P 251 Laboratory Activity III Graphical Analysis II Nonlinear Graphs

Graphical Analysis Exercise Determining the Relationship between Circumference and Diameter Procedure: 1. Measure the Circumference and diameter of five circular objects. 2. Analyze data using graphical analysis.

Plot a graph of Circumference versus diameter.

1. Is your graph a straight line? CALCULATIONS AND OBSERVATIONS: YES 2. Does the graph pass through the origin? YES…b = 0 3. Are circumference and diameter directly proportional? YES 4. Calculate the slope; Points Used: (4.8cm,15.4cm) & (11.5cm,36.2cm) Slope has NO units

What is the equation relating Circumference and diameter? Compare slope = 3.1 to  14)

Non-Linear Graphs

What procedure do we follow if our graph is not a straight line? Consider an experiment designed to investigate the motion of an object. We want to determine the relationship between the object’s distance traveled and time. We measure its distance each second for 10s. Here is the resulting data.

Data We then plot a graph of distance versus time.

Not a straight line but is a uniform curve

Compare graph to graphs of other functions of the independent variable

Plot a new graph where time squared is the independent variable: Distance, d versus Time Squared, t 2

Analysis of Graph

With units of m/s 2 the slope represents the acceleration of the object.

It will be difficult to determine the intercept from the graph!

Two Other Methods for Determining the Intercept 1. The intercept is the value of the dependent variable where the graph intersects the vertical axis. At this point the value of the independent variable is zero. Look at the data table to determine the value of d where t 2 equals zero. 2. Start with the partial equation: Solve for “b”: Choose any data pair and substitute the values of “d” and “t 2 ” into the equation for “b”: (25s 2, 127.5m)

Final Equation

Dependence of Radiation Intensity on Distance from Source PURPOSE: The purpose of this laboratory exercise is to investigate the transfer of energy by radiation and the dependence of intensity on distance.

INTRODUCTION: Radiation is the mechanism of heat (and other energy) transfer by electromagnetic waves. Electromagnetic radiation can be classified according to its frequency (f or  ) and the energy transferred. The energy transported by an electromagnetic wave is directly proportional to its frequency. Typically EM radiation is divided into eight categories called the EM spectrum. Listed in order of increasing frequency (increasing energy) the components are: 1) Radio, 2) Television, 3) Microwaves, 4) Infrared, 5) Visible Light,6) Ultraviolet, 7) X-Rays, 8) Gamma Rays. Infrared radiation is what we sense as heat. The visible light component can be further broken down into the visible light spectrum where different frequencies appear as different colors. Listed in order of increasing frequency: Red, Orange, Yellow, Green, Blue, Indigo, Violet

As radiation travels from a source it spreads spherically. As it spreads the intensity (brightness) decreases. How does the intensity depend on the distance? Source

Experimental Apparatus The radiation detector converts radiation emitted by the light bulb into an electrical voltage which is measured by the multimeter. Turn Selector counterclockwise to 200 m

Step 1. Set the Radiation Detector next to the meter stick. Align the detector opening with the height of the light bulb and 20 cm away. Procedure Step 2. Turn on the light to maximum brightness. Slide the ring on the radiation detector forward to uncover the aperture. Turn multimeter selector counterclockwise to 200m (V). Step 3. Record the detector's voltage output in the data table. Step 4. Move the detector to 30 cm from the bulb and record the detector's output. Step 5. Repeat Step 4 for distances to 100 cm in 10 cm increments.

65.3

Complete the extended data table. Each group member do a different graph. Plot graphs of Radiation, R versus:

Conclusion Put a 4 by the proportion that gives the relationship between radiation intensity, R and distance from the source, d. Suppose the radiation intensity was proportional to the distance squared, If the distance from the source was doubled (multiplied by 2) the radiation intensity would be multiplied by 2 2 = 4. if the distance was multiplied by 3 (tripled) the intensity would be multiplied by 3 2 = 9. If the distance we cut in half (multiplied by 1/2) the intensity would be multiplied by (1/2) 2 = 1/4.

Suppose that at 50cm from the light bulb the light intensity was 100 mV, according to your graphical analysis, at a distance of 100cm the intensity would be ______mV. Suppose that at 50cm from the light bulb the light intensity was 100 mV, according to your graphical analysis, at a distance of 25cm the intensity would be ______mV.