Calculate the wavelength of light that produces its first minimum at an angle of 36.9º when falling on a single slit of width 1.00 μm .
Answers
To solve this problem, we can use the formula for calculating the position of the first minimum in a single-slit diffraction pattern:
sinθ = λ / (wavelength) = (m + 1/2)λ / (width of slit)
where θ is the angle of the first minimum, λ is the wavelength of the light, and m is the order of the minimum (in this case, m = 0).
Plugging in the given values, we get:
sin(36.9º) = λ / (1.00 μm) = (0 + 1/2)λ / (1.00 μm)
Solving for λ, we get:
λ = (1.00 μm) * sin(36.9º) / 0.5
λ ≈ 0.603 μm
Therefore, the wavelength of light that produces its first minimum at an angle of 36.9º when falling on a single slit of width 1.00 μm is approximately 0.603 μm.
To calculate the wavelength of light that produces its first minimum at an angle of 36.9º when falling on a single slit of width 1.00 μm, you can use the single-slit diffraction formula:
sin(θ) = mλ / a
Where θ is the angle of the first minimum (36.9º), m is the order of the minimum (m=1 for the first minimum), λ is the wavelength of the light, and a is the width of the slit (1.00 μm).
Step 1: Convert the angle to radians.
θ = 36.9º × (π/180) = 0.644 radians
Step 2: Plug the values into the formula.
sin(0.644) = 1 × λ / 1.00 μm
Step 3: Solve for the wavelength.
λ = sin(0.644) × 1.00 μm = 0.601 μm
The wavelength of light that produces its first minimum at an angle of 36.9º when falling on a single slit of width 1.00 μm is approximately 0.601 μm.
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Related Questions
calculate the wavelength (in m) of a 650.00 hz sound in air at room temperature and pressure, where the velocity of sound is 344 m/s.
Answers
The wavelength of a 650.00 Hz sound in air at room temperature and pressure, where the velocity of sound is 344 m/s, is approximately 0.529 m.
What is the wavelength of a 650.00 Hz sound in air at room temperature and pressure?Sound waves travel through a medium by creating compressions and rarefactions. The wavelength of a sound wave is the distance between two consecutive points that are in phase, such as two compressions or two rarefactions. To calculate the wavelength, we can use the formula: wavelength = velocity of sound / frequency.
In this case, the frequency of the sound is 650.00 Hz, and the velocity of sound in air at room temperature and pressure is 344 m/s. Plugging these values into the formula, we get: wavelength = 344 m/s / 650.00 Hz = 0.529 m.
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A train is moving to the right. The force of air resistance and the surface friction from the tracks totals 259,800 N . In order for the train to keep moving at a constant velocity, how much forward force is the engine providing?
Answers
The engine is providing a forward force of 259,800 N to keep the train moving at a constant velocity.
What is forward force?
Forward force is the force applied in the direction of motion, which causes an object to move or maintain a constant velocity.
Constant velocity refers to the motion of an object moving in a straight line at a steady speed, without changing its direction. The velocity of the object is constant when its speed and direction remain unchanged over time, regardless of whether the object is moving or stationary.
Since the train is moving at a constant velocity, the net force acting on the train is zero. Therefore, the forward force provided by the engine must be equal in magnitude and opposite in direction to the force of air resistance and surface friction.
So, the magnitude of the forward force provided by the engine is:
Magnitude of forward force = Magnitude of force of air resistance and surface friction
Magnitude of forward force = 259,800 N
Therefore, the engine is providing a forward force of 259,800 N to keep the train moving at a constant velocity.
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What is the momentum of a toy car
with a mass of 100 g moving at 0.5
m/s?
Answers
The toy automobile has a momentum of 0.05 kg*m/s.
How can I determine momentum?p = m v . The equation demonstrates that momentum is directly related to an object's mass (m) and velocity. (v). As a result, an object's momentum increases with increasing mass or velocity. The momentum of a large, swift object is larger than that of a small, slower item.
