The seasons are reversed in the southern hemisphere because one part of the planet is more directly exposed to the rays of the Sun than the other.
The northern and southern hemispheres always experience the opposing seasons, regardless of the time of year. This is due to the fact that, depending on whether it is summer or winter, one region of the planet is alternately more directly exposed to the Sun's rays than the other.
A season is a division of the year based on variations in the local climate, ecology, and number of daylight hours. The axial parallelism of Earth's inclinated orbit around the Sun causes seasons on Earth. Seasons are distinguished by differences in the amount of sunlight that reaches Earth's surface in temperate and polar regions. These fluctuations may lead some animals to migrate or go into hibernation while others may cause vegetation to fall dormant.
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A toy rocket is launched from a 5.6 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h= - 4.97t^2+ 38.5t + 5.6. How long will it take for the rocket to hit the ground?
The time it will take the rocket to hit the ground is 7.92 seconds
What is the time of motion of the rocket?
The rocket will hit the ground when its height, h, is equal to zero. To find the time, t, when this happens, we can set h equal to zero and solve for t:
-4.97t^2 + 38.5t + 5.6 = 0
We can use the quadratic formula to solve for t:
t = (-b ± √(b^2 - 4ac)) / 2a
where
a = -4.97,
b = 38.5, and
c = 5.6
Plugging in these values, we solve for time of motion:
t = (-38.5 ± √(38.5^2 - 4(-4.97)(5.6))) / 2(-4.97)
t = (-38.5 ± √(1486.25 + 94.544)) / -9.94
t = (-38.5 ± √(1580.794)) / -9.94
t = (-38.5 ± 39.939) / -9.94
t = (-38.5 - 39.939) / -9.94
t = (78.439) / -9.94
t = 7.92 seconds
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A. An adaptive filter What type of digital signal processing filter is used to generate an SSB signal? A. An adaptive filter B. A notch filter C. A Hilbert-transform filter D. An elliptical filter
A Hilbert-transform filter is used to generate an SSB signal.
A Single Sideband (SSB) signal is generated by filtering one sideband of a modulated signal and suppressing the other sideband and the carrier signal. The most common way of generating an SSB signal is by using a Hilbert-transform filter.
This filter is used to shift the phase of the modulated signal by 90 degrees, effectively converting the upper sideband to the lower sideband, or vice versa. By filtering out one of the sidebands, the SSB signal can be generated. Therefore, option C is the correct answer.
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--The complete question is, What type of digital signal processing filter is used to generate an SSB signal?
A. An adaptive filter
B. A notch filter
C. A Hilbert-transform filter
D. An elliptical filter--
according to the kinetic theory, collisions between molecules in a gas_____
According to the kinetic theory of gases, collisions between the molecules in a gas are perfectly elastic.
It means that the total kinetic energy of the colliding molecules is conserved. This means that during a collision, the molecules may exchange energy and momentum with one another, but the total amount of energy and momentum remains constant.
In addition, according to the kinetic theory, the molecules in a gas are in constant random motion and travel in straight lines until they with each other or with the walls of their container.
The average kinetic energy of the molecules is proportional to the temperature of the gas, and the pressure of the gas is proportional to the number of collisions the molecules make with the walls of the container in a given amount of time. The kinetic theory provides a useful framework for understanding the behavior of gases at the molecular level.
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Balancing a centrifuge requires that all tubes in the load:
A. have an equal amount of liquid of the same viscosity.
B. are of equal size and shape.
C. have a partner directly across in the rotor holder.
D. All of the above
Every tube in the load must have a companion right across in the rotor holder in order for the centrifuge to be balanced.
In many laboratories, centrifuges are employed to separate fluids, gases, or liquids according to their densities. Centrifuges are often employed in clinical and research facilities for the purification of cells, organelles, viruses, proteins, and nucleic acids.
The separation of different components of whole blood using a centrifuge is an example of its usage in a clinical environment. Serum or plasma is required for several tests and can be obtained by centrifugation.
