Determine The Mass of our Water Rocket

Worksheet

I have created a worksheet of questions about the mass of our water rocket. It was written using Microsoft Word and you can find it here. Click on the word here

In this section we investigate and learn about the mass of our water rocket.
When we build our machines one of the most important characteristics is the size. That is generally stated as the mass. When making flying machines, mass may be the single most important attribute. When we intend to lift something off the ground, we need to know the force required to lift it.

Exercises

We all learn best when we do things. Everyone is encouraged to do the exercises described here. Further: This is for our STEM class. Science, Technology, Engineering, and Mathematics. It is in your advantage to be able to say: "I did the exercises." Much better is to be able to say: "Here are the steps I did and the results I discovered." Write down each step you performed and all the measurements you made. Take care as you write this down. Tomorrow, or a week or more later you want to be able to easily remember the meaning of what you wrote. You also wish to write so that others may understand and learn from what you have takent the time to write. Rather than writing down "42 grams," write down "The mass of the empty 1.25 liter bottle is 42 grams, not counting anything inside." Use complete and descriptive sentences.

Vocabulary

There will be some new words for you. Please expend the effort to look them up yourself before you accept the meanings I provide. Most words have more than one meaning so select the appropriate definition. Here are some new words that will be useful for our rocket discussions. Start with gross weight. It is a very useful word but probably not what you think. Then look up two companion words for gross weight: net weight and tare weight.

After finding those definitions write this sentence and fill in the blank: "The tare weight of our rocket is ______." You can probably guess it, but please look it up and be certain. You have sufficient information to write that down. We will get to the gross mass and net mass shortly.

Think about things I may have left out and measurements I might have done, and even mistakes I might have made. Write those down and make those measurements. Please bring your documents and your ideas to class.

Mass of our Water Rocket

We start by determining the characteristics of our water rocket. In particular, its mass.

Special Attention Needed

In these new few paragraphs we will perform some simple arithmetic. The numbers will not be very complicated. However, the concepts will be new and may not be easy for everyone. You will definitely need to think about what we do. If you have questions, please pause and write them down right away. If in class, raise your hand and ask for an explanation.
Let us begin!

We will begin with the easiest one first, the mass of our bottle. The water rocket kit was purchased from Hobby Lobby. I filled the bottle with water then measured the amount to be 1.25 liters. Not having a small scale, an Internet search revealed that the mass of a 1.25 liter plastic water bottle is 42 grams. We will make some rockets with two liter bottles. Do some Google searches and discover their mass.

Water

Water has many properties of interest but we will concentrate on those of mass and volume.

Water is very important to scientific standards. 1 cm3 of water has a mass of 1 gram. That relationship was created on purpose and did not just happen that way.
If we make a cube of water that is 10 cm on each of the sides, the volume of the box is 10cm * 10cm * 10cm or 1000 cm * cm * cm or 1000 cm3. That is one liter of water. It contains 1000 cm3 of water. Therefore it has a mass of 1000 grams or one kilogram.

Exercise

Get a ruler and draw a square 10 cm on each side. Then stand the ruler on end and imagine a box that size. That is the size of one liter of water. Its mass would be one kilogram. Just in case you don't have a metric ruler, 10 cm is about 3.9 inches. Drawing that box and thinking about it a little bit will help you understand a liter and a kilogram.

Find out if you have a measuring cup in the house and see if it has liters marked on it. If not you can search the Internet and discover that one quart is about 0.95 liters. A quart is just a little bit smaller than a liter and a little bit less mass. How many drinking glasses will a liter of water fill?

The word kilogram is the word gram with the prefix kilo added to it. Kilo means one thousand so one kilogram is 1000 grams. For reference, one kilogram weighs about 2.2 pounds. A gram is pretty small. One medium sized paper clip has the mass of about one gram.

We estimated that the best flight was with our rocket filled about half full of water. For convenience let us presume we are starting with 500 cc of water which has a mass of 500 grams. (Note: cc is short for cubic centimeter or cm3.)

How much volumn is left over for the air? Please calculate it yourself before you continue. And write it down in complete sentences.

To calculate the answer remember that the bottle capacity is 1.25 liters. Convert that to cc and the bottle volume is 1250 cm3.
When 500 cm3 are occupied by the water there are 750 cm3 remaining for the air.

Mass Of The Air

Challenge
See if you can discover the mass of air on your own. You can use a dictionary, encyclopedia, or an Internet search. Do not ask anyone, discover for yourself. It means more when you do it yourself.
Please do that before you continue.
Hint
Start a Google search and enter the phrase density of air. My Google search presented a nice definition right at the top. It is more complex that you might expect but please read it carefully a couple of times.

