AP Physics ----Administrative Chores

·  Pass out Syllabus

·  Comments on contact methods, web page, textbook, lectures, quizzes, homework.

·  Grading policy, grading scale, labs.

·  Course outline -- complete version on Thursday.

·  Calculators.

·  Study:

o  Establish and keep to a regular study schedule.

o  Read the assigned sections before lecture.

o  Attempt the assigned problems before quiz section.

o  Bring questions to lecture, quiz sections, or office hours.

o  It can be helpful to work problems with friends -- but avoid the temptation of letting your friends do all the work for you.

o  Physics is like sports: if you want to be good at it you must practice.

Chapter 1

What Is Physics?

From Webster's Dictionary:

From Greek, physikos, meaning of nature,

1 : a science that deals with matter and energy and their interactions
2 a : the physical processes and phenomena of a particular system b : the physical properties and
composition of something

We will be most concerned with (1). So, physics is the science that deals with matter and energy and their interactions. What isn't covered by this definition? Nearly everything around us is either matter or energy, so this definition is rather broad. In this course we will be concerned with the topics of mechanics, thermodynamics, and optics. We begin with mechanics.

Dimensions: Length, Mass, and Time

Mechanics deals with the motion of objects. To describe the motion of something, we need to know where it is at some instant in time, i.e. we need to know distances (length) and times. Additionally, when looking at what causes or controls motion, we will need to refer to the mass of objects -- the same cause of motion will have different effects on objects of different mass.

As a convenience, we will use international standards for length, mass, and time: the meter, second, and kilogram.

Definitions for length, mass and time are given in the text.

Tables showing the range of values for masses, lengths, and times. Notice that these quantities can have enormous variations from small to large.

Prefixes for Metric Units ------See table in the text on page 5 .
Building Blocks of Matter

Matter is composed of molecules which are made of atoms. Atoms are composed of a positive nucleus surrounded by a cloude of negatively charged electrons. The nucleus is composed of protons and neutrons which are in turn composed of quarks. And it is now hypothesized that electrons and quarks are actually small vibrating strings that exist in an 11 dimensional universe!

Dimensional Analysis or "You Can't Add Apples and Oranges"

We can treat the dimensions of quantities almost like variables. A length (L) divided by another length (L/L), is unit-less, since the two lengths cancel. Length divided by length squared (L/L2) is one over length. The example from the text demonstrates an application, where, without knowing what acceleration is, we can check that at least the dimensions work out properly.

Chapter 1, cont'd

55mi/hr = 24.6m/s

Coordinate Systems

It is often useful to use coordinate systems to define where things are. For instance, to specify the location of a chair in a room (a rectangular room), we can give the (perpendicular) distances of the chair from two adjacent walls

as shown to the right. Here I have labeled one of the distances X and the other Y, and we write the location of the chair as (X,Y). If the chair is 2m from the left wall and 5m from the bottom wall, then it's location is (2m, 5m). This type of coordinate system is known as a rectangular or Cartesian coordinate system. Notice that this type of coordinate system needs:

  1. an origin, in this case, the corner of the room from which the distances are measured,
  2. 2 (or 3) coordinate axes, in the case of the room the walls serve as the axes,
  3. and a distance scale in which to measure along the axes.

In this example, distances are measured in meters.

Show example with "standard" x-y coordinate system, and mark some positions on the plane.

Another way to specify a location is to give its distance from the origin, and its angle from a reference line, usually taken to be the x-axis. This is commonly called an r-theta, or polar coordinate. Show some examples of locating points with polar coordinates.

Trigonometry

We will have many occasions to make use of the properties of right triangles.

Recall that for a right triangle, such as the one pictured here, Pythagoran's theorem states that

a2 + b2 = c2

And, from trigonometry, we have the relations:

sinq = a / c

cosq = b / c

tanq = a / b

We will have many occasions to use these relations to:

·  find the distance between two points

·  decompose a vector (velocity, acceleration, or force) into x and y components

·  find the length and direction of a vector when we have the x and y components.

Problem Solving Strategies

Students should read through this now. I will return to this topic when I work examples.

Chapter 2: Motion in One Dimension

Mechanics is divided into two areas: dynamics, a cause and effect analysis of motion; and kinematics, the description of motion. We begin with kinematics of motion in one dimension.

Displacement

To descripe motion, we need to keep track of how the position of an object changes. A change in position is called a displacement, and is defined as the difference between the final and initial positions:

Dx = xf - xi

This calculation requires that first you establish a coordinate axes for measuring the position x.

Sketch a displacement, and show an example of how to calculate a positive and negative displacement.

Displacement is a vector. A vector is a quantity that has both a magnitude (value) and a direction. In the one dimensional case, the direction is rather easy, it is either positive or negative (right or left). In 2 dimensions, you must be more precise to indicate the direction.

Average Velocity

We define the average velocity of an object to be its displacement divided by the time interval for that displacement:

vavg = Dx / Dt = (xf - xi) / (tf - ti)

Example: P2.2

A swimmer crosses a 50m pool in 20s, and returns to her starting point in an additional 22s. (a) What is her average velocity for the first half of the swim?

  1. Read the problem.
  2. Make a sketch of the problem.
  3. Identify the data: length of pool is the displacement, is 50m, and the time interval is 20s
  4. Choose equation: vavg equation given above
  5. Solve the equation: vavg = 50m/20s = 2.5m/s
  6. Check answer.

(b) What is her average velocity for the second half of the swim?

Follow the same steps as above, but now the displacement is in the opposite direction, so let's call it -50m, and the time interval is 22s. Now vavg = 2.3m/s.

(c) What is her average velocity for the round trip?

