The power, the resistor and time is I²₀R e-2Rt/L and - I₀²R e-2Rt/L .
Work rate or energy delivery time is expressed as W/t, where W is the quantity of work completed or energy delivered, and t is the time interval.
A passive electrical device with two terminals that controls or limits the flow of electricity across electrical circuits. The main function of a resistor is to lower the voltage and reduce the current flow in a specific area of the circuit.
a) L di/dt + iR = 0 -Rt/L
= I = I₀ e
At t=0. I = I₀
= Pr = I²R = I₀ R e = -2Rt/t
= Pr (t) = I²₀R e-2Rt/L
b) Energy of inductor = 1/2 L I²
= 1/2 L I₀² e-2Rt/L
Power, Pl (t) = dE/dt
= d/dt (1/2 LI₀² e-2Rt/L)
= 1/2 t I₀² ( e-2Rt/L) e-2Rt/L
Pl (t) = - I₀²R e-2Rt/L
Therefore, the power, the resistor and time is I²₀R e-2Rt/L and - I₀²R e-2Rt/L .
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what inductance must be connected to a 17 pf capacitor in an oscillator capable of generating 550 nm (i.e., visible) electromagnetic waves? comment on your answer.
The inductance that must be connected to a capacitor is 5* 10⁻²¹ H.
If f is the frequency and λ is the wavelength of an electromagnetic wave, we know the relation between them as v = f * λ
The frequency is same as the frequency of oscillation of the current in the LC circuit of the generator.
f = 1/(2π* √LC)
where, C is the capacitance
L is the inductance
So, λ/(2π* √LC) = c
Given that, λ = 550* 10⁻⁹ m
C = 17 * 10⁻² F
c is the speed of light
Making L as subject, we have
L = λ²/(4π² C* c²) = (550* 10⁻⁹)² / [4π²(17 * 10⁻²) (3* 10⁸)²] = 5* 10⁻²¹ H
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if an object doubles its luminosity in 10 hours, how large can the emitting source of light be?
If an object doubles its luminosity in 10 hours, emitting source of light can be about 10 light hours across.
Luminosity, L, is a measure of the total amount of energy radiated by a star or other celestial object per second. This is therefore the power output of a star. A star's power output across all wavelengths is called its bolometric luminosity. A star's luminosity can be determined from two stellar characteristics: size and effective temperature. The difference between luminosity and apparent brightness depends on distance.
Since, the luminosity of the object doubles in 10 hours, emitting source of light can be about 10 light hours across.
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a sky diver jumps from a plane traveling horizontally at 55 m/s at an altitude of 1500 m. when she reaches an altitude of 425 m, she is falling at a terminal velocity of 52 m/s. how much work has been done by air resistance during this time?
The work that has been done by air resistance during this time is 55800 k m²/s².
To determine the work done by air resistance during the skydiver's fall, we can use the equation:
W = F × d
where W is the work, F is the force of air resistance, and d is the distance traveled.
The force of air resistance on the skydiver is given by the equation:
F = k × v²
where k is the drag coefficient, which is a measure of the resistance of the air to the movement of the object, and v is the velocity of the skydiver.
To determine the work done by air resistance, we need to determine the distance traveled by the skydiver and the force of air resistance at each point in her fall. The skydiver falls from an altitude of 1500 m to an altitude of 425 m, a distance of 1075 m.
At an altitude of 1500 m, the skydiver is falling at a terminal velocity of 52 m/s. Plugging these values into the equation for the force of air resistance gives us:
F = k × v² = k × (52 m/s)²
To determine the work done by air resistance at this point in the skydiver's fall, we can plug the value of F and the distance traveled into the equation for work:
W = F × d = (k × (52 m/s)²) × 1075 m = 55800 k m²/s²
The work done by air resistance at this point in the skydiver's fall is 55800 k m²/s².
At an altitude of 425 m, the skydiver is falling at a terminal velocity of 52 m/s. Plugging these values into the equation for the force of air resistance gives us:
F = k × v² = k × (52 m/s)²
To determine the work done by air resistance at this point in the skydiver's fall, we can plug the value of F and the distance traveled into the equation for work:
W = F × d = (k × (52 m/s)²) × 1075 m = 55800 k m²/s²
The work done by air resistance at this point in the skydiver's fall is 55800 k m²/s².