The formula for calculating an object's momentum (p) is the product of its mass (m) and velocity (v):
p = m * v
Plugging in the values given:
p = 0.1 kg * 0.5 m/s
p = 0.05 kg*m/s.
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What happens to digital signals sent wirelessly over long distances?
A. The signals become stronger the farther they are from the
recipient.
B. The signals change so that data are less likely to be reliable.
C. The signals become weaker as they move away from the source.
D. The signals are more likely to be affected by noise.
Answers
Answer: C!! <3
Explanation: (a p e x)
In wireless transmission, the digital signals become weaker as they move away from the source. Hence, option (C) is correct.
What is wireless transmission of digital signals?Although most people take wireless data transfer for granted, when one stops to think about how it truly works, it does appear miraculous. Of course, there is a scientific explanation that a non-WLAN expert can comprehend.
In essence, the manipulation of radio waves allows for wireless data transmission. These waves are produced by creating electrical pulses in a natural way. Then, in order to transmit sound or data, these radio waves might have their amplitude or frequency altered. This procedure can be enhanced to increase the amount of data that can be communicated and the speed at which it can be transmitted.
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A box is placed on a 30o frictionless incline. What is the acceleration of the box as it slides down the incline
Answers
Answer:
2.78m/s²
Explanation:
Complete question:
A box is placed on a 30° frictionless incline. What is the acceleration of the box as it slides down the incline when the co-efficient of friction is 0.25?
According to Newton's second law of motion:
\(\sum F_x = ma_x\\F_m - F_f = ma_x\\mgsin\theta - \mu mg cos\theta = ma_x\\gsin\theta - \mu g cos\theta = a_x\\\)
Where:
\(\mu\) is the coefficient of friction
g is the acceleration due to gravity
Fm is the moving force acting on the body
Ff is the frictional force
m is the mass of the box
a is the acceleration'
Given
\(\theta = 30^0\\\mu = 0.25\\g = 9.8m/s^2\)
Required
acceleration of the box
Substitute the given parameters into the resulting expression above:
Recall that:
\(gsin\theta - \mu g cos\theta = a_x\\\)
9.8sin30 - 0.25(9.8)cos30 = ax
9.8(0.5) - 0.25(9.8)(0.866) = ax
4.9 - 2.1217 = ax
ax = 2.78m/s²
Hence the acceleration of the box as it slides down the incline is 2.78m/s²
draw a figure of a simple pendulum explain its amplitude and effective length ?
Answers
Answer:
Explanation:
A simple pendulum consists of a mass (usually represented as a small object or bob) attached to a string or rod of negligible mass. The mass is free to swing back and forth under the influence of gravity.
In the figure, the point of suspension is denoted by "O," and the mass (bob) is represented by the small circle. The string or rod is represented by the vertical line connecting the point of suspension to the bob.
Amplitude:
The amplitude of a pendulum refers to the maximum displacement or swing of the bob from its equilibrium position. In the figure, the amplitude can be represented by the angle formed between the vertical position and the position of the bob when it swings to its maximum distance on one side. It is usually denoted by the symbol "A."
Effective Length:
The effective length of a pendulum refers to the distance from the point of suspension to the center of mass of the bob. It represents the distance over which the mass swings back and forth. In the figure, the effective length can be measured as the length of the string or rod from the point of suspension to the center of the bob. It is usually denoted by the symbol "L."
It is important to note that the amplitude and effective length of a simple pendulum affect its period of oscillation (the time taken for one complete swing). The relationship between these parameters and the period can be described by mathematical formulas.
Overall, the simple pendulum is a fundamental concept in physics and provides a simplified model for understanding oscillatory motion and the principles of periodic motion.
Rosa pours a cup of boiling water into a pot of room temperature water. According to the second law of
thermodynamics, what will occur?
O Thermal energy from the room temperature water will continuously flow to the boiling water.
O Thermal energy from the room temperature water will flow to the boiling water until all of the water in the pot is at
a single temperature.
Thermal energy from the boiling water will continuously flow to the room temperature water.