A full blood sample is allowed to clot at room temperature in order to get serum. The clot is subsequently removed from the sample by centrifugation, leaving a serum supernatant behind.
Plasma, in contrast to serum, is made from whole blood that has not been allowed to clot; it contains serum as well as clotting factors. A full blood sample is taken in tubes that have been anticoagulant-treated in order to get plasma.
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5. Express the following quantities in their basic dimensions: a) Electric resistance (2), (R = V = q = 1xt) b) Universal Gas constant (J/K mol) 1
Answer:
a) Electric resistance: The basic dimensions of electric resistance are resistance (R) which has the dimension of [mass] x [length]^2 / [time]^3.
b) Universal Gas Constant: The basic dimensions of the Universal Gas constant (R) are [energy]/[temperature x amount of substance]. These dimensions can be expressed as [mass] x [length]^2 / [time]^2 / [temperature] x [amount of substance].
Explanation:
we place a potential difference 6.11 v across a and b, how much charge is present on the c2 capacitor?
We cannot calculate the charge on the C2 capacitor without knowing the capacitance of the capacitor.
To determine the charge present on the C2 capacitor, we need to know the capacitance of the capacitor and the potential difference across it.
Assuming that the circuit is in steady state and neglecting any resistive losses, the potential difference across both capacitors will be equal to the applied potential difference of 6.11 V.
Let's call the capacitance of C2 as C2.
Then the charge present on the C2 capacitor can be calculated using the formula:
Q = C2 * V
where Q is the charge on the capacitor,
C2 is the capacitance of the capacitor, and
V is the potential difference across the capacitor.
Plugging in the values,
we get:
Q = C2 * V = C2 * 6.11 V
We cannot calculate the charge on the C2 capacitor without knowing the capacitance of the capacitor.
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r is not a readily measurable quantity for a given field. but we may have a sense of how large r is relatively for different fields. for example, field a is a subfield in physics that has very thorough background knowledge, with a small community, and the scientists have a good way of figuring out what hypotheses are important and should be tested. field b is a subfield of genetics which has attracted a lot of attention recently and is still in the exploratory phase of finding fruitful relations. which field has higher r?
Field A has higher r than field B, as the former has had more time to establish reliable methods and a more stable consensus within the scientific community.
Let's assume that "r" refers to the replicability of results within a given scientific field. That is, how likely it is that the results of a given study will be replicated in subsequent studies.
Based on the information given, we can infer that field A has a smaller community of scientists and a well-established set of hypotheses and theories. This indicates that the field has had more time to develop and refine its methods and that there is a higher degree of consensus among the scientific community about what research questions are important and how to approach them. These factors suggest that the replicability of results in field A is likely to be higher.
On the other hand, field B is described as being in an exploratory phase, with a larger community of researchers and a more recent influx of attention. This suggests that the field is still in the process of establishing a set of well-defined hypotheses and methods, which may lead to more variability in research results and lower replicability.
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An object is moving along a frictionless track and has a total energy of 210,000 J. At some point along the track, the object's potential energy is 92,000 J. Calculate how much kinetic energy the object has at that same point in the track. Explain how this follows the law of conservation of energy.
Answer:
118,000 J
Explanation:
The law of conservation of energy states that the total energy in a system remains constant, it can be transformed from one form to another, but the total energy remains the same.
Given that the total energy of the object is 210,000 J, and its potential energy at a certain point along the track is 92,000 J, we can use the law of conservation of energy to find the kinetic energy of the object at that point.
The total energy of the object is equal to the sum of its kinetic energy (KE) and its potential energy (PE):
E_total = KE + PE
Substituting the given values:
210,000 J = KE + 92,000 J
Solving for KE:
KE = 210,000 J - 92,000 J = 118,000 J
So, the object has a kinetic energy of 118,000 J at the same point where its potential energy is 92,000 J.
This follows the law of conservation of energy because the total energy of the object remains constant, and the change in potential energy is equal to the change in kinetic energy.
consider a cold canned (typically cylindrical in shape) drink left on a table. would the heat transfer be steady or transient? would you model the heat transfer as one-, two-, or three-dimensional? also, which coordinate system would you use to analyze this heat transfer problem?