To determine the total work done by air resistance during the skydiver's fall, we can add the work done at each point in the fall:
W_total = W_1500m + W_425m = 55800 k m²/s² + 55800 k m²/s² = 111600 k m²/s²
The total work done by air resistance during the skydiver's fall is 111600 k m²/s².
Note that this calculation assumes that the drag coefficient k is constant throughout the skydiver's fall. If the drag coefficient changes during the fall (for example, if the skydiver deploys a parachute), additional calculations will be needed to determine the total work done by air resistance.
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at what point does the terminal side of the angle 7π4 in standard position intersect the unit circle?
At point [tex](\frac{\sqrt{2}}{2} ,- \frac{\sqrt{2}}{2} )[/tex] the terminal side of the angle [tex]\frac{7\pi}{4}[/tex] in standard position intersect the unit circle.
A unit circle is divided into four quadrants, each of which has an angle of 90°, 180°, 270°, and 360° (in degrees) or π/2, π. 3π/2, and 2π (in radians) respectively.
A unit circle angle is always measured from the positive x-axis, with the vertex at the origin. Its initial side is on the x-axis, while the terminal side is formed by the ray that begins at the origin and coincides with the point on the unit circle. When an angle is measured anticlockwise from the x-axis, it has a positive value.
Quadrant 1 – (0 – 90°) : X is positive, Y is positive
Quadrant 2 – (90° – 180°) : X is negative, Y is positive
Quadrant 3 – (180° – 270°) : X is negative, Y is negative
Quadrant 4 – (270° – 360°) : X is positive, Y is negative
Given,
The radius of circle = 1 unit
The terminal side of angle = \frac{7\pi}{4}
[tex]\frac{7\pi}{4}=\frac{7*180}{4}=315\textdegree[/tex]
here, the angle 315° lies in the fourth quadrant, and we know that in 4th quadrant the x is positive and y is negative.
So, from the given options, the point [tex](\frac{\sqrt{2}}{2} ,- \frac{\sqrt{2}}{2} )[/tex] lies in the 4th quadrant.
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Your question is incomplete, here is the complete question.
At what point does the terminal side of the angle 7π/4 in standard position intersect the unit circle?
a) (-√2 / 2, -√2 / 2)
b) (-√2 / 2, √2 / 2)
c) (√2 / 2, -√2 / 2)
d) (√2 / 2, √2 / 2)
Ebo throw the ball at an initial velocity of 18m/ but thi time at an angle of 53 to the ground
a. Work at the velocity in component vector form
b. Why will the ball pend alonger time in the air than it did before. C. Calculate the range of the ball
The velocity is 6.52 m/s, and the velocity in component vector form is vcos.
"The pace at which an item changes its location" is described by a vector number known as velocity. Consider someone walking swiftly, one step ahead, one step back, and beginning each stride in the same place. Velocity is measured as a vector quantity. As a result, velocity is aware of direction. When calculating an object's velocity, the direction must be considered. A speed of 55 miles per hour does not provide enough information. To accurately represent the velocity of an object, the direction must be taken into account. Simply simply, the direction of the velocity vector describes the object's motion.
velocity in vector form
= vcos vector form
=18cos53 v
=16.52 m/s
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what is the minimum amount of hydrogen gas, in grams, required to completely hydrogenate 18.0 kg of 2-butene?
The minimum mass of hydrogen gas required is 641.64 grams.
Hydrogenation is a chemical reaction between molecular hydrogen and another compound or element, usually in the presence of a catalyst such as nickel, palladium, or platinum. This process is commonly used to reduce or saturate organic compounds.
2-butene = C4H8
maximum hydrogenation = C4H10
then we require 2 H, that is 1 mol ofH2
2-butene +H2 --> butane
MW of butene = 56.106
mol of butene = mass/MW = 18000/56.106 = 320.8213mol
then we require 1:1 ratio
320.8213 mol of H2
mass = mol*MW = 320.8213*2 = 641.64 g of H2
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during the game, the metabolism of basketball play- ers often increases by as much as 30.0 w. how much perspiration must a player evaporate per hour to dissipate this extra thermal energy?
Basketball players' metabolisms frequently accelerate by up to 30.0 w while they are playing. To release this extra thermal energy, a player must perspire 4.78x10-2kg.
Given that players release 30 J/s of heat (Q)
Heat is lost each hour given that
U=(30J/s)(3600s/h)=1.08x105J of thermal energy is lost per hour.
The amount of water that would be vaporized by this energy transmission is given by the formula:
m = U/Lwater
m=(1.08x105J)/(2.26X106J/kg)=4.78x10-2kg.
