God's Laws in the Universe
Be amazed by the fact that the Universe actually makes sense.
38 verses
theHARO
April 1, 2021
English
0
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Examples of longitudinal waves
A Bright Idea: AS Level Physics: Waves
Sound waves.
Primary seismic waves (P-waves). -
Excess pressure over atmospheric pressure
AS Level Physics
Difference between pressure at surface of liquid and pressure at a certain depth h in a fluid, that has a density, that exists within a certain g
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Hooke’s law: NIV
AS Level Physics
<p class="MsoNormal" style="font-size: 18.72px; margin-left: 72pt; text-indent: -72pt;"><span lang="EN-US">The extension of a body (e) is proportional to the applied load (F) provided the proportionality limit is not exceeded<o:p></o:p></span></p><p class="MsoNormal" style="font-size: 18.72px; margin-left: 72pt; text-indent: -72pt;"><span lang="EN-US"> F IS DIRECTLY PROPORTIONAL TO e<o:p></o:p></span></p><p class="MsoNormal" style="font-size: 18.72px; margin-left: 72pt;"><span lang="EN-US">F EQUALS K e </span></p>
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Hooke’s law (the name of the law is Hooke’s law, not spring constant or Young modulus)NIV
AS Level Physics
The extension of a body (e) is proportional to the applied load (F) provided the proportionality limit is not exceeded. F IS DIRECTLY PROPORTIONAL TO e.
F EQUALS K e.
Spring constant = gradient of force-extension graph.
</span></p> -
How to answer the following question: Excess pressure something over something else
A Bright Idea: AS Level Physics: Motion
The difference between the two quantities.
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How to change from one range to another in a lever balance with a circular scale
AS Level Physics
Rotate the hinged arm
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How to derive the equation for work:NIV
AS Level Physics
<h2>
</h2>
<p class="MsoNormal"><span lang="EN-US">Combine the
following equations:<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo1"><!--if !supportLists--><span lang="EN-US" style="font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
Symbol;mso-ansi-language:EN-US">·<span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 7pt; line-height: normal; font-family: "Times New Roman";">
</span></span><!--endif--><span lang="EN-US">Work
(W) EQUALS Average force (1/2F) X Extension (e)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">(The force
that is required to extend the object increases in a linear way from zero to
the maximum force, THEREFORE Average force EQUALS 1/2F)<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo1"><!--if !supportLists--><span lang="EN-US" style="font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
Symbol;mso-ansi-language:EN-US">·<span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-stretch: normal; font-size: 7pt; line-height: normal; font-family: "Times New Roman";">
</span></span><!--endif--><span lang="EN-US">F=ke<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:180.0pt;text-indent:-180.0pt"><span lang="EN-US">Strain energy Work EQUALS 1/2ke^2 THEREFORE Is represented as the area under
the line of the graph of load (y axis) against extension (x axis) <o:p></o:p></span></p> -
How to derive the equation for work:
AS Level Physics
Combine the
following equations:
Work
(W) EQUALS Average force (1/2F) X Extension (e)
The force that is required to extend the object increases in a linear way from zero to
the maximum force, THEREFORE Average force EQUALS 1/2F
Strain energy
Work EQUALS 1/2ke^2 THEREFORE Is represented as the area under
the line of the graph of load (y axis) against extension (x axis) -
How to find the total v and total s for a projectile of a mass in a uniform gravitational field or a charge in a uniform electric fieldNIV
AS Level Physics
Total v = y component of v + x component of v
Total s = y component of s + x component of s
Remember: v and s are vector quantities, so use Pythagoras to add them together. -
How to obtain the average force from a problem involving impulse of force
AS Level Physics
Calculate change in momentum (impulse of force) logically. F=F(delta)t/(delta)t
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How to solve problems involving kinematicsNIV
A Bright Idea: AS Level Physics: Motion
1) Understand the situation
2) Note the quantities you need to find
3) Note the quantities you already have
4) Substitute the above into the equation that is composed of the relevant quantities.
Same goes if you need to draw a free-body diagram. -
k vs. ENIV
AS Level Physics
Spring Constant (k)
The proportion of force needed to achieve a given extension for a material. A material with a larger spring constant requires a larger force to achieve a given extension, and the inverse is also true.
