Psyche Probe on Its Way to Asteroid Belt

Image credit: NASA/JPL-Caltech/ASU/Peter Rubin

Powered by a Hall thruster producing "250 millinewtons of force — about the amount of force that you would feel from the weight of holding one AA battery." 

Newton's first law of motion states that an object continues in its state of rest or uniform motion in a straight line, unless acted on by an external force. So once you give something a push in space, it keeps going. That doesn't happen on Earth because the external force in this case is drag, due to friction from the air. That slows an object down. Newton's second law of motion basically says that acceleration is proportional to force, so while the quarter-newton propulsion force is small and provides little acceleration, velocity increases over time. So unlike conventional rocket propulsion which generates high acceleration for a short period of time, Hall thrusters gently accelerate spacecraft for periods of months or years, to slowly build up velocity.

You can read more about the Psyche mission in this article on the NASA website. 

Beam Steering in the LHC: New Magnets Reach Full Power

View of the LHC tunnel sector 3-4
Maximilien Brice (CERN), CERN Document Server, Attribution-Share Alike 3.0 Unported

Within the 8.5 km-diameter Large Hadron Collider (LHC), sub-atomic particles are accelerated to close to the speed of light by electric fields in radiofrequency (RF) cavities.

Teeth Are Harder Than Steel

Hardness of various materials
Infographic created by Grok

Did you know that on a modified Mohs hardness scale that runs from 1 to 10, tooth enamel would rank at 5? That's harder than mild steel at 4.0 to 4.5 and softer than glass at 5.5.

What Are Clicks?

Image made by Grok.

What's the difference between a click or thump sound (e.g. when you hit something with a stick or hammer a nail) compared to striking a bell or a string in a musical instrument? It's mainly due to the amount of damping involved.

How To View What's Behind Your Washer Drum

© Eugene Brennan

You can check what's between the inner and outer drums of a washing machine, or check for limescale build-up on the heating element, by spinning the drum and illuminating it with a bright torch.

Three Reasons the Summer is Warmer Than the Winter

Created with ChatGPT.

A common misconception is that the Earth is closer to the Sun in summer, but it's actually further away. Diagrams would be better for explaining this. I'll get around to it, but I'll try to do it with words for now. 

Immersion Heaters and Potential Fire Risks

Immersion heater terminal box. (AI enhanced as the original photo was blurry)
© Eugene Brennan

So I was doing some gardening for the sister today and she mentioned a smell that was coming from her immersion. This immediately rang alarm bells in my engineering head, knowing what was likely to have happened—So I investigated.

How Can Insects Survive Falling From a Height?

Forces on a falling insect. © Eugene Brennan

One of the reasons insects don't hurt themselves when they fall is because they have a low terminal velocity and are travelling relatively slowly when they reach the ground.

Why Is Most of an Iceberg Under Water? And How Much?

Original uncaptioned image Lurens, public domain image via Pixabay.com

Ninety Percent of an Iceberg Is Below the Waterline

Icebergs can be massive, but did you know that you're only seeing literally the tip of them above the water? Yes, up to 90% of an iceberg's volume can be under water. But why does that amount sink and not just float above sea level like the rest of it? In this article we explore why.

The Andromeda Galaxy: "It's Big, And Also Faaarrr Away"

The apparent size of the Andromeda Galaxy, compared to that of the Moon. AI image created by Grok.

At a distance of 2.5 million light-years, or 24 million trillion km, the Andromeda Galaxy is the most distant object visible to the naked eye. We can see it because space is mostly empty, and light from the stellar object reaches us relatively unchanged, unlike what happens when we view distant objects on the horizon on Earth.

A Child Can Push Harder Than a Lawn Mower Blade

AI image generated by Google Gemini.

