When an excited electron from a higher energy level returns to a lower energy level by releasing energy in the form of light, a bright-line spectrum of sodium is created.
What is energy?In physics, energy is the quantitative quality that is imparted to a body or a physical system and is visible in the form of heat and light. The law of conservation of energy holds that energy can be transformed in form but cannot be generated or destroyed. Energy is defined by scientists as the ability to do tasks. People have learnt how to convert energy from one form to another and then utilize it to conduct labor, which makes modern civilization feasible. Energy is the ability to do tasks. It can take the form of a potential, kinetic, thermal, electrical, chemical, nuclear, or other energy.
Here,
The sodium bright-line spectrum is formed when an excited electron from a higher energy level returns to the lower energy level by releasing energy in the form of light, resulting in a sodium bright-light spectrum.
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Drag the correct arrow to the diagram.
The diagram shows a series of volcanic islands and a hot spot. Determine the direction of movement of the tectonic plate that helped form the islands.
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ocean
series of volcanic islands
motion of plate
hot
spot
Convergent boundaries occur when two plates move in the opposite direction until they collide and create mountains and volcanoes. In the image, the arrows direction is horizontal and oposite to each other.
What are convergent boundaries?
Collision area between two plates. The collition might occur between,
Two oceanic platesOne oceanic plate with a continental one, Two continental plates.When two oceanic plates collide, magma rises to the surface by crevices, creating volcanic arches. In these boundaries occur vertical movements and might originate from protruding areas. There is compressional stress between plates.
In the image, the arrows direction is horizontal and oposite to each other.
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Explain the dynamic characteristics of instruments
Answer:
speed of response and response time , lag , fidelity,and dynamic errors are the dynamic characteristics of instruments.
Need the answers can someone help me please
An update can be caused by changes to props or state. These methods are called in the following order when a component is being re-rendered.
what is the co ordinates of initial and terminal points?
The length of the arrow indicates the magnitude of the vector, and the direction of the arrow is the direction of the vector. The point at the tail of the arrow is called the initial point of the vector, and the tip of the arrow is called the terminal point.Vectors are identified by magnitude, or the length of the line, and direction, represented by the arrowhead pointing toward the terminal point. The position vector has an initial point at (0,0) and is identified by its terminal point ⟨a,b⟩.Zero vector A vector whose initial point and terminal point both lie at the origin; denoted by 0 = 〈0, 0〉.
The terminal point p(x, y) on the unit circle determined by the giving value of t = -3π/4 is determined to be P (1/√2, -1/√2 ).To learn more about coordinates refers to:
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if the bar has mass m , find the distance d that the bar must move along the rails from rest to attain speed v .
If the bar has mass m , find the distance d that the bar must move along the rails from rest to attain speed v is v²m/2ILB
Velocity MeaningAccording to the velocity meaning, it can be defined as the rate of change of the object’s position with respect to a frame of reference and time. It might sound complicated, but velocity is basically speeding in a specific direction. It is a vector quantity, which means we need both magnitude (speed) and direction to define velocity. The SI unit of it is metre per second (ms-1). If there is a change in magnitude or the direction of the velocity of a body, then it is said to be accelerating.
Initial and Final VelocityInitial velocity describes how fast an object travels when gravity first applies force on the object. On the other hand, the final velocity is a vector quantity that measures the speed and direction of a moving body after it has reached its maximum acceleration.
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What term describes speeding up,
slowing down, and changing
direction?
A. acceleration
B. neither
C. speed
Answer:A: Acceleration
Explanation: I hope this helps!
using conversions and data in the chapter, determine the number of hydrogen atoms required to obtain 1.0 kg of hydrogen. a hydrogen atom has a mass of 1.0 u.
The number of hydrogen atoms required to obtain 1.0 kg of hydrogen is 6.022 x 10^30.
1 kilogram is equal to 1000 grams and 1 atomic mass unit (u) is defined as one twelfth of the mass of a carbon-12 atom, which is 1.6605 x 10^-27 kg.
