P 251 Laboratory Activity II Graphical Analysis I.

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Presentation transcript:

P 251 Laboratory Activity II Graphical Analysis I

Graphical Analysis The analysis of experimental data to determine mathematical relationships between measured quantities 1. Constructing the Graph 2. Analyzing the Graph

Constructing the Graph

Summary: Problem: To determine the relationship between mass and volume, if one exists. Measurements: Mass and volume of five different aluminum objects Suppose that we think that there is a relationship between the mass of an object and its volume. We also think that this relationship will depend on the object's composition. We might look for several objects that are made of the same material, such as aluminum, and measure their masses and volumes. We could then use graphical analysis to determine if a relationship between mass and volume exists, and if it does what is its mathematical form.

DATA Volume and Mass of Aluminum Objects Choose Volume as independent variable Choose Mass as dependent variable

Mass versus Volume, Aluminum Objects Independent Variable Dependent Variable Graph Title 51 divisions 34 divisions mass, g Volume, cm 3 Construct and Label Axes

Scales do not have to be the same for both axes. Scales should be chosen so that the graph covers as much of the sheet as possible Determine scales for each axis.

Step 1: From the data table select the largest volume: 160cm 3 Step 2: Count the number of divisions on the horizontal axis: 34 divisions Step 3: Divide the largest volume by the number of divisions: Step 4: Round UP to a convenient number:

Step 1: From the data table select the largest mass: 432g Step 2: Count the number of divisions on the vertical axis: 51 divisions Step 3: Divide the largest mass by the number of divisions: Step 4: Round UP to a convenient number:

Plot data 0 origin Label Each Axis with its Scale

Graphing First data pair

Practice 1 1. Determine the best scale for each axis. 2. Label each axis with its scale. 3. Plot the first data pair.

Practice 2 1. Determine the best scale for each axis. 2. Label each axis with its scale. 3. Plot the first data pair.

Analysis of the Graph

Dependent variable Independent variable

V 1 M 1 V 2 M 2

Since the graph is (1) a straight line and (2) passes through the origin, we can say the the mass and volume are directly proportional.

Final Equation

Practice 3 Points Chosen for Slope: (0.2s,16.2m) ; (3.4s,83.4m) Intercept, b = 12m (speed) Equation: 1. Choose two points on the graph and determine the slope. 2. From the graph determine the y- intercept. 3. Write the equation relating d and t.