The Inductance and Inductive Reactance of the conductor is 1.315 x 10⁻⁶H/m and 0.496ohm/km respectively.
A type of inductor is a device that runs on magnetism or magnetic fields. Transformers, coils, motors, and generators are examples of inductors. Current and voltage can become out of phase and inefficient when an inductor is used in a circuit if the problem isn't fixed.An EMF is continuously produced in an inductive AC circuit where the current is constantly changing. This EMF's impact is measured in ohms because it fights against the ongoing change in the flowing current. Inductive reactance (XL) is the term used to describe this resistance of the inductance to the flow of an alternating current.The inductance of the circuit and the rate at which the current is changing through the circuit both affect the value of XL in any circuit. The applied voltage's frequency affects this rate of change.The mathematical illustration of XL is shown in the equation below.
XL = 2πfL.
Ds=0.0123mDe=8.819m
L= 2 x 10⁻⁷ x log [8.819/0.0123]
L=1.315 x 10⁻⁶H/m
XL=2 x 3.14 x 60 x 1.315 x 10⁻⁶=0.496ohm/km
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33. easy student solutions manual a 5.00-kg ball, moving to the right at a velocity of 2.00 m/s on a frictionless table, collides head-on with a stationary 7.50-kg ball. find the final velocities of the balls if the collision is (a)elastic and (b)completely inelastic
Easy student solutions manual a 5.00-kg ball, moving to the right at a velocity of 2.00 m/s on a frictionless table, collides head-on with a stationary 7.50-kg ball. find the final velocities of the balls if the collision is
(a)elastic and (b)completely inelastic
An act or instance of colliding : conflict. : an encounter among particles (which includes atoms or molecules) resulting in alternate or transformation of strength. collisional.
Velocity (vɪˈlɒsɪtɪ) / noun plural -ties. pace of movement, action, or operation; rapidity; swiftness. physics a measure of the fee of movement of a frame expressed because the rate of exchange of its function in a specific route with time.
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A star can give off white light. Why is this evidence that a star is a blackbody radiator?.
Answer: This is evidence that a star is a blackbody radiator because white light is made up of many different wavelengths of light.
A particle accelerator accelerates an electron to a kinetic energy of 6.5 MeV. a) How fast is the electron moving? b) How many times is its mass greater than its rest mass?
(a) The speed of the electron is 1.5 x 10⁹ m/s.
(b) The mass of the electron is 12.75 times greater than the rest mass energy.
What is the speed of the electron?
The speed of the electron is calculated by applying the following equation;
K.E = ¹/₂mv²
where;
m is mass of electronv is the speed of the electronv² = 2K.E/m
v = √(2K.E/m)
where;
K.E is the kinetic energy = 6.5 MeV = 6.5 x 10⁶ x 1.6 x 10⁻¹⁹ J = 1.04 x 10⁻¹² J
v = √(2 x 1.04 x 10⁻¹²/9.11 x 10⁻³¹)
v = 1.5 x 10⁹ m/s
The rest mass energy of an electron is 0.51 MeV
0.51x = 6.5
x = 6.5/0.51
x = 12.75
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The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
The absolute value equation is |x - 430| ≤ 20.
What is equation?An equation is a formula that is express the equality of two equation.
b) Solution: 410 ≤ x ≤ 450
Explanation:
1) Call x the variable, actual weight of the soccer ball
2) Recomended weight: 430 g
3) Difference using absolute value is | x - 430|
4) The accepeted variation (difference) is up to 20 g means that the difference has to less than or equal to 20 g ⇒ | x - 430| ≤ 20
5) Solution:
i) start: |x - 430| ≤ 20
ii) as per the definition of absolute value: -20 ≤ x - 430 ≤ 20
iii) addition property of inequalities: add 430 to all the parts:
- 20 + 430 ≤ x - 430 + 430 ≤ 20 + 430
iv) do the operations: 410 ≤ x ≤ 450
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dentical rays of light in air are refracted upon entering three transparent materials: (a) water, where the speed of light is 0.75c ; (b) ethyl alcohol; speed 0.7c ; and (c) crown glass; speed 0.6c .
