A wave on a string is traveling to the right. At this instant, the motion of the piece of string marked with a dot is up and down. The piece of string marked with a dot will experience a wave motion of up and down when a wave on a string travels to the right.
This is because a transverse wave moves perpendicularly to its direction of propagation or the direction in which the wave travels. When a wave travels along a string, the string moves in the direction of the wave. The motion of the string is transverse to the direction of wave propagation.
At any given point on the string, the wave moves up and down. Therefore, the piece of string marked with a dot will move up and down when a wave on a string travels to the right. In summary, when a wave on a string travels to the right, the motion of the piece of string marked with a dot is up and down.
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Which galaxy helps show scientists how stars and star cluster are formed
how do air masses contribute to the formation of air fronts?
Air masses contribute to the formation of air fronts because air masses are large bodies of air that have similar characteristics in terms of temperature, humidity, and stability.
When two air masses with different characteristics come into contact, they form a boundary known as an air front. The characteristics of the two air masses determine the type of air front that forms.
There are four types of air fronts: cold fronts, warm fronts, stationary fronts, and occluded fronts.
Cold fronts occur when a cold air mass displaces a warm air mass, causing the warm air to rise and cool, which leads to cloud formation and precipitation. Warm fronts occur when a warm air mass displaces a cold air mass, causing the warm air to rise gradually over the cold air, leading to gradual cloud formation and precipitation. Stationary fronts occur when two air masses with different characteristics meet but do not move, leading to prolonged periods of precipitation. Occluded fronts occur when a cold front overtakes a warm front and lifts the warm air mass off the ground, leading to cloud formation and precipitation.Air masses play a significant role in the formation of air fronts because they determine the characteristics of the air mass that will form at the boundary between the two air masses. This, in turn, determines the type of air front that will form and the type of weather that will result. For example, a cold, dry air mass coming into contact with a warm, moist air mass will likely result in a cold front and a period of heavy precipitation.
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Heat transfer between two substances is affected by specific heat and the
O chemical composition of the substances.
O state of matter of the substances at room temperature.
othermal equilibrium of the substances.
O amount of time and area of physical contact between the substances.
The correct answer is D. Amount of time and area of physical contact between the substances.
Explanation:
Heat transfer refers to the flow of thermal energy or heat between two or more objects. This process involves multiple factors and implies heat from the hottest object goes to the coldest one until there is an equilibrium. To begin, heat transfer depends on the amount of thermal energy in the objects because objects must have a different amount of thermal energy for heat to flow.
Besides this, the amount of energy that flows depends on the time and the contact between the substances of objects. Indeed, objects need to be in contact or close to each other for heat to transfer, and the time needs to be enough for the process to occur. For example, if you place a pot over the fire just for a few seconds it is likely the heat transferred is minimal, which does not occur if you leave the pot more time. At the same time if the pot is in close contact with fire more heat will be transferred.-
Answer:
the answer is D on edginuity.
Explanation:
how do i multiply 9.6 by 3/2
Solve the given problem as
\(\begin{gathered} x=9.6\times\frac{3}{2} \\ =9.6\times1.5 \\ =14.4 \end{gathered}\)8\%) Problem 9: The maximum horizontal distance that Jean can throw a baseball is 58.2 m : D Assuming she can throw with the same initial speed at all launch angles, to what maximum height (measured in meters above the release point) will the ball rise if she throws it straight upward?
The maximum height the ball will rise if Jean throws it straight upward is 0 meters above the release point.
To find the maximum height the ball will rise if Jean throws it straight upward, we can use the concept of projectile motion. The key idea is that the vertical component of the initial velocity is zero at the highest point of the trajectory.
Given that the maximum horizontal distance is 58.2 m, we can assume that the initial speed (also known as the magnitude of the initial velocity) is constant for all launch angles.
Let's denote the maximum height as "h" (measured in meters above the release point). At the highest point of the trajectory, the vertical velocity component will be zero.
