Double Slit Ahead of Single Slit?

This is similar to my earlier query regarding the sequence of topics that are introduced. My earlier post was the order of introducing the concept of energy and the concept of momentum. In this post, it is the issue of the sequence of introducing the double slit interference ahead of the single-slit diffraction.

This sequence is done in Knight's text "Physics for Scientists and Engineers". I don't follow that sequence because I prefer to introduce the single-slit diffraction first, show the diffraction pattern, and then introduce the double slit. The fact that the double slit pattern has interference pattern inside a single-slit diffraction envelope is easier to explain after the students already know about the single-slit diffraction.

What do you think? How did you teach this topic, or how did you learn this topic?

Zz.

Livestream of Total Solar Eclipse 2024

The US National Science Foundation (NSF) will be livestreaming the total Solar Eclipse of 2024. Here is the blurb from them:

Don't just watch the eclipse — explore it. On April 8, the U.S. National Science Foundation and the NSF National Solar Observatory are hosting an educational livestream all about the science of the sun.  

The livestream is a free resource that educators can use in their classrooms to share the excitement of science.  

You'll hear from scientists about the unique experiments happening during the eclipse. As we count down to the moment of totality, you'll learn about:  

• The different layers of the sun, from the core to the corona. 
• The world's largest, most advanced solar telescope.  
• How massive solar eruptions generate space weather. 

It all happens on YouTube on April 8 starting around 11 a.m. PDT/noon MDT/1 p.m. CDT/2 p.m. EDT.

 https://www.youtube.com/live/qAZmtbTTQAE?si=AKttYJOJT32g-Q3O

 

Doppler Ultrasound Uses Confusing Color Scheme

In my algebra-based General Physics courses, I get many Biology/Pre-med/Life Science majors, so of course many of the examples that I choose tend to be related to those areas. When we cover traveling waves and Doppler effect, I dive into medical diagnostics to show a few of the applications of Doppler effect in that area.

Interestingly enough, in Doppler Ultrasound, the color scheme that they use tend to be a bit confusing with what we use in physics. In the Doppler effect, when the source of a wave, or the source that is reflecting the wave, is moving away from the observer, the wavelength will be longer than the original wave. We popularly say that the wave has been "redshifted". This is because in the visible spectrum, the longest wavelength is toward the red color.

Conversely, if the object is moving toward the observer, then the wavelength will be shortened, and thus, "blueshifted", since blue (or violet) is the shortest wavelength in the visible spectrum.

But this is not the color scheme adopted in the field of Doppler Ultrasound, as represented in this video:

It seems that if the flow is toward the transducer, it is given the red color while if the flow is going away from the transducer, it is given a blue color.

Obviously, this is not a source of confusion for people in that field since they don't normally encounter those color-shifted lexicon, but for students who are studying this topic for the very first time, this takes a bit of an effort to make sure they do not become confused with the contradicting color scheme. The first time I used the Doppler ultrasound example was, unfortunately, right after I discussed an example from astronomy where I indicated that most of the light from the galaxies are redshifted and thus, a strong evidence that the universe is expanding since those galaxies are moving away from us. You can imagine that the students who were paying attention got a bit confused because the blood flowing away from the transducer is now being labeled with blue color instead of red.

Does anyone know why this field adopts this color scheme? 

Zz.

AI Will Pick Nobel Prize Winners in Physics

Please read the article carefully before you freak out. Hint: look at the date.

Zz.

What's In A Physics Word?

This is a rather fun article in this week's Nature. It reveals some of the fascinating origin of words used in Physics and how they may not match the more common usage of the word.

All of us in physics (and in science) know of this, where we may use the same words that are used in everyday language, but they have very different meanings in physics. Unfortunately, for many people outside of physics, this can lead to a lot of confusion or misuse if they do not investigate or understand the meanings of those words as used in the context of physics. The word "spin" comes to mind when talking about the quantum spin of elementary particles.

Z.

My Favorite Web Application - Part 8

Previous posts:

My favorite web applications - Part 1

My favorite web applications - Part 2

My favorite web applications - Part 3

My favorite web applications - Part 4

My favorite web applications - Part 5

My favorite web application - Part 6

My favorite web application - Part 7

This is another one of my favorite web application because it has a ability to assign random values to various parameters in the problem.

