Balloon Experiment Using Coulomb’s Law

Title: How Many Electrons?

Theory:

-See Attached

Objective:

-To determine the charge and number of excess electrons on a balloon by applying Coulombs law and Newton’s 3rd Law of motion.

Materials:

-Balloons.

-Thread.

-Masking Tape.

-Protractor.

-Ruler.

-Scale.

Procedure:

  1. Mass the two balloons.
  2. Blow up balloons.
  3. Tie balloons together with string (~ 6 feet / 2 meters in length)
  4. Hang balloon system from ceiling such that the balloons will be at the same height.
  5. Charge up balloons completely with “Fluffy” or other suitable means including your own hair.
  6. Measure the length of string from the ceiling to the center of each balloon (this number should be the same for each balloon).
  7. Measure the angle that the balloons make with each other directly with a protractor, or indirectly through by measuring the distance that they are separated from one another and basic trigonometry.

Analysis:

  1. Draw a free-body diagram identifying the forces acting on the balloons.
  2. Calculate the charge on each balloon using Coulomb’s Law.*
  3. How many electrons are there (qe = 1.6 x 10-19 C)?*
  4. What is the electrostatic force?*
  5. What are some sources of error in your measurements?

Conclusions:

Data

Mass of Balloon #1 / Mass of Balloon #2 / L / r / θ
Average Mass of Balloons

* Do all calculations on a separate piece of paper. Be sure to include the formula with proper substitution and units.
Theory & Solution:

Newton’s third law says that for every action there is an equal and opposite reaction. Therefore, the force acting on A due to B is equal to the force acting on B due to A. We can hence reason that F = FA = FB. Now, using vector analysis, we can derive the charge on each balloon since we know the weight of them and the length of string, and the angle or distance between the two balloons. However, to do this, we will only look at one side of the system.

To determine F, we have to use what we already know. We have the weight of each balloon, the length of the string, and either the distance between them or the angle that they form. If the angle between them is used:

F = mg tan (θ/2)

F = kq1q2 = mg tan (θ/2)

r2

If we assume that the charges on both balloons are equal, this equation reduces to:

F = kq2 = mg tan (θ/2)

r2

The charge on each balloon can now be determined by rearranging the terms to solve for q.

q = mgr2 tan (θ/2)

k

Once the value for q is determined in Coulombs, the number of electrons can be estimated by dividing q by 1.6 x 10-19C/electron.