The transition from less dense air to denser glass or water causes light to slow down.
What happens to a ray of light as it passes through air and enters water?A beam of light (a collection of perpendicular rays) will move straight through the air when it is shone at it. Until they come into contact with an object, light rays typically go in straight paths.A sheet of glass's surface will reflect some light when a light ray strikes it, so this happens. However, because glass is transparent, a large portion of the light will flow through the glass.Light beams are similarly impacted by water. While some light will reflect off the water's surface, the translucent water will let in the majority of the light.The direction of a light ray changes when it travels through glass from the atmosphere. As it travels through the glass' surface, the light ray seems to bend.Similar effects occur when a light beam travels from air into water: the light ray is twisted as it collides with the water's surface.Refraction describes the "bending of a ray of light" when it travels through one substance and then another.When a light beam exits glass or water and enters the atmosphere, it will also bend.To Learn more About slow down refer to:
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does the field [that is caused by a straight wire] have an axial component? does it have a radial component?
The field caused bt a straight wire have only axile component, B parallel Δl = μ₀I. The radial component of the field is perpenidular length.
A magnetic field is a vector subject that describes the magnetic effect on moving electric charges, electric currents, and magnetic materials. A transferring price in a magnetic area stories a pressure perpendicular to its very own pace and to the magnetic discipline.
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric-powered currents, and magnetic substances. A transferring rate in a magnetic field story a pressure perpendicular to its own velocity and to the magnetic area.
The magnetic discipline is the place around a magnet wherein the impact of magnetism is felt. We use the magnetic discipline as a tool to explain how the magnetic force is shipped in the area around and inside something magnetic in nature.
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The expansion of the universe after its origin takes place by a phenomenon called.
Expansion of the universe after its origin takes place by a phenomenon called inflation.
What is inflation?In physical cosmology, a theory of exponential expansion of space in the early universe is called inflation.Prior to the Big Bang, the universe underwent a breathtaking cosmic expansion, doubling in size in a fraction of a second. This rapid inflation, fueled by energy that permeated empty space and left the universe desolate and cold.The Big Bang theory explains how the universe got from the hot dense state of the early universe to the cold dense state whereas cosmic inflation is an explanation of some properties of the cosmic microwave background radiation.Phenomena can be defined as “observable events that occur in a natural or designed system.” They are everywhere around us, but some are easier to notice than others. Common examples of natural phenomena include lightning, earthquakes, tsunamis, volcanic eruptions, tornadoes, and similar.The natural phenomena in the given crossword are cyclone, thunder, storm, lightning, typhoon and hurricane.To learn more about phenomenon refer to:
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fingerprints left on a piece of glass such as a windowpane can show colored spectra like that from a diffraction grating. why?
The skin oils from the finger will deposit on smooth surfaces in the pattern of the closely spaced ridges when the finger contacts them.
What is diffraction ?The Huygens-Fresnel principle, which views each point in a propagating wave front as a collection of unique spherical wavelets, describes the diffraction phenomenon in classical physics. When a wave from a coherent source (such a laser) comes into contact with a slit or aperture that is roughly the same size as its wavelength, the characteristic bending pattern is most noticeable.
There are numerous closely spaced ridges and swirls on the skin of a fingertip. The skin oils from the finger will deposit on smooth surfaces in the pattern of the closely spaced ridges when the finger contacts them. In order to create a crude diffraction grating and create a coloured spectrum of the light travelling through or reflecting from the glass surface, open intervals between the lines of deposited oil can be used as slits.
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a 21 g bullet is accelerated in a rifle barrel 66.5 cm long to a speed of 968 m/s. use the work energy theorem to find the average force exerted on the bullet while it is being accelerated. answer in units of N.
The force on the bullet of mass 21 g is 14795.12 N.
What is force?Force is the product of mass and acceleration.
To calculate the force exerted on the bullet while it is being accelerated, we use the work energy relation below
Formula:
F = mv²/2d...........Equation 1Where:
F = Forcem = Mass of the bulletv = Velocity of the bulletd = DistanceFrom the question,
Given:
m = 21 g = 0.021 kgv = 968 m/sd = 66.5 cm = 0.665 mSubstitute these values into equation 1
F = 0.021×968²/(2×0.665)F = 14795.12 NHence, the force on the bullet is 14795.12 N.