The constant Force per extension for a particular material, that would enable us to find the extension if we know the load and the dimensions of the object. Different specimens of the same object with different shapes will have a different spring constant
Measured in Newton-metres
calculated by Force divided by extension
calculated by the gradient of a force/extension graph
Young Modulus (E)
The proportion of force needed to achieve a given extension for a material. . A material with a larger Young Modulus requires a larger force to achieve a given extension, and the inverse is also true.
The constant stress per strain, for a particular material, that would enable us to find the extension if we know the load and the dimensions of the object, regardless of its shape
Measured in Newton-meters squared OR Pascals
Calculated by:
Stress/Strain
=(Force/Area) TIMES (original Length/extension)
=(Force/extension) TIMES (original Length/Area)
=spring constant TIMES (original Length/Area)
=gradient of Force-extension graph X the other two quantities that affect the Young modulus
=(Young modulus TIMES Area/ original Length) X (original Length/Area)
=(Force TIMES original length)/(Area TIMES extension) -
k. vs. E.
AS Level Physics (Z notes)
Spring Constant (k)
The proportion of force needed to achieve a given extension for a material. A material with a larger spring constant requires a larger force to achieve a given extension, and the inverse is also true.
The constant Force per extension for a particular material, that would enable us to find the extension if we know the load and the dimensions of the object. Different specimens of the same object with different shapes will have a different spring constant
Measured in Newton-metres
calculated by Force divided by extension
calculated by the gradient of a force/extension graph
Young Modulus (E)
The proportion of force needed to achieve a given extension for a material. . A material with a larger Young Modulus requires a larger force to achieve a given extension, and the inverse is also true.
The constant stress per strain, for a particular material, that would enable us to find the extension if we know the load and the dimensions of the object, regardless of its shape
Measured in Newton-meters squared OR Pascals
Calculated by:
Stress/Strain
=(Force/Area) TIMES (original Length/extension)
=(Force TIMES Original length) DIVIDED BY (Area X Extension)
=(Force/extension) TIMES (original Length/Area)
=spring constant TIMES (original Length/Area)
=gradient of Force-extension graph X original length DIVIDED BY AREA (the other two quantities that affect the Young modulus)
=(Young modulus TIMES Area/ original Length) X (original Length/Area)
=(Force TIMES original length)/(Area TIMES extension) -
Pressure
A Bright Idea: AS Level Physics: Motion
Force per unit cross-sectional area where force acts perpendicularly to area
Symbol: p
Measured in Newtons per square metre
Pressure at a specified depth in a fluid (liquid or gas):
Pressure = Depth X Density X Gravitational field strength.
Pressure increases with the depth below the surface of the fluid (the easiest quantity to vary between depth of fluid, density of fluid and g)
Derivation:
Volume of fluid = Cross-sectional area X Height
Mass of fluid = Density X Volume
= Density X Area X Height
Weight of fluid (force exerted on fluid) = Mass X Gravitational field strength
= Density X Area X Height X Gravitational field strength
Pressure on fluid = Force DIVIDED BY Area
= Density X Area X Height X Gravitational field strength DIVIDED BY Area
= Density X Height X Gravitational field strength.
Difference in pressure between two gases using a manometer:
Difference in height between the water in the two tubes TIMES Density of liquid TIMES g.
The side of the manometer with the lower level of liquid is connected to the gas of a higher pressure. -
Pressure of a substanceNIV
AS Level Physics
Force per unit area where force acts perpendicularly to area
Symbol: p
Measured in Newtons per square metre
Proportional to the depth below the surface of the liquid (the easiest quantity to vary between depth of liquid, density of liquid and g) -
Principle of moments
AS Level Physics
For a body to be in rotational equilibrium, the sum of the clockwise moments about any point must equal the sum of the anticlockwise moments about the same point. How to find the sum of the moments in a particular direction: Calculate each moment separately, then add the moments together.
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Progressive waves
AS Level Physics
Properties:
Transfer energy along the direction of wave propagation without the movement of matter.