Using the equation for the vertical displacement in projectile motion, we have:
Vertical displacement = (Initial vertical velocity * time) + (0.5 * acceleration due to gravity * time^2)
Since the ball is thrown straight upward, the initial vertical velocity is positive (upward). The acceleration due to gravity is negative (downward). Therefore, the equation becomes:
h = (0 * t) + (0.5 * (-9.8 m/s^2) * t^2)
Simplifying the equation, we have:
h = -4.9t^2
To find the time it takes for the ball to reach its highest point, we need to use the equation for the vertical component of the velocity:
Vertical velocity = Initial vertical velocity + (acceleration due to gravity * time)
Since the vertical velocity is zero at the highest point, we have:
0 = 0 + (-9.8 m/s^2) * t
Solving for t, we find:
t = 0
This means that at the highest point of the trajectory, the ball has been in the air for 0 seconds.
Substituting t = 0 into the equation for h, we find:
h = -4.9(0)^2
h = 0
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When Jean throws the ball straight upward, it will not rise to any height above the release point. It will only reach the same level as the release point. To determine the maximum height the ball will reach when thrown straight upward, we need to use the concept of projectile motion. When the ball is thrown straight upward, it experiences a vertical motion under the influence of gravity.
First, we need to find the initial vertical velocity of the ball. Since the ball is thrown straight upward, the initial vertical velocity is equal to zero.
Next, we need to find the time it takes for the ball to reach its maximum height. We can use the equation:
t = (final velocity - initial velocity) / acceleration
The final velocity is zero, the initial velocity is zero, and the acceleration due to gravity is -9.8 m/s^2 (taking downward as negative). Therefore, the time taken to reach the maximum height is zero.
Now, we can use the equation for vertical displacement:
Δy = (initial velocity * t) + (0.5 * acceleration * t^2)
Substituting the values, we get:
Δy = (0 * 0) + (0.5 * -9.8 * 0^2)
=> Δy = 0
This means that the maximum height the ball will rise is 0 meters above the release point. The ball will reach the same level from where it was thrown, but not higher.
In conclusion, when Jean throws the ball straight upward, it will not rise to any height above the release point. It will only reach the same level as the release point.
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a flashlight emits 2.9 w of light. as the light leaves the flashlight in one direction, a reaction force is exerted on the flashlight in the opposite direction.
When a flashlight emits 2.9 W of light, it is also simultaneously producing a reaction force in the opposite direction. This reaction force is produced due to Newton's Third Law of Motion: This Law states that for every action there is an equal and opposite reaction.
In this situation, the action is producing light in one direction and the reaction is the production of an equal and opposite force in the opposite direction. This opposition force results from the momentum of the light particles leaving the flashlight in one direction.
The magnitude of this reaction force is determined by the amount of energy being produced, which in this case is 2.9 Watts. This reaction force aids in propelling the flashlight forward, and could be used in the design of light-based propulsion systems.
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Paco was driving his scooter west with an initial velocity of 4 m/s. He accelerates at 0. 5 m/s2 for 30 seconds. What is his final velocity? 2 m/s 8 m/s 19 m/s 60 m/s.
Answer:
Final velocity = 19 m/s
Explanation:
Initial velocity (u) = 4 m/s
Acceleration (a) = 0.5 m/s²
Time (t) = 30 s
Final velocity (v) = ?
In this question, you must use the formula:
v = u + at
Substitute the values into the formula.
v = 4 + (0.5 × 30)
v = 4 + 15
v = 19 m/s
Why is copper particularly useful in electrical circuits?
a very good conductor of heat
support burning
very reactive metal
A concave makeup mirror has a radius of curvature equal to 40 cm. How far away must your face be from the mirror so that your virtual image is twice the size of your actual face?.
Answer: 10 cm
Explanation:
\($$The focal length is: \\ \\ \begin{aligned}f &=\frac{R}{2} \\&=-\frac{46}{2} \\f &=-20 \mathrm{~cm}\end{aligned}$$\)
\($$ Since the image is virtual: \\ \\ :\begin{aligned}\frac{v}{u} &=m \\\Rightarrow & v=m u \\\Rightarrow &v=2 u\end{aligned}$$\)
\($$ Using: \\ \\ \begin{aligned}&\frac{1}{l}=\frac{1}{v}+\frac{1}{u} \\&\frac{1}{20}=-\frac{1}{2 u}+\frac{1}{u} \\&\frac{1}{2 u}=\frac{1}{-20} \\&\Rightarrow u=-10 \\&\therefore u=10 \mathrm{~cm}\end{aligned}$$\)
Therefore, you must be 10 cm away from the mirror so that your virtual image is twice the size of your actual face
_____ is a measure of the force of gravity pulling down on an object. it is measured in newtons (N), the common unit for measuring force
By definition, Weight is a measure of the force of gravity pulling down on an object. it is measured in newtons (N), the common unit for measuring force.