This is a simulation of a motional emf in the form of a rail gun. It actually is a straight-forward application of magnetic force acting on a straight current. One may also solve this using Faraday's law, but it is not as straight-forward to solve because the magnetic flux (or rather, the area) does not change uniformly since the rod is accelerating.

What I also like about this simulation is that one can also tie in with what the students learned in Physics 1, i.e. they may verify their answer using kinematics, since we know the rod's mass, and it starts moving from rest. Knowing how far it travels and a good estimate of the time of travel gives us the value of the acceleration, and thus, the force acting on the rod. This should match with the magnetic force.

Zz.

I Baked Cookies For My Students

A while back, I wrote an article on how to impress upon the students of the need have units in most of the numbers that they write in physics. I gave them a recipe for a banana bread, but I left out all the units of measure. It was the students themselves who noticed what was wrong with the recipe, so in the process, I managed to convey to them that (i) without units, these numbers are meaningless and (ii) this is not just something in physics (or science) but rather something common that we encounter and take for granted.

Over the Summer, I did the same thing but I showed them a recipe for my often-requested Chewy Oatmeal Cranberry cookies. Same reaction. But the difference happened at the end of the arduous and intense 8-week summer session. On the 2nd to last day of the class (last day was the final exam), after we did our review, I showed them again the cookie recipe and asked them if they remembered why I was showing them the recipe. All of them did.

I then whipped out a container that had the very same cookies, from the recipe, that I had baked the day before. Oh yeah, they were pleasantly surprised! We basically came full circle, and had a lovely time the last 15 minutes of class time as we sat around chatting and munching on the cookies. Even the coffee machine was nearby and a few of us got some coffee to go along with the cookies.

It was a wonderful end to the class, in my opinion. I am considering this Fall semester if I want to do that again. I just might, if I can find the time.

Zz.

The Unseen Impact of Physics In Healthcare

This is a nice news article that provides a basic summary of the applications of physics in healthcare and medicine. It's another one of those where if someone thinks physics only deals with esoteric and useless ideas, show him/her this. I've mentioned many examples of similar medical/health/etc. applications and concepts that came directly from physics, such as this one.

As someone who often teaches general physics to life science/premed/bio/kinesiology major, this is definitely another useful evidence to get them to realize that the physics class they are taking has a direct relevance to their area of study.

Zz.

Since When Does A "Proposal" Become "Evidence"?

It's one of the reasons why I groan at popular media's reporting of science.

This article is reporting on a paper that proposes a possibility of finding evidence of large-scale symmetry breaking from the  data ".. in current and upcoming surveys such as those undertaken by Dark Energy Spectroscopic Instrument, the Euclid satellite, and the Vera C. Rubin Observatory.... ". Yet, the article is trumpeting the "Incredible new evidence...." as if it has been found. This is similar to accepting speculation as the truth.

Over-selling and over-hyping science does no one any good, other than making it a click-bait.

Z.

The First 12 Months of the James Webb Space Telescope

Many of us knew that it would be a significant instrument. We just didn't know that in its early days, it would make this many discoveries.

In case you were asleep for most of the past 12 months, here is an article that will highlight some of the groundbreaking discoveries made by the JWST. It will not be hard to guess that there will be more earth-shattering (universe-shattering?) discoveries to be made in the next 12 months.

Zz.

ChatGPT and Projectile Motion, Part 2

If you missed my previous physics questions to ChatGPT, check them out here and here. 

In this particular case, I asked ChatGPT a rather common question, and ended up having an argument with it. My questions are in red while ChatGPT's responses are in blue.

Three projectiles of the same mass are launched from the top of a cliff with the same initial speed. The first projectile is launched at an angle of 20 degrees above the horizontal. The second is launched horizontally. The third is launched at an angle 20 degrees below the horizontal. Which projectile hit the ground with the largest speed?

All three projectiles are launched with the same initial speed, which means they all have the same initial kinetic energy. The only difference is the angle at which they are launched.

The maximum range of a projectile launched at a given speed is achieved when it is launched at an angle of 45 degrees above the horizontal. This means that the first and third projectiles will have the same range, but the second projectile, launched horizontally, will have a shorter range.
However, the question asks which projectile hits the ground with the largest speed, not which has the greatest range. To answer this question, we need to consider the vertical component of each projectile's velocity at impact.

