Measurement, Calculation and the Experimental Setting

Resources

The sections in this table will be considered knowledge the student should have prior to beginning a course in physics. A good review of much of this can be found in Unit 01 Chemistry and Unit 05 Chemistry.

Measurement using the Metric System

Unit 01 Chemistry

Fundamental Units of Measurement

  • time (sec)
  • length (m)
  • mass (kg)
  • temperature (K)

Common Prefixes Used in the Metric System

  • Nano = 1/1,000,000,000
  • Micro = 1/1,000,000
  • Milli=  1/1,000
  • Centi = 1/100
  • Kilo = 1,000
  • Mega = 1,000,000
  • Giga = 1,000,000,000

Exponential (Scientific) Notation

Unit 05 Chemistry

  • writing very large or very small numbers
  • converting exponential notation into regular notation
  • converting regular notation into exponential notation computations using scientific notation (+,-,x,/)

Mathematics Skills

  • basic algebra (rearrange equations to solve for a variable)
  • use of a scientific calculator: order of operations
  • trigonometry of right triangles (Pythagorean Theorem, Sine, Cosine, Tangent, Law of Sines and Cosines)

Error in Measurement 

  • accuracy vs. precision
  • relative error

Significant Figures Unit 01 Chemistry

  • expressing a measurement to the correct number of significant digits
  • the 4 rules for determining how many significant digits there are in a number
  • computations with significant figures

Converting Between Units Unit 01 Chemistry

  • factor label or dimensional analysis

Presenting Data Graphically

One of the most effective tools of visualizing data is the graph. Constructing a graph enables to identify quantitatively, how one variable affects another.

When we plot a graph, it is usually between 2 variables.

  • the dependent variable and is plotted on the y-axis.
  • the independent variable and is plotted on the x-axis.

The dependent variable is the quantity that is measured at set intervals of the independent variable. The independent variable is the variable that the experimenter has complete control over.

Relationships Between Variables

When we make a graph, we can determine the mathematical relationship between the variables and propose an equation that relates the two variables. When appropriate, the slope and or area beneath the curve will also have some significance. Whenever possible, we will perform experiments that give us data that we can plot on a graph so that we can discover the relationship between variables and the equation involved. We can determine the relationship by finding the equation that represents the function plotted.

Some Examples:

1. Measure the position of a car at various times as it travels on the interstate.
This graph is a straight line which means that the equation is y = mx + b. In this case y represents the change in position, x represents time in min, b represents the y intercept which is the initial position, and in this case is 0. The slope has units of km/min, which represents velocity. The specific equation becomes

d = v t (or v = d/t. )

We can use this equation to make predictions about where the car is at what time and what time it will be at a specific place.

2. How does the volume of a gas vary with pressure?

The curve appears to be a hyperbola which indicates an inverse relationship between Volume and Pressure.


A hyperbola suggests that a test plot be made of V vs 1/P. The resulting graph is shown below:
The result is a straight line with a y intercept of 0. The equation for this straight line is : V = m(1/P) or VP = m

In this case, m represents the slope (not mass) and is a constant.

 3. How is the area of a circle affected by its radius?.
This graph is NOT a straight line but instead a top opening parabola. This indicates a quadratic relationship. We can verify this relationship by plotting area vs. the square of the radius

Since the A vs r2 graph is linear with a y intercept of zero, the equation relating area and radius must be

A = mr2

Of course, m in this case has the value of pi, p.

 

4. How does stopping distance vary with speed?
The curve appears to be a side opening parabola. A parabola indicates a quadratic relationship. Because it is side opening, we can do a test plot of v2 vs d.
A straight line confirms our guess. The equation that relates speed to stopping distance would be v2 = md. In this case, the y intercept is zero. 

Resources

 

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