The critical angle for Lucite is 41.8°. What is Brewster's angle for Lucite?
33.7°
26.3°
48.2°
56.3°

Answers

Answer 1

The Brewster's angle for Lucite having a critical angle for Lucite is 41.8° is 56.3°.

What is Brewster's angle?

Brewster's angle is the angle of incidence for which the reflection of p-polarized light vanishes entirely. It is named after Sir David Brewster, a Scottish physicist who discovered it in 1812. The Brewster angle is described as the angle of incidence at which the reflected light is polarized at a right angle to the refracted light.

In order to determine Brewster's angle for Lucite, we need to know its refractive index. According to the given information, the critical angle for Lucite is 41.8°.

The critical angle (θc) is defined as the angle of incidence at which the refracted ray is parallel to the surface of the medium. When θi = θc, θr = 90°, and the refracted ray barely grazes the surface of the medium. Therefore, sin θc = 1/n (where n is the refractive index of the medium).

sin θc = 1/n

n = 1/sin θc = 1/sin 41.8°n = 1.495 (approx)

The equation for Brewster's angle (θB) is tan θB = n, where n is the refractive index of the medium.

θB = tan⁻¹(n)

θB = tan⁻¹(1.495)

θB = 56.3° (approx)

Hence, the correct option is 56.3°.

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Related Questions

Explain why the Earth and the rest of the Solar System are thought to have formed from essentially the waste products of earlier generations of stars (rather than from the primordial products of the Big Bang)

Answers

According to modern cosmology, the universe was born in a Big Bang, which began almost 14 billion years ago. The Big Bang started with a singularity that evolved into the universe we see today. While the Big Bang created some of the universe's light elements, it didn't create any heavier elements like carbon, nitrogen, and oxygen.

The solar system is thought to have originated from the debris left over from a supernova explosion that occurred approximately 5 billion years ago, according to the nebular hypothesis. This idea states that a giant cloud of gas and dust began to compress under its own gravitational pull, causing the cloud to rotate and eventually flatten into a disk. The center of the disk became hotter and denser until it ignited into a star (the Sun). The remaining material in the disk formed into planets and other solar system bodies, like moons and asteroids.

Astronomers believe that this disk was made up of debris from an older star that exploded in a supernova. The supernova explosion generated heavy elements like carbon, nitrogen, and oxygen, which were incorporated into the solar nebula. This is why the Earth and the rest of the solar system are believed to have originated from the "waste products" of earlier generations of stars.

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Describe how perceptual errors, cognitive biases, or emotions
have negatively affected you in a negotiation. Share at least three
examples (one perceptual error, one cognitive bias, and one
emotional)

Answers

Perceptual errors, cognitive biases, and emotions can indeed have negative effects on negotiations. Here are three examples illustrating each:

1. Perceptual error: One common perceptual error is the halo effect, where an overall impression of a person or situation influences the perception of specific attributes or qualities. In a negotiation, I may have made the mistake of perceiving my counterpart as more competent and trustworthy due to their confident demeanor and well-dressed appearance. This perceptual bias may have led me to underestimate their true intentions or overlook potential risks.

2. Cognitive bias: Confirmation bias is a cognitive bias where we seek and interpret information in a way that confirms our pre-existing beliefs or expectations. During a negotiation, I might have had a confirmation bias that my proposed solution was the best option. As a result, I might have selectively paid attention to information that supported my viewpoint and dismissed or ignored evidence that challenged it. This bias could have hindered open-mindedness and prevented me from considering alternative solutions.

3. Emotion: Emotions play a significant role in negotiations and can impact decision-making. For example, I might have experienced strong frustration during a negotiation due to the slow progress and lack of cooperation from the other party. This emotional response could have impaired my ability to think rationally and objectively, leading to impulsive or aggressive behavior. It might have also hindered effective communication and collaboration, potentially damaging the negotiation process.

In negotiations, it's important to be aware of these potential pitfalls and actively work to mitigate their effects. Developing self-awareness, practicing empathy, seeking diverse perspectives, and employing logical analysis can help counteract the negative impact of perceptual errors, cognitive biases, and emotional responses.