The first projectile is launched at an angle of 20 degrees above the horizontal, so it will have a significant vertical component of velocity at impact, causing it to hit the ground with a larger speed than the third projectile, which is launched at an angle of 20 degrees below the horizontal and will have a smaller vertical component of velocity at impact.

The second projectile, launched horizontally, will have no vertical component of velocity at impact, so it will hit the ground with the smallest speed of the three projectiles.

Therefore, the first projectile, launched at an angle of 20 degrees above the horizontal, will hit the ground with the largest speed.

It started off so well, realizing that all three have the same KE. But then, after it answered something that wasn't asked (the range), it went on to be obsessed with the vertical component of the velocity.

I decided to challenge its answer.

But they all have the same initial energy in the beginning. Shouldn't they have the same energy at the bottom when they hit the ground?

You're correct that all three projectiles have the same initial kinetic energy, and conservation of energy tells us that the total energy of the system must be conserved throughout the motion. Therefore, at the bottom of the cliff, all three projectiles will have the same total energy as they did at the top of the cliff.

However, the question specifically asks which projectile hits the ground with the largest speed, not which has the most kinetic energy. The speed of a projectile at any point during its motion depends not only on its kinetic energy but also on its direction and the effects of external forces such as gravity and air resistance.

In the case of these three projectiles, they all have different launch angles, which means they will follow different trajectories and experience different vertical and horizontal components of acceleration due to gravity. These differences will cause the projectiles to hit the ground with different speeds, even though they all have the same initial kinetic energy.

It's a bit puzzling what it is thinking at this point. If they have the same KE in the end, via conservation of energy, then should they also have the same speed?

But kinetic energy is 1/2*m*v^2. If they have the same kinetic energy, they should have the same speed.

Yes, you are correct that the kinetic energy of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. If three projectiles of the same mass are launched from the top of a cliff with the same initial speed, they will all have the same initial kinetic energy, and therefore the same total energy throughout their motion.
 

However, as the projectiles follow their different trajectories, they will experience different amounts of air resistance and vertical and horizontal components of acceleration due to gravity. These differences in the forces acting on the projectiles will affect their velocities as they reach the ground.
The projectile launched horizontally will experience no vertical acceleration due to gravity, so it will not gain any speed in the vertical direction as it falls, only in the horizontal direction. The first and third projectiles, on the other hand, will experience significant vertical accelerations due to gravity, which will affect their speeds at impact.
 

Therefore, even though all three projectiles have the same initial kinetic energy, the projectile launched at an angle of 20 degrees above the horizontal will hit the ground with the largest speed due to the combination of its initial horizontal velocity and the vertical velocity gained as it falls.

How can the projectile launched horizontally not experience vertically acceleration due to gravity? After all, it is falling to the ground!

You are correct that a projectile launched horizontally will experience vertical acceleration due to gravity, and it will also fall to the ground just like the other two projectiles.

What I meant to say is that the horizontal component of the velocity of the projectile launched horizontally will remain constant throughout its motion, since there are no external forces acting on it in the horizontal direction. This means that the horizontal velocity of the projectile will be the same at the top of the cliff and at the moment it hits the ground.

However, the vertical component of the velocity of the projectile launched horizontally will increase due to the acceleration of gravity. At the top of the cliff, the vertical component of the velocity is zero, but as the projectile falls, the vertical velocity will increase, and the projectile will hit the ground with a non-zero vertical speed.
 

Therefore, while the horizontal velocity of the horizontally launched projectile remains constant, the vertical component of its velocity will increase due to gravity, resulting in a non-zero speed at impact. However, since the horizontal velocity of the projectile remains constant, it will hit the ground with the smallest speed of the three projectiles.
 

The question asks about the speed, not the velocity. All three gain in speed as it falls to the ground. If their kinetic energy is the same, their speeds must be the same.

You are correct that the question asks about the speed of the projectiles, not the velocity. The speed of an object is the magnitude of its velocity, and it is calculated by taking the absolute value of its velocity vector.
 

If all three projectiles have the same initial kinetic energy, then they must have the same initial speed. As the projectiles fall, they will gain speed due to the force of gravity.
 