The heat transfer in this situation would be transient, as the temperature of the room, the can, and the drink inside the can are all changing over time.
The heat transfer can be modeled as a two-dimensional problem, since the can is cylindrical in shape and the temperature of the can and the drink inside the can will only depend on the vertical and horizontal components of heat transfer. The coordinate system used to analyze the heat transfer problem would be cylindrical, since it is the most appropriate for modeling a cylindrical object. In this system, the radial direction is along the circular circumference of the can, and the axial direction is along the length of the can. The temperature of the can and the drink inside the can can then be calculated using the two-dimensional equations of heat transfer, which consider both the radial and axial components of heat transfer.
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(a) Why the maximum tidal range (spring tide) occurs during a new moon and full moon phases?(b) Why the minimum tidal range (neap tide) occurs at first-quarter and third-quarter moons?
(a) The maximum tidal range (spring tide) occurs during a new moon and full moon phases because the sun and moon's gravitational pulls are aligned and amplified.
(b) The minimum tidal range (neap tide) occurs at first-quarter and third-quarter moons because the sun and moon's gravitational pulls are at right angles.
(a) As the sun and moon's gravitational pulls are aligned and amplified during the new moon and full moon phases, the maximum tidal range, or spring tide, occurs during these periods. With the moon and sun on opposing sides of the Earth, the sun, moon, and Earth are all in a straight line during a new moon. Due to the moon's proximity to Earth, its gravitational pull on the planet is at its greatest. Due to its alignment with the moon and Earth, the sun's gravitational pull also contributes to this. A broader tidal range results from the seas bulging due to this alignment, which also generates higher peak tides and lower low tides.
(b) As the sun and moon's gravitational pulls are at right angles during the first and third quarters of the moon, the shortest tidal range, or neap tide, occurs at these periods. With the sun and moon on opposing sides of the Earth, the sun, Earth, and moon make a straight angle during a first-quarter moon. The gravitational pull of the sun partially cancels out the gravitational pull of the moon on Earth, reducing the tidal range. When the moon is quartered, the same thing takes place. There is a narrower tidal range at these periods because the high tides are lower and the low tides are higher.
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If a neighbor pushes a lawnmower four times
exerts only half the force, which one of you
as far as you do but
does more work and by
how much?
It is quite easy.
Say that the work you did was w, so that the force you exert is F.
Furthermore, the displacement is s.
How can you explain this situation?AT THIS TIME
the work you(w)=Fs
Now, AT YOUR NEIGHBOR'S CASE.
Let his work be credited as W
IF, then force is half, or F/2.
with five times the displacement.
therefore, work done (W)=F/2*5s
hence, W=2.5Fs
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What happens to the time period of a simple pendulum if the amplitude is doubled?
When producing modest swings, the amplitude frequently has no impact at all on the pendulum's period. There is a tiny but insignificant rise in the period when the pendulum's amplitude is greater.
What alter on time period pendulum if amplitude changed?The distance to travel increases as the amplitude rises, but when the restoring force rises as well, the acceleration rises correspondingly.
This implies that the mass can move faster and cover a bigger distance. Since these qualities cancel one another, amplitude has no bearing on period.
A straightforward harmonic oscillator's period is independent of its amplitude. with the graphs of acceleration and velocity produced by the time derivatives. These oscillators also show how kinetic and potential energy can be transferred.
Therefore, the length of time is unrelated to the vibration's magnitude. Time period is unchanged by doubling the oscillation's amplitude.
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The current through a dryer is 12 A. If the input voltage is 220 v. What electrical energy does it make in 1.5 min?
The electrical energy consumed by the dryer in 1.5 minutes is 237,600 joules.
What is electrical energy?
Electrical energy is a form of energy that results from the movement of electric charge. It is the energy that is transferred or converted when electric current flows through a conductor or a circuit.