Did you know that a child can probably produce more torque using their arm, than a lawn mower engine can generate to turn the blade? Surprisingly, the figure for the torque of a 5 hp engine used on a mower is 7 to 10 foot-pounds (ft·lbf) in the imperial system or 11.5 to 13.6 newton-meters (Nm). Applied torque is simply force multiplied by distance, so 1 pound-force applied over a distance of 1 foot from a pivot is 1 foot-pound. In the metric system, the unit of torque is the newton-metre (Nm). A torque of 1 Nm is equivalent to one newton—the SI unit of force—applied over a distance of one metre. The speed of a lawn mower blade is more important than torque, and blades are driven directly by the crankshaft without reduction or overdrive gearing. Blades typically spin at the engine speed of around 3000 RPM, giving a blade tip speed of around 200 mph, or 90 metres per second.

As we saw in the article Interesting Facts - What is Torque?

power = torque x angular rotation speed

So while a child may be able to exert more torque with their arm than a mower engine can exert on a blade, they wouldn't be able to match its power. Another piece of the jigsaw is that the quoted figure of 11 to 13 Nm is for the drive torque from the engine. Since a blade is spinning at around 3000 RPM, it has a lot of inertia. The technical term for this when a rotating body such as a flywheel or blade is involved is moment of inertia. When a blade slows down as it impacts grass, the change in angular momentum creates a force, just like the way a car or any linearly-moving object creates a force as it slows down due to friction, or when it hits something (think of the huge force produced by a hammer, typically many tonnes, when it hits a nail). So the force produced by a blade as it impacts and shears grass is much greater than the force that the engine itself could have generated.

Note: You may be wondering why "newton" in "newton-metres" above isn't capitalised.  The unit is named after the English scientist Isaac Newton. It's not a typo. In the International System of Units (SI), or Système international d'unités, units named after a person are not capitalised. However, the symbol is, N in this case, Units are normally lower case, as are prefixes. However, prefixes over one million are capitalised—so kilometres is km, but gigahertz is GHz.

Driving Slower to Reduce Fuel Consumption

Created by ChatGPT

In theory, according to Newton's first law, a body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force. So if you kicked a ball in space and there were no planets or stars to influence the ball, it would go on forever. That's how deep-space probes work: during launch, engines fire to create thrust and increase velocity typically up to 10 km/s or more. When the engine cuts out, a probe will coast indefinitely, following a curved path due to the gravitational pull of planets and the Sun. Without gravity, the trajectory would be a straight line.

How to Use a Multimeter to Measure Voltage, Current, and Resistance

© Eugene Brennan

What Is a Multimeter?

Multimeters are measurement instruments widely used by professionals in several fields including industrial maintenance and testing, research, appliance repair, and electrical installation. However, a digital multimeter (or DMM) is also an invaluable test instrument for home and DIY use.

What Are the Applications of Multimeters?

The instrument can be used for measuring voltage, current, and resistance and can check the following:

• Battery voltages in equipment
• Current through cables or components
• Vehicle electrics and electronics
• Continuity of cables and power cords
• Home appliances and electronic devices
• Fuses

Conversations With ChatGPT: Air Drag and Surface Topology

Created by Grok.

Eugene: Is it possible to make a material that has a huge amount of drag that could allow a human to float? And what topology of surface has the most drag, a plane? I know that drag is proportional to cross-sectional area and also that there is a coefficient that depends on the surface shape of an object.

ChatGPT: Oh, yes, you can make a material or object with enormous air drag, but it’s a combination of material, surface topology, and shape, not just the “material” itself. Let’s break it down carefully.

Special Relativity and Angle Grinder Disks

© Eugene Brennan

The theory of special relativity was postulated by Einstein in his 1905 paper, "On the Electrodynamics of Moving Bodies". While things behave seemingly "normal" at speeds we experience in our daily lives, bizarre things happen at near-light speeds. One of these is time dilation. So for an object that's moving at super-high velocity, time slows down. You may have heard of the thought experiment in which there are two twins and one of them goes off on an interstellar space journey while the other twin remains on Earth. When the first twin returns home years later, he finds that his brother has aged much more than him. The theory was proven by placing an extremely accurate atomic clock on an aircraft while keeping a similar clock stationary on the ground (though it was slightly more complicated, with two aircraft, one travelling east and the other travelling west). Before the experiment started, both clocks were synchronised. On checking the clocks after the flight ended, it was discovered that the clock on the aircraft had run slower than the clock on the ground by a tiny fractions of a second. For a 4 1/2" angle grinder disc, it works out that if a disk were running constantly for 10 years, the perimeter of the disk would age slower than the centre by 7 microseconds. This may seem minor, but relativistic effects must be accounted for when doing GPS calculations to ensure accuracy, due to the satellites' velocity.