Weight is called the action exerted by the force of gravity on the body.
The mass (amount of matter that a body contains) of an object will always be the same, no matter where it is located. Instead, the weight of the object will vary according to the force of gravity acting on it.
The formula that allows you to calculate the weight of any body is:
P = m×g
where:
P = weight measured in N. m = mass measured in kg. g = acceleration of gravity measured in m/s². The acceleration of gravity g is the same for all objects that fall due to gravitational attraction, regardless of their size or composition. For example, as an approximate value on Earth, g = 9.8 m/s².
Then, the weight of an object is the force of gravity on the object, that is, the weight will vary according to the force of gravity that acts on it. So the correct answer is:
Weight is a measure of the force of gravity pulling down on an object. it is measured in newtons (N), the common unit for measuring force.
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brainly.com/question/15566515?referrer=searchResults brainly.com/question/15271930?referrer=searchResults brainly.com/question/4735812?referrer=searchResultsAñadir mayor cantidad de gas a un tanque, la presión interna aumentará debido a que al incrementar el número de partículas,
Translation-Adding more gas to a tank, the internal pressure will increase because by increasing the number of particles?
Adding more gas to a tank, the internal pressure will increase because by increasing the number of particles increases collision between particles.
The frequency of collisions between gas particles and the container walls determines the gas pressure. The number of collisions and consequently the pressure will rise if we fill the container with more gas particles.
The Avogadro Principle (V N) states the frequency of collisions with the container walls must increase as the number of gas particles increases. The pressure of the gas then rises as a result of this. Pressure rises as the number of gas molecules rises while the volume of the container stays the same. Gas pressure rises as container volume decreases. The pressure rises as the temperature of a gas inside a rigid container rises.
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A crate (m = 100 kg) is pulled across a floor to the right with a rope horizontal to the floor. The tension in the rope is 400 N. The coefficient of kinetic friction is 0.4. What is the acceleration? If started from rest, what was the velocity after 3 seconds?
Answer:
Explanation:
Force of friction acting on the crate = μ mg
= .4 x 100 x 9.8 = 392 N
Net force acting on the crate = 400 -392 N = 8 N .
acceleration = net force / mass
= 8 N / 100 kg
= .08 m /s²
velocity after 3 s.
v = u + at
= 0 + .08 x 3
= 0.24 m/s .
1. A ball is moving at 6 m/s and has a momentum of 24 kg-m/s. What is the ball's mass?
Answer:
4.0 kg
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Table 15.3 in the textbook gives an estimate for the sound intensity of a whisper at 1.0 m. What is the sound intensity of a whisper at a distance of 2.5 m , in W/m2?
What is the corresponding sound intensity in dB?
The corresponding sound intensity in dB is 12 dB. The sound intensity of a whisper at a distance of 2.5 m is calculated using the formula: I₁/I₂ = (r₂/r₁)²
What is sound intensity?Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.
I₁/I₂ = (r₂/r₁)²
Where I₁ is the sound intensity at a distance of 1.0 m,
I₂ is the sound intensity at a distance of 2.5 m,
r₁ is the distance from the source to the listener at 1.0 m and
r₂ is the distance from the source to the listener at 2.5 m.
sound intensity of a whisper at 1.0 m = 10^-10 W/m²
Formula to find the sound intensity of a whisper at 2.5 m:
I₁/I₂ = (r₂/r₁)²I₂
= I₁ (r₁/r₂)²I₂
= 10^-10 × (1/2.5)²I₂
= 10^-10 × (0.4)²I₂
= 10^-10 × 0.16I₂
= 1.6 × 10^-11 W/m²
The corresponding sound intensity in dB:
β = 10 log (I/I₀).