So, 1 u = 1.6605 x 10^-27 kg
Therefore, 1.0 kg of hydrogen is equal to 1.0 x 10^3 / 1.6605 x 10^-27 = 6.022 x 10^30 hydrogen atoms.
So, the number of hydrogen atoms required to obtain 1.0 kg of hydrogen is 6.022 x 10^30.
A conversion factor converts one unit to another by utilizing your knowledge of unit relationships. For example, if you know that there are 2.54 centimeters in an inch (or 2.2 pounds in a kilogram or 101.3 kilopascals in an atmosphere), converting between those units becomes simple algebra. It is critical to understand some common temperature, size, and pressure conversions, as well as metric prefixes.
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two lightweight metal spheres are suspended near each other from insulating threads. one sphere has a net charge; the other sphere has no net charge. the spheres will exert no net electrostatic corce on each other. attract each other. repel each other. do any of these things depending on the sign of the net charge on the one sphere.
From insulating threads, two thin metal spheres are suspended close to one another. One sphere has a net charge while the other sphere has no net charge. The spheres will exert no net electrostatic force on each other. The correct option is A.
The uncharged balloon in an experiment advances toward the charged rod. The net charge from the charged sphere distributes onto both evenly, so they are each charged with same sign. The positive and negative charges neutralise, any residual charge is spread evenly. So, both spheres are charged with same sign. If there is no residual charge, both remain neutral.
Suppose the sphere is positively charged, the neutrally charged sphere becomes is negatively charged. The other sphere is polarised by the positively charged one, with a negative charge on the side that is nearest to the first sphere. Now the second sphere moves towards the first sphere.
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(a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in Figure P19.2, as shown. (b) Repeat part (a), assuming the moving particle is an electron
As the curved path is confined to the XY plane the component of magnitude.
Find the direction of the force on a proton ?
we can see the direction of magnetic force on the proton is towards right and on electron is towards left. Hence, the magnitude of force on electron and proton under the same conditions is equal but the direction of magnetic force is opposite due to opposite signs of these charges.The right hand rule states that: to determine the direction of the magnetic force on a positive moving charge, point your right thumb in the direction of the velocity (v), your index finger in the direction of the magnetic field (B), and your middle finger will point in the direction of the the resulting magnetic force .Electron will move anticlockwise and proton moves clockwise.We need the direction angle of F, i.e. the counterclockwise angle F makes with the positive x axis. Hence, the magnitude is 658 N and the direction angle is 233.9°.
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Elastic and (for our purposes) Nearly Elastic Collisions:
Select all that apply
conserve the momentum of each object
conserve the total kinetic energy of the system
conserve the total momenta of the system
conserve the kinetic energy of each object
For elastic collision: conserve the total kinetic energy of the system and conserve the total momenta of the system.
option B and C.
What is elastic collision?
This is a type of collision in which the two objects move with a different velocities after the collision.
In elastic collision both momentum and kinetic energy is conserved unlike the inelastic collision where only momentum is conserved and the kinetic energy of the system is not conserved.
Thus, we can conclude that in an isolated system during elastic or inelastic collision the sum of the initial momentum of the system is equal to the sum of the final momentum of the system.
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A train starts from rest and speeds up for 15 minutes until it reaches a constant velocity of 100 miles/hour. It stays at this speed for half an hour. Then it slows down for another 15 minutes until it is still. Which of the following correctly describes the position vs time graph of the train’s journey?
A: The first 15 minutes is a curve that is concave upward, the middle portion is a straight line with slope 100 miles/hour, and the last portion is a concave downward curve.
B: The first 15 minutes is a curve that is concave downward, the middle portion is a straight line with slope 100 miles/hour, and the last portion is a concave upward curve.
C: The first 15 minutes is a curve that is concave upward, the middle portion is a straight line with slope zero, and the last portion is a concave downward curve.