The temperature affects how hot water vaporizes. It is 2.257 x 106 J/kg at the boiling point (100C), but it is more like 2.40 x 106 J/kg at 37C.
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the anti-lock brake system engages every time the driver applies the brakes. group of answer choices true false
with the use of an example, fully and clearly discuss your understanding of the concepts of reversibility and irreversibility in a thermodynamic system. why do we study reversible thermodynamic systems?
The reversible process is the one that can be reverted back and an reversible process is the one that cannot back towards initial state.
In the field of thermodynamics the processes are defined as reversible or Irreversible.
Practically speaking, process is that one which occurs slowly slowly and reversible process is the one which occurs suddenly. Irreversible processes cannot be reverted back and reversible processes can be reverted back.
An example of reversible process is the change of state of water and an example of Irreversible process is the change in colour often iodine containing sample at the addition of starch.
We study the reversible processes in order to understand the thermodynamical perspective of the process and the energy change associated with the system.
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green light strikes a metal and electrons are ejected. yellow light results in no electrons. which color light would you expect to produce electron ejection in this metal?
The relationship between light frequency and wavelength is inverse. No matter how powerful, yellow light simply lacks the necessary energy per photon to excite any electron sufficiently to liberate it from the metal.
Since yellow and red light have longer wavelengths than green light and lower frequencies than green light, when yellow or red light strikes metal, no photoelectrons are produced. Yellow light makes a green thing appear green. Under cyan light, a red object seems to be black. Cyan light makes a blue thing appear blue. Red and green light are also present in yellow light, which likewise reflects both colors.
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A football player pushes a training sled 20 meters while pushing with a constant force of 300 Newtons. If this is accomplished in 7.5 seconds, what power was exerted?
The Power exerted will be 800W
What is Power?Power is the quantity of energy that is transferred or transformed in a certain length of time. The watt, which is equal to one joule per second as in the International System of Units is the unit of power. A scalar concept is a power.
Using te formular;
Power = (Force x distance) / time
P = (F x d) / t
where F = 300N
d = 20m
t = 7.5s
P = (300 x 20) / 7.5
P = 800W
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workers expect inflation to fall from 4% to 1% next year. as a result, this should
Workers expect inflation to fall from 4% to 1% next year. as a result, this should Shift the short-run aggregate supply curve to the right.
Option (B) is the correct choice.
The SRAS curve demonstrates that the amount of real GDP that will be generated in an economy grows as the price level rises as you move along the SRAS.
A movement to the right indicates an increase in the SRAS.
In the near run, decreasing wages, increasing the stock of physical resources, lowering inflation, and advances in technology would move the aggregate supply curve to the right.
The short term aggregate supply will move to SRAS2 on the left if businesses and labour anticipate price increases.
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The complete question may be:
Workers expect inflation to fall from 4% to 1% next year. As a result, this should
A) shift the short-run aggregate supply curve to the left.
B) shift the short-run aggregate supply curve to the right.
C) move the economy up along a stationary short-run aggregate supply curve.
D) move the economy down along a stationary short-run aggregate supply curve.
The 20-kg crate is lifted by a force of F = ( 100 +{ 5t }^{ 2 }) NF=(100+5t 2)N, where t is in seconds. Determine how high the crate has moved upward when t = 3 s, starting from rest.
4.23 m is the height the crate can move in 3s.
At t = 0,
force F = 100 N.
the time taken to move upward is 3s
Since at this moment,
2 F = 200 N > W = 20(9.81) = 196.2 N2F=200N>W=20(9.81)=196.2N,
the crate will move at that moment force F is applied. Referring to the Free body diagram of the crate,
[tex]m(v_y)_1 + \sum\int\limits^{t_2}_{t_1} {F_y} \, dt=m(v_y)_2[/tex]
=> [tex]0+2\int\limits^t_0 {100+5t^2} \, dt-20(9.81)t=20v[/tex]
=>[tex]2(100t+\frac{5}{3} t^3)-196.2t =20v[/tex]
=> v={0.1667[tex]t^3[/tex] + 0.19 t} m/s
The displacement of the crate can be calculated by integrating
ds = v dt with the primary condition s = 0 at t = 0.
