WHAT IS PHYSICS? The goal of physics is to use a

small number of basic concepts, equations, and assumptions to describe the physical world.

These physics principles can then be used to make predictions about a broad range of phenomena.

Physics discoveries often turn out to have unexpected practical applications, and advances in technology can in turn lead to new physics discoveries.

THE SCIENTIFIC METHOD There is no single

procedure that scientists follow in their work. However, there are certain steps common to all good scientific investigations.

These steps are called the scientific method.

CONTROLLED EXPERIMENTS A hypothesis must be tested in a

controlled experiment.

A controlled experiment tests only one factor at a time by using a comparison of a control group with an experimental group.

SI STANDARDS

SI PREFIXES In SI, units are

combined with prefixes that symbolize certain powers of 10. The most common prefixes and their symbols are shown in the table.

DIMENSIONS AND UNITS

Measurements of physical quantities must be expressed in units that match the dimensions of that quantity.

In addition to having the correct dimension, measurements used in calculations should also have the same units.

For example, when determining area by

multiplying length and width, be sure the

measurements are expressed in the same units.

ACCURACY AND PRECISION

Accuracy is a description of how close a measurement is to the correct or accepted value of the quantity measured.

Precision is the degree of exactness of a measurement.

A numeric measure of confidence in a measurement or result is known as uncertainty. A lower uncertainty indicates greater confidence.

SIGNIFICANT FIGURES

It is important to record the precision of your measurements so that other people can understand and interpret your results.

A common convention used in science to indicate precision is known as significant figures.

Significant figures are those digits in a measurement that are known with certainty plus the first digit that is uncertain.

Even though this ruler is marked in only

centimeters and half-centimeters, if you

estimate, you can use it to report

measurements to a precision of a millimeter.

RULES FOR DETERMINING SIGNIFICANT ZEROS

RULES FOR CALCULATING WITH SIGNIFICANT FIGURES

MATHEMATICS AND PHYSICSTables, graphs, and equations can

make data easier to understand.

GRAPHICAL METHODSquantitative graph - shows the relationship

between two variables in the form of a curve

For the relationship: y =f (x)x- the independent variable

plotted along horizontal axis positive values to the right of the origin is the one over which the experimenter has complete control

y- the dependent variable plotted along vertical axis positive values above the origin the one that responds to changes in the independent

variable

Ex: In an experiment where given amount of gas expands when heated at a constant pressure, the relationship between the variables, V and T, may be graphically represented as follows

It is proper to plot V= f(T) rather than T= f(V)

The experimenter can control the temperature of the gas,

but the volume can only be changed by changing the

temperature

CURVE FITTING The process of matching an equation to a curve is

called curve fitting. The desired empirical formula, can usually be

determined by inspection, and requires an assumption that the curve represents a linear or simple power function.

If data plotted on rectangular coordinates yields a straight line, the function y= f(x) is said to be linear and the line on the graph could be represented algebraically by the slope-intercept form:

y = mx+b where: m -is the slope b –is y-intercept

Consider the graph of velocity vs. time

The curve is a straight line, indicating that v =f(t) is a linear relationship

v =mt +b

where slope m =(Δv) / (Δt)= (v2-v1) /(t2-t1)

from the graph m = (8.0m/s)/(10.0s)= 0.80 m/s2

The curve intercepts the v-axix at v =2.0 m/s ( velocity when the first

measurement was taken)

when t =0, b =v0 =2.0m/s The general equation, v =mt +b can be rewritten as

v =(0.8 m/s2)t + 2.0m/s

Consider the graph of Pressure vs. Volume:

The curve appears to be a hyperbola (inverse function). This function suggest a test plot of P vs 1/V.

The equation for this straight line is: P= m(1/V) +b

where b =0, P =m(1/V)

when rearranged, this yields PV = constant which is known as Boyle’s Law

Consider the graph of distance vs. time. The curve appears to be a top-opening parabola This function suggest that a test plot be made

of d vs. t2

Since the plot is linear d =mt

2+b

The slope m =(Δd) / (Δt2

) =(.80m)/(.50s)2

=

1.6m/s2

b=0 (curve passes through the origin)

The mathematical expression that describes the motion of the object is: d

=(1.6m/s2

)t2

Consider the graph of distance vs. height The curve appears to be a side-opening

parabola. This function suggest a plot be

made of d2

vs. h

Since the graph is linear, the expression

is:d2

= mh +b The slope m =Δd

2 / Δh

m =2.5 cm2

/ 5.0 cm= 0.50cm b=0 (the curve passes through origin) The mathematical expression is: d

2 = (0.5

cm)h