AP Physics 2 - fundamentals review #3

With three weeks to go before the AP physics exams, it's worth remembering that our students don't need MORE practice problems; rather, they need to pay careful attention to the practice problems they do.  This is my application of a John Dewey principle, that we don't learn by doing; we learn by paying attention to what we do.  

My first-year students in physics 1 are in a cycle of AP problem / quiz based on AP problem / corrections to AP problem if their quiz or problem shows they didn't get it the first time.  In AP Physics 2, which is a second-year course, students have already internalized that they must pay attention to what they do.  And, P2 students have a level of earned confidence in their skills that my 9th grade P1 folks lack.  So truly all we're doing is these daily quizzes, in-class experimental and problem solving work, and each week one take-home 25 minute "quiz" with 5 multiple choice and one free response.  Less is more when dealing with upperclasspeople in the spring.

P2 Fundamentals Review #3

21. A battery is connected to two resistors in series.  The resistors each take 20 V of voltage across them.  What is the voltage of the battery?

22. Write the first law of thermodynamics, which is an expression for the change in internal energy.

23. Two waves are initially in phase with one another.  One wave has traveled a small extra distance than the other.  Under what conditions does constructive interference occur?

24. Define the period of a wave.

25. What is the equation relating the image and object distances for a convex mirror?

26. Two light waves undergo constructive interference.  What physical effect will be observed?

27. Name two items that can produce a magnetic field.

28. A battery is connected to two resistors in series.  The resistors each take 20 mA of current through them.  What is the current provided by the battery?

29. A gas consists of molecules moving around.  What feature of these molecules’ behavior causes the macroscopic effect called pressure?

30. What is the physical quantity that means energy produced in one second?

AP Physics 2 - fundamentals review #2

My AP Physics 2 class is an ungraded honors course.  There's not even a contract.  There is a careful selection process - students are selected not based on their previous grades, but holistically based on their demonstrated authentic interest in the subject.  Basically, if a student passed P1, wasn't a jerk, and put forth reasonably consistent effort, we take them into the P2 class.  

Even without published grades, the ground state of our class is to begin with a 4-5 minute fundamentals quiz.  We grade the quiz; students tell me their scores.  The quiz grades have no extrinsic meaning, won't be seen by parents or counselors or universities.  So what!  Motivated students still care about getting things right.  But, with no published grades, the students are insulated from the shame or world-ending dread of receiving a published grade that is not an A.  If someone gets 3/10 - which happens somewhat regularly! - they don't have to fear that someone is waiting with a (hopefully figurative) cane for their poor performance.  They just should try to do better next time.

P2 Fundamentals Quiz #2

11. Light is incident on a thin film.  Under what conditions does the light change phase?

12. An ammeter measures ____.  It is connected in _____ with a resistor.

13. Write the equation for induced emf.  

14. And electric field points →.  A positron moves ← in the electric field.  Sketch the path of the positron, and describe briefly how it moves.

15. An electric field points from position A to position B.  Which position is at higher electric potential?

16. A gas expands adiabatically.  What is the sign of the work done on the gas during this process?

17. Write the units of electric field.

18. Kirchoff’s loop rule is a statement of conservation of _____.

19. A concave mirror has radius 50 cm.  What is the focal length of this mirror?

20. For a convex (diverging) mirror, how does a ray parallel to the principal axis reflect?

(Solutions will be in the comments in a few days!)

Fundamentals checks for AP Physics *2*

Last year I wrote a bunch of fundamentals checks in preparation for the AP physics 1 or C-mechanics exams.  This year, I'm teaching a physics 2 section.  So, I'm writing daily quizzes for P2 now!  I'll post the quizzes here, then follow up a couple of days later with the answers in the comments.

Quiz 1:

1.       A substance has index of refraction 1.5.  What is (or how do I figure out) the speed of light in this substance?

