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
Click to view answer
Answer: D.
The triangle OPQ is equilateral, so the angle $\angle QOP$ = 60° or $\dfrac{2\pi}{6}=\dfrac{\pi}{3}$ rad.
As OQ is displaced clockwise from OP, angular displacement $\theta = 2\pi – \dfrac{\pi}{3} = \dfrac{5\pi}{3}$ rad.
A siphon operates through the combined effects of gravity and air pressure, which work together to move liquid from a higher elevation to a lower one. Gravity is the primary force driving the flow, as it pulls the liquid from the higher container down through the siphon tube to the lower container. The liquid’s potential energy, due to its elevated position, is converted into kinetic energy as it flows downward.
Air pressure plays a crucial supporting role by maintaining the continuous flow of liquid. Atmospheric pressure on the liquid’s surface in the higher container pushes the liquid into the siphon tube. This pressure counteracts gravity’s pull that might otherwise cause the liquid to fall back into the higher container. As the liquid moves downwards, it creates a partial vacuum in the upper part of the tube, allowing atmospheric pressure to push more liquid into the tube, sustaining the flow.
Thus, a siphon can continue to operate as long as the outlet is lower than the liquid surface in the source container, the tube remains filled with liquid, and atmospheric pressure supports the flow.
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.”
This demonstration can be modified for use as a magic trick.
Materials:
Glass of water
Piece of cardboard that is larger than the mouth of the glass.
Procedure:
Fill the glass up with water.
Place the piece of cardboard over the mouth of the glass.
Holding the cardboard against the mouth of the glass, invert the glass.
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:
Drill a small hole in a plastic cup, near the base.
Seal the hole with your thumb and fill the cup with water.
Place the cardboard over the mouth of the cup.
Invert the cup together with the cardboard, while keeping your thumb over the hole.
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.
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
Empty aluminum drink can
Pair of tongs
Stove or bunsen burner
Tank of water
Procedure
Heating the Can over a Flame
Put about a teaspoon of water into the drink can and heat it upright over the stove or Bunsen burner.
Prepare a tank of water and place it nearby.
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.
You should observe the can being crushed instantaneously.
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.
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.
Outline for Measuring the Speed of Sound Using a Tuning Fork and a Hollow Pipe Submerged in Water:
Equipment Setup:
Obtain a tuning fork of known frequency and a hollow pipe that can be partially submerged in a column of water.
The pipe should be open at the top and closed at the bottom by the water surface.
Strike the Tuning Fork:
Strike the tuning fork on a soft surface to make it vibrate. This produces a sound wave of a specific frequency, known as the fundamental frequency of the tuning fork.
Submerge the Hollow Pipe:
Submerge the hollow pipe vertically in a large container filled with water. The length of the air column inside the pipe can be adjusted by raising or lowering the pipe in the water.
Create Resonance:
Hold the vibrating tuning fork above the open end of the pipe. Slowly raise or lower the pipe in the water while listening for the loudest sound, which indicates resonance.
Resonance occurs when the length of the air column in the pipe is such that it forms a standing wave with the frequency of the tuning fork. This usually happens when the length of the air column is a quarter of the wavelength of the sound wave.
Measure the Air Column Length:
When resonance is achieved (indicated by a significant increase in sound amplitude), measure the length of the air column from the water surface to the top of the pipe. This length corresponds to one-quarter of the wavelength of the sound wave in air.
Calculate the Wavelength:
Multiply the measured length by 4 to determine the wavelength of the sound wave.
Determine the Speed of Sound:
Use the formula Speed of Sound = Frequency × Wavelength ($v = f\lambda$) to calculate the speed of sound in air. The frequency is given by the tuning fork, and the wavelength is obtained from the previous step.
Explanation:
The speed of sound in air can be measured using the relationship between the frequency of the sound wave and its wavelength, which are connected by the speed of sound. When the tuning fork vibrates, it creates sound waves that travel through the air. When these waves enter the hollow pipe, they reflect off the water surface, and at certain lengths, they create a resonance condition, amplifying the sound. The resonant length corresponds to one-quarter of the wavelength because the pipe is effectively closed at the bottom (by the water), forming a node at the water surface and an antinode at the open end. By measuring this length and knowing the frequency of the tuning fork, the speed of sound can be calculated.
