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Lift off!

Helium balloons float because the helium gas inside is much lighter than the air outside. And you can use the balloons to lift anything--from your eraser to an elephant! The trick: You need enough balloons so that the helium's buoyancy (the upward force on a floating object) pulling the object is larger than the force of gravity (the downward force that pulls objects towards Earth). The buoyant force of helium can lift about one gram per liter of the gas. Now, with a few simple calculations, you can figure out how many balloons you need to lift some objects from your classroom-- including you!

You need:

* 10 helium balloons (same size and with strings attached) * 1 meter stick * calculator * scale * paper clip * rubber band * ruler

Part A:

Calculate the volume of gas in a party balloon

We know that one liter of helium can lift one gram. But how many liters of helium are in one balloon? Your balloon probably has a funny shape. But to simplify the calculation, we will pretend that it's a perfect sphere. Here's the formula to calculate the volume of a sphere:

V = 4/3 x [pi] x r x r x r (r = radius of the sphere)

Don't panic! The formula may look complicated, but you can easily calculate your balloon's volume by following the steps below.

1. Measure the diameter (the distance from one side of a circle to the other side) of your balloon in centimeters. (Hint: Measure in the middle of the balloon, at the fattest part.)

Diameter = -- cm

2. Calculate the radius of your balloon: r = diameter / 2

Answer: r = -- cm

3. Use a calculator to find the balloon's volume:

V = 4/3 x [pi] x r x r x r (Hint: [pi] [approximately equal to] 3.14)

Answer: V = -- cubic cm

4. Now convert volume into liters: (answer in Step 3) / 1,000 (Reason: 1,000 cubic cm is equal to 1 liter.)

Answer: V = -- liters

Part B: Calculate how many balloons are needed to lift objects

Now that you know how many liters a balloon holds, you can calculate how many balloons you will need to lift any object.

1. Look at each object you have collected from your classroom (paper clip, tack, pencil, rubber band, ruler, etc.). Then create a data table, (See SW 9/22/03 for help.)

2. Guess how many balloons you would need to lift each object. Record your guess guesses in the table.

3. Now weigh each object, and record the data in the table.

4. Using the calculated volume of a balloon and the rule that one liter of helium can lift one gram, how balloons are needed to lift each object? many balloons are needed to lift each object? Number of balloons = weight in grams) / (answer from Step 4, Part A)

5. Record your calculations in the table.

6. Now test your calculations. Tie balloons one by one to each object until it lifts off the table.

7. You probably don't have room in your classroom for the thousands of balloons that it would take to lift an elephant, but you can still calculate how many you would need to lift some hefty things. How many Would you need to lift a: 4,000 g (9 lb) rabbit?-- 10,000 g (22 lb) desk?-- 1,400 kg (3,090 lb) Porsche?-- 6,000 kg (13,230 lb) elephant?--


Did your calculations of the number of balloons needed to lift the objects in your classroom match how many it actually took to lift each object? If not, what factors might have impacted your results?

Don't stop now:

How many balloons would it take for you to lift off?
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Title Annotation:Math Skills/Hands-On Activity
Publication:Science World
Date:Nov 3, 2003
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