How is electricity generated?Electricity is generated at power plants using various sources of energy such as fossil fuels, nuclear power, or renewable energy sources like wind, solar, or hydroelectric power. This electrical energy is then transmitted through high-voltage power lines and distributed to homes.
First we should calculate the power:
power = voltage x current
power = 220 V x 12 A = 2640 W
Now we can calculate the electrical energy consumed by the dryer in 1.5 minutes:
Electrical energy = power x time
= 2640 W x 90 s
= 237,600 joules (J)
The electrical energy consumed by the dryer in 1.5 minutes is 237,600 joules.
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In the opposite electric circuit, if the reading of the
voltmeter is 6 V, the resistance of R equals
Answer:
[tex]2\; {\rm \Omega}[/tex].
Explanation:
The lower case "[tex]r = 1\; {\rm \Omega}[/tex]" in the circuit diagram indicates that the internal resistance of this [tex]12\; {\rm V}[/tex]-battery is [tex]1\; {\rm \Omega}[/tex].
In practice, the rated [tex]12\; {\rm V}[/tex] voltage drop across this battery is split across not just the resistors in the external circuit, but also across the internal resistance of the battery.
The voltameter in this circuit measures the voltage drop across the [tex]3\; {\rm \Omega}[/tex] resistor and the unknown resistor [tex]R[/tex]. The voltage drop across the internal resistance and the other resistor (a total of [tex]1\; {\rm \Omega} + 4\; {\rm \Omega} = 5\; {\rm \Omega}[/tex]) would be [tex]12\; {\rm V} - 6\; {\rm V} = 6\; {\rm V}[/tex].
Divide the voltage drop by the resistance to find the current:
[tex]\begin{aligned}I &= \frac{V}{R} \\ &= \frac{6\; {\rm V}}{5\; {\rm \Omega}} = 1.2\; {\rm A}\end{aligned}[/tex].
Since this circuit is serial, current would be the same everywhere in the circuit. Given that voltage drop across the [tex]3\; {\rm \Omega}[/tex] resistor and the unknown resistor is [tex]6\; {\rm V}[/tex], the resistance of that part of the circuit would be:
[tex]\begin{aligned}\frac{6\; {\rm V}}{1.2\; {\rm A}} = 5\; {\rm \Omega}\end{aligned}[/tex].
Subtract the [tex]3\; {\rm \Omega}[/tex] from the resistance to find the value of [tex]R[/tex]:
[tex]R = (5\; {\rm \Omega} - 3\; {\rm \Omega}) = 2\; {\rm \Omega}[/tex].
Nichrome is used as a heating element in electric iron. give reason
Nichrome is used as a heating element in electric irons
High resistanceCorrosion resistanceGood temperature stabilityWhy Nichrome is used as a heating element?High resistance: Nichrome has a high electrical resistance, which means that it converts electrical energy into heat energy efficiently. This makes it ideal for use in heating elements where heat generation is the primary requirement.
Good temperature stability: Nichrome has a high melting point and a low coefficient of thermal expansion. This means that it can maintain its structural integrity even at high temperatures and does not deform or break easily.
Corrosion resistance: Nichrome is resistant to corrosion, which makes it suitable for use in electrical appliances that are exposed to moisture, such as electric irons.
Long lifespan: Nichrome has a long lifespan and does not degrade easily even with repeated use. This makes it a reliable and durable choice for heating elements.
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Define Resonance Physics
Answer:
Resonance is a phenomenon that occurs when the frequency at which an external force is applied to an object is equal to the natural frequency of vibration of that object.
In physics, resonance is a common occurrence in mechanical, electrical, and acoustical systems.
What does the resolution limit of an optical system depend on? Choose all answers that are correct. (a) The wavelength of light (b) The diameter of the aperture (c) The distance to the object being viewed (d) The distance from the aperture to the light detectors
The resolution limit of an optical system depends on both (a) The wavelength of light and (b) The diameter of the aperture. These two factors determine the diffraction limit, which is the smallest distance between two points that can be resolved by the optical system.
