Reviewed ideas of General Relativity from Friday - in particular the kindergarten approach to time ticking slower near source of gravity.
Calvin and Hobbes intro to Principle of Equivalence.
Principle of Equivalence worksheet.
Pound Rebka worksheet.
Test tomorrow.
Monday, April 21, 2008
Friday, April 18, 2008
Friday, April 18, 2008
Went over problems 14 in problem sheet.
Went over Giancoli problems in relativity. Students did well on them.
Showed graphs of mass vs speed and speed vs time for a constant force (both Newtonian and Relativistic).
Introduced General Relativity.
Sprang from the mind of Einstein in 1916 paper.
General, because it handles acceleration, whereas the special theory of relativity only dealt with the special case of reference frames moving with respect to each other at constant velocity.
Life on Flat World skit.
We live on a sphere so it is possible to head off in opposite directions and meet.
Happens also in space. Satellite above Earth sends off two probes in opposite directions. They meet because they both orbit the Earth. Newton attributes this to gravity. Einstein said space itself is curved.
Mass tells space how to curve, space tells objects how to move. If you have a rubber sheet with nothing on it, it is flat. If you place objects on the sheet, it will sag. Objects moving on the sheet are affected by the sags and tend to be deflected towards the depressions.
Kindergarten view of General Relativity:
1. Light has energy
2. Energy and mass are connected (E = mc^2)
3. Mass is affected by gravity.
4. Light is affected by gravity.
5. Show thick light beam. If no mass, the beam is straight. If there is mass, the beam is bent. A runner around the track on an inside lane has an advantage because the path is shorter. The inner part of the light beam travels a shorter distance. But...since the speed of light is the same for all observers, the clock for the inner beam ticks more slowly (less ticks). Clocks run slow near sources of gravity!!
Note the difference between clocks in special relativity and those in general relativity. In special relativity, as you go by, I see your clock ticking slow. You are at rest in your rest frame and see me going by. You see my clock as ticking slow. We each see each others clock as ticking slow.
In general relativity, I am in the attic and you in the cellar. I see your clock ticking slow, you see my clock ticking fast. We each see our own clocks ticking correctly but see the differences in the other person's clock.
A black hole is a strong source of gravity. As you approach the black hole, I see your clock running slow, you see my clock running fast. You look back and see the entire future of the universe.
For homework, please look at Hewitt Relativity.
Went over Giancoli problems in relativity. Students did well on them.
Showed graphs of mass vs speed and speed vs time for a constant force (both Newtonian and Relativistic).
Introduced General Relativity.
Sprang from the mind of Einstein in 1916 paper.
General, because it handles acceleration, whereas the special theory of relativity only dealt with the special case of reference frames moving with respect to each other at constant velocity.
Life on Flat World skit.
We live on a sphere so it is possible to head off in opposite directions and meet.
Happens also in space. Satellite above Earth sends off two probes in opposite directions. They meet because they both orbit the Earth. Newton attributes this to gravity. Einstein said space itself is curved.
Mass tells space how to curve, space tells objects how to move. If you have a rubber sheet with nothing on it, it is flat. If you place objects on the sheet, it will sag. Objects moving on the sheet are affected by the sags and tend to be deflected towards the depressions.
Kindergarten view of General Relativity:
1. Light has energy
2. Energy and mass are connected (E = mc^2)
3. Mass is affected by gravity.
4. Light is affected by gravity.
5. Show thick light beam. If no mass, the beam is straight. If there is mass, the beam is bent. A runner around the track on an inside lane has an advantage because the path is shorter. The inner part of the light beam travels a shorter distance. But...since the speed of light is the same for all observers, the clock for the inner beam ticks more slowly (less ticks). Clocks run slow near sources of gravity!!
Note the difference between clocks in special relativity and those in general relativity. In special relativity, as you go by, I see your clock ticking slow. You are at rest in your rest frame and see me going by. You see my clock as ticking slow. We each see each others clock as ticking slow.
In general relativity, I am in the attic and you in the cellar. I see your clock ticking slow, you see my clock ticking fast. We each see our own clocks ticking correctly but see the differences in the other person's clock.
A black hole is a strong source of gravity. As you approach the black hole, I see your clock running slow, you see my clock running fast. You look back and see the entire future of the universe.
For homework, please look at Hewitt Relativity.
