Aviation Mathematics and Physics
What is the cause for the change in seasons throughout the year?
Ans : The axis of rotation of the Earth is tilted.
Notes:
The seasons on Earth have nothing to do with the specific shape of Earth’s orbit around the Sun.
What causes day and night?
The Earth rotates around a line through the north and south poles once every 24 hours.
Only half of the globe is lit by the Sun at any given moment. On the half of Earth facing the Sun, it is day; on the other side, people experience night.
Suppose a planet with no atmosphere, how will temperature vary on its surface?
The hot/cold asymmetry between the lit side and the dark side is the defining thermodynamic feature of a planet.
Earth’s atmosphere is practically transparent to visible light radiation (high frequency) from the Sun, neither absorbing nor blocking much of its transmission to and from Earth.
By contrast, the atmosphere absorbs infrared radiation (low frequency) with near-perfect efficiency.
Earth’s surface absorbs light with good efficiency (~70%) though, the earth’s surface converts visible light to infrared radiation and it is re-radiated – this boosts the atmospheric absorption of incoming radiation.
High air pressure zones can result from the excess weight of high density pockets, but also from the downward movement of columns of air.
Likewise low pressure zones can develop due to local drops in the density of air or from the bulk movement of air out from a zone, leaving a vacuum of sorts in its wake.
heat capacity of a substance tells us how much heat energy it takes to increase the temperature of a substance.
Coriolis effect is significant when rotation is significant compared to the movement of an object. For this reason, humans don’t usually experience the Coriolis effect
What could be the cause of tides in the ocean?
Tides are the alternating rise and fall in sea level with respect to the land, produced by the gravitational attraction of the moon and the sun both.
Suppose that at a given time, some location on Earth is in high tide. What should it be on the opposing point on Earth? Must it also be in high tide?
High tide heppens at a given time at both side of the earth – way of thinking about this is that the gravitational force of the Moon causes the Earth to accelerate slightly towards the Moon, causing the water to be pulled towards the Moon faster than the solid rock on the side nearest the Moon. On the far side, the solid Earth ‘leaves behind’ some of the water, which is not as strongly accelerated towards the Moon as the Earth is. This produces the bulge on the ‘back side’ of the Earth.
What’s “spring tide” ?
Spring Tide, which has nothing to do with the season of spring – when the Sun, the Moon, and the Earth are colinear, the gravitational tidal pull from the Moon and the Sun act along the same direction and their effects add, enhancing the ocean bulge. Because the Sun and Moon have additive effect, high tides are at their highest and low tides are at their lowest.
Notes: Full or New Moon produce tidal bulges in same manner
What’s neap tide?
Neap tide occurs during the moon’s quarter phases – the Sun and Moon work at right angles, causing the bulges to cancel each other. The result is a smaller difference between high and low tides
To produce lift on the airplane, in which direction do the wings bend the incoming air?
Ans: By Newton’s third law, the air pushes the airplane in the upward direction, opposing the pull of gravity.
How does the lift dumper immediately reduce lift and prevent the plane from dangerous bounces during landing?
The lift dumper forces air upward immediately resulting in a downward force on the wing, “spoiling” the lift that previously held it aloft.
Lift dumpers also increase air drag on the plane, working in conjunction with the brakes to gradually slow the airplane. Turbulent vortices that form in the wake of the spoiler rapidly carry energy away from the plane.
What happens if the tires of landing gear did not make an adequate grip on the road?
The control and handling of the car depends on the force of friction between the surface and the tires.
Without grip, regardless of how fast the tires spin, the car will move in one direction. If you try to turn the steering wheel, it will not respond. Nowhere is this more clear than on a snowy, icy, or wet road. If the tires cannot get a grip, you are not able to control the vehicle.
how does a slightly dirty cup help water boil?
The presence of random particles in the water provide nucleation sites for bubbles to expand without having to spend as much energy – this is why adding sugar to or even just bumping superheated water can provide rapid vaporization of the liquid.
Why do beam bridges have limited spans between supports?
The torque produced by a force or load increases as the distance from the support increases.
Can we increase the span of a beam bridge by building stronger abutments (the supports on which the deck of the beam bridge is placed)?
we cannot increase the span of beam bridges by strengthening the abutment, again —the further apart we place the abutments, the greater the bending force on the deck.
In what ways the beam design could distribute the load of traffic and eliminate the long range torque?