Thermal energy from the boiling water will flow to the room temperature water until all of the water in the pot is at
a single temperature.
Answers
Answer: D. Thermal energy from the boiling water will flow to the room-temperature water until all of the water in the pot is at a single temperature.
Explanation:
This is because thermal energy moves from warmer objects to cooler objects, until they are at the same level of thermal energy or temperature.
Answer:
Answer is D
Explanation:
Edge 2020
Which property of sugar makes it different from white crystalline sand?
Answers
Answer:
The property of sugar which makes it different from sand is that sugar can dissolve in water. Explanation: however the power of dissolving of sand is not present. This is due to the presence of interaction between sugar and water.
Explanation:
I hope that was useful
A soda can rolls off a table top and lands 0. 225 m away 0. 416 s later. How tall was the table
Answers
According to the given statement ,we can use the equations of motion and the concept of free fall. Therefore, the height of the table is approximately 0.085 meters.
To determine the height of the table, we can use the equations of motion and the concept of free fall.
First, let's identify the known values:
- The distance the soda can rolled horizontally, 0.225 m.
- The time it took for the soda can to land, 0.416 s.
- The acceleration due to gravity, which is approximately 9.8 m/s².
Since the can was rolling horizontally, we can ignore any initial vertical velocity and consider only the vertical motion of the can.
Using the equation of motion for vertical displacement:
s = ut + (1/2)at²
Where:
- s is the vertical displacement
- u is the initial vertical velocity (which is zero in this case)
- t is the time
- a is the acceleration due to gravity
In this case, we want to find the height of the table, which is the vertical displacement. So we can rearrange the equation to solve for s:
s = (1/2)at²
Plugging in the values:
s = (1/2) * 9.8 m/s² * (0.416 s)²
Simplifying:
s = (1/2) * 9.8 m/s² * 0.173056 s²
s = 0.085 m
Therefore, the height of the table is approximately 0.085 meters.
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Explain the differences between Specific Latent Heat and Specific Heat Capacity.
Answers
Answer:
Specific latent heat means, the amount of heat energy needed to convert a phase completely to another phase of a unit mass of a substance. Heat capacity is dependent on the amount of substance. Specific heat or specific heat capacity (s) is the heat capacity which is independent of the amount of substances.
Specific Heat Capacity involves temperature change, while Specific Latent Heat is for phase change without temperature change. Both measure energy requirements in different contexts.
Explicit Intensity Limit (SHC) and Explicit Idle Intensity serve unmistakable jobs in portraying substances' warm ways of behaving. SHC alludes to the intensity energy expected to build the temperature of a unit mass by one degree Celsius, mirroring the substance's capacity to store heat during temperature changes.
Then again, Explicit Inactive Intensity relates to the intensity energy expected for a substance to go through a stage progress, like liquefying or vaporization, without changing its temperature. It implies the energy important to defeat intermolecular powers during these progressions in state at a steady temperature.
Generally, SHC is significant while examining temperature varieties and energy stockpiling, while Explicit Idle Intensity becomes critical during stage shifts, where substances retain or deliver energy to progress between strong, fluid, or vaporous states while keeping a consistent temperature.
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how is geothermal energy trapped? state a draw back of this kind of energy.
Answers
Answer:
Geothermal energy can be trapped using geothermal plants that utilizes steam escaping from the earth surface to make electricity.
The limitations include :
depletion of the geothermal sourcehigh costs of investments required for geothermal systemsExplanation:
Geothermal energy originates in form of heat/steam escaping from the inner parts of the earth surface. The steam trapped is converted to electricity through turbines. The hot water pumped by heat pumps can be used to heat homes or for heating purposes in industries.
The limitations of geothermal energy are high initial capital costs for installing the systems, depletion of geothermal sites after sometime, environmental concerns due to greenhouse gases emissions and land requirements for geothermal projects.
In a democracy how is rule of law regarded
Answers
Answer:
It is respected as leaders are accountable to the people. The rule of law within a democratic country will dictate what actions is considered wrong and punishable to do in that country. This will prevent people from harming and violating each other to get what they want and form a stable and safe society
Which waveform should be used as the input in subtractive synthesis to obtain a clarinet sound?