Thursday, April 17, 2008
Thursday, April 17, 2008
Went over homework problems 8-13.
Reassigned problem 14 for homework. Handed out Giancoli problem packet.
Hope to wrap up Special Theory of Relativity and start General Theory tomorrow.
Test on Tuesday.
Reassigned problem 14 for homework. Handed out Giancoli problem packet.
Hope to wrap up Special Theory of Relativity and start General Theory tomorrow.
Test on Tuesday.
Wednesday, April 16, 2008
Wednesday, April 16, 2008
Handed back time dilation quiz. Asked students who did not get it correct to redo it on back and hand in.
Introduced Length Contraction with Thought Experiments. Came up with equation for length contraction. Showed by proof by contradiction that the length is contracted only in the direction parallel to the direction of motion, NOT in a direction perpendicular to the motion.
Redid the quiz first using time dilation and then using length contraction to calculate what the astronaut's "odometer" would read. The results were consistent as they must be.
Introduced idea of increase in mass with speed along with the mass equation.
Used examples of bouncer with roll of quarters, Andy and Bill trying to punch each other, and Bonnie and her sister.
Like other waves, light has energy, but unlike other waves, light also has momentum (comet tails always point away from the Sun). If light has energy, it also has mass. It has mass because it has energy.
The total energy of an object is, from Einstein's equation, E = mc^2 = mo c^2 + KE
where mo is the rest mass. You cannot use KE = 1/2 m v^2 when dealing with relativistic speeds.
Assigned problems 8-13 for homework.
Test next Tues/Wed
Introduced Length Contraction with Thought Experiments. Came up with equation for length contraction. Showed by proof by contradiction that the length is contracted only in the direction parallel to the direction of motion, NOT in a direction perpendicular to the motion.
Redid the quiz first using time dilation and then using length contraction to calculate what the astronaut's "odometer" would read. The results were consistent as they must be.
Introduced idea of increase in mass with speed along with the mass equation.
Used examples of bouncer with roll of quarters, Andy and Bill trying to punch each other, and Bonnie and her sister.
Like other waves, light has energy, but unlike other waves, light also has momentum (comet tails always point away from the Sun). If light has energy, it also has mass. It has mass because it has energy.
The total energy of an object is, from Einstein's equation, E = mc^2 = mo c^2 + KE
where mo is the rest mass. You cannot use KE = 1/2 m v^2 when dealing with relativistic speeds.
Assigned problems 8-13 for homework.
Test next Tues/Wed
Tuesday, April 15, 2008
Tuesday, April 15, 2008
Reviewed simultaneity. If Bonnie sends signals to light lamps at either end of her spacecraft, she will be illuminated by each at the same time. You too will see her illuminated by both at the same time but you will see the rear light light first and then the front light.
Went over homework problems.
Quiz on time dilation.
Hewitt video on Time Dilation.
No homework for this evening.
Went over homework problems.
Quiz on time dilation.
Hewitt video on Time Dilation.
No homework for this evening.
Monday, April 14, 2008
Monday, April 14, 2008
Went over Waves Test.
Talked about Hugh Hunter Scholarship.
Around the room review of topics covered last time in relativity.
Went over homework problems.
Continued relativity - finished simultaneity.
Derived time dilation equation from light clocks. Showed graphical example.
Handed out Han Solo problem.
Assigned problems 4,5,6,7 (7 is hard).
Talked about Hugh Hunter Scholarship.
Around the room review of topics covered last time in relativity.
Went over homework problems.
Continued relativity - finished simultaneity.
Derived time dilation equation from light clocks. Showed graphical example.
Handed out Han Solo problem.
Assigned problems 4,5,6,7 (7 is hard).
Thursday, April 10, 2008
Thursday, April 10, 2008
Didn't have time to grade tests so didn't hand them back today.
Intro to Relativity.
Gave intro
Went through first 6 thought experiments.
Discussed relativistic correction to the relative velocity equation.
Students did worksheet on simultaneity. Went over worksheet.
Handed out problem sheet. Assigned problems 1-3 for homework - due Monday.
Intro to Relativity.
Gave intro
Went through first 6 thought experiments.
Discussed relativistic correction to the relative velocity equation.
Students did worksheet on simultaneity. Went over worksheet.
Handed out problem sheet. Assigned problems 1-3 for homework - due Monday.
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