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(ρfluid)(Vsub)g
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Fbuoy=
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Voltage
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V=ΔΦ
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Micro?
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10^-6
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CAH quick
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A=H(cos8)
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Liquid Pressure
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p=hdg
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LeverarmXF so, LF
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Torque=
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I
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density*Q or density *Av
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formula for speed
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speed= distance/time
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Angular Speed
ω
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Velocity / Radius
v/r
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What is average acceleration?
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Picture.
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Vsub/V= ρobject/ρfluid
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Equilibrium on the surface=
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trig func
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SOH , CAH, TOA
Sine=opposite/hypotenuse, Cosine=Adjacent/Hypotenuse, Tangent= Opposite/Adjacent
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Stress
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Force/Area (tensile or compressive stress = F⊥/A ; shear stress = Fμ /A so [stress] =N/m²
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adiabatic
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Q = 0
ΔU = -W
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Weight
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- Gravitational force an object experiences when near a much larger body, i.e., the earth
W = mg
W = Fd
∴ mg = Fd
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Volume expansion (when fluids are heated, ΔV=)
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βVΔT
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________ gravity is the nominal acceleration due to gravity at the Earth's surface at sea level.
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Standard
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Work is zero
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Theta = 90 then
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power and focal point
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p = 1/f
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fusion
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combine smaller nuclei into larger nucleus
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longtitudinal wave
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wave that changes parallel to direction of displacement
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What do boiling points correspond to?
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Intermolecular forces
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Potential Difference
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Also called Voltage (ΔV). Difference in electric potential between two points in an electric field
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Snell's Law
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Equation describing the angle of refraction for a light ray passing from one medium to another, given by n₁sinθ₁ = n₂sinθ₂, where n is the index of refraction.
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________, jolt, surge or lurch, is defined as the rate of change of the acceleration.
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Jerk
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1) Transitional 2) Rotational
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2 types of equilibrum?
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harmonic frequency
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common frequency of traveling waves that will produce a standing wave
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electromotive force (emf)
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voltage difference across terminals when no current is flowing
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When do current carrying wires attract to each other in a magnetic field?
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weight − Fbouy
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Apparent weight of object in water?
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Straight-Wire Magnetic Field
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Magnetic field produced at a perpendicular distance r, from a straight current-carrying wire, calculated by: B = µ₀i/2∏r
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Temperature
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Measure of heat content that a body possesses, measured in Kelvin, Celsius or Fahrenheit.
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________ is defined as the rate of change of the position.
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Velocity
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Positive
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Always call toward the center in UCM positive or negative?
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Acceleration (a)
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rate of change of velocity = Δv/Δt
Units: m/s²
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(T/F) The total mechanical energy of a body is the sum of its kinetic and potential energies.
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True
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Pascal's principle
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change in pressure is transmitted to every portion of the fluid
F1d1 = F2d2
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What are Elastic collisions?
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◦Perfectly elastic collisions: conservation of both momentum and kinetic energy.
◦Conservation of kinetic energy: total kinetic energy before = total kinetic energy after.
◦Kinetic energy is scalar, so there are no positive / negative signs to worry about.
What is not true concerning elastic collisions is that the speed of all colliding objects do not always remain unchanged. Even though the kinetic energy is conserved, and KE = 1/2 mv^2, the speed can change before and after the objects collide. For example, when one pool ball elastically collides with a second at rest, the first stops while the second continues at the original velocity of the first. All that is conserved is KE - how the velocity plays out remains to be calculated. Only conservative forces are involved in elastic collisions. Since KE is conserved, then the KE could be converted back to PE, which could mean that if the object was dropped or thrown from a height, it could return back to the same height. When an object collides with another object, causing that object to move, then it does work on the object. So even with elastic collisions, and even though KE is conserved, as long as the objects are moving, work is being done on them. The objects that move individually have a change in KE, and that change in KE is the work done on each object, but the total KE of the system is the same before and after the collision (it's conserved). Realize that speed and velocity are different if the objects are of different masses and could collide and move in different directions after the collision. Just because it's an elastic collision and KE and momentum are conserved doesn't mean they will go in the same direction - one object may have a huge mass, so the other object may bounce back. In this case, if the question asks for speed, use KE to calculate the speed before and after because KE is scalar and speed is scalar. If the question asks for velocity, use momentum to calculate the velocity before and after because momemtum is a vector and velocity is a vector.