The wavelength of light affects the resolution limit because shorter wavelengths are able to resolve smaller details than longer wavelengths. The diameter of the aperture also affects the resolution limit because a larger aperture allows for more light to enter the system, which can improve the resolution.
The distance to the object being viewed (option c) and the distance from the aperture to the light detectors (option d) do not affect the resolution limit of an optical system. These factors may affect the overall image quality, but they do not determine the smallest distance between two points that can be resolved by the system.
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The stored energy that can be used to do work is called ______ energy, while the energy of motion used to do work is called ________ energy.
The stored energy that can be used to do work is called Potential energy
while the energy of motion used to do work is called kinetic energy.
Potential energy is simply stored energy that, depending on its surroundings or circumstances, a thing may use. Potential energy is the energy that is held inside a system of physically interacting things, to use terminology more closely related to physics.
Kinetic energy, often known as the energy of motion, may be seen in the motion of things and subatomic particles. Kinetic energy may be found in all particles and moving objects. Examples of kinetic energy in action include a person walking, a baseball flying through the air, food tumbling off a table, and a charged particle in an electric field. Everything contains kinetic and potential energy. Kinetic energy is the ability to move anything (KE). Energy is a potential form of energy (PE).
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Can someone help me with this ?
The first image shows a speed - time relation in which the speed is zero and the the object is not moving. The second graph shows a constant velocity and the third one shows an increasing velocity with time.
What is speed - time graph ?A speed - time graph represents the change in speed of an object with respect to the time. The speed can be increasing with time or decreasing. Speed of an object is dependent on the path through which it is moving and the mass, frictional force etc.
Here, the first image shows no no values for the y - axis and and thus, the image is not moving. The second graph shows a parallel line which is showing there is no change in speed with the time. This indicates that the object is moving with a constant speed.
The graph C plots an increasing speed with respect to time. The straight line diagonal to the x, y axis indicates the increasing speed.
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assuming the only force acting is the force of collision, which one experiences the most force during the crash - the car or the dump truck?
They experience the same size force. Both car and dump truck will experience the force of same magnitude. The main difference is the change in acceleration which is greater for smaller car.
Collision is when two or more objects collide with each other, either directly or indirectly. In physics, collision is defined as the interaction between two or more bodies, where the total kinetic energy of the two bodies before the collision is greater than the sum total of the entire kinetic energy of the two bodies after the collision.
Collisions can involve two or more objects and can be elastic or inelastic. Elastic collisions involve objects that bounce off of each other and inelastic collisions involve objects that stick together after the collision. Collisions can also involve two or more particles, where the particles interact and exchange energy, momentum and angular momentum.
Both car as well as the dump truck will experience the force of same magnitude.
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Assertion - Rainbow is a natural phenomenon showing dispersion.
Reason - Splitting light is known as dispersion of light
Rainbow is a natural phenomenon showing dispersion. Splitting light is known as dispersion of light. The reason is correct for the given assertion.
What is Dispersion of light?Dispersion is the phenomenon in which the phase velocity of a light wave depends on its frequency. It is sometimes also termed as chromatic dispersion, which is used for the specificity to optics in particular. A medium having this common property may be termed as a dispersive medium.
A rainbow is a meteorological phenomenon which is caused by the reflection, refraction and dispersion of light in the water droplets resulting in a spectrum of light appearing in the sky. This takes the form of a multicolored circular arc. Rainbows are caused by the sunlight which always appear in the section of sky directly opposite the Sun.
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Your question is incomplete, most probably the complete question is:
Assertion - Rainbow is a natural phenomenon showing dispersion.
Reason - Splitting light is known as dispersion of light
What is right answer?
acceleration is a vector and has direction. when the object moves to the right and speeds up, what is the direction of the acceleration? group of answer choices to the right. to the left. up. down. in the direction of the force that is causing the change of speed. in the direction of the gravitational force.
An object that is travelling to the right would accelerate in the same direction as its motion, which would be to the right. This is so because acceleration, which encompasses both speed and direction of motion, is the rate at which velocity changes.