[tex]\int\limits^s_o \, ds =\int\limits^t_o {0.1667t^3+0.19t} \, dt[/tex]
=> s={0.04167[tex]t^4[/tex]+0.095[tex]t^3[/tex]}m
At time t = 3 s,
s=0.04167 ( [tex]3^4[/tex] ) + 0.095 ( [tex]3^3[/tex])
=> s = 4.23 m
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the fruits are tossed in the air and spin back to the ground acting like small helicopters, which part of the fruit allows for this
The wall of a fruit, advanced from the ovary wall. The ripened and variously changed partitions of a plant ovary.
Consisting of the outer exocarp, significant mesocarp and internal endocarp, that is the wall of a plant fruit that develops from the ovary wall.
Pericarp: ↑ The a part of the fruit that surrounds the seed(s). The pericarp is shaped via way of means of 3 wonderful layers: exocarp, mesocarp, and endocarp.
Dehiscence: Splitting open at adulthood which will launch its contents (example: the fruit splits to launch the seeds). Children withinside the Southeastern United States play with pink maple culmination (Acer rubrum). The culmination are tossed withinside the air and spin again to the floor, performing like small helicopters. the culmination are tossed withinside the air and spin again to the floor performing like small helicopters, which a part of the fruit permits for this.
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If 2.5 minutes is the maximum access time for a magnetic tape, ____ is the average access time.
a. 0.5 minutes c. 1.25 minutes
b. 1 minute d. 2 minutes
The average access time of the magnetic tape is 1.25 minutes
What is access time of a magnetic disc?Disk access time is defined as the total time required by the computer to process a read/write request and then retrieve the required data from the disk storage.
The access time may be counted in nanoseconds for a semiconductor device, in milliseconds for a magnetic disk, or in minutes if the file containing the required data is on magnetic tape.
A magnetic field sensing read head and a magnetic field inducing write head are used for accessing data on each recording surface.
The average time of the magnetic tape is :
(0+2.5)/2
average access time = 2.5/2 = 1.25 minutes
Therefore the average access time of the magnetic tape is 1.25minutes.
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in a photoelectric effect experiment at a frequency above the cut-off frequency, the number of electrons ejected is proportional to
In a photoelectric effect experiment at a frequency above the cut off frequency the number of electrons ejected is proportional to the number of photons that hit the sample per second.
The photoelectric current is measured in relation to the intensity of the incident radiation at a specific frequency and potential between the metal plate and collector. It demonstrates that incident radiation intensity and photoelectric current are inversely correlated. The photoelectric current shows how many photoelectrons are released each second.
The idea of light as a wave cannot be used to explain the photoelectric effect. However, the particle nature of light, which can be visualized as a stream of electromagnetic energy-containing particles, can provide an explanation for this phenomenon. These particles of light are called as photons.
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An Lois Lane weighs 480 N on Earth. Superman takes Lois Lane to the planet Krypton to meet the parents. Krypton has a mass and diameter each 10 times that of Earth. Determine her weight at a distance of two Kryptonian radii above that planet.
Krypton was soon revealed to have formerly been a planet like Earth, only older by eons and possessing. All the advantageous advancement that entailed, starting in the Superman comic strip (though the downside was the hint that Krypton exploded due mainly to old age).
What Kryptonian radii above that planet?Superman's ability to defy gravity is also explained by another school of thinking, although with a slight variation. Krypton was a gigantic planet with a gravity so strong that typical humans would be crushed beneath its gravitational pull because it was about 1000 times bigger than Earth.
Therefore, Krypton, which was about 1.5 times the size of Earth and was located 50 light-years from the Sun, orbited the red star Rao.
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Which of the following best describes an electromagnet?
Need a Hint?
A) permanent magnet
B) insensitive to electrical currents
C) unchanging magnetic properties
D) temporary magnet
An Electromagnet can be best described as a temporary magnet.
An Electromagnet is called a non permanent magnet or a temporary magnet.
It is called so because of its property of getting magnetized and demagnetized.
Electromagnet behaves like a magnet only in the presence of the electric current their magnetic properties disappear as soon as the current in them stops.
Electromagnet are used in various devices like headphones and loudspeakers, induction cookers, data storage devices MRI machines and magnetic locks.
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Resistors R1, R2, R3, and R4 are arranged in a circuit as shown in the figure above. The direction of positive currents I1, I2, I3, and I4 through the resistors are shown. (i.e., negative current values correspond to currents in the opposite direction to that shown above). The values for the resistors and the batteries in the circuit are: R1 = 100 ?, R2 = 200 ?, R3 = 30 ?, R4 = 400 ?, V1 = 4 V, and V2 = 12 V.What is the value of I2, the current through R2? (remember I2 is a signed number) I2 = ?