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Three dogs are fighting over a bone. One is pulling to the left with a force of 20N, another
to the right with a force of 35N and the third upward with a force of 15N. What is the net
force on the bone? This is a multiple-select problem: You must select a magnitude for the
force and an angle for the force.

Answers

Answer:

Net force = 21.12 N

angle for the force α = 45°

Explanation:

In this problem, we will take the left as the negative x-axis, the right as the positive x-axis, and the upward direction as the positive y-axis.

The 20 N force to the left has an x component of -20 N, and y component of 0 N

The 35 N force to the right has a x component of 35 N, and a y component of 0 N

The 15 N upwards has an x component of 0 N, and a y component of 15 N

We resolve the forces into the x and y components.

for the x component Fx

Fx = -20 + 35 + 0 = 15 N

For the y component Fy

Fy = 0 + 0 + 15 = 15 N

Net force Fn = \(\sqrt{Fx^{2} + Fy^{2} }\)

\(Fn = \sqrt{(15)^{2} + (15^{2} ) }\)

Net force Fn = 21.21 N

for the angle,

\(tan\alpha = \frac{Fy}{Fx} = \frac{15}{15}\)

\(tan\alpha = 1\)

α = \(tan^{-1}\) 1

angle for force α = 45°

kisses has mass of 57 kg runs up a flight of stairs with a vertical heighy of 28 m. if the trip takes 32 seconds to complete, calculate kisses power?

Answers

Kisses' power is approximately 490.13 Watts.

Power (P) is defined as the rate at which work is done. The formula to calculate power is:

P = W / t

P is the power,

W is the work done,

t is the time taken.

The work done (W) can be calculated as the product of force (F) and distance (d):

W = F * d

In this case, the force is the weight of Kisses, which can be calculated using the formula:

F = m * g

m is the mass of Kisses,

g is the acceleration due to gravity (approximately 9.8 m/s^2).

m = 57 kg

d = 28 m

t = 32 seconds

g = 9.8 m/s^2

First, calculate the work done:

W = F * d

W = (m * g) * d

Next, calculate the power:

P = W / t

Substituting the given values:

W = (57 kg * 9.8 m/s^2) * 28 m

W ≈ 15684.24 J

P = 15684.24 J / 32 s

P ≈ 490.13 W

Therefore, Kisses' power is approximately 490.13 Watts.

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Which of these structures is made up of all of the others?

Which of these structures is made up of all of the others?

Answers

Answer:

systems

Explanation:

You can't see anything if time stop..
Explain​

Answers

You can't see anything if time would stop:

This is in fact true...if time stops then photons will also stop and they will unable to reach your eyes, so would your metabolism and cellular activity. Thus you won't be able to see anything.

Hope this helped you- have a good day bro cya)

You can't see anything if time stop..Explain

Answer:

You can't see anything if time stop..

Explanation:

IG

pls class 10 th hepl me with this project​

pls class 10 th hepl me with this project

Answers

Answer: Sad y’all have holiday homework

calculate the torque procured by the same 75N force when a pipe extends the length of the wrench to 0.5m

Answers

Answer:  37.5 N-M

Explanation:

Help me please, I need help!!!

Help me please, I need help!!!

Answers

Adding resistance in a series circuit increases the total resistance, resulting in a decrease in the overall current flow.

When you add resistance in a series circuit, the flow of current is affected. The addition of resistance increases the total resistance in the circuit, which in turn reduces the overall current flowing through the circuit. This relationship is governed by Ohm's Law, which states that the current (I) flowing through a circuit is directly proportional to the voltage (V) applied across the circuit and inversely proportional to the total resistance (R) of the circuit.

Mathematically, Ohm's Law can be expressed as:

I = V / R

Where:

I = Current (in amperes)

V = Voltage (in volts)

R = Resistance (in ohms)

By increasing the resistance (R) in a series circuit, you effectively decrease the current (I) flowing through the circuit, assuming the voltage (V) remains constant. This relationship can be observed in a simulation or real-world scenario where adding resistance leads to a decrease in the overall current flow.