Therefore, at the moment of impact, all three projectiles will have the same kinetic energy, which means they will have the same speed. The angle at which the projectiles are launched and the resulting trajectories they follow may affect their final velocities, but their final speeds will be the same since they all have the same kinetic energy at impact.

So, to answer the original question, all three projectiles will hit the ground with the same speed, even though they were launched at different angles.

Phew!! That felt like pulling teeth!

It was as if it doesn't know the difference between speed and velocity, and I'm wondering if it was arguing with me about the vertical component of the velocity. It still makes no sense because clearly I explicitly mentioned "speed" at the very beginning.

Once again, if you don't know what you are looking for, there is no guarantee that you'll get the correct answer and consistent explanation.

Zz.

ChatGPT and Buoyant Force

I posted previously about ChatGPT's response to a projectile motion question. It got the answer correct, but with a wrong starting point, which made the whole response rather puzzling, inconsistent, and self-contradictory.

This time, I decided to ask a question that I had asked my students in a poll during a lesson on buoyancy and Archimedes principle.

A block of Styrofoam floats on water while a lead block of the same size block lies submerged in the water. Which one has the larger buoyant force?

The buoyant force on an object is equal to the weight of the fluid displaced by the object. The Styrofoam block is less dense than water and floats because it displaces an amount of water equal to its own weight, which is equal to the buoyant force acting on it. On the other hand, the lead block is more dense than water and sinks because it displaces an amount of water that is less than its own weight.

Therefore, the Styrofoam block has a larger buoyant force acting on it than the lead block of the same size because it displaces more water.

This time, ChatGPT got the answer wrong. Unlike the first time, it started out with the correct idea, which is that the buoyant force is equal to the weight of the displaced fluid.

However, in this case, the Styrofoam is displacing a very small amount of fluid because it is floating above the surface, while the lead block is completely submerged in the water, displacing its entire volume. This means that the lead block is displacing a larger volume of the fluid, and thus, having a larger buoyant force, despite it sinking in the water.

So in this case, ChatGPT once again exhibits its inconsistent and self-contradictory behavior.

I followed up trying to correct this error.

This is incorrect. The lead block displaces more water than the Styrofoam.

You are correct, I apologize for the mistake in my previous answer. The buoyant force acting on an object is equal to the weight of the fluid displaced by the object, and the amount of fluid displaced depends on the volume of the object. Since the lead block and the Styrofoam block have the same volume, the lead block will displace more water than the Styrofoam block because it is denser.

Therefore, the lead block has a larger buoyant force acting on it than the Styrofoam block of the same size, even though it is submerged in the water while the Styrofoam block floats on the surface.

It gets it now, but it is arguing that the lead block displaces more water than the Stryrofoam because it is "denser". While that is somewhat correct, it is not the reason why it displaces more water. It is because it is completely submerged in the water and displaces a volume of water equal to its volume.

If I reshape the same mass of lead into the shape of a bowl, the object itself will have the same "density", but this time, it can float on the water. It now displaces enough of the water such that the weight of the displaced water is equal to its weight, and thus, it will float. Granted that the whole "object" now includes the air that it encompasses so that its "total" density is less than the density of water, but the density of the lead itself hasn't changed. It is still denser than water but this time it floats!

Once again, if you don't know the material, it is hard to know whether you are being given not just the correct answer, but whether the whole response is consistent and not self-contradictory.

More to come.....

Zz.

ChatGPT and Projectile Motion

In my previous post, I mentioned an exercise that I often give to my General Physics students that are learning about projectile motion. Using a PhET application, they found out that two different scenarios produced a projectile motion that has the same maximum height and same time of flight. I asked the students to figure out why.

I decided to post the same question to ChatGPT. The result was a bit of an eye-opener. I will show my question (in red) and its response below:

Why does a projectile shot with initial velocity of 20 m/s and angle 30 degrees with respect to the horizontal reach the same height as the projectile shot with initial velocity of 10 m/s and angle 90 degrees?