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What are Elastic collisions?
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Elastic collisions are collisions where the mechanical energy is conserved. In an elastic collision, no energy is dissipated to internal energy.
Ui + Ki = Uf + Kf where the sum of the mechanical energies
before the collision is equal to the sum of the mechanical energies after the collision.
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What kinds of images can Converging (convex) lenses create?
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Real & Virtual
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Virtual Image
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An image produced at a point where light does not actually pass or converge. For mirrors, this would be the opposite side of the object; for lenses, it would be on the same side as the object.
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Modes of Thermal expansion
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1. Conduction-Which occurs within a substance
2. Convection- Where air or another fluid carries heat off or to the surface of a substance
3. Radiation- Where heat emanates from a body, often in a vacuum
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Momentum (p)
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linear momentum = mass x velocity
p = mv ; momentum is a vector quantity
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Bernoulli's Equation
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For streamline flow of an ideal fluid at a steady flow rate, the quantity P+ρgh + ½ρv² is constant along a streamline.
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What creates a magnetic field?
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moving charges or a magnet
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What is pitch?
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•Pitch is the human perception of the frequency of sound.
•Higher frequency = higher pitch.
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Newton's First Law
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A body at rest or constant velocity will remain so unless acted upon by an outside net force.
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Magnetic Field Strength SI symbol and units
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telsa (T) 1 T=1N/A*m
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Newton's Third Law
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For every acting force there exists a reacting force of equal magnitude but in the opposite direction.
F(action) = F(reaction)
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Huygen's Principle
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each pt. on a wave front may be regarded as a new source of disturbance
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What is impulse?
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•Impulse = FΔt, where F is force and t is the time interval that the force acts.
•Impulse = average force from the change in momentum of colliding bodies: Ft = mΔv.
When a force is applied to a rigid body it changes the momentum of that body. A small force applied for a long time can produce the same momentum change as a large force applied briefly, because it is the product of the force and the time for which it is applied that is important. Also, the same force can produce the same CHANGE in momentum of different objects, because what is variable is t. So if the same force were applied to a 5 kg ball moving at 9 m/s and a 7 kg ball moving at 7 m/s, even though their individual masses and velocities aren't the same, since the same force is applied to them, their change in momentum could be the same as long as the time for each is different. Change in momentum is proportional to the force and change in momentum is proportional to time. So if the same time was applied to 2 different objects, the change in momentum would be the same. The force used for impulse is the net force on an object. This net force can be frictional force. So if you are given an equation about an object that is moving at a certain initial velocity (like 30 m/s) on a pavement and stops in a certain amount of time (like 7s), and you need to figure out the coefficient of friction and you are not given the mass of the object or the distance, then instead of trying to solve the problem with W = change in KE, use Ft = mΔv. The beauty with this equation is that you don't need mass or distance! Why? Because the frictional force that you use F = μmg and the masses cancel out. Frictional force is F = μN, and the normal force here is mg.
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What is impulse?
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Impulse is the change in momentum or the force of a collision multiplied by the duration of the collision (FΔt).
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P2 = Patm + ρgD since P1(at surface)=Patm
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Container open at rest
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is the single point at which, for the purposes of a simple mechanics problem, the force of gravity can
be applied to the entire mass. If gravity is the only force, the result will be the same
regardless of the orientation of that mass.
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center of gravity
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What is the speed of light in vacuum
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3.0 x 10^8 m/s
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What is refraction index and Snell's law?
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Snell’s law (n1sinθ1 =n2sinθ2)
The refractive index of a medium (such as water, air, glass, the vacuum of space, etc.) is a measure of how much the speed of a wave is reduced inside that medium compared to the speed of the wave in some reference medium. When a light ray travels from one medium (such as air) into another medium (such as glass), the difference in the refractive indices between these two media can change the direction (and intensity) of the light ray, a phenomenon that is characterized by Snell's Law. Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different media. The law says that the ratio of the sines of the angles of incidence and of refraction is a constant that depends on the media. The law is used to compute the angles of incidence or refraction or find the refraction index.
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What is refraction index and Snell's law?