Therefore, In a series circuit, adding resistance raises the total resistance, which reduces the overall current flow.

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A bowling ball rolls without slipping up a ramp that slopes upward at an angle β to the horizontal. Treat the ball as a uniform, solid sphere, ignoring the finger holes.

Part A:

What is the acceleration of the center of mass of the ball?

Express your answer in terms of the variable β and appropriate constants.

Part B:

What minimum coefficient of static friction is needed to prevent slipping?

Express your answer in terms of the variable β and appropriate constants.

Answers

Friction is an opposing force that works on a body's surface and tries to stop it from moving. Newton (N) is its unit.

What is the friction force?

Friction is the force created when two surfaces of two things come into contact and slide against one another.

It is described mathematically as the product of the normal reaction and the coefficient of friction.

The equation becomes balanced once the provided force and acceleration in the various components have been resolved. elements moving in the x-direction

To find acceleration on an inclined plane

Ma(sin∅) - F = ma

mg(cos∅) = R

F = μR

To prevent slippage, the frictional force must be less than the maximum static friction force. We'll use constants to represent the ratio of the ramp's opposite and adjacent sides.

At this point, the frictional force equals ma. It was previously discovered that a=gsin

The frictional force is thus mgsin∅. The maximum static friction force, or normal force, is defined as kmgcos∅, where k is the minimal static friction coefficient.

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So if any of ya got like, screenshots of all the answers for Edge, 2020. Lab-Kinetic Energy-student guide, That would be really helpful. If you could help me, then I will mark you brainliest. And for you trollers out there who just want the points, could you not steal them for this one? Anyways, thanks ya'll!

Answers

Answer:

has any one finished the lab yet?????

Explanation:

Currently, electricity is the form of energy we use most in our daily lives. This means we are always using energy resources that can be transformed to electrical energy. You are an electrical engineer exploring different resources for producing electricity while also making sure to pick resources that are least harmful to the environment. Create a PowerPoint to include the below information:
1. What are the disadvantages of using fossil fuels for producing electricity?
2. Why do we depend so heavily on fossil fuels to produce electricity even when they cause air pollution?
3. Which energy resources seem to be the least harmful for the environment (this includes harmful to air, water, or living things)? Explain how you reached this conclusion.
4. Renewable energy resources affect the environment as well. Pick one renewable energy resource and describe how and why it affects the environment.

Answers

The drawbacks of burning fossil fuels to generate power include their role in climate change and air pollution, their limited supply, and the environmental harm that their extraction and transportation create.

Why do we depend so heavily on fossil fuels to produce electricity even when they cause air pollution?

Our infrastructure is essentially based on the usage of fossil fuels, which are relatively cheap, and abundant, and on which we rely extensively to produce electricity. Furthermore, many individuals might not be aware of the harmful effects that using fossil fuels has on the environment or might not have access to alternate energy sources.

Which energy resources seem to be the least harmful to the environment (this includes harmful to air, water, or living things)? Explain how you reached this conclusion.

Because they emit few to no greenhouse gas emissions or other pollutants, renewable energy sources like solar, wind, and hydropower are typically regarded as the least damaging to the environment. Furthermore, they do not generate toxic waste or need to mine or dig for fuel. Yet, depending on elements like the location of the power generation facilities and the materials employed in the manufacture of renewable energy technology, the environmental impact of renewable energy sources might change.

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At a regional airport with an elevation of 76 meters below mean sea level, the observed station pressure is 1015 mb.

Using the equations presented in the activity, _____ mb must be _____ the station pressure to correctly determine the sea level pressure value in mb.

a. 10.15 mb, subtracted from

b. 10.15 mb, added to

c. 7.6 mb, subtracted from

d. 7.6 mb, added to

Answers

The answer is option c: 7.6 mb must be subtracted from the station pressure to correctly determine the sea level pressure value in mb.

To determine the sea level pressure value, we need to adjust the observed station pressure for the difference in elevation between the station and sea level.

