, circle, parabola, ellipse Math Review Vectors Unit vectors Adding, subtracting, finding components Dot product Cross product Derivatives Integrals http://people.virginia.edu/~ral5q/classes/phys631/summer09/math-practice.html

Arc Length and Radians S is measured in radians

Pythagorean Theorem EXAMPLE

Trigonometry EXAMPLE

Simultaneous Equations FIND X AND Y

Cramer’s Rule

Cramer’s Rule

Quadratic Formula EQUATION: SOLVE FOR X: SEE EXAMPLE NEXT PAGE

Example

Derivation Complete the Square

Small Angle Approximation A useful simplification of the laws of trigonometry which is approximately true for very small angles. For EXAMPLE

How would you estimate the radius of the Earth roughly? Chap 1-33