Where Does Water Come From in an Air Compressor Tank?

Graph of temperature versus max water storage capacity of air.

Anyone who owns an air compressor knows that one of the regular maintenance chores is to drain the tank to release water. This is essential to prevent eventual corrosion of the tank.

Water accumulates naturally as air is compressed. Air can only hold a certain amount of water at a given temperature before it starts to condense out. Relative humidity (RH) is defined as the amount of water vapour in air as a percentage of the maximum amount of water that air can hold at a specific temperature. So 100% RH means air is saturated and 0% RH means it is totally dry. As temperature increases, air can hold more water per unit volume and vice versa. When air is compressed, it takes up less space, and because there is a limit to the amount of water a certain volume can hold, it will eventually condense out if volume is reduced sufficiently. Water vapour density in the metric system is usually specified in g/m³.

Question:
2 cubic metres of air at 20°C is at a water vapour density of 7 g/m³ (50% RH at this temperature). The air is compressed by a factor of 10 and allowed to cool back to 20°C. How much water condenses out?

Answer:
Initial water content = 2 m³ × 7 g/m³ = 14 g

Compressed volume = 2 / 10 = 0.2 m³

Maximum water content at 20°C = 15 g/m³
So 0.2 m³ can hold = 0.2 × 15 = 3 g

Water that condenses = 14 − 3 = 11 g

Summary of Ideal Gas Laws

Thanks to ChatGPT for creating the table to my design. There's a long discussion with ChatGPT about the gas law equations here, where I revise my limited knowledge from school. (which was basically just understanding Boyle's Law and Charles's Law)

Law / Equation	Form / Equation	Derived From	Notes / Conditions
Boyle’s Law	P V = constant	Ideal Gas Law P V = n R T, with T = constant	Isothermal: pressure inversely proportional to volume
Charles’s Law	V / T = constant or V ∝ T	Ideal Gas Law P V = n R T, with P = constant	Isobaric: volume directly proportional to temperature
Gay-Lussac’s Law	P / T = constant or P ∝ T	Ideal Gas Law P V = n R T, with V = constant	Isochoric: pressure directly proportional to temperature
Ideal Gas Law	P V = n R T	Fundamental definition of ideal gases	Connects pressure, volume, temperature, and moles
Combined Gas Law	P V / T = constant P1 V1 / T1 = P2 V2 / T2	Ideal Gas Law, general form combining Boyle, Charles, Gay-Lussac	Relates pressure, volume, and temperature for a fixed amount of gas
Adiabatic PV Relation	P Vγ = constant	First Law dU = -P dV + Ideal Gas Law, γ = Cp/Cv	No heat transfer; pressure rises faster than 1/V
Adiabatic T–V Relation	T Vγ-1 = constant	PV adiabatic relation + Ideal Gas Law	Temperature rises when volume decreases (or vice versa)
Adiabatic T–P Relation	T = constant × P(γ-1)/γ	From PV and T–V adiabatic relations	Temperature as a function of pressure
Adiabatic PV Relation (states)	P1 V1γ = P2 V2γ	PV adiabatic relation applied to two states	Useful for calculating compression/expansion between two points
Adiabatic T–V Relation (states)	T1 V1γ-1 = T2 V2γ-1	T–V adiabatic relation applied to two states	Temperature change for volume change between two states
Adiabatic T–P Relation (states)	T2 = T1 (P2/P1)(γ-1)/γ	T–P adiabatic relation applied to two states	Temperature change for pressure change between two states

What Would Happen if You Fell Down a Hole That Went Through the Centre of the Earth?

Created by Grok

Well you'd be incinerated as you pass through the hot and molten core! But imagine if the core wasn't there or you had a special suit that protected you from the heat—what would happen then? Would you suddenly stop when you got to Oz?