If an object is going to the right and then accelerates, the acceleration would also be moving to the right, following the motion. This is so because acceleration, which encompasses both speed and direction of motion, is the rate at which velocity changes. While the item in this instance is moving faster, its velocity is rising in the same direction as its motion, and consequently, the acceleration is likewise moving faster. The other possible solutions don't work in this case.The rate at which velocity changes is known as the acceleration, which is a vector quantity. The speed and direction of motion of an object are described by a vector called velocity.
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a machine of velocity ratio 5 requires 1000joules of work to raise a load of 450newton through a vertical distance of 2meter . calculate the efficiency
The efficiency of the machine is 90%.
What is the efficiency of the machine?
The efficiency of a machine is defined as the ratio of output work to input work.
Output work = Force x Distance x Load
Output work = 450 N x 2 m
Output work = 900 J
The input work is the work done by the machine, which is equal to the product of the force applied to the machine and the distance through which it moves
Input work = Force x Distance = 1000 J
The efficiency of the machine is the ratio of output work to input work:
Efficiency = Output work / Input work
E = 900 J / 1000 J
E = 0.9
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What is moving faster, a 450 kg horse with a momentum of 765 kgm/s or an object with a different mass and momentum?
Therefore, the answer to this question is that it cannot be determined without more information.
The answer to this question can be determined by comparing the velocity of the two objects.
The formula for momentum is:
momentum = mass × velocityWe can rearrange this formula to solve for velocity:
velocity = momentum / mass For the horseWe can plug in the given values:
velocity = 765 kgm/s / 450 kg velocity = 1.7 m/sFor the other object, we do not have enough information to determine its velocity. We would need to know its mass and momentum in order to calculate its velocity and compare it to the horse's velocity. Without this information, we cannot determine which object is moving faster. Therefore, the answer to this question is that it cannot be determined without more information.
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webassign astronomy light from the sun takes 8 minutes to reach earth. how long (in min) does it take to reach saturn, 9.55 au from the sun?
The required time for the light to reach Saturn from the Sun is calculated to be 76.4 min.
It is given that the light takes 8 minutes to reach the Earth from the Sun.
We are told to determine how long it takes for light to travel from the Sun to Saturn.
The distance between the Saturn and the Sun is given as 9.55 au.
Distances in solar system are measured in astronomical units.
The separation between the Earth and the Solar is 1 au.
For 1 au, it takes 8 minutes.
So, for 9.55 au it takes, 9.55(8) = 76.4 min.
As a result, it takes some time for the radiation from the Sun to reach Saturn.
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You kick a soccer ball with an initial vertical velocity of 14 m/s and a horizontal velocity of 18 m/s. What is the initial resultant velocity of the soccer ball?
Answer:
Explanation:
ij42fom2k jjnjmiok3ofnf jnk jn kj j vjk v
imad sets the charge of both particles to zero, then varies the charge on the left particle. what does jacob report on what he observes?
Jacob reports that as he varies the charge on the left particle, he observes that the force between the two particles changes.
Specifically, when the charge on the left particle is positive, the force between the two particles is attractive, and when the charge on the left particle is negative, the force between the two particles is repulsive. This is because opposite charges attract and like charges repel. As the magnitude of the charge on the left particle increases, the force between the two particles increases as well. The force of attraction is strongest when the charges on both particles are the same, and the force of repulsion is strongest when the charges on the particles are opposite.
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. a common statistic in car tests is the standing (starting from rest) quarter-mile performance. a modern sports car can achieve a terminal speed (speed at the end of the quarter-mile) of 120 mph (193 km/h). how does the average acceleration compare to g? (0.25 mile
The required acceleration of the car compared to g is 0.36 times the value of g.
The velocity v of the car is given as 193 mph = 193× 18/5 = 53.61 m/s.
