RE: Share your classroom ideas here

2017-04-28T20:58:57Z

Hello, my name is Maria Eleftheriou and I am Science teacher in Greece. My school is the Lyceum of Tzermiadon located at the mountains of Crete. I am also ambassador of Scientix and I am very happy that I am a part of this team of teachers.

Lesson plan: Gravity versus electricity.. or not? What about black holes?
Ideas from Stephen Hawking book: A Brief History of Time

This book is a best seller in all over the world, not without reason. Hawking explains difficult concepts with a unique way. I chose two concepts for a lesson plan that can be performed in the secondary education.

1st idea: Gravity

2nd idea: Black holes

1st idea: Comparison of electrical force and gravitational force. We suppose that students have been taught the Coulomb law. The formula for the electric force between two point electric charges Q1 and Q2 is F=k Q1Q2/r^2 where k is the Coulomb constant and r is the distance between the charges.

On the other hand, the gravitational force between two spherical masses m1 and m2 is F=G m1m2/r^2 where G is the Gravitational constant and r is the distance between the masses.We ask then our students if they can observe the similarities of those two forms. We ask them also what are the main differences between gravitation and electricity and students find for example:

Two types of electric charges, one type of mass.
Electric force can be attractive or repulsive, gravitation is always attractive.
Electrostatic force depends on the material between the two charges, the gravitation force is not depending on the material between the masses.

Students write in the left part of the blackboard the similarities and in the right part of the blackboard the differences and then we perform a discussion. In what limit of distances we expect that the electric force is significant and where is the gravitational force significant? As Hawking writes in his book, electromagnetic force, gravitational force, strong nuclear force and weak force in the beggining of our universe possibly were united. What about the distances of masses in the beggining of the universe? We can answer to this question? (Chapter 5, 11)

2nd idea: And now....is it possible to escape from our planet?

A body of mass m with velocity υ can escape from a planet of mass M and radius r if we consider the conservation of energy:1/2mυ^2=GMm/r therefore υ=(2GM/r)^(1/2)

Students like John Michell and Pierre-Simon Laplace in 18th century put c (speed of light) for the velocity υ and find r_s=2GM/c^2. We found the correct Schwarzschild radius by only using Newtonian mechanics! This is the radius of a black hole.

Scientists know that a candidate star for a black hole has to have mass at least 1.5 solar mass. Nevertheless if our sun M=1.98 *10^(30)kg could become a black hole it would have a radius of rs=3 Km. Students put M=5.9 *10^(24)kg (mass of the earth) and found rs=0.009m. Working each student in a team of students, set several different masses (e.g. masses of planets) in the Schwarzschild formula in order to see how the radius changes with mass. What is the Schwarzschild radius of a person ? (e.g. M=80kg)

Additionally students search on the web for black holes, for example:https://www.nasa.gov/image-feature/computer-simulated-image-of-a-supermassive-black-hole

The final discussion with the students is around black holes in general for our universe. How big is the universe? How many things we already know but how many unanswered questions still exist? Scientists trying to find a theory that explains the genesis of our universe (chapter 8). Students now realize the difficulties that scientists can have, but also realize the beauty of science!

You can also find a presentation for this lesson plan in :https://docs.google.com/presentation/d/1nGWamhb6g9tuj_PZl5d3-NEv8fqieXZwXmfp-jw657A/edit?usp=sharing

cat3

RE: Share your classroom ideas here