The current of the resistor 2 from a circuit of four resistors is calculated to be 2 A.
A resistor is an electronic component that is designed to reduce the flow of electricity in a circuit. It is typically used to limit the amount of current flowing through a circuit, and it can also be used to regulate the voltage in a circuit. Resistors are typically composed of a conductive material, such as carbon, metal, or ceramic, and they are available in a variety of shapes and sizes.
I₂ is found using Ohm's Law. I₂ = (V₂ - V₁)/R₂, where V₂ and V₁ are the voltage across R₂ in the same direction as current I₂, and R₂ is the resistance of resistor 2. Substituting the given values gives
I₂ = (12 - 4)/200 = 8/200 = 0.04 A = 2 A.
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(a) an electron has a kinetic energy of 3. 0 ev. Find its wavelength. (b) also find the wavelength of a photon having the same energy.
Its wavelength is 8.47 x 10-11 m and wavelength of a photon having the same energy is 1.01 x 10-7 m.
What is wavelentgh?Wavelength length is a distance between two consecutive peaks of a wave it is most commonly associated with light and sound wave but can also refer to electromagnetic radiation like gamma rays x-rays and radio wavelentgh is usually measured in meters or nanometers.
(a) The wavelength of an electron with a kinetic energy of 3.0 eV can be calculated using the formula λ= h/√(2mKE) , where h is Planck's constant (6.62607 x 10-34 Js), m is the electron's mass (9.10938 x 10-31 kg), and KE is the kinetic energy (3.0 eV). Plugging in the values gives us a wavelength of 8.47 x 10-11 m.
(b) The wavelength of a photon with the same energy as the electron can be calculated using the equation λ= hc/E, where h is Planck's constant (6.62607 x 10-34 Js), c is the speed of light (299792458 m/s), and E is the energy of the photon (3.0 eV). Plugging in the values gives us a wavelength of 1.01 x 10-7 m.
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when the first astronauts travel to mars they will be traveling for long periods of time with no external time cues. you would predict that the circadian rhythms for these astronauts would
Based on the provided information, it can be predicted that the circadian rhythms for the astronauts would be drift toward a slightly longer cycle. (Option A)
A circadian rhythm, also known as circadian cycle, refers to a natural, internal process that regulates the sleep–wake cycle and is repeated roughly every 24 hours. It can refer to any process that originates within an organism and responds to the environment. These natural processes respond primarily to light and dark and affect most living things. A zeitgeber refers to any external cue or environmental cue that synchronizes an organism's biological rhythms such as circadian rhythm, usually naturally occurring and serving to entrain to the Earth's 24-hour light/dark and 12-month cycles. Circadian rhythms that are expressed in the absence of any 24-hour signals from the external environment are called free running, which are slightly longer cycle than usual. Hence, in the absence of external cue, the circadian rhythms for the astronauts would drift toward a slightly longer cycle.
Note: The question is incomplete as it is missing options which are a. They would drift toward a slightly longer cycle. b. They would become sporadic and show no definite pattern. c. They would stay synchronized with a 24-hour cycle. d. They would become synchronized with the light pattern around Mars.
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a ball is thrown upward. at a height of 10 meters above the ground, the ball has a potential energy of 50 joules (with the potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 joules. air friction is negligible. the maximum height reached by the ball is most nearly: group of answer choices 40 m
The maximum height reached by the ball thrown upwards with kinetic and potential energies specified is nearly 20 m.
Utilising the principle of energy conservation, we can solve this problem.
While the KE is largest at the surface and 0 at the top, the PE is zero at the surface and maximum at the top.
From the above data,
PE = mgh = 50 J ----(1)
m g* 10 = 50
m* g = 50/10
m* g = 5
The total energy at that point = PE + KE = 50 + 50 = 100 J
The PE will therefore be 100 J at the highest point.
m g H = 100 J , H is the needed height
Using the above-mentioned value of m* g, we have
H = 100/5
H = 20 m
So, the maximum height reached by the ball is 20 m.
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Approximately how much work do you do when you lift your 10.0 kg sister to a height of 1.5 m?
The amount of work done in lifting the sister to a height of 1.5m is approximately 147 J.
The height to which the sister of mass 10.0 Kg is lifted is 1.5m.