The distance covered = 0.25 miles = 0.25× 1609 m/ 1 mile = 402.336 m
Initial velocity u = 0
Let us find the acceleration of the car using the equation of motion.
v² - u² = 2 a s
where,
v is final velocity
u is initial velocity
a is acceleration
s is distance
Entering values in the above equation, we have,
53.61² - 0 = 2 a (402.336)
804.672 a = 2874.03
a = 3.57 m/s²
Let us compare it with the value of 'g',
a/g = 3.57/9.8 = 0.36
So, a = 0.36 g
Thus, the acceleration of the car is 0.36 times the value of g.
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7. A fisherman sees a lobster cage on the sea floor and tries to retrieve it by lowering a winch directly
over where the cage appears to be. The winch lands behind the cage.
a) Explain why the cage isn't exactly where he thought it was.
b) The fisherman uses an underwater camera to get a better view. Light travels from the
lobster cage and hits the camera lens at an angle of 37.2° to the normal. If water has a
refractive index of 1.40 and the lens has a refractive index of 1.49, at what angle to the
normal will the refracted ray in the camera lens be?
Explanation:
a) The fisherman sees the cage at a different location than where it actually is because of the refraction of light in water. When light travels from air into water, its speed decreases, causing the light to bend or refract. This means that the light entering the fisherman's eyes is coming from a slightly different direction than the actual position of the cage, making it appear as if the cage is in a different location.
b) To calculate the angle of the refracted ray in the camera lens, we can use Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two materials.
Using this formula, we can calculate the angle of refraction in the lens:
sin(θ2) / sin(θ1) = n2 / n1
where n1 is the refractive index of water (1.40), n2 is the refractive index of the lens (1.49), and θ1 and θ2 are the angles of incidence and refraction, respectively.
Solving for θ2, we find:
θ2 = sin^-1(sin(θ1) * n1 / n2) = sin^-1(sin(37.2°) * 1.40 / 1.49) = 35.0°.
So, the refracted ray in the camera lens will be at an angle of 35.0° to the normal.
Two large, charged plates with charge density ±30µC/m^2 face each other with a separation of 5.0 mm. The negative plate is grounded, and defined as 0 potential. Find the electric potential at a location 8.0mm from the negative plate, 3.0mm from the positive plate.
V=3.39×10⁶ ×d for 0≤d≤0.005 m, 7.73x10⁷ m/s is the electric potential at a location 8.0mm from the negative plate, 3.0mm from the positive plate
a. Identify the unknown:
The potential everywhere
List the Knowns:
Charge density of the two plates: σ = ±30×10⁻⁶ C/m²
Distance between the two plates: d=5×10⁻³ m
Permittivity of free space: ε₀=8.85×10⁻¹² C²/N⋅m²
Set Up the Problem:
Since the σ are equal and opposite, this means that in the region outside of the two plates, the electric fields cancel each other out to zero: E = 0 The electric field between the plates is this strong:
E = σ/ε₀ = 30×10⁻⁶/8.85×10⁻¹² = 3.39x10⁶N/C
Possible variations between the positive plate and the negative plate include:
ΔV=Ed=3.39×10⁶ ×0.005=1.7×10⁴ V
Assuming the negatively charged plate is at the origin (d=0) and has no potential, the electric field is directed away from the positively charged plate and towards the negatively charged plate, the positive plate is at (d=+0.005 m) and have 1.7×10⁴ V
Solve the Problem:
V=0 for d<0
V=3.39×10⁶×d for 0≤d≤0.005 m
V=1.7×10⁴ V for d>0.005m
b. Identify the unknown:
when an electron leaves a state of rest at the negative plate and strikes the positive plate, how quickly it moves
List the Knowns:
Electron charge: e=1.6×10⁻¹⁹ C
Electron mass: m=9.11×10⁻³¹ kg
Set Up the Problem:
Potential and electric potential energy have the following relationships: = U/q
U=qV
To move the drop, this potential energy is converted to kinetic energy:
1/2mv²=qV
v = √2qV/m
Solve the Problem:
v = √(2×1.6×10⁻¹⁹×1.7×10⁴/9.11×10⁻³¹) = 7.73x10⁷ m/s
Learn more about Electric potential here:
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