Ans: truss design
What’s truss design? And benefit?
truss is a framework, typically consisting of rafters, posts, and struts, supporting a roof, a bridge, or another structure – in simple words: designs feature big triangular structures.
load is distributed into multiple beams of the truss, it is not concentrated at any given point. So, bridge is able to sustain heavier weight
Why would triangular shapes be preferred over other polygons on truss design?
The triangular structure can only be deformed if the screws are removed or broken. Thus, the geometry of a triangle is rigid.
What if structure of a square on truss design?
Square can easily bend about the connected bolts as shown and takes the shape of a rhombus.
Why are there so many vertical cables attached to the main cables of a suspension bridge?
vertical cables take the load of the bridge and pass it to the main cable which stretches, compressing the vertical abutments. As the number of vertical cables increases, the load on any one of them is reduced, as is the torque on the road.
Notes: The abutments support the vertical component of the load from the bridge.
How to prevent skyscrapers from toppling due to wind or earthquake?
Main support beams (a heavy slab) for the skyscraper are driven into a massive hole with dense concrete, so that the heavy slab counterweighs the above-ground portions of the skyscraper. In fact, the slabs are so heavy that in many skyscrapers the center of mass is below the surface.
What’s torque?
Torque is a measure of the twisting force on an object about a pivot point.
The quantitative measure of torque is given by:
T = FR
where F is the strength of the twisting force, and R is the distance from the point at which the force is applied to the pivot point.
What’s angular velocity(w) ?
Angular velocity (w) is an object’s speed and its rate of spin. To show in formula, angular velocity is simply w = travel distance / time
Unlike the linear velocity of a given point on the axe, the angular velocity is an intrinsic property.
If the tangential velocity of an object’s center of mass is Vtan.
Once around the circle, an object travels a distance 2 pi r
Distance/time = Speed;
So, T = 2 pi r / Vtan
In going around the circle the object moves through an angle of 360 degree = 2pi
Again, Distance/time = Speed;
So, w = 2pi / T
w = 2pi x (Vtan/2pi r)
w = Vtan/r
For an n-loop throw to work out, the distance it travels during n rotations must be equal to the distance to the target.
Distance/time = Speed;
So, Distance = speed x Time
D = Vtan x T
D = Vtan x (2 pi r/Vtan)
D = 2 pi r
D which is (somewhat amazingly) independent of the speed at which we throw an object, or the nature of its rotation. Instead, the distance for one loop is fundamental, and is imposed upon the object regardless of how we throw it.
No matter how hard or soft we throw the object, it will always require the same distance to go through one-loop and thus it is a quantity over which we have no control.
what’a temperature?
temperature is a measure of the motion of the microscopic particles that make up all matter – it describes average molecular kinetic energy.
formula for kinetic energy:
K. E = m(v^2)/2
temperature is a measure of molecular kinetic energy, and molecular kinetic energy is a function of molecular speed, temperature is dependent on the speed of molecular motion.
What’s heat?
Heat is the thermal energy that’s transferred between two systems at different temperatures. Unlike temperature, heat is not a physical quantity but rather a process quantity, meaning it is defined in the context of a process – Aheat is the thermal energy that’s transferred between two systems at different temperatures. Unlike temperature, heat is not a physical quantity but rather a process quantity, meaning it is defined in the context of a process. A cup of tea does not haveheat. Instead, we talk about the heat transferred from the cup to its surroundings.
What’s thermal equilibrium?
The point at which two systems at different temperatures have exchanged enough energy to reach the same temperature (AND same average K. E)
Prefixes usually apply to metric system units, which are also known as standard international (SI) units
Perimeter is a one dimensional, linear measurement. Therefore, it increases with the same scale factor as the dimensions – If each of the side lengths of a triangle triples, then the perimeter will triples
If both the length and width of a rectangle double, then the area will increase by a factor of 4.
Absolute change, the difference between measurements at two different times.
Relative change (or sometimes percent or fractional change) is the ratio of change in percentage of its initial or reference value.
Example : sth original value is 0.2 unit, if it is increased by 400%, then:
0.2 x 4 = 0.8
However, 0.8 is just the relative change and the absolute change should be rel change + ori = 0.8+0.2 =1
In other words, “increased by 400%” = x5 (5 times)
Another formulas appear:
(New – Old) /Old = Relative Change
temperature measures the average kinetic energy
K. E = (1/2)mv2
Data is typically divided into two categories:
- qualitative data and
- quantitative data
Qualitative data is used to describe qualities. Qualitative data is observed or sensory perception.
Quantitative data is used to measure the magnitude of quantities.
Instead of multiplying by 5, it might be easier to multiply by 10 – :
e.g 86 x 5 = 43 x 10