Answers
A "single-reed instrument" waveform should be used as the input in subtractive synthesis to obtain a clarinet sound.
Subtractive synthesis involves starting with a complex waveform and then filtering out certain frequencies to create a desired sound. To create a clarinet sound, a waveform that simulates the sound of a single reed instrument, such as a clarinet or saxophone, should be used as the input. This waveform can then be filtered using subtractive synthesis techniques to remove unwanted frequencies and shape the sound to closely resemble the timbre of a clarinet. Other parameters, such as envelope and modulation settings, can also be adjusted to further refine the sound.
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A uniform plank of mass 10kg and length 10m rests on two supports, A and B as shown. A boy of weight 500N stands at a distance of 2m from A. Find the reaction forces U¹ and U² at the supports A and B respectively
Answers
Answer:
U² = 142.86 N
U¹ = 357.14 N
Explanation:
Taking summation of the moment about point A, we get the following equilibrium equation: (taking clockwise direction as positive)
\(W(2\ m) - U^2(7\ m) = 0\)
where,
W = weight of boy = 500 N
U² = reaction ay B = ?
Therefore,
\((500\ N)(2\ m)-(U^2)(7\ m)=0\\U^2=\frac{1000\ Nm}{7\ m}\\\)
U² = 142.86 N
Now, taking summation of forces on the plank. Taking upward direction as positive, for equilibrium position:
\(W-U^1-U^2=0\\500\ N - 142.86\ N = U^1\\\)
U¹ = 357.14 N
Due to our ozone layer, ultraviolet astronomy must be done from space, true or false?
Answers
True, due to the protective nature of the ozone layer and the absorption of UV radiation, conducting ultraviolet astronomy from space is necessary to gather accurate and detailed data about celestial objects and phenomena emitting UV light.
The ozone layer plays a crucial role in protecting the Earth's surface from harmful ultraviolet (UV) radiation. It absorbs a significant portion of the Sun's UV rays, preventing them from reaching the surface and potentially causing damage to living organisms.
As a result, to observe and study ultraviolet astronomy, which involves the detection and analysis of celestial objects and phenomena emitting UV radiation, observations must be conducted from space. By observing from space, astronomers can bypass the Earth's atmosphere, including the ozone layer, and directly capture the UV light from celestial sources.
UV astronomy satellites and telescopes, such as the Hubble Space Telescope and the International Ultraviolet Explorer (IUE), have been specifically designed and deployed to conduct observations in the ultraviolet spectrum. These instruments are situated above the Earth's atmosphere, enabling them to capture and analyze UV radiation without interference from atmospheric absorption.
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Which statement best describes the motion of the box when the forces pull on the box
Answers
the required net force acting on the box is the difference between the two forces, which is 7 N to the left.
What is force?Force is a physical quantity that describes the interaction between two objects. It is a vector quantity, meaning it has both magnitude and direction.
The net force acting on the box is the difference between the two forces, which is 14 N - 7 N = 7 N to the left.
According to Newton's second law of motion, an object will move in the direction of the net force acting on it, so in this case, the box will move to the left. The magnitude of the acceleration of the box will be proportional to the magnitude of the net force, so the greater the net force, the greater the acceleration of the box.
Thus, the required net force acting on the box is the difference between the two forces, which is 7 N to the left.
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A wire whose resistance is R is stretched so that its length is tripled while its volume remains unchanged.
Determine the resistance of the stretched wire.
Express your answer in terms of R and appropriate constant
Answers
When a wire is stretched so that its length is tripled, its cross-sectional area decreases by a factor of 3, since the volume of the wire remains the same.
The resistance of a wire is given by the equation:
R = ρ L / A
where R is the resistance, ρ is the resistivity of the wire (a constant that depends on the material), L is the length of the wire, and A is the cross-sectional area of the wire.