Amplitude along the wave can be constant, or it can be changed, but there is naturally no changing pattern of amplitudes.
No phase change occurs. -
Projectile motion and air resistance
AS Level Physics (Z notes)
A) In the absence of air resistance:
1) Horizontal component moves with a constant velocity
THEREFORE
final velocity = initial velocity in the kinematic equations
acceleration = 0
2) Vertical component moves with a constant acceleration
THEREFORE
initial velocity = 0 in the kinematic equations
3) Use Pythagoras’ theorem to combine the two components to calculate the required quantity
B) In the presence of air resistance:
1) Horizontal motion: Velocity decreases to 0
2) Vertical motion: Acceleration decreases to 0 -
Properties of all waves
AS Level Physics
Can be:
Reflected
Refracted
Diffracted
Can:
Produce interference patterns
How these properties can be demonstrated:
Using a ripple tank, as the motor turns, the wooden bar or small dipper vibrates, creating ripples on the surface of the water that are lit by a light FROM ABOVE. The waves cast shadows on a viewing screen LYING UNDERNEATH THE WAVES. The shadows correspond to a particular point on the wave, and are called wavefronts -
Quadratic equations: Solving other equations in quadratic form
AS Level Physics (Z notes)
Substitute for another variable (come on!)
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Reflection
AS Level Physics
When waves hit a plane surface and change direction
Example: When straight waves hit a curved barrier, they could be made to converge, and then diverge again. -
Refraction
AS Level Physics
When the depth of the medium changes. If the depth of the medium decreases, the waves will slow down by: Wavelength decreases, but frequency (number of waves passing a point per second remains the same).
Why this makes sense:
Mathematically: Speed EQUALS Wavelength TIMES Frequency
THEREFORE, if wavelength decreases, but frequency remains the same, speed will decrease.
Logically: If the waves are travelling slower, but the same number of waves need to pass a point per second, the waves need to be shorter, hence the shorter wavelength to maintain the same frequency -
Rotational equilibrium
AS Level Physics
When a body has no tendency to change its speed of motion
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Significant figures (how to handle)
AS Level Physics (Z notes)
Note: Uncertainty is recorded to only 1 significant figure.
Calculated answer from measured quantities:
Number of decimal places in uncertainty = Number of decimal places in answer.
Number of significant figures in measured quantities = (OR 1 more of, but never less of) Number of significant figures answer. -
SI units: Why certain calculations may not work
AS Level Physics (Z notes)
They may not take pure numbers into consideration.
Pure numbers: Infinitely accurate numbers that have no unit -
Speed vs. Velocity
AS Level Physics (Z notes)
Textbook definitions:
Average speed:
Distance moved by a particle divided by total time taken.
Average velocity:
Change in displacement of a particle divided by total time taken. Not displacement of a particle in unit time.
Derivation:
We measure the displacement of a particle from the position it was at when we first started counting.
Philosophical note:
The earlier you check, the greater the change that you will see. So don’t just come and judge when you have no idea how far we have come. -
Strain energy
AS Level Physics (Z notes)
The potential energy stored in or the work done by an object when it is elastically deformed
Measured in joules
Calculated by:
Work = 1/2 X spring constant X extension squared
Derivation:
Original equation:
Work = Force X extension
Think logically about force:
Force increases from 0 to maximum value THEREFORE Average force = 1/2 maximum force
Substitute into original equation:
Work = 1/2 maximum force X extension
Use force:
Force = spring constant X extension
Substitute into equation:
Work = 1/2 X spring constant X extension squared -
Strain (the result of stress)
AS Level Physics (Z notes)
Fractional increase in the original length of a material
Measured in no units (units of length cancel each other out)
Calculated by
Extension DIVIDED BY Original length -
Stress (the cause of strain)
AS Level Physics (Z notes)
Force applied per cross-sectional area of material
Measured in newtons per square metre OR pascals
Calculated by: Force DIVIDED BY Cross-sectional area
NB! When calculating strain from a graph of force to extension at a given extension, use the exact force at the exact extension (strain = force DIVIDED BY cross-sectional area), not average force (strain = half force DIVIDED BY cross-sectional area). -
Uncertainties for measuring instruments
AS Level Physics (Z notes)
Pipette/ burette: 0.05 squared centimetres
Mercury-in-glass thermometer: 1 degree Celsius
Thermocouple: 0.5 degrees Celsius
Voltmeter: 0.01 volts
Ammeter: 0.01 amps -
Wavelength ranges (approximate) for the electromagnetic spectrum
AS Level Physics (Z notes)
In ascending order of wavelengths:
Gamma rays: 10 TO THE POWER OF -16 metres TO 10 TO THE POWER OF -10 and shorter
X rays (overlap): 10 TO THE POWER OF -12 to 10 TO THE POWER OF -9 metres and shorter
UV rays: 10 TO THE POWER OF -9 to 10 TO THE POWER OF -7 metres only
Visible light: 10 TO THE POWER OF -7 to 10 TO THE POWER OF -6 metres only
Philosophical note:
Ultraviolet light:
“It is the visual capacity of their human eyes that decide where I end and you begin. They can’t see me, yet they blame me for causing their death. So therefore they call me invisible.”