D: The first 15 minutes is a curve that is concave downward, the middle portion is a straight line with slope zero, and the last portion is a concave upward curve.
Answer:
The correct answer is: B: The first 15 minutes is a curve that is concave downward, the middle portion is a straight line with slope 100 miles/hour, and the last portion is a concave upward curve.
Explanation:
The first 15 minutes of the journey, the train is accelerating from rest to reach a constant velocity of 100 miles/hour. The position vs time graph of this portion of the journey would be a curve that is concave downward, as the acceleration is positive and the velocity is increasing.
The middle portion of the journey, the train is moving at a constant velocity of 100 miles/hour. The position vs time graph of this portion of the journey would be a straight line with slope 100 miles/hour, as the velocity is constant.
The last 15 minutes of the journey, the train is slowing down to come to a stop. The position vs time graph of this portion of the journey would be a curve that is concave upward, as the acceleration is negative and the velocity is decreasing.
a block is at rest on a disk that spins about its center, as shown. a student must determine the centripetal acceleration of the block when the block spins with the disk as a result of the force of static friction. what measuring devices, when used together, could be used to determine the centripetal acceleration of the block? select two answers.
The student can use a meterstick and stopwatch to measure the centripetal acceleration.
Acceleration of an object on a circular orbit. Velocity is a vector quantity (that is, it has both magnitude, velocity, and direction), so as an object moves along a circular path, its direction changes constantly, and so does its velocity, causing acceleration. increase. Centripetal acceleration is defined as the property of motion of a body through a circular orbit. An object that moves in a circle and has an acceleration vector pointing to the center of the circle is called centripetal acceleration. Spinning a ball on an overhead string causes it to experience centripetal acceleration.
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I NEED HELP AND PLS BE QUICK
A positively charged object hovers a few
centimeters above a positively charged
platform. The object is not moving because
the repulsive force of the platform balances
the object's weight. What will happen if the
object is pushed down and then released?
Answer:It will shoot back up
Explanation:It is not going to change from positive to negative because you pushed it! It will stay positive and repel away from the positive.
a phenomenon is modeled using n dimensional variables with k primary dimensions. the number of non-dimensional variables would be question 2 options: a. k b. n c. n-k d. n k
A phenomenon is modeled using n dimensional variables with k primary dimensions, so the number of non-dimensional variables would be option c. n-k.
Measurements with quantitative data and distinct sizes are referred to as dimensional variables. Variables with dimensions and yet no constant value are called dimensional variables. Non-dimensional variables, on the other hand, are things that lack both dimensions and a variable value.
Quantities with dimensions but no constant value are called dimensional variables. Non-dimensional variables, on the other side, do not have the value of any variable or even the dimensions. Physical quantities with changing values but no dimensions are typically considered to be dimensionless variables.
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A 24kg is accelerated by a constant force up a frictionless plane that makes an angle of 37° with the horizontal. Starting from rest at the bottom, it covers a distance of 18 metres in 3 seconds. What is the average power required to accomplish the process
WHY do stars turn hydrogen into heavier elements such as helium, beryllium etc?
Answer: Stars turn hydrogen into heavier elements through a process called nuclear fusion. This occurs when the nuclei of hydrogen atoms come together under intense heat and pressure, releasing a large amount of energy in the form of light and heat. This process is triggered by the intense gravity at the core of a star and continues until the star runs out of fuel and eventually dies.
Explanation:
A boy slides down a hill on a sled (total mass of 32 kg) and coasts onto a flat plain with a speed of 5.5 m/s. Friction between the sled and the snow exerts an average force of magnitude 32 N on the sled. How far (in m) does the sled travel before stopping? (Note: First, find the acceleration of the boy using Unit Two material, then use this to compute the distance using Unit One material.)
The distance which the sled which is weighing 32 kg and has a speed of 5.5 m/s will travel before stopping is 15.1 meters.
What is Friction?
Friction is the force which resists the sliding or rolling of one solid object over the another object. Frictional forces, such as the one traction needed to walk without slipping, may be beneficial, however they also present a great measure of opposition to the motion of object.