In this case, the regional airport is located 76 meters below mean sea level. The standard atmosphere assumes a decrease of approximately 1 mb for every 10 meters of elevation gain. Therefore, we need to subtract the equivalent pressure decrease caused by the elevation difference.

Given that the observed station pressure is 1015 mb, we can calculate the adjustment by dividing the elevation difference (76 meters) by 10 and multiplying it by the pressure decrease per 10 meters (1 mb). So, (76 / 10) * 1 = 7.6 mb. Therefore, we must subtract 7.6 mb from the observed station pressure of 1015 mb to correctly determine the sea level pressure value.

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in a single slit experiment, what effect on the central minimum in the diffraction pattern would result as the wavelength of the light is decreased?

Answers

In a single-slit experiment, decreasing the wavelength of light would result in a narrower central minimum in the diffraction pattern.

The width of the central minimum in a single-slit diffraction pattern is inversely proportional to the wavelength of light. When the wavelength decreases, the angle at which the first minimum occurs increases according to the formula

θ = λ / a, where θ is the angle, λ is the wavelength, and a is the slit width.

As the angle increases, the width of the central minimum becomes narrower. This change in the diffraction pattern can be observed as the separation between adjacent bright fringes, or maxima, increases when the light wavelength is decreased.

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NEED HELP TODAY

Which of the following is true about the speed of light?
A. It depends on the wavelength
B. In a vaccum, it is a constant value that does not depend on the observer
C. It is the slowest in a vacuum unless the observer is moving towards the source
D. In a vacuum, it varies depending on the color of the light

Answers

Answer:

I am pretty sure it is B My friend hope you are well

Explanation:

Answer:

B- It is a constant when the light is traveling in a vacuum.

Explanation:

"Light in a vacuum always travels at the same speed." Those additional three words in a vacuum are very important. A vacuum is a region with no matter in it. So a vacuum would not contain any dust particles (unlike a vacuum cleaner, which is generally full of dust particles)

How much work is required to move an electron

through a potential difference of 3.00 volts?

(1) 5.33 × 10^–20 J (3) 3.00 J

(2) 4.80 × 10^–19 J (4) 1.88 × 10^19 J

Answers

Answer:

(2) the work required to move the electron is 4.8 x 10⁻¹⁹ J.

Explanation:

Given;

potential difference, V = 3.00 volts

charge of electron, q = 1.6 x 10⁻¹⁹ C

The work required to move an electron is calculated as;

W = Vq

where;

W is the work done in Joules

Substitute the given values and solve for W;

W = (3.00)(1.6 x 10⁻¹⁹)

W = 4.8 x 10⁻¹⁹ J.

Therefore, the work required to move the electron is 4.8 x 10⁻¹⁹ J.

If x(n) is passed through an ideal d/a converter, what is the reconstructed signal ya(t)?

Answers

If x(n) is passed through an ideal d/a (digital-to-analog) converter, the reconstructed signal ya(t) will be an analog signal that approximates the original discrete-time signal x(n). The d/a converter converts the discrete-time samples into a continuous-time signal.

To reconstruct the signal ya(t), the d/a converter needs to perform the following steps:

1. Sample and Hold: The d/a converter first samples the discrete-time signal x(n) at regular intervals. This means that it takes snapshots of the signal at specific points in time.

2. Quantization: The sampled values are then quantized, which means they are approximated to a limited set of values. The number of bits used for quantization determines the resolution of the reconstructed signal.

3. Digital-to-Analog Conversion: The quantized values are converted into corresponding analog voltage levels. This process involves reconstructing a continuous-time signal that closely resembles the original waveform.

The reconstructed signal ya(t) is a continuous-time approximation of the original signal x(n). It is important to note that the accuracy of the reconstructed signal depends on the sampling rate and the resolution of the d/a converter. A higher sampling rate and resolution generally result in a more accurate reconstruction.

