The following section is an excerpt from the example laboratory report, titled Proper Inflation of a Basketball. (The entire example report is available in either  Microsoft Word Format for printing, or  HTML format for online viewing.)

Data and Analysis

The specific results from this experiment allow us to determine the proper number of strokes of our hand pump needed to properly inflate the basketball, and to calculate the proper number of strokes to use with any pump.

Experimental Results

Some typical data describing the rebounding of the basketball are shown in Table 1. From these data we can see that there is a small amount of variation in the rebound height from one trial to another, even for identical conditions. This is most probably due to variations in the initial height from which we dropped the ball. For each set of trials, we took the average of the individual rebound heights to represent the rebounding of the ball at that amount of inflation. We took the standard deviation of the five trials to be the uncertainty in each of these averages.

Table 1. Typical data describing the rebounding of the basketball. These data were taken for the case of 15 strokes having been used to inflate the ball.
 

rebound height h [m]					average  h [m]	uncertainty  [m]
trial 1	trial 2	trial 3	trial 4	trial 5
1.31	1.34	1.34	1.34	1.36	1.34	0.02

Figure 3 shows the variation of rebound height h as a function of the number of strokes of the pump used to inflate the basketball. We used the "trendline" feature in Microsoft ExcelÒ to fit the data to a polynomial function. The functional fit we found was
 

(1)

where N is the number of strokes of the pump and h is measured in meters. From these data, we see that the proper number of strokes to inflate the basketball is N = 12.
 
 
 

Figure 3. Rebound height h as a function of the number of strokes of the pump used to inflate the basketball.

Theoretical Analysis

It is important to realize that the number of strokes needed to properly inflate the basketball is valid only for the particular pump that we have used. The important quantity is the pressure of the air that is in the ball. Fortunately, we can use the ideal gas law to determine the pressure in the ball from our measurements. The ideal gas law states that (Serway 1997, p. 542)
 

(2)

where P is the pressure of an amount of gas, V is the volume the gas occupies, n is the number of molecules in this amount of gas, T is the temperature of the gas, and k is Boltzmann's constant. In SI units, k = 1.38 ´ 10- ²³ J/K (Serway 1997, p. 542). In this equation, the temperature is measured on the absolute scale of degrees Kelvin or K.

When we use a pump to inflate a basketball, we take a fixed number of air molecules, n, initially at room temperature and pressure, and squeeze them into a smaller volume. Although the process of compressing the gas heats it, it quickly looses this heat and returns to room temperature. Since n and T in Equation (2) are constants, we can rewrite this equation as
 

(3)

where the subscripts "1" and "2" refer to the initial and final conditions of the gas. Here, the initial pressure of the gas is atmospheric pressure at room temperature, P_atm. The initial volume of the gas is the volume of the basketball, V_ball, and N times the volume of the pump, V_pump. Recall that N is the number of strokes of the pump we used to inflate the ball. The situation is described graphically in Figure 4.
 
 
 

Figure 4. When we use a pump to inflate a basketball, we take a fixed amount of air and squeeze it into a smaller volume.

The relative increase in the pressure of the ball, using Equation (3), is just
 

(4)

Because we know the dimensions of the ball and the pump, we can calculate these volumes. The volume of the pump is its cross-sectional area times the length of its stroke, or
 

(5)

and we can find the volume of the ball from the formula for the volume of a sphere, so
 

(6)

This tells us that the increase in pressure that makes the ball bounce properly is P₂/P_atm = 1.57. With this knowledge, we can use Equation (4) to derive a formula that is useful in general for the number of strokes to properly inflate the ball, namely
 

(7)

where we use Equations (5) and (6) to calculate the volume of the pump and the ball, respectively.

Note what's here:

• Sample data in a table. A representative set of a larger data set can be useful to explain your methods, but present raw data sparingly.
• Complete data in a graph. A graph is the way to display a large data set.
• Equations. You can also explain the theory behind the experiment in the introduction. Choose the location that makes reading your paper the clearest.

• All of the raw data. Do not display all of your raw data in a table, unless the data set is very small.