But do not get too side-tracked. If you have many burning questions, write them down on another sheet of paper and look them up after you finish this section about our rockets. Bring your questions to class so we can hear what else you discovered.

As we saw in our very first experiment, the air we breathe has mass. The density of air at sea level is 1.225 kilograms/m3. We live very close to sea level so that value will do nicely.

How much air is that? Measure a square on the floor that is about 39 inches on each side. Then measure up for 39 inches and imagine a cardboard box that size. That is a pretty big box. The volume of air inside would be one cubic meter or 1m3

Challenge: How many liters of air are in a cubic meter?

Hint: A liter is a cube that is 10 centimeters on a side. A centimeter is a combination of two phrases: centi and meter. The phrase centi means one hundred. There are one hundred centimeters in a meter. If we have ten liters of air in perfect cubes, then how many do we line up to make a line one meter long. That would be 10. Now how many of these cubes would it take to cover the bottom of our cubic meter box?

Continue that line of thinking and you can do the calculations.

I'll wait for you.

Did you get 10 * 10 * 10 = 1000 liters per m3?
Hopefully so.

In this lesson we will be working with liters of air rather than a cubic meter. So what is the mass of air in one liter of volume?

Method Convert the mass of the cubic meter of air to grams rather than kilograms to get 1,225 grams. Divide 1,225 grams that by 1000 because there are 1000 liters in a cubic meter and we have 1.225 grams of mass per liter of air.

Just for fun, recall that a liter of air has 1.225 grams of mass and the same volume of water has 1000 grams of mass. Divide that 1.225 grams of air in one liter into the 1,000 grams of water in one liter and quotient is 800. Water is 800 times as dense as air.

Back to the air.

Our rocket started about half full of air. Then we forced more air into it. Let us begin before we pumped extra air in. The unpressurized rocket contains 750 cm3 of air at sea level pressure about 14.7 pounds/inch2. Calculate the mass of the air inside the bottle before we started pumping. I'll take a break while you do that.

Done?
Here is one way to figure it out. The volume of air was 750 cm3 while a liter of air has 1000 cm3. That means there there are 0.750 liters of air in the bottle. Multiply that by the mass of one liter of air 1.225 grams. The result is 0.91875 grams of air in the bottle.

You might have calculated the mass of air in one cc, then multiplied by 750 to get the result. If so, that was good thinking.

Understanding this is very important. Make sure you can do those calculations before you continue.

Now to pressurize our rocket
We used a pump to force more air into the bottle until the pressure was about 25 psi (pounds per square inch) more than normal air pressure. We will work on this for a while.

Pressure in Scientific Notation

We are going to do our calculations in scientific notation. But my bicycle pump is marked in PSI. One of the basic notations for air pressure is the pascal and its symbol is Pa. Do a Google search on what is a pascal of pressure and see what you get. I advise you to use that entire phrase because Pascal is the name of a famous person, its is the name of a computer programming language and probably some other stuff. Using the longer search phrase will help the Google search utility to filter out the things you don't want and show just what you do want.

After reading that, write a quick note from memory describing what a pascal of pressure is.

For completeness, I'll include it here. One pascal is enough pressure to press on one square meter with a force of one newton.

Do you remember the newton? When you hold an average size apple gravity pulls it down with the force of about one newton. One newton spread out over an entire square meter is not much force.

Convert PSI to Pascal

Do another search for convert psi to pascal If you select a conversion tool, you can enter 1 for psi and the tool will give you a conversion number. Multiply psi by that number to get pascals.

Explanation

The unit of measure we call psi is pressure on one square inch. A pascal is the pressure of one newton on one square meter. In one square meter there are 1550 square inches.
(Note: 1 meter is 39.3701 inches so one square meter is 39.3701 inches * 39.3701 inches or 1,550.00477401 inches2. That is close enough to call it 1550 in2. )
One psi on each of the 1550 square inches in a square meter is a lot of pressure, 1,550 pounds on that square meter.

We are not there yet, but we are getting closer. We have determined that 1 psi on a square meter is 1550 pounds. But pascals are a measure of newtons. Search for convert pounds to newtons.

I presume you found that one pound of force is is 4.44822162 newtons. Now multiply that 1550 number by this new 4.4 number to get: (Do it your self first,...) 6894.7647468545.

Important: We are almost done with our conversion, but we have an intermediate product that is very important. We know that one psi is equal to 6894.76 pascal. This is the conversion factor from psi to pascal. To convert psi to pascal, simply multiply the psi by this conversion factor. The result is the pressure in units of pascal.
Now we finish our problem calculating standard air pressure in psi to pascal.

Multiply our sea level air pressure of 14.7 by the conversion factor 6894.76 to get about 101,325. We have now reached our goal: Air pressure at sea level is 101,325 pascal.

That is a pretty big number so science often use the term kilopascal. That is 1000 pascal so our pressure becomes 101.3 KPa. That is easier to work with. (Note: When reading this you can say K P a, pronouncing each letter, or you can say kilopascal as one word.)

Back To Our Pump

Our pump showed the pressure as about 25 psi. To convert to pascal multiply 25 by the conversion factor we just found: 6894.75 to get 172,368.75 pascal.

Then divide by 1000 and round off to one decimal place to get 172.3 KPa. This is the approximate pressure in our rocket when it launched.

The end result is that we changed 25 psi to 172.3 KPa. Be sure you understand what just happened before we continue.

PSIA versus PSIG

When we used our pump to add air pressure, the gauge on our pump started at 0 and went up to 173 KPa. (That is after the conversion of course.) The zero did not mean there was no air pressure when we started. The zero meant that the air pressure inside the bottle was the same as outside the bottle. When we pump up the air pressure in the bottle, or maybe the air in your bicycle tire, we are not concerned with the air pressure everywhere. For the moment, we are concerned with how much more pressure there is inside the bottle than there is outside the bottle.

Think about why that is the case.
In order to push the water out of the bottle, the air pressure in the bottle must be greater than the air pressure outside the bottle. That larger pressure on the inside is what forces the water out.

The bicycle pump pressure gauge is a certain type of gauge known as psig which stands for Pounds per Square Inch Gauge. It shows the pressure above ambient. When we want to know the total pressure we use a gauge of the type psia or Pounds per Square Inch Absolute.

We will see why that is important now.

We pumped the air pressure up to 172.3 KPa according to the gauge. But the real total pressure was 101.3 KPa (sea level air pressure) plus what the gauge showed, 172.3 KPa for total of 273.6 KPa.

The next question is: How much did we increase the pressure by. We take our final pressure of 273.6 (Absolute and not Gauge) and divide it by our starting pressure of 101.3 (also absolute) to get about 2.7. If we had tried to start with zero, we would be dividing by zero and that does not work out well.

But that is not the entire story. Here is the complete division problem with units of measure.

	 273.6 KPa
	 _________
	 101.3 KPa
We divided a pressure by another pressure. Both must have the same units of measure. Observe that this division problem included KPa divided by KPa which is a factor of one. Remember that when multiplying and dividing we can remove factors of one.
The next step is to reduce our fraction. We divide both the numerator and the denominator by 101.3 and the complete result is:
	 2.7
	 ____
	 1
That is the ratio. We know that anything divided by 1 is itself so for convenience, we omit the vinculum and the denominator leaving us with our ratio of 2.7.

Cool. Right? Write down any question you have before your forget them.

Vocabulary

There is a new word in the above paragraph: vinculum See if you can determine its meaning from how it was used. Then look it up. After reading about it, use your own words and without looking at the definition, write down the meaning.

To Continue:

Here is the reason we did that.

From our notes above we discovered that the density of air is 1.225 kilograms/m3. We also discovered that the unpressurized mass of air in our bottle was about 0.6125 grams.

From just above, we know that we increased the pressure by the ratio of 2.7 to 1. By pressurizing the air we increased its density by a factor of 2.7. So to find our how much air we then had in our rocket, start with the unpressurized mass of 0.91875 and multiply by 2.7 to get about 2.48 grams of air.

Finally, The Total Mass

Add up all of our masses.
		 42    grams       the bottle
		500    grams       the water
		  2.48 grams       the air
	______________
	        544.48 grams       rocket at launch
	
This is the gross mass of our rocket at launch.

Exercise

Recall the three vocabulary words: net, gross, and tare. Our rocket has a number for each one. Determine each of those values and describe what each means. Write down what you discover.

Hint: To find something that you know is in this document, press and hold down the Ctl key, then press the F key. That will open a find window. Type what you are searching for in the window and press the enter key. The computer will show you the next instance of those characters.

Answer

The gross mass of our rocket is about 544 grams. The net mass is what the rocket carries. In this case it is the weight of the propellant, the water and the air. Add those up and see what you get. The tare weight is the empty rocket. You should know what that is by now. Write them all down in complete sentences.

You probably noticed that the mass of the fins are not included. How would you categorize their mass?

Thrust

The next step, and the next lesson, is to determine the thrust of our rocket. That page is here:
Water Rocket Thrust

12 Jan 2015
Bryan Kelly
send comments to: on line at bkelly dot ws