Where I₀ is the threshold of hearing (10^-12 W/m²)
β = 10 log (I/I₀)
β = 10 log (1.6 × 10^-11 / 10^-12)
β = 10 log (16)β = 10 × 1.2041
β = 12.041 ≈ 12 dB
Therefore, the corresponding sound intensity in dB is 12 dB.
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Which statement about velocity is true?
Answer: velocity is the study of how fast an object changes its place, or is displaced.
Explanation: An example would be how fast a basketball reaches the other side of a gym, the acceleration and speed are measured and calculated to find velocity
n airplane that flies at 100 km/h in a 100 km/h hurricane crosswind (i.e., the wind is blowing perpendicular to the direction the plane is pointing) has a ground speed of:
A) 200 km/h
B) 0 km/h
C) 141 km/h
D) 100km/h
The ground speed of the airplane is approximately 141 km/h. Option C is the correct answer.
The ground speed of an airplane flying in a crosswind can be determined using vector addition.
The airplane's ground speed is the vector sum of its airspeed (100 km/h) and the velocity of the crosswind (100 km/h). Since the wind is blowing perpendicular to the direction the plane is pointing, we can use the Pythagorean theorem to find the magnitude of the ground speed.
Ground speed = √(airspeed² + crosswind velocity²)
Ground speed = √(100² + 100²)
Ground speed = √(10000 + 10000)
Ground speed = √20000
Ground speed ≈ 141.4 km/h
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A positively charged light metal ball is suspended between two oppositely charged metal plates on an insulating thread as shown below. After being charged once, the plates are disconnected from the battery. Describe the behavior of the ball. Please use 3 content related sentences. (
Answer:
The positive ball would go first to the negatively charged plate.
Explanation:
After which, it would hold a more negative charge. Due to the negative charge, it would travel towards the positive plate. Thereby, it would transfer negative electrons to the positive plate once more. In doing so, it would transfer positive protons to the negative plate. After which, it would hold more negative electrons and be drawn towards the positive plate once more. The Process would continue until the once-positive and once-negative became neutral ( and were discharged.) Additionally, the ball hanging on the insulator thread would also be neutral and discharged.
What are the 7 polyatomic ions?
Polyatomic ions are ions (atoms or molecules that have a net electrical charge) that consist of multiple atoms bonded together.
There are many different types of Polyatomic ions, but the seven most commonly encountered in introductory chemistry are:
Ammonium (NH4+)
Nitrate (NO3-)
Acetate (C2H3O2-)
Carbonate (CO32-)
Sulfate (SO42-)
Hydroxide (OH-)
Phosphate (PO43-)
These polyatomic ions play important roles in many chemical reactions and processes, such as acid-base reactions, precipitation reactions, and metabolic processes. For example, nitrates are commonly used as fertilizers, hydroxides are used in the production of soaps and detergents, and carbonates are used in the production of cement.
It's important to note that polyatomic ions are not simple molecules, as the atoms within them are held together by covalent bonds, not ionic bonds. This means that they have specific properties, such as charge and molecular weight, that are different from those of simple ions.
In conclusion, the seven most commonly encountered polyatomic ions in introductory chemistry are ammonium, nitrate, acetate, carbonate, sulfate, hydroxide, and phosphate. These ions play important roles in many chemical reactions and processes, and have specific properties that are different from those of simple ions.
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Why is the potential difference higher between any two points on a single E-field line than between two points the same distance apart on different E-field lines
While moving over a separate electric field line, however, has a non-zero value. If the test charge is transferred in a direction perpendicular to E, no work is done and the electric potential does not change. A smooth equipotential surface characterizes every such path.
Why is the potential difference higher between any two points on a single E-field line than between two points the same distance apart on different E-field lines?Generally, The equation of the potential difference is mathematically given as
\(V = Ed cos \theta.\)
Where
\(\theta=Angle\)
E=electric field
d= the varing distance
When the charge to be tested is transferred via an electric field line. Since =0, the maximum possible velocity (Vmax) is calculated.