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Choose the correct measuring device for gathering data from the list of tools in the drop-down menu. Heartbeats per minute time distance across the pond.
Measuring devices are used as follows -1. Thermometer, 2. Heart monitor, 3. Measuring cylinder, 4. Clock, 5. Tape measure
What are measuring devices?
The instruments that are used for the measurements of various specific items based on the laws and the theories of measurement are called measuring devices.
Specific measurements have specific measurement devices. These measure the value based on the specific unit of the measurement.
For example, an inch tape measures the length of something in inches. It also has scales of centimetres and meters.
For the measurement of length, scales and tape measures are used.
For the measurement of time, clocks are used.
For the measurement of volumes, graduated cylinders are used.
For the measurement of temperature, thermometers are used.
Therefore, the measuring devices vary according to the function it needs to perform. In this case, 1. Thermometer, 2. Heart monitor, 3. Measuring cylinder, 4. Clock, 5. Tape measure.
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Answer:
Answer:heart monitor
Stopwatch
Digital tape measure
Thermometer
Graduated cylinder
Explanation:
Sample response: t represents time, which is the input of the function, so we know that 10 is the time in minutes. H(t) represents the altitude, which is the output of the function after time, t. So, we need to substitute 10 into 210 – 15t in place of t. Simplifying 210 – 15(10), we get that 60 is the altitude in feet. So, after 10 minutes, the hot air balloon is at 60 feet. What did you include in your response? check all that apply. T represents time, which is the input of the function. H(t) represents the altitude, which is the output of the function. After 10 minutes, the hot air balloon is at 60 feet
Answer: Uh i do not know
Explanation:
A sports car is accelerated from 0 to 100 km per hour in 3 s. What is the acceleration of the car?.
The automobile accelerates at 0.9g.
Describe acceleration.acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight forward is accelerated when it accelerates or decelerates.
1 g equals 9.8 m/s2, as we are aware. Therefore, we must first convert 100 km/h to m/s. So that we may compare units like meters and seconds (we'll deal with s2 eventually).
100 km/h * (1 km) * (1 hour) * (1 minute) * (60 sec) = 27.778 m/s.
We are aware that this automobile needed three seconds to reach this speed. Since acceleration is a change in velocity, and we know that the car's velocity increased from 0 to about 27.8 m/s in 3 seconds, we may calculate the accelerationknow that our acceleration is:
(27.8 m/s - 0 m/s) / (3 s) = 9.259 m/s^2.
Now to find how many g’s, we know that 1 g = 9.8 m/s^2.
So we know that 9.259 m/s^2 / 9.8 m/s^2 = about 0.9. This will be 0.9 of 1 g, which is just 0.9 g.
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what makes astronomers think that impact rates for the moon must have been higher earlier than 3.8 billion years ago? a.the ancient sea basins on the moon, whose water has since evaporated, show a lot more cratering b.all the large craters on the moon come in pairs, while all recent craters are single c.all the radioactive rocks found on the moon so far give ages much younger than that, so the moon must have formed less than 3.8 billion years ago d.there are ten times more craters on the older highlands than the younger maria e.we see many more craters on the moon that have been eroded by wind and rain
Option (4) is correct: There are ten times more craters on the older highlands than the younger maria.
Who are astronomers?
Astronomers are scientists in the field of astronomy, who focus their research on a particular problem or area outside the realm of the Earth. Observe celestial bodies such as stars, planets, moons, comets, and galaxies either by observation (by analyzing data) or by theoretical astronomy. Examples of topics and fields studied by astronomers include planetary science, solar astronomy, the origin and evolution of stars, and the formation of galaxies. A related but different field is physical cosmology, which studies the universe as a whole.
Therefore, Option (4) is correct: There are ten times more craters on the older highlands than the younger maria.
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what is the tension in a string of mass 0.83\;\mathrm{kg}0.83kg and length 12.29\;\mathrm{m}12.29m if when plucked, waves travel at 28.5\;\mathrm{m/s}28.5m/s?