The key to understanding this phenomenon is to recognize that the vertical motion of the projectile is independent of its horizontal motion.
For both projectiles, the initial vertical velocity is zero. The only force acting on the projectile in the vertical direction is gravity, which causes the projectile to accelerate downward at a rate of 9.8 m/s^2. The vertical displacement of the projectile can be determined using the formula:
Δy = v0y*t + (1/2)at^2
where Δy is the vertical displacement, v0y is the initial vertical velocity, a is the acceleration due to gravity, and t is the time elapsed.
Since the projectile that was shot with an initial velocity of 10 m/s at an angle of 90 degrees goes straight up, it reaches its maximum height when its vertical velocity becomes zero. At this point, the time elapsed is given by:
t = v0y/a
where v0y is the initial vertical velocity. Substituting in the values, we get:
t = (10 m/s) / (9.8 m/s^2) = 1.02 s
Using this value of t in the above formula, we get:
Δy = (0 m/s)(1.02 s) + (1/2)(9.8 m/s^2)*(1.02 s)^2 = 5.1 m
So, the projectile reaches a maximum height of 5.1 m before falling back down to the ground.
For the projectile that was shot with an initial velocity of 20 m/s at an angle of 30 degrees, we can break down its initial velocity into its horizontal and vertical components:
v0x = v0cos(30) = 17.3 m/s
v0y = v0sin(30) = 10 m/s
The horizontal motion of the projectile is uniform, meaning it moves with a constant velocity of 17.3 m/s. The time taken for the projectile to reach its maximum height is the same as the time taken for it to reach half the range of its motion (i.e., the distance it travels horizontally before hitting the ground). The formula for the time of flight is:
t = 2*v0y/a
Substituting in the values, we get:
t = (2*10 m/s) / (9.8 m/s^2) = 2.04 s
The horizontal distance traveled by the projectile can be calculated using the formula:
R = v0x*t
Substituting in the values, we get:
R = (17.3 m/s)*(2.04 s) = 35.3 m
The maximum height reached by the projectile can be determined using the formula for vertical displacement:
Δy = v0y*t + (1/2)at^2
Substituting in the values, we get:
Δy = (10 m/s)(2.04 s) + (1/2)(9.8 m/s^2)*(2.04 s)^2 = 5.1 m
So, the projectile that was shot with an initial velocity of 20 m/s at an angle of 30 degrees reaches the same maximum height of 5.1 m as the projectile that was shot with an initial velocity of 10 m/s at an angle of 90 degrees, despite traveling much farther horizontally before hitting the ground.

Now, the answer is correct. In fact, it gave me more than what I asked for, i.e. it included the actual calculation of even the range, which I did not ask for.

However, its starting point is incorrect, and in fact, it is self-contradictory. It starts of by saying that the initial vertical velocity for both projectile is ZERO. This is clearly wrong.

Yet, a few lines down, it then mentioned and even found the vertical component of the initial vertical velocity, all while it was oblivious to what it just said in the beginning. So while the answer in the end may be correct, the reasoning, if we were to go by what it said, is puzzling and inconsistent.

I decided to challenge it by pointing out its mistake:

You are mistaken about the initial vertical velocity being zero. For both projectiles, the initial vertical velocity is not zero.

You are correct, I apologize for the mistake. The initial vertical velocity for the projectile shot with an initial velocity of 20 m/s and angle 30 degrees with respect to the horizontal is:
$v_{0y} = v_0 \sin \theta = 20 \text{ m/s} \sin 30^\circ = 10 \text{ m/s}$
And the initial vertical velocity for the projectile shot with an initial velocity of 10 m/s and angle 90 degrees with respect to the horizontal is:
$v_{0y} = v_0 \sin \theta = 10 \text{ m/s} \sin 90^\circ = 10 \text{ m/s}$
So, both projectiles have an initial vertical velocity of 10 m/s. The rest of the explanation and calculations remain the same.

This is now correct. Unfortunately, it requires someone who actually understands projectile motion to spot this. A student learning about it may not notice the inconsistency of the reasoning.

This seems to be the most common issue that I've come across and read about as far as scientific questions being asked to ChatGPT. This was similarly observed in another post that I wrote about. ChatGPT response has correct parts, but there are also parts that are puzzling, contradictory, and often downright wrong, all within one response.

There's more. In my next blog on ChatGPT, I asked it about buoyant forces. You don't want to miss that!

Zz.