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Which statement describes an interacting force pair represented by the third law of motion? The force exerted by a cyclist equals the combined forces of friction and air resistance. A car exerts a force on a bug as they collide and the bug exerts an equal force on the car. Gravity exerts a downward force on a refrigerator and the normal force pushes up on the refrigerator. Two people pull on opposite ends of a rope, but the rope does not move because the people pull with equal forces.

Answers

Answer:

A car exerts a force on a bug as they collide and the bug exerts an equal force on the car.

Explanation:

Newton's third law of motion states that for every action there is an equal and opposite reaction.

Action-reaction force pairs make it possible for fishes to swim, birds to fly, cars to move etc,

Furthermore, take for example, While driving down the road, a firefly strikes the windshield of a car (Action) and makes a quite obvious mess in front of the face of the driver (Reaction) i.e The firefly hit the car and the car hits the firefly.

Hence, the statement which best describes an interacting force pair represented by the third law of motion is, a car exerts a force on a bug as they collide and the bug exerts an equal force on the car.

The ultimately implies that, in every interaction, there is a pair of forces acting on the two interacting objects in this case, the car and bug. The size of the force on the car equals the size of the force on the bug. These two forces are called action and reaction forces and are the subject of Newton's third law of motion.

Two balls, a foam ball and a golf ball, are placed into a pail of water. The golf ball sinks. Why does a foam ball float and a golf ball sink when both are placed into water?

Answers

Answer:

The golf ball has a greater mass than the foam ball

Explanation:

A bus accelerates for 25 s at a rate of 0.2 m/s². how much does its velocity increase?​

Answers

Answer: Velocity increase is, 5m/s.

Explanation: Given,

t = 25s, acceleration(a)=0.2m/s², assuming(required but not given) initial velocity = 0m/s.

According to laws of motion,

v = u + at,

v : Final velocity

u : Initial velocity

a : Acceleration

t : Time

Therefore, on putting values, as given, we get

v = 0 + (0.2)(25)

v = 5m/s

Therefore, velocity increase is 5m/s.

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From v=u+ at
V=?
Given
u=0
a=0.2m/second square
t=25second
Therefore ;
Velocity = 5m/s

which nonmetal forms a gas commonly found in our atmosphere? responses cl uppercase c lowercase l n n i i rn

Answers

Acc to the responses given in the query:

Nonmetal forms a gas commonly found in our atmosphere  is chlorine (Cl, element 17)

Many of the nonmetals are gases when they are in their elemental state. Example Hydrogen, Flourine, Oxygen, and Nitrogen. (H2, N2, O2, F,and Cl2.)

Describe a non metal.

A non-metallic chemical element that may create anions, acid oxides, acids, and stable hydrogen compounds. Examples include boron, carbon, and nitrogen. When compared to metals, nonmetals' electrons exhibit different behaviour. Elements with 4, 5, or 7 electrons in their outermost shell are considered non-metals. Non-metals include things like carbon, oxygen, chlorine, etc.

Describe a metal.

Metals are a type of element that typically has 1, 2, or 3 valence electrons. Metals are opaque, glossy elements that are effective heat and electrical conductors. Examples of some metals are sodium, potassium, copper, and others. The majority of metals are ductile and malleable, and they are often.

Hence, acc. to question, Nonmetal forms a gas commonly found in our atmosphere  is chlorine (Cl, element 17) .

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A tennis ball of mass m = 0.071 kg is thrown straight up with an initial speed v0 = 11 m/s. Let the gravitational potential energy be zero at the initial height of the tennis ball.
Randomized Variables
m = 0.071 kg
v0 = 11 m/s
Questions-
Part (a) What is the maximum height, h in meters, the ball reaches?
Part (b) What is the work done by gravity, Wg in Joules, during the ball's flight to its maximum height?

Answers

The maximum height of the ball is approximately 6.096 m and the work done by gravity is -4.95 J.

Given information,

m = 0.071 kg

V₀ = 11 m/s

(a) Finding the maximum height:

The initial kinetic energy of the ball is converted into potential energy at its maximum height.