54.85N is the tension in a string of mass [tex]$0.83 \mathrm{~kg}$[/tex] and length [tex]$12.29 \mathrm{~m}$[/tex] if when plucked, waves travel at [tex]$28.5 \mathrm{~m} / \mathrm{s}$[/tex].
What is tension?
In physics, tension is defined as the pulling force that is transmitted axially by a string, rope, chain, or similar object, or by each end of a rod, truss member, or other comparable three-dimensional object. Tension can also be defined as the action-reaction pair of forces acting at each end of the aforementioned elements.
[tex]\begin{aligned}& m=0.83 \mathrm{~kg} \\& l=12.29 \mathrm{~m} \\& v=28.5 \mathrm{~m} / \mathrm{s} \\& \mu=\frac{m}{l} \\& v=\sqrt{\frac{T}{\mu}}\end{aligned}[/tex]
[tex]\Rightarrow T=v^2 \mu=[/tex] [tex](28.5)^2 \times \frac{0.83}{12.29}[/tex] = [tex]54.85 \mathrm{~N}[/tex]
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A block of mass m lying on a rough horizontal surface is given an initial velocity of v0. After traveling a distance d, it makes a head-on elastic collision with a block of mass 2m. How far does the second block move before coming to rest? (Assume the coefficient of friction, µk, is the same for both blocks.)
Hence the block will travel for 8 cm before coming to rest.
An elastic collision is a collision in which there may be no net loss in kinetic energy inside the device because of the collision. both momentum and kinetic strength are conserved portions in elastic collisions.
In physics, an elastic collision is an come across between two bodies wherein the full kinetic strength of the two bodies stays equal. In a really perfect, flawlessly elastic collision, there's no net conversion of kinetic electricity into other forms together with warmth, noise, or potential electricity.
Whilst a ball at a billiard desk hits another ball, it's miles an example of elastic collision. while you throw a ball at the floor and it bounces again in your hand, there may be no internet change in the kinetic energy, and subsequently, it's far an elastic collision.
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an object sits at rest with no unbalanced forces acting upon it. what do we expect this object to do?
Unless acted on by an imbalanced force, an object is at rest can tend to stay as rest, and a motion should tend to maintain its current speed and direction.
Describe a force.A pull or pull that an object experiences as a result of interacting with another item is known as a force. Every time two items touch, a force is exerted on each of objects.
Which types of force are there?Forces acting and act at a range forces are the two different types of forces. Your daily use of force is evident. Essentially, thrust and pull are forces. You exert force on an object if you push against it or pull against it.
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in electronic circuits, when analyzing the effect of l or c on the wave shape of non sinusoidal voltages, what is useful?
It retains its wave shape when added to another sine wave of the same frequency and arbitrary phase and magnitude.
What has a sinusoidal wave form?Periodic waveforms known as sine waves can be represented graphically using the sine or cosine trigonometric functions. Electrical circuits that receive "AC" voltages and currents, or sinusoidal waveforms whose polarity alternates on each cycle.The strength of the magnetic field that forms around a wire or conductor while an electric current flows through it is inversely proportional to the current value. The movement of this single wire conductor through the magnetic flux induces a "EMF" (Electromotive Force) inside the conductor if it is moved or rotated within a stationary magnetic field.It retains its wave shape when added to another sine wave of the same frequency and arbitrary phase and magnitude. It is the only periodic waveform that has this property. This property leads to its importance in Fourier analysis and makes it acoustically unique.To learn more about sinusoidal wave, refer to
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unpolarized light with intensity 300 w m2 is incident on three polarizers, p1, p2, and p3 numbered in the order light reaches the polarizers. the transmission axis of p1 and p2 make an angle of 45◦ . the transmission axis of p2 and p3 make an angle of 30◦ . how much light is transmitted through p3?
Through p3, a light of equal power (60 W) is transmitted.
According to Malus's law, I = I0 cos2, the polarization phenomena is described.The angle between the direction of polarization of the light and the polarizer is, where I and Io are the transmitted and incident intensities, respectively.