In conclusion, Since no work is done when the test charge is shifted in a direction perpendicular to E, the electric potential does not shift in this case. Any such route is a smooth equipotential surface.
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You need to use your cell phone, which broadcasts an 833 MHz signal, but you're in an alley between two massive, radio-wave-absorbing buildings that have only a 15 m space between them.
What is the angular width, in degrees, of the electromagnetic wave after it emerges from between the buildings?
The electromagnetic wave's angular width after it emerges from between the buildings is 2.14 degrees. The reason is that the angular width of the electromagnetic wave emerging from between the buildings depends on the wavelength of the wave and the distance between the buildings.
The formula for calculating the angular width of the electromagnetic wave emerging from between the buildings is given as: `θ = 2λ / d`Where `θ` is the angular width, `λ` is the wavelength of the wave, and `d` is the distance between the buildings.In the question, the frequency of the signal is given as 833 MHz.
We can calculate the wavelength of the wave by using the formula `λ = c / f`, where `c` is the speed of light and `f` is the frequency of the wave. So the wavelength of the wave is:λ = c / f= 3 x 10^8 m/s / 833 x 10^6 Hz= 0.36 mNow, the distance between the buildings is given as 15 m. Using the formula above, we can calculate the angular width of the wave as:θ = 2λ / d= 2 x 0.36 m / 15 m= 0.048 radiansConverting from radians to degrees, we get:θ = 0.048 x (180 / π)= 2.14 degreesTherefore, the electromagnetic wave's angular width after it emerges from between the buildings is 2.14 degrees.
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a) Determine the mass of a student in kg who weighs 135 lbs. using the conversion factor 1 kg = 2.2 lbs. Round your answer to the nearest tenth. b) Convert 5.3 milligrams into grams.
Answer:
Below
Explanation:
135 lbs * 1 kg/2.2 lb = ~ 61.4 kg
there are 1000 mg in each gram
5.3 mg * 1 gm / 1000 mg = .0053 g
what is a projectile motion
Answer:
Projectile motion is the motion of an object projected vertically upward into the air and moving under the influence of gravity.
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\(\pmb{\underline{Projectile~motion}}\)
If an object given it's initial velocity and travel freely under the gravity only, This type of motion is called as Projectile motion.
Which is a characteristic of all waves
Waves share common characteristics such as wave motion, amplitude, wavelength, frequency, wave speed, and interactions with boundaries. These properties are fundamental to understanding the behavior and properties of various types of waves, including sound waves, electromagnetic waves, water waves, and seismic waves.
A characteristic of all waves is their ability to transfer energy without transferring matter. This fundamental property distinguishes waves from other forms of energy transfer, such as the movement of objects in a solid or the flow of fluids. Waves propagate through various mediums or through empty space, carrying energy from one location to another.
Waves exhibit several common characteristics, including:
1. Wave Motion: Waves involve the transfer of energy through periodic oscillations or vibrations. The particles or fields involved in the wave motion move back and forth around their equilibrium positions, transmitting the energy along the wave path.
2. Amplitude: The amplitude of a wave represents the maximum displacement or disturbance from the equilibrium position. It corresponds to the intensity or strength of the wave and can be measured as the maximum height, displacement, or value of a wave.
3. Wavelength: The wavelength of a wave is the distance between two consecutive points with the same phase or the distance covered by one complete cycle of the wave. It is commonly represented by the symbol λ and is usually measured in meters or other appropriate units.
4. Frequency: The frequency of a wave refers to the number of complete oscillations or cycles that occur per unit of time. It is denoted by the symbol f and is measured in hertz (Hz). The frequency and wavelength of a wave are inversely related and are related to the speed of the wave through the equation v = fλ, where v represents the wave velocity.
5. Wave Speed: The wave speed represents the rate at which a wave travels through a medium or through empty space. It is the product of the wavelength and the frequency of the wave and is usually denoted by the symbol v. The speed of a wave depends on the properties of the medium through which it travels.
6. Reflection, Refraction, and Diffraction: Waves can undergo interactions with boundaries or obstacles, resulting in phenomena such as reflection (bouncing off a surface), refraction (bending when passing through different mediums), and diffraction (spreading out or bending around obstacles).