If the length of the wire is tripled while its volume remains constant, the cross-sectional area of the wire must decrease by a factor of 3. Therefore, the new cross-sectional area of the wire is 1/3 of its original value.
Let A' be the new cross-sectional area of the wire. Then :--
A' = A / 3
Substituting this expression for A' into the equation for resistance gives:--
R' = ρ (3L) / (A/3) = 9ρL / A
Therefore, the resistance of the stretched wire is 9 times the resistance of the original wire. In terms of the original resistance R, we have:--
R' = 9R
So the resistance of the stretched wire is 9 times the resistance of the original wire.
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How is the law of conservation of momentum be displayed Rugby
The speech should be 3–5 minutes in length.
The speech should consist of three parts: an introduction of the topic, a body (including the
demonstration), and a conclusion to wrap it all up.
Include information about the following:
Momentum and impulse
How momentum and impulse are present in the sport
How conservation of energy is present within the sport
Will give brainliest
Answers
Today, I want to talk to you about the law of conservation of momentum and how it applies to the sport of Rugby.
First, let's define momentum and impulse. Momentum is a measure of the motion of an object, calculated by multiplying its mass and velocity. Impulse is the change in momentum that results from a force acting on an object for a certain amount of time.
Now, let's think about how momentum and impulse are present in Rugby. During a Rugby match, players are constantly running, tackling, and passing the ball. Each of these actions involves a transfer of momentum from one player to another. When a player runs with the ball, for example, they have momentum that is transferred to the ground. When they tackle an opposing player, they apply an impulse that changes the momentum of that player.
The conservation of energy is also present within Rugby. This law states that the total energy of a closed system remains constant over time. In Rugby, the players and the ball make up a closed system. The energy of the system is conserved as players pass the ball back and forth, run with the ball, or tackle each other.
Now, I want to demonstrate how the law of conservation of momentum works in Rugby. I have here a small Rugby ball and two equally weighted balls, one blue and one red. If I drop the Rugby ball onto the blue ball, the momentum of the Rugby ball is transferred to the blue ball, causing it to move. If I drop the Rugby ball onto the red ball, the momentum is transferred to the red ball, causing it to move instead.
This demonstration shows how the momentum of one object can be transferred to another object when they collide. In Rugby, this happens when players tackle each other or when they pass the ball.
In conclusion, the law of conservation of momentum plays a crucial role in the sport of Rugby. As players run, tackle, and pass the ball, they transfer momentum from one object to another. The conservation of energy is also present within the sport, as the total energy of the closed system of players and ball remains constant. Thank you for listening.
For an ideal gas of a given mass, if the pressure remains the same and the volume increases:_________
Answers
The temperature of the gas will increase due to the direct relationship between volume and temperature in accordance with Charles's Law.
According to the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. When the pressure of a given mass of gas is kept constant and the volume increases, we can observe the effect on temperature.
In this scenario, the gas is considered ideal, meaning it follows certain assumptions such as negligible intermolecular forces and volume occupied by gas particles. According to Charles's Law, which states that the volume of an ideal gas is directly proportional to its temperature (assuming pressure remains constant), if the volume increases, the temperature will also increase.
This relationship can be understood by considering the behavior of gas particles. As the volume expands, the gas particles have more space to move around, resulting in an increase in their kinetic energy. This increase in kinetic energy corresponds to an increase in temperature, as temperature is a measure of the average kinetic energy of gas particles.
In conclusion, for an ideal gas of a given mass, if the pressure remains constant and the volume increases, the temperature of the gas will also increase according to Charles's Law.
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What are the resources? assuming the order size is 1 dozen, what is the capacity of each resource?