In this problem, we are to utilize the kinematic equation in the form;
Vf² = Vi² + 2aD
where, Vi is the initial velocity, Vf is the final velocity, a is the acceleration and D is the distance traveled.
Given,
Mass of boy and sled (m) = 32 kg
Speed of boy and sled (Vi) = 5.5 m/s
Average force (F) = 32 N
Using the equation for Newton's Second Law of Motion with the friction force opposing the motion:
Fs = ma
a = Fs/ m
a = -32/ 32
a = -1m/s²
Plugging the values in the obtained acceleration into the kinematic equation, we get:
(0)² = (5.5)² + 2(-1)D
D = (5.5)²/ 2
D = 30.25/ 2
D = 15.1 meters
The distance which the sled will travel before stopping is 15.1 meters.
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do your graphs show the trends you expected based on what you know about absorbance and transmittance using a spectrophotometer? why or why not? (2 pts.)
It depends on the data. If the data matches what is expected based on the known properties of absorbance and transmittance using a spectrophotometer, then the graphs will show the expected trends.
If the data does not match what is expected, then the graphs may not show the expected trends.
A diagram or pictorial representation that organises the depiction of data or values is known as a graph. The relationships between two or more items are frequently represented by the points on a graph.
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Shannon has a mass of 60 kg and steps into an elevator on the top floor of a building with her bathroom scale. The elevator accelerates towards the lobby, 15 floors below, at 3 m/s2. When Shannon steps onto the scale, what does it read (in N)?
When Shannon's elevator (from the previous problem) reaches its cruising speed of 10 m/s downward, what is the reading on the scale (in N)?
Mass of woman: 60 kg , Mass of elevator and scale: 815 kg and Starting from rest means Vo = 0 m/s Force applied is 9410 Newtons in the positive y direction (making up positive y and down negative y) g = -9.8 m/s^2.
What is Force?Fy = m*a
Solution: Two forces acting on the elevator: Force of gravity against the force of the tension in the cable. Therefore: Sigma Fy = m*a Force of cable on the elevator + Force of gravity = (mass of the woman + mass of the elevator + mass of the scale)*Acceleration of the elevator.
9410 N + (mass of elevator + mass of woman + mass of scale)*(-9.8 m/s^2) = (mass of elevator + mass of woman + mass of scale) * a 9410 N + (815 kg + 60 kg)* (-9.8 m/s^2) = (815 kg + 60 kg)*a 9410 N + (-8575 N) = 875*a 835 N = 875 kg*a 835 N / 875 kg = a a = 0.95 m/s^2.
Therefore, Mass of woman: 60 kg , Mass of elevator and scale: 815 kg and Starting from rest means Vo = 0 m/s Force applied is 9410 Newtons in the positive y direction (making up positive y and down negative y) g = -9.8 m/s^2.
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A cart travels 4 meters east and then 4 meters north.
Determine the magnitude of the cartâs resultant displacement
Answer:
Displacement = √(4^2 + 4^2) = √(16 + 16) = √32 = 4√2 meters
Explanation:
To determine the magnitude of the cart's resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse (the displacement) of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
We can imagine the cart's displacement as the hypotenuse of a right triangle, where one side is 4 meters (the eastward displacement) and the other side is 4 meters (the northward displacement). Using the Pythagorean theorem, we can calculate the magnitude of the displacement as follows:
Displacement = √(4^2 + 4^2) = √(16 + 16) = √32 = 4√2 meters
So the magnitude of the cart's resultant displacement is 4√2 meters.
suppose a car's velocity is to the left, and its acceleration is to the right. which of the following describes this car's motion?
This car is undergoing negative acceleration, meaning that its velocity is decreasing as it moves to the left. The car's motion can be described as decelerating to the left.
