Heinrich Hertz and Wolfgang Pauli

Mr. Sandoe 4/1/1917 Heinrich Hertz and Wolfgang Pauli

Density of Sports Balls

Introduction Density is a unit that has been studied in the last few weeks of class. Many people commonly have misconceptions about density, such as something heavy must be dense and will sink when placed in water. Density, instead, is the ratio of mass and volume in an object. Misconceptions about density and density’s relationship with other variables will be studied in this lab with the help of different sports balls being measured and placed in water.

Procedure A sports ball was assigned to each lab group. The mass of the sports ball was recorded using an electronic balance. Based on the mass of the ball, a prediction was made as to whether the ball will sink or float in water.

Circumference of the ball was measured by wrapping a string around the center of the ball and marking how much string was used. The length of string used to wrap around the center of the ball was measured in centimeters, using a ruler.

The circumference value was used to solve for the radius of the ball using the equation C = 2πr. Radius was then used to find volume with the use of the equation V = (4/3)( π)(r3).

Using the measured mass of the ball and the calculated volume of the ball, density was calculated using the equation D = m/v.

Data was shared between all groups for each ball measured. The procedure was repeated, but with a different sports ball.

All balls were placed into a clear tub of water to test the sink/float predictions and make observations.

Discussion and Conclusion The idea that many misconceptions about density and mass exist was supported with evidence from the data of the lab. Many groups had predicted that the bowling ball would sink, solely based upon the mass of the ball. Upon testing in water, the bowling ball floated (density of 0.53 g/cm3). This shows that mass is not the determining factor about whether an object will float or not, it is density. Mass must be considered with the volume of the object to correctly find density and predict whether an object can float or sink.

It was possible to conclude the density of water after analyzing the collected lab data. All of the objects that floated had a density value lower than 1 g/cm3 and all of the objects that sank had a density value greater than 1 g/cm3 (see attached graph). From this observation, it is clear that the density of water will be very close to 1 g/cm3.

Density and mass misconceptions were successfully exposed and overturned during the course of this lab. A better understanding of what density is and how it is used was obtained.

Some error is likely in the circumference measurement of the sports balls. Using a string to wrap around the center of the ball was a difficult measurement to accurately make and most likely lead to a lot of variation between lab groups. A better method of calculating volume could be considered for the next time.

Post-Lab Questions 1. Examine the density values of the balls that sink. Do the same for the balls that float. By comparing the densities of these two groups (sinkers and floaters), what would you estimate the density of water to be and why?

After examining the sports balls, it seems that all of the balls that sink have a density value below 1 g/cm3 and all of the balls that sank have a density above 1 g/cm3. It can be concluded that water has a density of 1 g/cm3.

2. Find two balls used that have a similar mass, but one floats and one sinks. Compare the volume of both balls. Thoroughly explain why one sinks and one floats.

Two balls that have a similar mass are the small grey mouse ball at 25.64 g and the small green basketball at 25.50 g. The volume of the ball’s, however, varies a little bit more. The mouse ball has a volume of about 8.05 cm3 and the green basketball has a volume of about 13.74 cm3. The similar mass, but difference in volume leads to a difference in density which is why one ball floats but the other sinks.

3. Find two balls used that have a similar volume, but one floats and one sinks. Compare the mass of both balls. Thoroughly explain why one sinks and one floats.

The tennis ball and lacrosse ball have similar volumes (146.39 cm3 and 135.94 cm3, respectively). The mass values differ a little bit more, as the tennis ball has a mass of about 55.83 g and the lacrosse ball’s mass is about 149.36 g. The similar volume but big difference in mass leads to a difference in density. The lacrosse ball’s large density value is the reason it sinks while the tennis ball stays afloat.

4. Other than the method used in this lab, describe a method that we could use in our lab to experimentally figure out the density of water. Include equipment, steps, etc. To find the density of water, both the mass and volume would need to be known. A graduated cylinder would be placed on the balance and then the balanced be set to zero. Water would be added and the mass of the water recorded. The volume of the water in the graduated cylinder would be measured. The mass value and the volume would be used in the density equation to find the density of the water.

5. Assuming that it would have the same volume as the bowling ball we tested, how much mass would a new bowling ball need in order to sink in the water? Think about the density equation, and your estimation in question 3. Show all of your work. In order to sink, the new bowling ball would need a density greater than 1 g/cm3, as discussed in question 1. This would mean the mass needs to be greater than the volume. This new mass would need to be greater than 5544.92 g. A bowling ball with the same volume and a mass of 5545 g would sink in water. x 1 g/cm3 < 5544.92 g < x 5544.92 cm3

6. Using the density values of the two balls, give an explanation for what you saw in numbers 2 and 4 of the observation section.

In observation number 2, the mouse ball sank much faster than the golf ball did. This can be attributed to the density of each. The mouse ball has a density of about 4.97 g/cm3 and the golf ball’s density is about 1.09 g/cm3. The higher density of the mouse ball causes it to sink faster. In observation number 4, the small green basketball floated, but much lower in the water than the ping pong ball did. The green basketball’s density is about 0.84 g/cm3, meaning in barely floats. The ping pong ball’s density is about 0.017 g/cm3, meaning it floats very high on the water.

7. What was the benefit of having 2 different groups make measurements for each ball and then use an average value for making graphs and comparisons?

With two groups making measurements on the same ball, mistakes were much less likely. If one group made a significant error in measurement or calculation, the hope is that the second group performing the same work would notice the difference in answers and catch the mistake.

8. What are some likely sources of error that could have occurred during this lab? How would they have affected the data? One likely source of error in the lab is the circumference measurement performed by all lab groups. A lot of difficulty was found when trying to keep the string in the center of the ball while measuring exactly how much string was wrapped around the ball. It was also difficult to hold the exact mark on the string while measuring the length of the string with the ruler.