Answers
The following ingredients are required for the cookie making process:
combining ingredients in a food processorUsing cookie tray, place dough.oven for use in baking cookiescans used for packing biscuitsduration of participantsAssuming a 12-unit order, the capacity of each resource is as follows:
Up to three dozen cookies can be processed in one batch using a food processor (6 minutes to wash and mix).Cookie Tray: Each tray holds a dozen cookies and takes two minutes to prepare.Oven: Bakes one tray of cookies at a time (10 minutes total baking time).Each box holds a dozen cookies and takes two minutes to pack.It depends on how quickly and effectively everyone involved works.Learn more about capacity, here:
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Your question is incomplete, most probably the complete question is:
Mike’s Cookie Company You and your roommate are preparing to start Mike’s Cookie Company in your on-campus apartment. The company will provide fresh cookies to starving students late at night. You need to evaluate the preliminary design for the company’s production process to figure out how many orders to accept and how effectively your time, and that of your room mate, will be utilized. BUSINESS CONCEPT Your idea is to bake fresh cookies to order, using any combination of ingredients that they buyer wants. The cookies will be ready for pickup at your apartment within an hour. Several factors will set you apart from competing products such as store-bought cookies. First, your cookies will be completely fresh. You will not bake any cookies before receiving the order; therefore, the buyer will be getting cookies that are literally hot out of the oven. Second, you will have a variety of ingredients available to add to the basic dough, including chocolate chips, M&M’s, chopped Heath bars, coconut, walnuts, and raisins. Buyers will telephone in their orders and specify which of these ingredients they want in their cookies. You guarantee completely fresh cookies. In short, you will have the freshest, most exotic cookies anywhere, available right on campus. THE PRODCUTION PROCESS Baking cookies is simple: mix all the ingredients in a food processor; spoon out the cookie dough onto a tray; put the cookies into the oven; bake them; take the tray of cookies out of the oven; let the cookies cool; and, finally, take the cookies off the tray and carefully pack them in a box. You and your roommate already own all the necessary capital equipment: one food processor, cookie trays, and spoons. Your apartment has a small oven that will hold one tray at a time. Your landlord pays for all the electricity. The variable costs, therefore, are merely the cost of the ingredients (estimated to be $0.60/dozen), the cost of the box in which the cookies are packed ($0.10 per box; each box holds a dozen cookies), and your time (what value do you place on your time?). A detailed examination of the production process, which specifies how long each of the steps will take, follows. The first step is to take an order, which your roommate has figured out how to do quickly and with 100 percent accuracy. (Actually, you and your roommate devised a method using the campus electronic mail system to accept orders and to inform customers when their orders will be ready for pickup. Because this runs automatically on your personal computer, it does not take any of your time.) Therefore, this step will be ignored in further analysis. You and your roommate have timed the necessary physical operations. The first physical production step is to wash out the mixing bowl from the previous batch, add all of the ingredients, and mix them in your food processor. The mixing bowls hold ingredients for up to 3 dozen cookies. You then dish up the cookies, one dozen at a time, onto a cookie tray. These activities take six minutes for the washing and mixing steps, regardless of how many cookies are being made in the batch. The next step, performed by your roommate, is to put the cookies in the oven and set the thermostat and timer, which takes about one minute. The cookies bake for the next nine minutes. So total baking time is 10 minutes, during the first minute of which your roommate is busy setting the oven. Because the oven holds only one tray, a second dozen takes an additional 10 minutes to bake. Your roommate also performs the last steps of the process by first removing the cookies from the oven and putting them aside to cool for 5 minutes, then carefully packing them in a box and accepting payment. Removing the cookies from the oven takes only a negligible amount of time, but it must be done promptly. It takes two minutes to pack each dozen and about one minute to accept payment for the order. That is the process for producing cookies by the dozen in Mike’s Cookie Company.
What are the resources? Assuming the order size is 1 dozen, what is the capacity of each resource?
A boy is pushing on a heavy door, trying to slide it open. His friend stands behind him and helps him push.
How have the forces changed?
There will be less friction.
The net force applied will increase.
The applied force will not change.
The net force will decrease.
Answers
Answer:
I think the net force will increase
Answer:
2 one
Explanation:
What is the stopping potential if the incident light has a wavelength of 180nm?
Answers
The photoelectric effect's cutoff wavelength is 295.98 nm. (b) The stopping potential is 2.70625 V if the incident light has a wavelength of 180 nm.
