PHYSICAL SCIENCES

EXPERIMENT 2 (COMPUTERIZED VERSION)

 

THE LAW OF THE PENDULUM

 

NAME: ____________________________ ID#: ___________SECTION: ____ DATE: _____

 

INTRODUCTION:

 

                                A simple pendulum consists of a small heavy mass attached to a light string suspended from a rigid support.  The pendulum is set swinging by displacing the mass (called the bob) slightly and then letting go.  Make sure the bob has an unobstructed arc I which to swing.  Figure 2.1 illustrates the proper displacement of the bob and the swinging arc for a simple pendulum.  The 'simple' is use to describe the pendulum because most of the mass is concentrated at a point (the bob).  The system we will be using today is not ideal because there is some mass distribution within the bob and we are not accounting for the mass of the string.  The system does, however, allow us to closely approximate the Period of a pendulum.

 

                                The period of a pendulum is the time require for one swing of the bob and can be calculate using the formula:

 

                                                                      

 

                                                                        Equation 2.1

'T' is the term used to represent the period in seconds.

'L' is the length of the pendulum.

'g' is the acceleration due to gravity and is a constant with a value of 980 cm/s2 for this experiment.

 

 

 

 

 

 

 

 

 

 

 

 


                                                        Figure 2.1 Simple Pendulum

 

OBJECTIVES :

 

                                To study the use of a simple pendulum and to learn graphing techniques using a computer.

 

APPARATUS:

 

                                Simple pendulum, meter stick, timer and a lap top computer.

 

                                                                               

 

 

 

 

 

 

 

PROCEDURE:

 

                                Determine, experimentally, the period of a simple pendulum with a length of 98 cm.  Allow the bob to swing for five periods for each determination and record your data in TABLE 2.1.  TABLE 2.1 is an Xcel file on the lap top.  As you enter your raw data the computer has been programmed to calculate the period for each of your determinations and ultimately to determine your average period for the five determinations.

 

Table 2.1  (Imported from XCEL)

 

 

 

 

 

 

 

 

 

Your average from TABLE 2.1 is your experimental value for the pendulum.

 

a.        EXPERIMENTAL VALUE _______________ s.

 

USE THE CALCULATOR AND MAKE APPROPRIATE SUBSTITUTIONS IN EQ. 2.1 TO CALCULATE THE THEORETICAL VALUE FOR A 98 cm PENDULUM.  SHOW ALL MATH STEPS USED TO OBTAIN YOUR ANSWER.

 

 

 

 

 

 

 

 

 

b.   THEORETICAL VALUE                         _____________ s.

 

2.                             Use your data for the theoretical and experimental values for the pendulum to determine your percent error by substituting in EQ. 2.1 

 


                                                                               

PERCENT ERROR =______________

 

 

Equation 2.2

 

 

 

                                                                                                               

 

 

 

3.                             From your data in TABLE 2.1, calculate the percent difference among your values for the five determinations for the period using EQ. 2.3


                                                                               

PERCENT DIFFERENCE = __________________

 

 

 

Equation 2.3         

 

                                                               

 

4.  Reduce the length of your pendulum by successive halves (49.00, 24.50, and 12.25 cm respectively).   Let the pendulum swing for five swings, only, at each distance and record your data in TABLE 2.2 which can be found as an Xcel file on the lap top.  MAKE SURE TO INCLUDE YOUR 98 cm DATA FROM TABLE 2.1 INTO TABLE 2.2 FOR GRAPHING PURPOSES. 

 

Table 2.2 (Imported From XCEL)

 

 

 

 

 

 

 

 

a.  USING THE SQUARE ROOT OF LENGTH DATA (Y-AXIS) AND THE PERIOD (X-AXIS) COMPUTER GENERATE YOUR GRAPH AND DETERMINE THE SLOPE OF THE LINE. SEE YOUR COMPUTER DATA.

 

 

 

 

SLOPE: ______________                                                  

 

b.  DETERMINE THE VALUE FOR GRAVITY USING YOUR SLOPE AND EQUATION 1.  REARRANGING EQ. 1 WILL GIVE:  YOUR SLOPE IS COMPUTED FROM YOUR DATA BY THE COMPUTER                                 

                                               

 

 

 

 

                                                                                                                                                                GRAVITY: ____________

 

c.        USE EQ. 2.2 AND CALCULATE YOUR PER CENT ERROR FOR GRAVITY.

 

 

 

 

 

                                                                                                                                                PER CENT ERROR: ____________

 

d.        FROM YOUR GRAPH, DETERMINE THE PERIOD OF A PENDULUM IF ITS LENGTH IS 25 cm.

 

 

 

 

 

QUESTIONS:

 

1.       What is the length, in centimeters, of a simple pendulum that has a period of one second? 

 

 

 

 

 

 

 

 

 

 

 

 

2.       Distinguish between percent error and percent difference.

 

 

 

 

 


 

Determination #

Time For Five Swings (s)

Period (s)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LENGTH OF PENDULUM (cm)

SQUARE RT. OF L

FIVE SWINGS (s)

PERIOD (T)