What is acceleration?Acceleration is the rate of change of velocity. It is the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction. Acceleration can be caused by a number of forces, such as gravity, friction, and applied forces. In one dimension, acceleration is the change in velocity divided by the time it takes for the change to occur. In two dimensions, acceleration is the rate at which an object's velocity vector changes in magnitude and/or direction. Acceleration can be positive, negative, or zero. Positive acceleration occurs when an object speeds up, negative acceleration occurs when an object slows down, and zero acceleration occurs when an object's velocity remains constant.
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A glass cube of index 1.5 lies on a table. A coin is embedded in the glass cube near the surface of the table. When you look at the coin from above, which of the following is true?
The coin appears below the bottom of the cube.
The coin apparent location is the same as it’s real location.
The coin appears to be closer to the top of the cube.
Due to the refraction of light when we look the coin embedded in a glass cube it appears to be closer at the top of the cube.
Refraction is the bending of a light ray when it goes from an optically rare medium to an optically denser medium. It is determined by the refractive index. Refractive index of a substance is the ratio the speed of light in a vacuum to the speed of light in the substance.
So refractive index 1.5 tells that the speed of light in the glass will be 1.5 times slower than the speed of light in vacuum. That's why it will gets bent towards the normal when it will pass through the glass. So the coin will appear closer to the top surface of the cube.
Hence the option C is correct.
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based on this, which of the following materials would your state need in large quantities to expand future biopower production?
In order to expand future biopower production, states would need to acquire large quantities of biomass materials such as wood and agricultural crops like corn, switchgrass, and other grasses.
These materials are used in the production of biofuels, which is a type of renewable energy generated from organic matter. Biomass materials are typically converted into liquid fuels such as ethanol or biodiesel for use in vehicles, or burned for electricity generation. Additionally, states may need to acquire large quantities of organic waste materials like animal manure and food scraps for use in anaerobic digestion systems that generate biogas. Biogas is a type of renewable energy that can be used to produce electricity or heat.
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Matt is pouring grain into a bucket to feed the new horse. Due to the friction between pieces of grain as they rub against each other during the pouring process, one piece of grain picks up a charge of 3.0 E−15 C and another piece of grain picks up a charge of 3.5 E−15 C. What is the electric force between them if the pieces of grain are 4.0 cm apart? Please answer in a steo-by-step manner.
Use Coulomb's law: F = k q₁ q₂ / r² F = (9×10⁹) (6.0×10⁻¹⁰) (2.3×10⁻¹⁵) / (0.02 m)². F = 3.1×10⁻¹¹
What is Columb's law?The Coulomb's inverse-square law, sometimes known as Coulomb's law, is an experimental physical principle that measures the force exerted between two electrically charged particles that are stationary.
The rule was known earlier, but Charles-Augustin de Coulomb, a French physicist, published it for the first time in 1785, giving it its name. Because it made it possible to debate the amount of electric charge in a meaningful way, Coulomb's law was crucial to the development of the theory of electromagnetic, perhaps even its beginning point.
According to the rule, the electrostatic attraction or repulsion between two point charges has a magnitude that is directly proportional to the product of the charges'.
Therefore, Use Coulomb's law: F = k q₁ q₂ / r² F = (9×10⁹) (6.0×10⁻¹⁰) (2.3×10⁻¹⁵) / (0.02 m)². F = 3.1×10⁻¹¹.
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The electrostatic force between these two charges can be determined using Coulomb's law. The electric force acting here is
What is Coulomb's law ?According to Coulomb's law of force, the electrostatic force between two charges separated by a distance of r is given as follows:
Fc = Ke q1 q2 /r²
where Ke = 8.9 × 10⁹ Nm²/C²
Given the charge of grain = 3.0 × 10⁻¹⁵ C
charge of another grain piece = 3.5 × 10⁻¹⁵ C
distance r = 4 cm = 0.04 m
Then Fc = 8.9 × 10⁹ Nm²/C² ( 3.0 × 10⁻¹⁵ C ) ( 3.5 × 10⁻¹⁵ C)/(0.04 m)² = 5.8 × 10⁻¹⁷N
Therefore, the net electric force acting between the charged grains is 5.8 × 10⁻¹⁷N.