Again, follow the same steps as above. Since she returns to her starting point, xf = xi and the displacement is zero. The time interval is 20s+22s = 42s. Note a curious thing about our definition about the average velocity, even though there is motion during a time interval, if the ending point is the same as the starting point, then the displacement is zero, and the average velocity is zero. This is the case here. Her speed is never zero, it is on average 100m/42s = 2.4m/s. But due to the formal, Physics definition, her average velocity is zero!

Graphical Interpretation of Velocity

It may be helpful to visualize the above problem on a graph of position versus time.

On such a graph, the average velocity between two points is simply the slope of the line connecting the two points. The points represent the position of an object at a particular time. Note that even though the object moves in a straight line (along x), the line on the graph doesn't have to be straight. This is because the line doesn't represent the direction of motion, but shows the position as a function of time.

Instantaneous Velocity

In the above graph, the velocity changes from instant to instant. We can see this by choosing different final points, and noting that the average velocity (the slope of the straight line connecting the initial and final points) is not constant. What would the graph look like if the object were moving at a constant velocity? (ans. a straight line)

The instantaneous velocity, v, is defined as the limit of the average velocity as the time interval Dt becomes infinitesimally short:

v = limit as Dt goes to 0 [Dx/Dt]

Graphically, the instantaneous velocity at a point is given by the slope of the line tangent to the position versus time curve at that point.

The instantaneous speed is the magnitude of the instantaneous velocity.

Acceleration

Acceleration is probably a familiar concept to everyone. Most people are familiar with the feeling of acceleration in a car or bus. In Physics, acceleration has a formal definition that may sometimes differ from common usage. The average acceleration is defined as the change in velocity during an interval of time:

aavg = Dv/Dt = (vf - vi) / (tf - ti)

Note that acceleration can be positive (increasing velocity) or negative (decreasing velocity, also called deceleration). And when we work problems in more than one dimension, we can have acceleration even though the speed is constant -- the direction of the velocity changes, but the magnitude remains the same.

Example: P2.16

A car is travelling initially at +7.0m/s. It accelerates at a rate of +0.80m/s2 for 2.0s. What is the final velocity?

  1. Read the problem.
  2. Make a sketch.
  3. Identify the data: vi = 7.0m/s, a = 0.80m/s2, Dt = 2.0s.
  4. We will use the equation a = (vf - vi) / Dt
  5. Rewrite the equation to solve for vf = vi + aDt = 7.0m/s + (0.80m/s2)(2.0s) = 8.6m/s
  6. Check the answer.

Recall:

  1. Displacement: Dx = xf - xi
  2. Average velocity: vavg = Dx / Dt
  3. Instantaneous velocity: the average velocity in the limit the time interval goes to zero, also the slope on the position versus time graph.
  4. Average acceleration: aavg = Dv / Dt = (vf-vi)/(tf-ti). Note that vf and vi are instantaneous velocities.
Example: P2.16

A car is travelling initially at +7.0m/s. It accelerates at a rate of +0.80m/s2 for 2.0s. What is the final velocity?

  1. Read the problem.
  2. Make a sketch.
  3. Identify the data: vi = 7.0m/s, a = 0.80m/s2, Dt = 2.0s.
  4. We will use the equation a = (vf - vi) / Dt
  5. Rewrite the equation to solve for vf = vi + aDt = 7.0m/s + (0.80m/s2)(2.0s) = 8.6m/s
  6. Check the answer.

Motion Diagram

1-D Motion with Constant Acceleration

Free Fall

Chapter 3: Vectors and 2-D Motion --all the following topics are from last year

Vectors and Scalars

Some Properties of Vectors

Components of a Vector

Velocity in two dimensions

Projectile motion

Relative velocity

Recall: Kinematics

Displacement vector: Dr = rf - ri
Velocity vector: vavg = Dr/Dt
Instantaneous velocity: take the limit as Dt goes to zero.
Average acceleration: aavg = Dv/Dt

Example: P3-21

A car is on an incline that makes an angle of 24 degrees to the horizontal. The car rolls from rest down the incline with a constant acceleration of 4.00m/s2 for a distance of 50.0m to the edge of the cliff. The cliff is 30.0m above the ocean. Find (a) the car's position relative to the base of the cliff when the car lands in the ocean, and (b) the length of time the car is in the air.

  1. Reread the problem.
  2. Draw a sketch.
  3. Identify the data. For this problem, think in terms of (1) when the car is rolling down the incline, and (2) when the car is falling to the ocean.
  4. Choose the equations. For (1) vf=vi+at.
  5. Solve the equations.
  6. Check the answer.

Chapter 4: The Laws of Motion

We move from kinematics (description of motion) to dynamics (understanding the causes of motion, and the resulting effects). The causes of motion we call "forces". Some types of forces are familiar, like if you pull on a string or throw a ball. Other forces are just as real but less familiar, for instance, when you sit on a chair, the chair pushes upward, against your weight. Otherwise, you would fall through the floor!

Types of Forces

Forces can be classified as contact or field forces. Contact forces involve the contact of two objects, such as in the examples of someone pulling a string, throwing a ball, or sitting in a chair. Field forces are a bit more abstract. You may have heard the phrase "action at a distance" to describe gravity. Initially, most of the forces we will use are either contact forces or gravity.

Newton's Laws of Motion

The ideas embodied in Newton's three laws of motion were known to many. Newton gets credit primarily for sythesising what was then known into three laws, and demonstrating the power of his formulation by tackling the problem of planetary motion and gravitation.

Newton's First Law

What is the natural state of matter? Aristotle believed it is for matter to be at rest. But anybody who's driven on icy Michigan roadways can attest to the fallacy of that blief. Galileo proposed that the natural state is to resist acceleration, and this idea is formalized in the first law: