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.
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.
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 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.
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.
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?
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.
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.
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.
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 KPaWe 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.
2.7 ____ 1That 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.
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.
42 grams the bottle 500 grams the water 2.48 grams the air ______________ 544.48 grams rocket at launchThis is the gross mass of our rocket at launch.
You probably noticed that the mass of the fins are not included. How would you categorize their mass?
12 Jan 2015
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