Initial kinetic energy = Potential energy at maximum height

(1/2)mv₀² = mgh

(1/2)(0.071 kg)(11 m/s)² = (0.071 kg)(9.8 m/s)h

h = (0.5)(11²)/(9.8) ≈ 6.096 m

Part (b) Calculating the work done by gravity:

The work done by gravity during the ball's flight to its maximum height is equal to the change in potential energy. Since the gravitational potential energy is defined as zero at the initial height, the work done by gravity is equal to the negative of the potential energy at the maximum height.

Wg = -mgh

Wg = -0.071 × 9.8 × 6.096

Wg ≈ -4.95 J

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please help me with this!!!

please help me with this!!!

Answers

Answer:

I think the answer is C :)

Explanation:

at what height above the ground must a body of mass 10kg be situated in order to have potential energy equal in value to the kinetic energy possessed by another body of mass 10 kg moving with a velocity of 10 ms-1​

Answers

Answer:

The body must have to be situated at a height 5.10 m.

Explanation:

at what height above the ground must a body of mass 10kg be situated in order to have potential energy

The body of mass 10 kg must be situated at a height of approximately 51.02 meters above the ground.

What is conservation of energy principle?

The conservation of energy principle states that the total energy of a system is constant. In this case, we can equate the potential energy of the first body to the kinetic energy of the second body, as follows:

Potential energy = Kinetic energy

\(mgh = 1/2 mv^2\)

where m is the mass of each body, g is the acceleration due to gravity, h is the height above the ground, and v is the velocity of the second body.

Substituting the given values, we get:

\(10 kg * g * h = 1/2 * 10 kg * (10 m/s)^2\)

Simplifying this equation, we get:

\(h = (1/2 * v^2) / g\\h = (1/2 * 10 m/s * 10 m/s) / 9.81 m/s^2\\h = 51.02 meters\)

Therefore, the body of mass 10 kg must be situated at a height of approximately 51.02 meters above the ground to have potential energy equal in value to the kinetic energy possessed by the other body of mass 10 kg moving with a velocity of 10 m/s.

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A generation is about one-third of a lifetime. approximately how many generations have passed since the year 0?

Answers

A generation is about one-third of a lifetime. Approximately 10^2 generations have passed since the year 0.

According to Guinness world records the most generations alive in a single family has been seven. Mrs. Fitzgerald stated she became "flabbergasted" to end up a super-great-fantastic grandmother.

The most normally accepted fee is four generations in keeping with the century, meaning that tracing backward by way of 10 generations could locate ancestors who lived approximately 250 years ago, inside the middle of the 18th century.

It is believed to have originated with the Iroquois – top notch regulation of the Iroquois – which holds suitable to assume seven generations ahead (about 525 years into the future, that's counted through multiplying the seventy-five years of a median human lifespan through 7) and determine whether or not the decisions they make these days would benefit.

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A group of students were investigating the force of gravity. They began by dropping a foam ball from a height of 3 meters into a bucket of sand. The ball hit the sand in 0.306 seconds. They dropped additional balls of approximately the same diameter, but of different masses. Here is the data they collected. Based on this experiment and the collected data, what would their conclusion be?
A) Gravitational attraction is dependent on the mass of an object.
B) The greater the mass of the object the greater the acceleration due to gravity and the faster it will fall.
C) Mass does not affect the speed of falling objects assuming there is only the force of gravity acting on the objects.
D) Mass becomes a factor affecting the speed of a falling object when the object is dropped a great distance from the surface of the Earth.

Answers

Answer:B

Explanation:

The force of gravitation depends on the mass of the object. As the mass increases, the speed of the falling object also increases because it experience more gravitational pull from earth. Thus, option D is correct.

What is gravitational force?

Gravitational force is a kind of force by which an object attracts other objects into its center of mass. We are all standing on the ground because of the gravitational pull of earth.

Gravitational force is directly proportional to the mass of the objects and inversely proportional to the distance from the surface. Therefore, the force exerted by earth on massive body is greater than that on a light body.

Here, the ball with greater  mass hit the ground with less time compared to the one with less mass. Hence, the mass becomes a factor  affecting the speed of a falling object when the object is dropped a great distance from the surface of the earth. Thus, the massive body will be pulled more by earth.