Half of the unpolarized light that enters the first polarizer (I0 I1 = 12 300 I1 = 150 W) is transmitted.
I2 = I1 cos2 1 I2 = 150 cos2 45 I2 = 75 W is the transmission through the second polarizer (P2).
I3 = I2 cos2 2 I3 = 75 cos2 30 I3 = 56.25 W is the third polarizer's (P3) transmission.
The closest response, A, corresponds to 60 W and represents the light that the 56 W system transmits.
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When a piece of metal is heated to high temperatures, it begins to glow red, and then white, as its temperature increases. Does this phenomenon provide evidence for the wave model or the particle model of light? why?.
Answer:
The particle model, because the metal is only absorbing radiation. of specific frequencies.
Explanation:
When a piece of metal is heated to high temperatures, it begins to glow red, and then white, as its temperature increases.
what is the moment of inertia of the object starting from rest if it has a final velocity of 5.4 m/s? express the moment of inertia as a multiple of mr2 , where m is the mass of the object and r is its radius.
The moment of inertia of is the object starting from rest if it has a final velocity of 5.4 m/s is 0.344 M R²
You can then use the energy conservation equation to calculate the moment of inertia of an object that starts at rest and has terminal velocity.
Then Ek1 + Ep1 = Ek2 + Ep2, where
Ek1 = kinetic energy of the object before rolling
Ep1 = potential energy of the object
Ek2 = kinetic energy when the object falls
Ep2 = potential energy of the object below.
Mgh = Iv² +Mv²
2R² 2
19.6M = 14.58 I + 14.58 M
R²
5.02 M R² = 14.58 I
0.344 M R² = I
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a salesperson claims a 960 kg car has an average acceleration of 5 m/s2 from a standing start to 100 km/h. what average net force is required to do this?
The average net force will be 4.8× [tex]10^{3[/tex] N
What is acceleration?Acceleration describes the speed and direction changes in velocity over time. Acceleration refers to the change in speed or direction of an item or point traveling straight forward.
The average force is what?The force applied by a body that's travelling at a definite velocity (rate of speed) for a definite period of time is the average force. Force is a vector quantity that has both magnitude and direction.
The vehicle weighs 960 kg, or m. The car's average speed is
a = 5m/s2 Newton's Second Law of Motion states that a particle's mass times its typical acceleration equals the average force that is applied 5 m/s2.
average net force (F) operating will be
F = ma
F = 960*5
F = 4.8× [tex]10^{3[/tex] N
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What is the power needed to change the speed of a 1600-kg sport utility vehicle from 15. 0 m/s to 40. 0 m/s in 4. 00 seconds?.
2725 Watt, is the power needed to change the speed of a sport utility vehicle.
What is the Power?
The quantity of energy moved or converted per unit of time is known as power. The watt, or one joule per second, is the unit of power in the International System of Units also it is a scalar quantity.
What are the Calculations?
Mass of the sport utility = 1600kg
Initial velocity ([tex]v1[/tex]) - 15m/s, ([tex]15^{2}[/tex] = 225)
Final velocity ([tex]v2[/tex]) - 40m/s, ( [tex]40^{2}[/tex] = 1600)
To find the energy required, Kinetic energy (K.E) = [tex]\frac{1}{2}[/tex] [tex]mv^{2}[/tex]
K.E = final K.E - initial K.E
= [tex]\frac{1}{2} (v2 - v1 )[/tex]
= [tex]\frac{1}{2} 1600 * (1600 - 225)[/tex]
= 80 * 1375
= 11000 J
Power = [tex]\frac{Energy (E)}{Time (t)}[/tex] = [tex]\frac{1100 joule}{ 4 sec}[/tex]
= 2725Watt.
Hence, 2725Watt, is the power needed to change the speed.
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You redo the primitive yo yo experiment (Figure 1), but instead of holding the free end of the string stationary, you move your hand vertically so that the tension in the string equals 2M /3. What is the vertical acceleration of the yo yo's cena of mass? Does it accelerate upward or downward? Express your answer to three significant figures and include the appropriate units. Enter positive value of the acceleration is directed upward and negative value if the acceleration is directed downward.