The work done to lift sister is given by,
W = MgH
Where,
M is the mass of the sister,
g is the acceleration due to gravity,
H is the height to which the sister as lifted,
The value of acceleration due to gravity of earth is 9.8m/s².
Now, putting all the values accordingly,
W = 10.0 x 9.8 x 1.5
W = 147 Joules.
So, the amount of work done in lifting the sister is 147 J.
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A mass of sunken lead is resting against the bottom in a glass of water. You take this lead, put it in a small boat of negligible mass, and float the boat in the water.
1.) Which of the following statements are true? (There may be more than one correct choice.)
A. The sunken lead displaces a volume of water equal to the lead's own volume.
B. The floating lead displaces a volume of water equal to the lead's own volume.
C. The sunken lead displaces a volume of water whose weight equals the lead's weight.
D. The floating lead displaces a volume of water whose weight equals the lead's weight.
The sunken lead displaces a volume of water equal to the lead's own volume. The floating lead displaces a volume of water whose weight equals the lead's weight.
What is Mass?
It is the most fundamental characteristic of matter and one of the fundamental quantities in physics. Mass is a term used to describe how much matter is there in a body. The kilograms is the SI unit of mass (kg).
A body's mass does not alter at any point in time. only in rare instances where a significant quantity of energy is supplied to or taken away from a body. A nuclear reaction, for instance, results in the mass of the substance being reduced as a very little amount of matter is transformed into a very large amount of energy.
This law provides a numerical description of how a force might alter a body's motion.
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imagine that you are an olympic sprinter, running at a speed of 11 m/s around the curve of a circular track with a radius of 36.5 m. what is your centripetal acceleration?
When an Olympic sprinter runs around the curve of a circular track with a radius of 36.5 m, they experience centripetal acceleration of 3.31m/s2.
Given that the runner's speed(v) = 11 m/s
Circular track radius (r) equals 36.5 meters
Centripetal acceleration (ac) is calculated as follows:
(11x11)/36.5 = 3.31 m/s2.
Centripetal acceleration is a characteristic of an object's motion along a circular path. Centripetal acceleration applies to any item travelling in a circle with an acceleration vector pointing in the direction of the circle's center. The centripetal acceleration, denoted by the symbol AC, has a magnitude equal to the square of the velocity of the body along the curve divided by the radius of the circle, denoted by the symbol r. This is also known as the formula ac = v2/r.
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a particle has potential energy u(x)=x+sin((2rad/m)x) as a particle moves over the range 0m≤x≤πm.
A particle has potential energy U(x)=x+sin ((2 rad/m) x) as a particle moves over the range 0 m \leq pi m The equilibrium positions in this range will be a=(pi/3), x=(2pi/3).
Potential energy and equilibrium are related in that the body's potential energy is lower in such an equilibrium.
In this case, the state generates a force that does not resist the displacement when a little distance displaces the body.
When the body shifts from its initial posture in such a situation.
Potential energy is a form of stored energy that is dependent on the relationship between different system components.
When a spring is squeezed or extended, its potential energy increases.
If a steel ball is lifted above the ground as opposed to falling to the ground, it has higher potential energy.
A particle has potential energy u(x)=x+sin 2 x
Now differentiating with respect to x.
[tex]\Rightarrow \frac{d u}{d x}=1+2 \cos 2 x \\\\[/tex]
for equilibrium point
[tex]\frac{d u}{d x}=0 \\\\\Rightarrow (1+2 \cos 2 x)=0 \\\\\Rightarrow \cos 2 x=-\frac{1}{2}[/tex]
[tex]$$\begin{aligned} \Rightarrow \cos 2 x=\cos \left(\pi-\frac{\pi}{3}\right) \\\Rightarrow 2 x=\frac{2 \pi}{3} \Rightarrow x=\frac{\pi}{3} \\\cos 2 x=\cos \left(\pi+\frac{\pi}{3}\right) \\\Rightarrow 2 x=\frac{4 \pi}{3} \Rightarrow x=\frac{2 \pi}{3}\end{aligned}$$[/tex]
Hence, a=(Pi/3), x=(2pi/3) is correct,
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The correct questions should be:
A particle has potential energy U(x)=x+sin ((2 rad/m) x) as a particle moves over the range 0 m [tex]\leq[/tex] pi m.
Where are the equilibrium positions in this range?