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a 0.15kg baseball travel at a rate of 35m/s and collide and stick to a catcher milt and hand. the milt and hand are intally at rest and have a mass of 10kg. what is the final volcity of the mitt,hand,and ball?
Answer:
4.57 m/s
Explanation:
mass of baseball (m1) = 0.15kg
velocity of baseball (v1) = 35 m/s
mass of milt and hand (m2) = 10kg
velocity of mitt and hand (v2) = 0 m/s
final velocity of mitt, hand, and ball = vf
Conservation of momentum since they are colliding and sticking together after collision:
Pb = Pa
m1v1 + m2v2 = (m1+m2)vf
plug in:
(0.15kg)(35m/s) + (10kg)(0m/s) = (0.15kg + 10kg)vf
5.25 = 1.15vf
vf = 4.57 m/s
What is the coefficient of static friction if it takes 44 N of force to move a box that weighs 86 N?
Answer:
0.5
Explanation:
The coefficient of static friction (μs) can be calculated using the formula:Friction Force = μs x Normal ForceWhere Normal force is the weight of the object = 86 NThe force required to move the box is 44 N, which is the Friction forceSo,44 N = μs x 86 NTherefore, the coefficient of static friction (μs) = 44 N / 86 N = 0.5The coefficient of static friction between the box and the surface is 0.5.
suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit (in dollars) of the product according to the following formula. y= 32/ (3p+1 (-2/5)) , p>0 (a) What is the rate of change in sales volume when the price is $20? (Round your answer to three decimal places.)
(b) Interpret your answer to part (a). (Round your answer to the nearest whole number.)
If the price increases $1, the sales volume will decrease by _____ units.
When the price is set at $20, the rate of change in sales volume is -0.086. The number of units sold will fall by 86.
What is volume?Volume is defined as the space occupied by an item inside the confines of three-dimensional space. It is also known as the object's capacity. Volume is a measurement of an object's capacity. For example, the capacity of a cup is 100 ml if it can carry 100 ml of water up to the brim. Volume is also the amount of space filled by a three-dimensional object. Volume and mass are the two fundamental qualities of matter. Volume is simply the amount of space occupied by a thing. There are several methods for measuring volume depending on the physical condition of an item.
Here,
dy/dp = -174/5 [3p + 1]^-7/5
Substitute p = 20 in the above equation, we get
dy/dp = -0.086
(b) The sales volume will decrease by 86 units.
The rate of change in sales volume when the price is $20 is -0.086. The sales volume will decrease by 86 units.
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it is a scale which intensifies 10 times over as it increase by a value?
It is not a proper scale to measure which intensifies 10 times over as it increases by value. The scale which have a short and regular intervals are more accurate.
What are measuring scales ?There are various kinds of measuring gadgets which can be used in appropriate occasions. For example in a chemical lab, there are graduated beakers, measuring vessels, electronic balances, burettes, pipettes etc.
Each type of measuring vessels are used in different situations. In all cases, measuring devices with small regular interval of scale is very easy to use and helps for an accurate measurement especially in the case small volume samples.
Therefore, it is not a proper scale which intensifies 10 times over as it increase by a value. We can't take the intermediate values properly with this scale.
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Water flows inside a horizontal pipe so that at the beginning of the pipe its velocity vi is lower than the velocity at the end of the pipe v2. Compare the pressures at the beginning P1 and at the end of the pipe P2. Pi < P2 P1 = P2 P1 > P2 Not enough information.
The pressure at the beginning and the end of the pipe cannot be determined without additional information.
What is velocity?Velocity is a vector quantity that measures the rate of change of an object’s position in a given direction. It is the rate of displacement over time, or the speed at which an object is moving. Velocity is the speed of an object in a particular direction. It is measured in meters per second (m/s) or kilometers per hour (km/h). Velocity is a combination of both speed and direction, and it can also be represented by an arrow pointing in the direction of motion.