The direction of acceleration is downward, and its magnitude is 3.27 m/s².
Given:
Tension, T = 2M/3
The gravitational force is exerted downwards, and the tension force is exerted in the opposite direction of the gravitational force.
The total force is given by:
mg - T = ma
The torque is given as:
T × R = MR²/2 × α
Here, α is centripetal acceleration;
The centripetal acceleration is given by:
α = a/R
Substitute values:
MG - 2mG/3 = ma
a = g/3
The direction of acceleration is downward.
a = 9.8/3
a = 3.27 m/s²
Hence, the direction of acceleration is downward, and its magnitude is 3.27 m/s².
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which of the following is likely to break a wave? a) the wind increases its speed near shorelines b) random molecular motion in wave forms c) the bottom interferes with its oscillatory motion d) the sediment load of water is greater near the shore e) the density of water increases closer to shore
The wave can be broken in c) the bottom interfering with its oscillatory motion.
In fluid mechanics, a breaking wave or breaker is a wave whose amplitude reaches a critical level where a large amount of wave energy is converted into turbulent kinetic energy. At this point, simple physical models describing wave dynamics, especially those that assume linear behavior, are often invalid.
The most commonly known type of breaking wave is a water wave that breaks on the shore. In general, wave breaking occurs when the amplitude reaches the point where the crest of the wave actually flips over. Another particular effect in fluid dynamics is also called "wave breaking", partly by an analogy to waves on water. In meteorology, atmospheric gravitational waves are said to break down when the wave creates a region of potential temperature drop with altitude, resulting in energy dissipation due to convective instability.
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Finally, Joe turns his attention to the mountain in the distance but finds that he cannot bring the mountain into focus. This is because he is nearsighted. But when Joe puts on his glasses, he can see the mountain clearly. To adjust for his nearsightedness, his glasses must contain _____ lenses.
Mountain --- Tree --- Squirrel --- Joe
converging
diverging
Finally, Joe turns his attention to the mountain in the distance but finds that he cannot bring the mountain into focus. This is because he is nearsighted. But when Joe puts on his glasses, he can see the mountain clearly. To adjust for his nearsightedness, his glasses must contain diverging lenses.
An image of an object is formed when its light rays are recorded on the retina. The lenses in the eye focus these rays onto the retina, making the phenomenon of vision possible.
Joe is nearsighted- or in other words, he has myopia. Myopia is a defect in normal vision where one cannot see nearby objects clearly and distinctly.
The image of the mountain (distant object) is formed at the retina properly for Joe as he can see distant objects distinctly. But for nearby objects, he cannot see clearly, because he suffers from nearsightedness.
The inability of the ciliary muscles to arbitrarily increase or decrease the focal length of the lens results in nearsightedness and farsightedness. Therefore, his eyes must be able to focus on the image of the distant mountains naturally due to the corrective diverging lenses.
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Two identical cars, one on the moon and one on earth, are rounding banked curves at the same speed with the same radius and different angles. The acceleration due to gravity on the moon is 1/6 that of earth. How do the centripetal accelerations of each car compare?.
The acceleration due to gravity on the moon is 1/6 that of earth, then the centripetal forces are the same for each car.
What is centripetal force?A force that keeps objects moving in a circular path is called centripetal force .
The centripetal force on an object is given by :
F= mv²/R
where,
F is centripetal force,
m is mass of the object,
and v is speed,
r is radius of the circular path.
Centripetal force primarily depends upon three factors, that are, mass of object, speed and radius of the circular path.
The speed of cars and the radii of the circular paths are given to be same. Hence, the centripetal force acting on both cars must also be same.
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which of the following is considered to be a boundary between two different air masses? group of answer choices cold front warm front both warm front and cold front none of these
A front denotes the separation of two air masses with dissimilar characteristics in terms of temperature, wind, and moisture.
Distinguish between warm and cold fronts.
Both warm and cold fronts are intricate weather phenomena, necessitating a thorough explanation in order to fully comprehend their similarities and distinctions. A cold front develops on the edge of a cold air mass flowing into a warmer area, whereas a warm front develops on the edge of a warm air mass moving into a colder area. A cold front is often linked to a low-pressure system, whereas a warm front is linked to a high-pressure system.