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Notice that in Snell's law, the angle of incidence and refraction are not specified; it makes no difference is light is moving from medium 1 to medium 2 or from medium 2 to medium 1. When light crosses into a new medium, the frequency remains the same and the wavelength changes. If the medium's index of refraction is higher, the wavelengths become shorter; if the index is lower, then the wavelengths become longer. The frequency remains the same because the energy remains the same (E = hf), but the velocity of the light through the medium is different (v = fλ because n = c/v, where n is the index of refraction). To have a higher n, you need a smaller velocity in the medium, to get that, you need a shorter wavelength. To have a lower n, you need a larger velocity, to get that, you need a longer wavelength.
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Tension in a static system
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• defined as the Force in one direction
ex: horse tied to a tree is pulling against with 500 N
∴ overall tension = 500 N
• tension can only be as great as the force at one end
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Newton's 1st law
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A body at rest tends to stay at rest, a body in motion tends to stay in motion
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Lens Power
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P = 1/f ; f = focal length in meters
[P]=diopters (D); 1D= 1m⁻¹
P total = sum of individual powers
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What is Potential difference (ΔV)?
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■ΔV = VB - VA . Potential difference is used in scenarios such as the difference in potential between the two plates of a capacitor, or the positive and negative terminals of a battery. Consider the task of moving a positive test charge within a uniform electric field from location A to location B as shown in the diagram. In moving the charge against the electric field from location A to location B, work will have to be done on the charge by an external force. The work done on the charge changes its potential energy to a higher value; and the amount of work which is done is equal to the change in the potential energy. As a result of this change in potential energy, there is also a difference in electric potential between locations A and B. This difference in electric potential is represented by the symbol V and is formally referred to as the electric potential difference. By definition, the electric potential difference is the difference in electric potential (V) between the final and the initial location when work is done upon a charge to change its potential energy. The standard metric unit on electric potential difference is the volt, abbreviated V. One Volt is equivalent to one Joule per Coulomb. If there are 3 point charges, and you need to figure out the voltage or potential of 1 of them, with the others as given, what you do is find the potential of the charge to 1 of the charges, then the potential of the same charge to the other charge, and then add them together. That is the potential that the charge of interest. Force of an electric field is F = Eq.
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What is Potential difference (ΔV)?
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Voltage (V) is the potential for work by an electric
field in moving any charge from one point to another: V = Ed. Voltage is given in units of volts (V), and is a scalar. You should also recognize voltage in units of J/ c. Voltage of a point charge is also V = kq1/r. That's why Voltage is: V = Ed, E = kq1/(r^2), and you multiply it by distance and get voltage.
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For a transverse wave, the sine fun ction represents
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vertical displacement of the medium with respect to time or displacement of the wave.
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What is the unit of power?
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Watt (W) which is equal to (1 Joule/sec)
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What are the Conditions for total internal reflection?
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◦Going from a medium of HIGH index of refraction to a medium of LOW index of refraction. Angle of incidence > critical angle. Find the critical angle by: n1*sinθc = n2*sin90°. n1 > n2. θc = critical angle. Total internal reflection (TIR) is the phenomenon which involves only the reflection of all the incident light off the boundary and no refraction. TIR only takes place when both of the following two conditions are met: 1) the light is in the more dense medium and approaching the less dense medium. 2) the angle of incidence is greater than the so-called critical angle. Total internal reflection will not take place unless the incident light is traveling within the more optically dense medium towards the less optically dense medium. TIR will happen for light traveling from water towards air, but it will not happen for light traveling from air towards water. TIR would happen for light traveling from water towards air, but it will not happen for light traveling from water (n=1.333) towards crown glass (n=1.52). TIR occurs because the angle of refraction reaches a 90-degree angle before the angle of incidence reaches a 90-degree angle. The only way for the angle of refraction to be greater than the angle of incidence, is for light to bend away from the normal. Since light only bends away from the normal when passing from a more dense medium into a less dense medium, then this would be a necessary condition for total internal reflection. Total internal reflection only occurs with large angles of incidence. Question: How large is large? Answer: larger than the critical angle.
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What are the Conditions for total internal reflection?