The scenario is an example of a simple harmonic oscillator—other examples being a swinging pendulum and a weight bobbing up down, suspended from a spring. Both of the latter rely on interchange of energy and its change in form, from kinetic energy due to motion of an object, to stored potential energy. In the example of a weight suspended from a spring, the potential energy is manifested as tension in the spring. Energy in physics is defined as "the ability to do work". "Work" in physics also has a specific meaning: work is done when a force moves a body through a distance. The stored potential energy in a spring can do work, which is how a clock spring can move the hands of the clock.

Simple harmonic oscillators as the name suggests oscillate or move backwards and forwards indefinitely. For an ideal spring-mass system in a vacuum, with a perfect spring and no friction,  the mass will bounce up and down forever, with energy being interchanged as described above. Simple harmonic oscillators have a natural frequency that depends on the magnitude of the mass and the stiffness of the spring (how hard it is to stretch or compress it). In real life, systems are lossy and due to mechanical friction in a spring and drag from air, oscillations eventually die out. Technically this is known as damping. Dampers are actually used as components in your washing machine's drum suspension and also vehicle suspension systems to smooth out oscillations.

Back to the hole in the Earth that goes all the way to Australia—if you jumped in and there was no air in the hole, you would fall and accelerate, your velocity increasing as you drop downwards. In fact, you'd free fall under the influence of gravity, being continually accelerated. This differs from the situation of falling in air, because in that case, you eventually reach a constant velocity—known as terminal velocity—when the downward force of gravity is balanced by the upward drag, resulting in no net acceleration. As you continue to fall closer to the centre of the Earth, your velocity increases until you reach maximum velocity at the centre. Due to inertia however, you overshoot and pass through the centre. However, from now on, there's "less Earth" in front of you and more behind you. So now you're being decelerated and the gravitational force of the Earth is having a braking effect. Your velocity decreases after you pass through the centre, and it keeps decreasing until it falls to zero as you emerge from the hole on the other side, just like the way a ball kicked up into the air pauses momentarily when it reaches the apex of its trajectory. Once your velocity reaches zero, you start to fall back down the hole and the process is repeated as you fall back to where you started from. Without any losses due to friction, you would keep moving from one side of the planet to the other indefinitely, and it works out that the transit time would be 42 minutes. In reality, if such a hole was a civil engineering possibility, which is highly unlikely and it was filled with air, your oscillations back and forth would be damped and you'd eventually settle and float at the centre of the Earth, weightless. 

How Much Thrust?

SLS rocket. Image credit: NASA

8.8 million pounds, 4.0 million kilos or 17.3 million newtons (the SI unit of force). That's 15% more thrust than the Saturn V rocket, used for the Apollo missions to the Moon in the late '60s and early '70s.
The SLS or Space Launch System is the rocket that's being used for the Artemis missions that will once again carry astronauts to the Moon. (Artemis was Apollo's twin brother in Greek mythology).
Huge amounts of thrust are needed to accelerate spacecraft, so that they can escape Earth's gravity. The escape velocity of planet Earth is 11.2 km/s or 25,000 mph. We can't simply use rockets to travel point-to-point to the Moon as it would be inefficient and require continuous rocket firing and fuel use. By travelling fast enough initially, hence the massive engines and fuel tanks, we can "coast" there, like a car with one's foot on the clutch. The principle is based on Newton's first law of motion—so once an object starts moving, it keeps moving uniformly, unless another force acts on it, Earth's gravity in this case. (That's why the Voyager spacecraft are still moving out beyond the Solar System). Technically, a spacecraft is falling back to Earth under the influence of the latter's gravity, but in the case of lunar missions, the Moon and its gravity "take over" when the craft is close enough, allowing it to be injected into lunar orbit. 

Earth Speeding Through the Universe and How is Speed Measured in Spacecraft

AI image generated by ChatGPT

Did you know that we're travelling at 600,000 km/hr on planet Earth as our home galaxy, the Milky Way, orbits the Local Group, a group of neighbouring galaxies? That's somewhat faster than the mere 1000 km/hr velocity of a point on the island of Ireland, due to the Earth turning on its axis. We don't experience the effects of constant velocity on our bodies, only acceleration and deceleration. So we can't tell whether we're stationary or moving.