What’s heavier: A pound of feathers or a pound of rocks? This is is a trick question! A pound of anything is the same weight as a pound of anything else, but it would take WAY more feathers to make up a pound than a pound of rocks. This has to do with density.
Density is determined by how tightly the atoms in an object are packed together. An object with very tightly packed atoms is denser than an object with atoms that have more room in between each other. Take a look at the image below. Which is denser, object A or object B?
We have learned about density in some of our previous blogs, such as when you built a a liquid rainbow in a jar using liquids of different densities. Check it out to learn more! http://discoveryexpress.weebly.com/homeblog/rainbow-in-a-jar-learning-about-liquid-density
An object that is denser is also heavier than an object that is less dense. For example, stainless steel has a density of 7.8g/cm^3. Aluminum has a density of 2.7g/cm^3. Because steel has a higher density, it is heavier, more sturdy, and is used to build objects that need to last a long time, such as bridges or ships, while aluminum, a lighter, more flexible metal, is used more to make items such as cans or baking sheets.
A similar example is muscle versus fat. Take a look at the image below. Which is denser, muscle or fat?
So let’s get back to our question of the day: Do bowling balls sink or float? The answer seems obvious, doesn’t it? Clearly, heavy objects such as rocks should sink while lighter objects such as feathers would float, right? Well, it’s not as simple as it may seem. A bowling ball seems pretty heavy, but the determining factor of whether the ball (or any object, for that matter) will sink or float is its density. If an object is denser than water, it will sink. If an object is less dense than water, it will float. Water has a density of approximately 1g/cm^3. Just how do you figure out an object’s density? Let’s find out!
circumference = 2 * π * radius
volume = 4/3 * π * radius^3
(Remember, the symbol π is pi. Pi is approximately 3.14)
YOU WILL NEED:
- Two bowling balls (one lighter than 11 pounds and one heavier than 13 pounds)
- Tape measure
- Bath tub or large container filled with water
- A scale
Here’s what to do!
- Fill the tub or container with water.
- Predict whether the bowling balls will sink or float. Why do you think this?
- Place the heavier bowling ball in the water. What happens? Is this what you thought would happen?
- Place the lighter bowling ball in the water. What happens? Does this surprise you? Why or why not?
- Now that you’ve observed what happens with each ball, you are going to actually determine their densities.
- Use a tape measure to find the circumference of your ball. To find the circumference, you need to wrap the tape measure all the way around the widest part of the ball. Make sure the tape measure is flat against the ball. Every ball should be right around 27 inches. Once you measure the ball, convert the inches to centimeters. 1 inch = 2.54 centimeters.
For example, if your ball is 26 and 3/4 inches, then you would multiply 26.75 by 2.54.
26.75 inches x 2.54 = 67.945 centimeters
7. After you find the circumference, solve for radius.
67.945 = 2 x 3.14 x r
67.945 = 6.28 x r
67.945/6.28 = r
10.819 = r
The radius is 10.819cm.
8. After you find the radius, you can solve for volume using the volume equation.
volume = 4/3 * 3.14 * r^3
volume = 4/3 * 3.14 * 10.819^3
volume = 5301.878cm^3
Now you have the volume of the ball... IF the bowling ball were a perfect sphere, but it’s not. Bowling balls have finger holes, so you need to find the volume of the finger holes and then subtract the finger holes volumes from the volume you just found.
9. Use the volume equation for cylinders below:
volume = π * radius^2 * height
To complete this equation, you need to find the height and radius of the finger hole. Find the height by sticking a pencil eraser-first into the hole until it hits the bottom, marking the point on the pencil at the finger hole’s top, then measuring the pencil from the eraser to the point where you marked it. This is your height. Let’s say you found out the hole was 2.5cm deep. Plug the number into the equation.
Volume = 3.14 * radius^2 * height
Volume = 3.14 * radius^2 * 2.5cm
10. Next you need to find the radius of the hole. The radius is half of the diameter (width of the hole). Remember to measure in centimeters! Let’s say you found out the diameter of the hole was 1.2cm. Because the diameter is 1.2cm, the radius would be 0.6cm. Plug the number into the appropriate spot in the equation.
Volume = 3.14 * .6^2 * 2.5
Volume = 2.826cm^3
11. There! You’ve now found the volume of a finger hole in the bowling ball. Check to see if the radius and height of each hole is the same. If they are all the same, you can just multiply the volume you found for the first hole by 3. If they are different, find the volume of the other two holes and then add them together to find the total volume for the three holes. For simplicity’s sake, let’s say that all three holes were the same and multiply our first number by 3.
Volume of three holes combined = 8.478cm^3
Now that you have the volume of the finger holes, subtract this number from the volume of the ball that you found earlier.
Volume of bowling ball - volume of finger holes = True volume
5301.878cm^3 - 8.478cm^3 = 5,293.4cm^3
True volume of the bowling ball = 5,293.4cm^3
12. Now you FINALLY have the volume of the bowling ball! BUT you still don’t have the density. To find the density, you need to weigh the ball. Remember to use a scale that measures in grams. If you don’t have one, 1 pound = 453.6 grams.
If your ball is 13 pounds, then you would multiply 13 by 453.6.
13lbs * 453.6 = 5,896.8g
13. Now that you have the weight, divide it by the volume of the ball in cubic centimeters to discover the density.
Weight of bowling ball / True volume of bowling ball = density
5,896.8g / 5,293.4cm^3 = 1.114g/cm
The density of your bowling ball is 1.114g/cm.
There you go! You now know how to find the densities of the two bowling balls. Do your results match up with what you predicted earlier? You should have found that the ball that floated had a density of less than 1g/cm while the ball that sank had a density of more than 1g/cm.