The pressure at the beginning of the pipe (P1) will be determined by the pressure of the source supplying the pipe, such as a pump, as well as the friction losses that occur along the pipe. The pressure at the end of the pipe (P2) will be determined by the available pressure of the source supplying the pipe, the friction losses that occur along the pipe, and the velocity at the end (v2). As such, without knowing the source pressure, the friction losses, and the velocities, it is impossible to determine whether P1 is less than, equal to, or greater than P2.
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you have been hired to design a spring-launched roller coaster that will carry two passengers per car. the car goes up a 12-m -high hill, then descends 20 m to the track's lowest point. you've determined that the spring can be compressed a maximum of 2.1 m and that a loaded car will have a maximum mass of 400 kg . for safety reasons, the spring constant should be 11 % larger than the minimum needed for the car to just make it over the top.
a) what spring constant (k) should you specify ?
b) What is the maximum speed of a 350 kg car if the spring iscompressed the full amount.
An object can encounter some resistance when moving through the fluid medium of air.
The drag force is the oppositional force applied by the air to a moving object. The size of the cross section A of the front face of the item, the density of the air, and the square of the object's velocity v all contribute to the drag force.
With motion exclusively in the vertical direction and letting
downward be positive, we have that
dv/dt = g - pv, where g = 32 ft/, and so
dv/dt + pv = g. The integrating factor is , so
d/dt( × v) = g× ----->
v = (g/p)× + C ----->
v(t) = (g/p) + C×
Now v(0) = (g/p) + C = 0, and so C = -g/p, giving us
v(t) = (g/p)×(1 - ).
Now we are given that lim(t->infinity)(v(t)) = 99 mi/h = 145.2 ft/s,
so since -> 0 as t -> infinity we have g/p = 145.2 ft/s ------>
p = 32 ft/s^2 / (145.2 ft/s) = 0.2204 s^-1 .
Next, since we have defined downward as positive, the expression
we have for v(t) will equal dy/dt where y(0) = 0 and y increases as
the paratrooper falls. So
dy/dt = v(t) = (g/p)×(1 - )), so
y(t) = (g/p)×(t + (1/p)×) + K.
Now y(0) = (g/p)×(0 + (1/p)) + K = 0 ----->
K = -(g/p^2) = 32 / 0.2204^2 = -658.76 ft, so
y(t) = (145.2)×(t + (4.5372)×e^(-0.2204×t)) - 658.76.
Next, y(6) = (145.2)×(6 + (4.5372)×e^(-0.2204×6)) - 658.76 = 444.84 feet.
The computed drag coefficient is substantially higher than anticipated.
The free fall distance is the longest distance an individual can travel in a predetermined amount of time. However, the distance covered in the time frame indicated in the news report is significantly greater than the greatest distance that could be covered. Consequently, the news story is exaggerated.
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some pairs of functions cannot be composed. some pairs of functions can be composed only for certain values of x. the domain of a composed function is either the same as the domain of the first function, or else lies inside it. the range of a composed function is either the same as the range of the second function, or else lies inside it.
Composed functions are useful for evaluating complex systems, but it is important to understand the range and domain of both functions to ensure that the composed form is valid.
Understanding how composed functions operate within a system is essential to understanding mathematics. Composed functions are essentially a combination of two functions, usually denoted as f(g(x)) or g(f(x)).
The domain of a composed function is the set of all possible input values from the first function, which can either be the same as the domain of the first function or a subset of it.
Similarly, the range of a composed function is the set of all possible output values from the second function, which can either be the same as the range of the second function or a subset of it.
For two functions to be composed, they must be compatible in the sense that the range of the first function is the same as the domain of the second function.
Otherwise, the composed form of the two functions would not make sense mathematically. In addition, some pairs of functions can be composed only for certain values of x, meaning that a composed function may not be valid for all possible input values.
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