Check all that apply.
x=pi/6 m
x=pi m
x=(pi/2) m
x=(pi/3) m
x=(2/3) pi m
The magnetic field is uniform over each face of the box shown in (Figure 1). Suppose B1 = 2 T, B2 = 2 T.Part AWhat is the magnetic field strength on the front surface?
[tex]B_{f}[/tex] = - 4T is the magnetic field strength on the front surface for the given details B1 = 2 T, B2 = 2 T .
In terms of direction, we know that by convention, the flux entering the surface is negative and the flux leaving the surface is positive.
Apply the following formula to all of the box's surfaces:
3T(2 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) =6* [tex]10^{-6}[/tex]T[tex]m^{2}[/tex] on the left surface
3T(2 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) = 6* [tex]10^{-6}[/tex] T[tex]m^{2}[/tex] for the right surface
-2T(2 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) = -4* [tex]10^{-6}[/tex] T[tex]m^{2}[/tex] top surface
-1T(2 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) = -2* [tex]10^{-6}[/tex] T[tex]m^{2}[/tex] bottom surface
-2T(2 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) = -2* [tex]10^{-6}[/tex] T[tex]m^{2}[/tex] back surface
Assume that the magnetic field strength on the front surface is [tex]B_{f}[/tex]
[tex]B_{f}[/tex]T(1 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) = [tex]B_{f}[/tex]* [tex]10^{-6}[/tex] T[tex]m^{2}[/tex] front surface
The net flux through all of the box's surfaces should be zero.
(6T +6T-4T-2T+BfT)([tex]10^{-6}[/tex][tex]m^{2}[/tex]) = 0
When we divide [tex]10^{-6}[/tex][tex]m^{2}[/tex] on both sides, we get:
12T-8T+[tex]B_{f}[/tex]=0
4T+[tex]B_{f}[/tex] = 0
[tex]B_{f}[/tex]= - 4T
On the front surface, the magnetic field strength is [tex]B_{f}[/tex] = - 4T.
Because it is negative, it indicates that the magnetic field is entering the front surface.
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B) Calculate the maximum force of static friction that could exist in this system.
two objects attract each other with a gravitation force of magnitude 3.80 x 10-8 n when separated by a distance of 0.350 m. if the difference in mass of the objects is 7.50 kg, what is the mass for each of these objects?
The mass for each of these objects is 12.91kg and 5.41kg.
Gravitational Force:
The traditional hypothesis that explains gravity is Newton's law of gravitation. Only the masses of two objects and their distance from one another are taken into account by this law. According to Newton's law of gravitation, the following is how much gravitational force there is between two objects.
F = GMm/r²
Where,
r is the radius.
M and m are the masses of the objects.
G = Universal constant = 6.67 × 10⁻¹¹ [tex]\frac{m^{3} }{kgs^{2} }[/tex]
Given,
Gravitational Force = 3.8 × 10⁻⁸ N
Distance between two objects = 0.35 m
Let,
The mass of one object is x kg.
Then,
The mass of the second object = (x - 7.5) kg.
Now,
F = GMm/r²
3.8 × 10⁻⁸ = 6.67 × 10⁻¹¹ × x × (x - 7.5)/[tex](0.35)^{2}[/tex]
x² - 7.5x - 575.76 = 0
x = 12.91, 5.41
Hence,
The mass for each of these objects is 12.91kg and 5.41kg.
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what is the phenomenon called when the center of a galaxy gets extremely bright due to lots of material falling into the supermassive galaxy at the center of a galaxy?
When this occurs, a supernova results. A supernova is a star that explodes and sends a portion of the star into space. Supermassive black holes are believed by scientists to have formed simultaneously with the galaxy they are in.
What is Galaxy ?
Galaxies are collections of stars and other celestial objects that are gravitationally bound. The cosmos contains more than 100 billion galaxies, each of which has stunning formations seen in photographs captured by telescopes of the far sky.
According to Jenna Samuel, a PhD candidate in astrophysics at the University of California, Davis, a galaxy may be conceptualised as a collection of stars, gas, and dark matter that are all gravitationally bonded to one another
A galaxy is a vast region of space bound together by gravity and made up of stars, dust, interstellar gas, stellar remains, and dark matter. The Greek word "galaxies" is the source of the English word "galaxy." It is challenging to gauge the size of the cosmos! There are numerous galaxies in the cosmos, and each one contains millions of stars that are constrained by a special force called gravitational pull. The cosmos contains about 70,000,000,000 stars. The Milky Way Galaxy contains the solar system in which our planet is located.
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