Angular Displacement - 2011 A-level question

A disc rotates clockwise about its centre O until point P has moved to point Q, such that OP equals the length of the straight line PQ. What is the angular displacement of OQ relative to OP?

A.   \frac{\pi}{3} rad

B.   \frac{2\pi}{3} rad

C.   \frac{4\pi}{3} rad

D.   \frac{5\pi}{3} rad

Static Electricity

image source: http://www.sxc.hu/photo/243992

This question is meant for TA 2B and 2C Physics students.

Other than the demonstrations we have tried out during class, could you think of any other way in which static electricity can be observed?

Please leave your comments below. You may need to log in to Facebook while doing so.

p-V diagram Sudoku time!

For the topic of Thermal Physics, JC1 students can try to make sense of p-V diagrams using the following exercise, which does not involve any calculation. They will need to fill in the cells in the table below with any of the three (+, - or 0) to indicate whether there is heat transfer, work done on the gas, or a change in internal energy.


Hooke's Law

Here are two applets students may like to try:

A. The first is a simple "experiment" showing that the extension of a spring is proportional to the force applied:

http://www.absorblearning.com/media/attachment.action?quick=5l&att=394

B. For the second applet, you can try:

  1. looking for the unknown masses.
  2. observing the potential energy at different extensions of each spring.
  3. varying the gravitational field strength.

http://phet.colorado.edu/sims/mass-spring-lab/mass-spring-lab_en.html

Wave-Particle Duality of Electrons

I find this video easy to understand and it may be useful for students to appreciate the wave property of matter and how it is observed via interference.  The video ends with a mind-boggling problem that when an attempt to detect the path of the electron, it goes back to behaving as a particle.

There's a whole series of "What the Bleep" videos that you might want to check out also. Be careful though, the rabbit hole is pretty deep.

Quoting from another website on what could have happened to each electron and to make the problem clearer (and hence more confusing):

The possibilities are: 1) the electron went through the left slit; or 2) the electron went through the right slit; or 3) the electron went through both slits. For the sake of logical rigor, we should add the possibility that 4) the electron went through neither slit (that is, it found some other way to get to the back wall). Now, one problem with possibility number 3 -- a single electron going through both slits -- is that, in nature, there is no such thing as half an electron. So if we found half an electron at both slits, we would have something really new; but that has to be a distinct possibility, considering that, in order to create the apparent interference pattern, something would have to radiate from both slits.

How are we going to find out? Well, we are going to put an electron detector at each slit. The electron detectors at the slits will be devices to keep watch over the passage through the slit. Every time an electron (or part of an electron) goes through, the detector will give a holler, "Hey, an electron (or part of an electron) just went through." In this way, we will be able to learn something about how the electrons get through the barrier in a double slit experiment.

As it turns out, when you put the electron detectors at the slits, the result is that the electron is always detected at one slit or the other slit. It is never found going through both slits. And it is never found going through neither slit. You send one electron through, you find it at one of the slits. We have eliminated possibilities number 3 (both slits) and number 4 (neither slit). The only results we find are possibilities number 1 (left slit) or number 2 (right slit), in equal proportions.

They call this phenomenon the measurement effect. When we measure something at the quantum level, the very act of measurement will have an effect on the thing itself.

This is a phenomenon that still has no classical explanation.

Even Richard Feynman called it "a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery."

Water in an Inverted Cup

This demonstration can be modified for use as a magic trick.

Materials:

  1. Glass of water
  2. Piece of cardboard that is larger than the mouth of the glass.

Procedure:

  1. Fill the glass up with water.
  2. Place the piece of cardboard over the mouth of the glass.
  3. Holding the cardboard against the mouth of the glass, invert the glass.
  4. Release the hand slowly.

Explanation

Water can remain in an inverted glass with the piece of cardboard underneath because atmospheric pressure is acting upward on the cardboard, holding it up together with the water. There is little air pressure within the g;ass, so the downward force acting on the cardboard is mainly the weight of the water, which is to the order of several newtons whereas atmospheric pressure exert an upward force of several thousand newtons.

Modification:

  1. Drill a small hole in a plastic cup, near the base.
  2. Seal the hole with your thumb and fill the cup with water.
  3. Place the cardboard over the mouth of the cup.
  4. Invert the cup together with the cardboard, while keeping your thumb over the hole.
  5. Using a magic word as the cue, shift your thumb slightly to allow a little air into the cup. This will cause the cardboard and water to fall. As the air pressure within the cup is equal to that of the atmosphere.

Crushing Can

We are usually unaware of the immense strength of the pressure due to the atmosphere around us, having taken it for granted. This demonstration will utilize atmospheric pressure to crush an aluminum can while introducing concepts such as the relationship between pressure and the amount of gas in a fixed volume.

Materials

  1. Empty aluminum drink can
  2. Pair of tongs
  3. Stove or bunsen burner
  4. Tank of water

Procedure

Heating the Can over a Flame
  1. Put about a teaspoon of water into the drink can and heat it upright over the stove or Bunsen burner.
  2. Prepare a tank of water and place it nearby.
  3. When steam is seen to escape from the drink can, use the pair of tongs to grab the drink can, inverting it and placing it just slightly submerged into the tank so that the mouth of the can is sealed by the water.
  4. You should observe the can being crushed instantaneously.
Crushing the Can

Physics Principles Explained

Two physics principles work in tandem to crush the can. The cooling of the air within the can will reduce the internal pressure of the can as the movement of the air particles will slow down with reduced temperature.

At the same time, the sudden cooling will cause the water vapour in the can that exists at just slightly above 100°C to revert to its liquid state, greatly reducing the amount of gases inside the can.

Water Vapour Condenses Rapidly

As air pressure depends on both the kinetic energies and amount of particles within the system, it is significantly reduced. Atmospheric pressure, being stronger than the internal pressure, will cause the can to implode.

Measuring Speed of Sound

Measuring the speed of sound can be done using several methods. The following makes use of the understanding of stationary waves in pipes with one closed end. Such a pipe will have a fundamental mode that looks like this:

Hanging Forks

This simple demonstration can be done anywhere at home using the following items:

  1. an empty glass
  2. a toothpick
  3. two forks
The video below demonstrates how to do it. When the forks are balanced on the mouth of the glass with the toothpick, the centre of gravity of the forks-and-toothpick system will adjust itself so that it lies vertically below the pivoting point. This is possible because the forks form a V-shape within which the centre of gravity can exist.