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With total internal reflection, the if the angle of incidence is large enough, none of the light will refract. This angle is the critical angle. The critical angle is when the angle of refraction is 90° to the normal and sin90° = 1. The angle of incidence is always equal to the angle of reflection. This angle of incidence in TIR is the critical angle and this critical angle is equal to the angle of reflection.
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Tangent to the field line passing through that point and its direction is the same as that of the field line
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The electric field vector at any point is always what?
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Characterize the direction of force exerted by a fluid on an area located within the fluid
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A fluid at rest exerts only a normal force on any area located in a fluid
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What are the resonance frequencies of closed and open tubes?
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For an open tube (a tube open at both ends) or a closed tube at both ends, resonance occurs when the wavelength of the wave (λ) satisfies the condition:
λ = 2L/n, where n = 1, 2, 3, 4,…. n is the harmonic (1st, 2nd, etc).
where L = tube length.
For a tube that is open at one end and closed at the other, resonance occurs when the wavelength of the wave (λ) satisfies the condition:
λ = 4L/n where n = 1, 3, 5, 7, 9,…. There are no even harmonics for pipes open at one end and closed at the other. n is the harmonic (1st, 3rd, 5th, etc).
Wavelengths are divided into 4 parts and you count each part for the length.
An open pipe has its fundamental, resonant wavelength at twice the length of the pipe. Both ends have displacement antinodes (maximum amplitudes) with a node in the middle of the pipe. Thus, an open pipe is half a wavelength long. The resonant wavelength is independent of the diameter of the pipe, but it depends on the length.
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What are the resonance frequencies of closed and open tubes?
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Notice when one end is an antinode (pipes with one open end and one closed end), the even numbered harmonics are missing. Why? There is no second harmonic for a closed-end air column. The next frequency above the fundamental frequency is the third harmonic (three times the frequency of the fundamental).
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magnetic force exerted on a charge
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F = q (v x B), v: velocity of charge
Magnitude: F = |q|vBsinϑ; F⊥both v and B, obeying right-hand rule
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What is the electric field of a parallel plate capacitor?
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When two plate of different charge are placed near each other, the two E-fields between the plates add while the E-field outside the plate cancel. When the plates are close to each other to form a capacitor, the E-field between the plates is constant through out the interior of the capacitor as long as one is not near the edges of the plates. Since the E-field is constant inside a capacitor, the magnitude of the Electric field has a very simple relation to the voltage between the plates and their separation d: E = V/d. This relationship is also true in an electrical wire were V is the voltage across the ends of the wire and d is the length of the wire. C = Q/V = εA/d. This equation for the capacitance of a parallel capacitor shows that C is a constant independent of the charge stored in on the plates or the voltage across the capacitor. By placing a thin insulating material (a dielectric) between the plates the separation d can be reduced thus increasing the capacitance of the capacitor and prevent the plates from touching. It takes more voltage to store the same amount of charge on a capacitor because of the presence of the dielectric. Typically a dielectric contains polar molecules which partially line up in the presence of the electric field. The dielectric creates an E-field in the opposite direction which reduces the overall E-field between the plates. The force of the electric field is also equal to F = E/q. V = Eq/r, where E is the electric field and you are just interested in the voltage near a point charge. Also, V = Eq[1/rB-1/rA] if you are interested in the voltages between two positions, where B and A are the two positions.
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Is it possible to have a net torque but no net force?
Is it possible to have a net force but no net torque?
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Yes, Yes.
eg. objects can spin w/o translating, or translate w/o spinning
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What does the graph of a capacitor charging look like?
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Thus, we see that the RC product is indeed a measure of time, and can properly be described as the time constant of this circuit. This in turn means that this curve can be used to determine the voltage to which any capacitor will charge through any resistance, over any period of time, towards any source voltage. It is the general curve describing the voltage across a charging capacitor, over time. Theoretically, C will never fully charge to the source voltage, V. In the first time constant, C charges to 63.2% of the source voltage. During the second time constant, C charges to 86.5% of the source voltage, which is also 63.2% of the remaining voltage difference between E and vC. This continues indefinitely, with vC continually approaching, but never quite reaching, the full value of V. However, at the end of 5 time constants (5RC), vC has reached 99.3% of V. This is considered close enough for practical purposes, and the capacitor is deemed fully charged at the end of this period of time. Mathematically, charging a capacitor takes an infinite amount of time.
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