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cruising far from the sun, we notice that the sun's apparent brightness has dimmed to 10 watts per square meter. we know that the apparent brightness at a distance of 1au is 1000 watts per square meter. how far from the sun are we?
100 watts x 10 apparent brightness = 100 au. Hence we are 100 au far from the sun.
Distance is a numerical and sometimes qualitative measure of how far apart an object or point is. In physics and everyday use, the distance may refer to physical length or an estimate based on other criteria. Distance is the overall movement of an object, regardless of direction. The distance can be defined as the distance an object has traveled regardless of its start or end point.
Distance is defined as the magnitude or amount of displacement between two positions. Note that the distance between two points is not the same as the distance traveled between the two points. The traveled distance is the sum of the traveled distances between the two positions. Distance traveled is not a vector.
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As A Plant Grows, it gains mass Which of the following provides the most matter that a plant uses for its growth?
As a plant grows, what provides the most matter that a plant uses for its growth is carbon from the air.
The correct option is C.
What are the requirements for the growth of a plant?
The requirements for the growth of a plant are those things that a plant needs in order to grow.
In order to thrive, plants require nutrients such as carbon from air, water, light, warmth, and air. One of these criteria may prevent a plant from growing or possibly cause it to perish. For instance, a plant left in a dark environment may grow tall and spindly in search of light before deteriorating and dying.
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Complete question:
As A Plant Grows, it gains mass Which of the following provides the most matter that a plant uses for its growth?
Minerals and nutrients from the soil
Light from the sun
Carbon from the air
why it is important to have a regular
supervision of the weight and measurement and in the market
A force of 24 N will stretch a rubber band 12 cm(0.12 m) Assuming that Hooke's faw applies, how lar will a 20 - N lorce stretch the rubber band? How much wokk does if take fo stretch the nubber band this far? How lar will a 20.N torce stretch the rubber band? B) (Sirnplify your answed) How mach work does ia take la stretch the rubber band this far? (Stmplify your answer)
Work required to stretch the rubber band by 0.10 meters will be negative, indicating that work needs to be done against the force applied to stretch the rubber band.
To determine how much the rubber band will stretch under a 20 N force and the work required to stretch it, we need to apply Hooke's Law. Hooke's Law states that the force applied to a spring or elastic material is directly proportional to the displacement it undergoes.
We can set up a proportion to find the stretch under Force 2:
(F1 / S1) = (F2 / S2)
Substituting the given values:
(24 N / 0.12 m) = (20 N / S2)
To find S2, we can rearrange the equation:
S2 = (20 N * 0.12 m) / 24 N
Simplifying:
S2 = 0.10 m
Therefore, a 20 N force will stretch the rubber band by 0.10 meters.
Now, let's calculate the work required to stretch the rubber band this far. The work (W) can be calculated using the formula:
W = (1/2) * k * (S2^2 - S1^2)
Where k is the spring constant.
However, we don't have the spring constant (k) given in the problem. So, we cannot determine the exact work without that information.
But, if we assume that the rubber band behaves as a linear spring and Hooke's Law applies, we can simplify the equation. Hooke's Law states that the force applied to a spring is equal to the spring constant (k) multiplied by the displacement (S).
F = k * S
Rearranging the equation:
S = F / k
Since the stretch (S) is directly proportional to the force (F), we can approximate the work required by assuming a constant k value:
W ≈ (1/2) * k * (S2^2 - S1^2)
W ≈ (1/2) * k * [(0.10 m)^2 - (0.12 m)^2]
Simplifying:
W ≈ (1/2) * k * (0.01 m^2 - 0.0144 m^2)
W ≈ (1/2) * k * (-0.0044 m^2)
Without the exact value of the spring constant, we cannot calculate the work precisely. However, we can still conclude that the work required to stretch the rubber band by 0.10 meters will be negative, indicating that work needs to be done against the force applied to stretch the rubber band.