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Identify each lettered part of the circuit, and explain what each part does.

Help please!!!

Identify each lettered part of the circuit, and explain what each part does.Help please!!!

Answers

The 3 main parts of an electric circuit and their functions are:

Power source - Either electrical or battery, provides the power to the load.

Conducting path - The wires, carry the power from the power source to the load

Load - The device using the electricity such as a computer, light bulb, power saw, etc. More complicated circuits use switches, such as light switches, to control the flow of electricity.

What is an electric circuit?

A circuit that solely has resistors and perfect current and voltage sources is said to be resistive. Analysis of circuits without capacitors and inductors is more difficult than analysis of circuits with those components. A DC circuit will result if the sources are constant (DC) sources. Any arbitrary resistor network's effective resistance and current distribution qualities can be characterised in terms of its graph measurements and geometrical characteristics.An electronic circuit is a network of functional electronic components. Since such networks are typically nonlinear, more sophisticated design and analysis methods are needed.

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What is the mass of an object traveling at 30. m/s if it has 33,750 J of energy?​

Answers

Answer:

\(30 \div 33750 = 0.008888\)

Consider again the company making tires for bikes is concerned about the exact width of their cyclocross tires. The company has a lower specification limit of 22.8 mm and an upper specification limit of 23.2 mm. The standard deviation is 0.15 mm and the mean is 23 mm. a. What is the probability that a tire will be too narrow? b. What is the probability that a tire will be too wide? c. What is the probability that a tire will be defective?

Answers

a. The probability that a tire will be too narrow is approximately 0.0918 or 9.18% , b. The probability that a tire will be too wide is approximately 0.0918 or 9.18% , c. The probability that a tire will be defective is approximately 0.8164 or 81.64%.

In order to determine the probabilities for the width of the cyclocross tires, we can use the concept of standard normal distribution. The mean width of the tires is 23 mm, and the standard deviation is 0.15 mm.

a. To find the probability that a tire will be too narrow (below 22.8 mm), we need to calculate the z-score corresponding to this lower specification limit. The z-score is given by the formula:

z = (x - μ) / σ

where x is the lower specification limit, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:

z = (22.8 - 23) / 0.15 = -1.33

Using a standard normal distribution table or a statistical software, we can find that the probability of a z-score being less than -1.33 is approximately 0.0918. Therefore, the probability that a tire will be too narrow is approximately 0.0918 or 9.18%.

b. Similarly, to find the probability that a tire will be too wide (above 23.2 mm), we calculate the z-score corresponding to the upper specification limit:

z = (23.2 - 23) / 0.15 = 1.33

Using the same table or software, we find that the probability of a z-score being greater than 1.33 is approximately 0.0918. Thus, the probability that a tire will be too wide is approximately 0.0918 or 9.18%.

c. To calculate the probability that a tire will be defective, we need to find the area under the normal curve outside the specification limits. This can be done by subtracting the sum of the probabilities obtained in parts a and b from 1:

P(defective) = 1 - P(narrow) - P(wide)

P(defective) = 1 - 0.0918 - 0.0918

P(defective) = 0.8164

Therefore, the probability that a tire will be defective is approximately 0.8164 or 81.64%.

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a weightless spring scale is attached to two equal weights as shown below. the reading on the scale will be

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When a weightless spring scale is attached to two equal weights, the reading on the scale will be zero. This is because the weights on both sides are balanced, resulting in no net force acting on the scale.



The reason for this is Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In this case, when one weight exerts a downward force on the spring scale, the other weight exerts an upward force of the same magnitude on the scale.

These opposing forces cancel each other out, resulting in a net force of zero. As a result, the spring scale does not experience any deformation and the reading remains at zero.

It is important to note that this only applies when the two weights are equal. If the weights were different, there would be an imbalance in the forces, causing the spring scale to register a non-zero reading.

In summary, when a weightless spring scale is attached to two equal weights, the reading on the scale will be zero due to the balanced forces acting on it.

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