Hence, the answer is both warm and cold front, since a front denotes the separation of two air masses with dissimilar characteristics in terms of temperature, wind, and moisture.
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in the context of spearman's two-factor theory of intelligence, an intermediate class of factors common to a group of activities but not to all is called .
The term "Group factor" refers to an intermediate class of factors that are shared by a group of activities but not by all in the context of Spearman's two-factor theory of intelligence.
What is the two-factor hypothesis of intelligence proposed by Spearman?
According to Spearman's two-factor theory, intelligence is divided into two categories: general intelligence ("g") and specific ability ("s"). Spearman proposed that the "s" component was particular to a certain feature of intelligence to account for variations in performance on various tasks.
What exactly are general and specific factors?
The "g" factor is associated with general aptitude, whereas the "s" factor is associated with aptitude for a particular task. The "s" factor is in charge of identifying a person's specific abilities, while the "g" factor measures a person's capacity for performing tasks requiring general mental ability.
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Wave motion is characterized by two velocities: the velocity with which the wave moves in the medium (e. G. , air or a string) and the velocity of the medium (the air or the string itself). Consider a transverse wave traveling in a string. The mathematical form of the wave is.
a) The velocity of propagation of the wave V=w/k
b) The y velocity v_y(x,t) of a point on the string as a function of x
v=-wAcos(kx-wt)
What is a wave?
A wave can be described as a disturbance that travels through a medium from one location to another location
y(x,t)=Asin(kx−ωt) defines the wave equation.
a)The velocity of propagation of the wave
We are asked to find wave speed (v)
Recall that v = fλ
From the wave equation above,
k = 2π/ λ where k is the wave number and λ is the wavelength, λ = 2π /k
ω = 2πf where f is the frequency and ω is the angular frequency.
f = ω/ 2π.
By substituting for λ and ω into the wave speed formulae, we have that
v =( ω/ 2π) × (2π /k)
v = ω/k
b)The y velocity v_y(x,t) of a point on the string as a function of x
y(x,t)=Asin(kx−ωt)
The first derivative of y with respect to x give the velocity (vy)
By using chain rule, we have that
v = dy/dt = A cos( kx −ωt) × (−ω)
v = - ωAcos( kx −ωt)
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A .530 kg block slides on a frictionless horizontal surface with a speed of 1.10 m/s. The block encounters an unstretched spring and compresses it 20.0 cm before coming to rest. Part A) What is the force constant of this spring? k=________N/m
Part B) For what length of time is the block in contact with the spring before it comes to rest?
t=________sec
Part C) If the force constant of the spring is increased, does the time required to stop the block increase, decrease, or stay the same.
Choices:
A) Increases
B) Decreases
C) Stays the same
The force constant of this spring is 16.03N/m; the length of time block is in contact with the spring before it comes to rest is 1.14s; If the force constant of the spring is increased, the time required to stop the block will decrease.
What happens if a block slides on a frictionless horizontal surface?
When a block slides over a horizontal surface without friction, it has kinetic energy. Before coming to rest, it runs into an untensioned spring and compresses it.
The energy is purely kinetic when the mass first comes into contact with the spring. Energy is transformed into spring potential energy as the spring is squeezed. To find the spring force constant, equate the energies. One-fourth of a period is represented by the motion. A stiffer spring will result in a smaller stopping distance for the mass, which will result in a faster stopping time.
(a)Equations: Conservation of energy using a spring.
Ei=Ef
1/2mvo2 = 1/2kA2
A= vo√m/k
K is force constant
k is 16.03N/m
(b) Time
T = 2∏√m/k
T = 1.14s
(c) The time to stop reduces as the force constant rises. A stronger spring and a greater stopping force result from a higher force constant, and a shorter stopping time follows. The compressed spring contains all of the energy left behind after the spring has stopped the block. The block will be accelerated back the way it came when the spring pushes back on it. The block will leave the spring moving in the opposite direction from where it first came into contact with it, but at the same speed. Equal to the stopping time is the accelerating time.
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