#ultraphobia
Infrared light: 10 TO THE POWER OF -6 to 10 TO THE POWER OF -2 metres only
Microwaves (overlap): 10 TO THE POWER OF -3 to 10 TO THE POWER OF -1 metres only
Radio waves: 10 TO THE POWER OF -1 to 10 TO THE POWER OF 4 metres and longer -
Work
AS Level Physics (Z notes)
Change in energy, when a force moves a mass through a distance, measures in Joules and calculated by:
1) Work = Average force (1/2F) X Extension (e)
Derivation:
The force that is required to extend the object increases in a linear way from zero to
the maximum force, THEREFORE Average force EQUALS 1/2F
2) Strain energy:
Work = 1/2ke^2
THEREFORE
Is represented as the area under
the line of the graph of load (y axis) against extension (x axis)
To understand what you have just heard, research Young’s modulus of a material.
3) Work = Force X Change in volume of a gas, provided that temperature remains constant, and change in pressure (indicated by motion of piston in a syringe) is so small that it can be assumed to be constant.
4) Work = Voltage X Charge
Derivation:
Work = Force X Displacement in the direction of the force
Electric field strength = Force DIVIDED BY Charge
Force = Electric field strength X Charge
THEREFORE
Work = Electrical field strength X Charge X Displacement
Electrical field strength = Voltage DIVIDED BY Distance between two oppositely charged horizontal parallel plates
Voltage = Electrical field strength X Distance
THEREFORE
Work = Voltage X Charge -
Work (equations with explanations and derivations cont.)
AS Level Physics (Z notes)
1) Work in the direction of displacement when it is applied at an angle to the direction of displacement:
W=Fs(cos)theta BECAUSE Cos(theta)=adj/hyp. Do not use opp, not even while trying to calculate it's work, because it does no work whatsoever
2) Work done by a gas:
Work = Force X Change in volume, provided that temperature remains the same, and change in pressure (indicated by movement of piston) is so small that pressure is assumed to be constant (similar to rtp, but constant, not necessarily room)
3) Work done on a charged particle by an electric field between to oppositely charged parallel horizontal metal plates:
Work = Voltage X Charge
Derivation:
Original equation:
Work = Force X Displacement
Use electrical field strength:
Electrical field strength = Force DIVIDED BY Charge
THEREFORE
Force = Electrical field strength X Charge
Substitute into original equation:
Work = Electrical field strength X Charge X Displacement
Recognise:
Voltage = Electrical field strength X Displacement
BECAUSE Electrical field strength = Voltage DIVIDED BY Displacement
THEREFORE
Work = Voltage X Displacement -
Young modulus for aluminiumNIV
AS Level Physics
7 X 10 to the power of 10
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Young modulus for copperNIV
AS Level Physics
1.1 X 10 to the power of 11
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Young modulus of glassNIV
AS Level Physics
4.1 X (10 to the power of 10)
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Young modulus of rubberNIV
AS Level Physics
5 X (10 to the power of 8)
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Young modulus of steelNIV
AS Level Physics
2.1 X (10 to the power of 11) (almost double that of copper)