2.       Write the equation relating focal length, image distance, and object distance for a mirror.

3.       Write the equation for the energy carried by a photon.

4.       Under what conditions is the image distance d_i positive, and under what conditions is it negative?

5.       The diagram shows light hitting a mirror.  What is the angle of incidence as the light hits the mirror?

6.       A resistor is connected to a battery, and the current in the circuit is measured.  The voltage of the battery is increased, and the current is measured again.  Which Ohm’s Law variable(s) remain unchanged after the voltage is increased?

7.       Under what conditions is the electric field given by the equation E = kQ/d²?

8.       One mole of monotomic ideal gas begins at pressure P₁ and volume V_1­.  Next, the pressure is increased to P₂ without changing the volume.  Write an expression (including a + or – sign) for the work done on the gas.

 9.       Write the equation for the capacitance of a parallel plate capacitor.

 10.   A photon initially has wavelength 500 nm.  The photon collides with a free electron which was initially at rest, giving the electron 3.0 eV of kinetic energy.  The photon bounces back opposite the direction it was initially moving.  What is the speed of the reflected photon?

Energy of various systems in an inelastic collision

 

I was asked about the situation above, in which two carts of different masses are released from rest and roll down frictionless ramps.  The carts collide and stick together on the flat surface.

Let's treat this as a goal-less problem:

Edna, Bertha, and Anthony by @Aldescary

Which way do the carts move after they collide?  

Well, Anthony (whom Edna calls a mean hippopotamus) says that the carts don't move after collision - they both have the same energy but in opposite directions, which cancel.

Oy.  So many things wrong with Anthony's answer.  Let's start with the fact that energy is a scalar quantity - energy can't have direction at all, let alone "cancel" other forms of energy.  And whenever we see a collision, energy should never be the first port of call - momentum should be.

It is true that the gravitational energy of each earth-cart system is converted to kinetic energy at the bottom.  And since the gravitational energy 2mgd is the same for both earth-cart systems, each cart will have the same kinetic energy before collision.

However, the momentums of each cart will be different.  I like to use the shortcut equation K = p^2 / 2m in this case to see that with the same kinetic energy, the cart with a greater mass will also have greater momentum.  You could also convert gravitational energy to kinetic energy to show that the speed at the bottom will root 2gh for both carts with mass canceling; then by p = mv twice as much mass with only 1.4 times as much speed means bigger momentum.

So the cart moving left has larger momentum than the cart moving right, meaning the two-cart system has a leftward momentum.  System momentum must be the same after collision as before, so the momentum is still leftward after collision... and that's the way the stuck-together carts will move.

Is mechanical energy of the both-carts-and-earth system conserved from release to just BEFORE the collision?

Anthony says mechanical energy is potential plus kinetic energy, and is always conserved, so yes.

Well, even a blind squirrel, or hippopotamus, finds a nut once in a while.  Anthony is pretty much correct.  Mechanical energy is conserved when no work is done by external forces and when no internal energy conversion occurs.  Here, the only external force acting on the carts-earth system is the normal forces of the surfaces on the carts.  These forces are perpendicular to the carts' motion, and so do no work.  Mechanical energy is, in fact, conserved here!

Is mechanical energy of the both-carts-and-earth system conserved from release to just AFTER the collision?

Anthony is perturbed... he already answered this question!  Mechanical energy is conserved, period, full stop, end of sentence.  Hemph.

Oh, Anthony... when carts collide and stick together, they undergo an inelastic collision by definition.  Mechanical energy may never be conserved in an inelastic collision - rather, some mechanical energy must be converted to internal energy.  

Is mechanical energy of the both-carts-only system conserved from release to just AFTER the collision?

Anthony says he's done answering these tricky questions involving systems.  He's gonna put his head down on his desk and listen to Edna for a change.

Edna thinks this one is pretty simple... because an object by itself can only possess kinetic energy!  (Potential energy can only exist when a spring or the earth is incl
uded in the relevant system.)  So the mechanical energy of the carts is just their kinetic energy.  On release from rest, the carts have no speed and therefore no kinetic energy.  After collision, the carts are moving, so they have kinetic energy.  The KE has gone from zero to not-zero, and therefore has increased.