What is the formula for calculating stopping potential?How to get KEmax=|eV0|, the equation for a photoelectron's stopping voltage. Hint: The stopping voltage (or stopping potential) refers to the voltage difference required to stop electrons from passing between plates and creating a flow in the photoelectric analysis.
How do you determine stopping potential photoelectric?Derivation of the Photoelectric Effect and the Stopping Potential Formula
According to Einstein's photoelectric equation
(0.6+2.14)eV
1242eVnm
=454nm
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Use the table to answer the question.
A
B
formed by oscillating source
formed by vibration of charged particles
requires a medium to transmit energy
can transmit energy through a vacuum
examples include sound waves
examples include light waves
What should column A be titled?
(1 point)
seismic waves
mechanical waves
surface waves
electromagnetic waves
Answers
Answer:
Mechanical Waves
Explanation:
I took the practice
A 1. 5-kilogram cart initially moves at 2. 0 meters
per second. It is brought to rest by a constant net
force in 0. 30 second. What is the magnitude of
the net force?
(1) 0. 40 N (3) 10. N
(2) 0. 90 N (4) 15 N
Answers
The initial velocity of a 1.5-kilogram cart is 2.0 meters per second. It is brought to a stop in 0.30 seconds by a constant net force.To solve this problem, you must first recall the formula F = ma, where F is force, m is mass, and a is acceleration.
We can rearrange the formula to solve for force as follows:F = maWhere F is force, m is mass, and a is acceleration.We can use the formula to solve for force since we know the mass of the cart and its acceleration.First, we must calculate the acceleration, which can be found using the formula a = Δv / Δt, where a is acceleration, Δv is the change in velocity, and Δt is the time taken. We can substitute the values that we know into the equation:
a = Δv / Δt= (0 m/s - 2 m/s) / 0.30 sa = -2/0.3a = -6.67 m/s²
We obtained a negative acceleration because the velocity of the cart decreases during the time interval of 0.30 seconds.To determine the net force on the cart, we can now use the formula F = ma:F = ma= 1.5 kg x -6.67 m/s²= -10.0 N (approximately)Therefore, the magnitude of the net force on the cart is 10 N. Answer (3) is correct.
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(Newton's Law of Cooling): The mathematical formulation of Newton's empirical law of cooling/warming of an object is given by the linear first-order differential equation
dt
dT
=k(T−T
s
), where k is a constant of proportionality, T(t) is the temperature of the object at any time t≥0, and T
s
is the surrounding environmental temeperature, that is, the temperature of the medium around the object. (i). Assuming that T
s
is constant, find the temeperature of the object as a function of time if T(0)=T
0
. (ii). Then what is the temepretauer of the object after 5 minutes?
Answers
Newton's Law of Cooling is described by the first-order linear differential equation dt/dT = k(T - Ts), where T(t) is the temperature of the object at time t, Ts is the surrounding environmental temperature, and k is the constant of proportionality.
The temperature of an object, governed by Newton's Law of Cooling
(i) To find the temperature of the object as a function of time, we first solve the differential equation dt/dT = k(T - Ts). This is a separable differential equation, and the solution can be obtained by rearranging and integrating:
dt/dT = k(T - Ts)
dt = k(T - Ts) dT
∫ dt = ∫ k(T - Ts) dT
t = k * ∫ (T - Ts) dT
t = k * (T^2/2 - Ts*T) + C
Now, we apply the initial condition T(0) = T0. At t=0, the temperature of the object is T0:
T(0) = T0
k * (\(T0^2\)/2 - Ts*T0) + C = T0
C = T0 - k * (\(T0^2\)/2 - Ts*T0)
C = T0 - k * (\(T0^2\)- 2 * Ts * T0) / 2
C = T0 - k * (\(T0^2\) - 2 * Ts * T0) / 2
So, the equation becomes:
t = k * (\(T^2\)/2 - Ts*T) + (T0 - k * (\(T0^2\)- 2 * Ts * T0) / 2)
(ii) Now, we can find the temperature of the object after 5 minutes (t = 5 minutes). We'll use the initial condition T(0) = T0 and the formula obtained in part (i):
t = 5 minutes = 5/60 hours = 1/12 hours
T(t) = Ts + (T0 - Ts) * exp(-kt)
T(1/12) = Ts + (T0 - Ts) * exp(-k * (1/12))
This equation gives us the temperature of the object after 5 minutes, considering the given initial temperature T0 and the surrounding environmental temperature Ts.