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Monochromatic light from a distant source is incident on a sif 0.710 mm wide. On a screen 2.03 m away, the distance from the central maximum of the diffraction pattem to the first minimum is measured to be 1.35 mm For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Single-slit diffraction. Part A Calculate the wavelength of the ight. Express your answer in meters. X Incorrect; Try Again; One attempt remaining
Width of slit, a = 0.710 mm = 0.710 × 10⁻³ m Distance from the slit to screen, L = 2.03 m Distance between the central maximum and the first minimum, y = 1.35 mm = 1.35 × 10⁻³ m We know that for a single slit of width a, the intensity of light as a function of the angle θ from the central maximum is given by I (θ) = Iₒ sinc²(πa sinθ/λ)
Where Iₒ = Intensity of the light at the center of the diffraction patternλ = Wavelength of lightθ = Angle from the central maximum sin c = Sine cardinal function For the first minimum, we have θ = λ/a Putting this in the equation for I(θ), we get I (minimum) = Iₒ (πa/λ)²This is the equation for the minimum intensity of light in the diffraction pattern.
Now, using the given value of y, we can find θ sinθ = y/L = (1.35 × 10⁻³)/2.03 = 6.65 × 10⁻⁴Using the value of θ, we can find the wavelength asλ = a sinθ= (0.710 × 10⁻³) × (6.65 × 10⁻⁴)= 4.72 × 10⁻⁷ m Therefore, the answer isλ = 4.72 × 10⁻⁷ m. The explanation of the calculation has been provided above.
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An electric field of 4.0 muV/m is induced at a point 2.0 cm from the axis of a long solenoid (radius = 3.0 cm, 800 turns/m). At what rate is the current in the solenoid changing at this instant?
The answer should be 0.40 A/s
The rate at which the current in the solenoid is changing at this instant is 4.4 A/s.
To determine the rate at which the current in the solenoid is changing, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (emf) is equal to the negative rate of change of magnetic flux through a circuit. In this case, the solenoid acts as a circuit.
The induced electromotive force (emf) is given by:
emf = -dΦ/dt
Where:
emf is the induced electromotive force,
dΦ/dt is the rate of change of magnetic flux.
For a long solenoid, the magnetic flux (Φ) can be calculated as:
Φ = B * A
Where:
B is the magnetic field strength,
A is the area of the solenoid.
The magnetic field strength inside a solenoid is given by:
B = μ₀ * n * I
Where:
μ₀ is the permeability of free space (4π × 10^-7 T·m/A),
n is the number of turns per unit length (turns/m),
I is the current flowing through the solenoid.
Let's calculate the magnetic field strength (B) inside the solenoid:
B = μ₀ × n × I
= (4π × 10^-7 T·m/A) × (800 turns/m) × I
= (3.1831 × 10^-4) × I T
The area (A) of the solenoid can be calculated using the formula for the area of a circle:
A = π × r^2
Where:
r is the radius of the solenoid.
Let's calculate the area (A) of the solenoid:
A = π × r^2
= π × (0.03 m)^2
= 0.002827 m^2
Now, substitute the values of B and A into the formula for magnetic flux:
Φ = B × A
= (3.1831 × 10^-4) × I T × 0.002827 m^2
= 9.0 × 10^-7 × I Wb
Next, we differentiate the magnetic flux (Φ) with respect to time (t) to find the rate of change of magnetic flux:
dΦ/dt = d/dt (9.0 × 10^-7 × I)
= 9.0 × 10^-7 × dI/dt Wb/s
Finally, we can equate the rate of change of magnetic flux (dΦ/dt) to the induced electromotive force (emf) given in the problem statement:
emf = -dΦ/dt
= -9.0 × 10^-7 × dI/dt Wb/s
Given that the induced electromotive force (emf) is 4.0 μV/m = 4.0 × 10^-6 V/m, we can solve for the rate of change of current (dI/dt):
4.0 × 10^-6 V/m = -9.0 × 10^-7 × dI/dt
\(\frac{dI}{dt} = \frac{-(4.0) (10^-6 V/m)}{(9.0) (10^-7)} = -4.4 A/s\)
Therefore, the rate at which the current in the solenoid is changing at this instant is 4.4 A/s.
For more questions on solenoid
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can ya pls answer dis rq!
Answer:
I don't even know can u tell me how to ask questions