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why is fundamental unit called derived unit ?
Answers
Since fundamental units are elementary in nature and cannot be reduced further, so it can not be reduced further, so it cannot be expressed in other units
Compare two sound waves, a and b. the frequency of wave a is one third that of wave b. how does the period of wave a compare with the period of wave b?
Answers
If the frequency of wave 'a' is one-third of that of wave 'b', then the time period of wave a will be three times as compared to the time period of wave 'b'
The frequency of a wave is inversely proportional to its time period, and it is defined as the number of oscillations per second.
which means F ∝ 1/T
If we remove the proportionality we will need to add a constant.
which makes the relation F = k/T
Time period is defined as the total time taken by a wave to complete one oscillation.
Now as per the data we have,
let the frequency of wave b be 'F', and the time period of b be 'T'
\(F_{a}\) = F/3 and \(T_{a}\) = T/3
Arranging the data into the formula we get
\(\frac{F_{a}}{F_{b}} = \frac{T_{b}}{T_{a}}\)
Which gives us \(T_{b}\) = 3\(T_{a}\)
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A 3. 2 kg cannon ball at rest is fired from a cannon. The cannon ball leaves the cannon with a speed of 6. 0 m/s. Determine the force provided by the cannon if it
takes 0. 55 seconds to launch the cannon ball
0 10,6 N
0 27,8 N
0 34 9 N
0 159 N
Answers
The force provided by the cannon to launch a 3.2 kg cannonball at rest with a speed of 6.0 m/s in 0.55 seconds is 34.88 N.
To determine the force, we'll first need to find the acceleration of the cannonball using the formula:
final velocity (vf) = initial velocity (vi) + acceleration (a) * time (t).
Then, we'll use Newton's second law of motion (F = m * a) to find the force.
Step 1: Calculate the acceleration.
Given: vi = 0 m/s (cannonball at rest), vf = 6.0 m/s, t = 0.55 seconds
Formula: vf = vi + a * t
Rearranging the formula: a = (vf - vi) / t
Step 2: Plug in the given values.
a = (6.0 m/s - 0 m/s) / 0.55 seconds
a = 6.0 m/s / 0.55 seconds
a ≈ 10.9 m/s²
Step 3: Calculate the force using Newton's second law of motion.
Given: mass (m) = 3.2 kg, acceleration (a) ≈ 10.9 m/s²
Formula: F = m * a
Step 4: Plug in the given values.
F = 3.2 kg * 10.9 m/s²
F ≈ 34.88N
Thus, the force provided by the cannon is approximately 34.88 N.
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what do you think explains the pattern of planet density in the solar system
Answers
Answer:
If density is greater, the object sinks. Saturn is mainly composed of the lightest two gases known, hydrogen and helium. It is the only planet in our solar system whose density is less than water
Explanation:
Planet density are uneven they all have different density.
What is density?Mass per unit of volume is referred to as density. Although the Latin letter D can also be used, the sign most frequently used for density is. Mass divided by volume is how density is mathematically defined:
If density is greater, the object sinks. Saturn is mainly composed of the lightest two gases known, hydrogen and helium. It is the only planet in our solar system whose density is less than water
Planet density are uneven they all have different density.
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the apparent weight of a body wholly immersed in water is 32N and its weight in 96N and calculate volume of the body
Answers
Answer:
0.0065 m³
Explanation:
Apparent weight = weight − buoyancy
32 N = 96 N − (1000 kg/m³) (9.8 m/s²) V
V = 0.0065 m³