Hence, work done over the particle is 26
According to the given information
Consider a particle that moves on the line segment from (1,0,0) to (3,4,2)
The objective is to find the work done by the force field [tex]$F(x, y, z)=\langle y+z, x+z, x+y\rangle$[/tex] on the particle.
The particle moves on the line segment joining the points (1,0,0) to (3,4,2).
Recall that the work done over the particle is given by the integral as follows:
[tex]W=\oint_C F \cdot d r[/tex]
The curve C represents the line segment from the point (1,0,0) to (3,4,2).
Calculate the vector function which represents the segment such as,
[tex]& r(t)=\langle 1,0,0\rangle+t\langle 3-1,4-0,2-0\rangle \\[/tex]
[tex]& r(t)=\langle 1,0,0\rangle+t\langle 2,4,2\rangle \\[/tex]
[tex]& r(t)=\langle 1+2 t, 4 t, 2 t\rangle[/tex]
The vector [tex]$\vec{r}(t)=(1+2 t) \vec{i}+(4 t) \vec{j}+(2 t) \vec{k}$[/tex]
Compare the above equation with [tex]$\vec{r}(t)=x \vec{i}+y \vec{j}+z \vec{k}$[/tex]
Evaluate the value of x, y, z by above equations.
x=1+2 t, y=4 t, z=2 t
Since, [tex]$F(x, y, z)=\langle y+z, x+z, x+y\rangle$[/tex]
Substitute the values of equation (2) to get,
[tex]x & =y+z \\[/tex]
[tex]& =4 t+2 t \\[/tex]
[tex]& =6 t \\[/tex]
[tex]y & =x+z \\[/tex]
[tex]& =1+2 t+2 t \\[/tex]
[tex]& =1+4 t \\[/tex]
[tex]z & =x+y \\[/tex]
[tex]& =1+2 t+4 t \\[/tex]
[tex]& =1+6 t[/tex]
Find the derivate of the vector as,
[tex]d r(t)=(2 \vec{i}+4 \vec{j}+2 \vec{k}) d t[/tex]
Here [tex]$0 \leq t \leq 1$[/tex]
Substitute the values in equation (1) as follows:
[tex]& \oint F \cdot d r=\int F(r(t)) \cdot r^{\prime}(t) d t \\[/tex]
[tex]& =\int_0^1 F(r(t)) \cdot r^{\prime}(t) d t \\[/tex]
[tex]& =\int_0^1((6 t) \vec{i}+(1+4 t) \vec{j}+(1+6 t) \vec{k}) \cdot(2 \vec{i}+4 \vec{j}+2 \vec{k}) d t \\[/tex]
[tex]& =\int_0^1(12 t+4+16 t+2+12 t) d t[/tex]
[tex]& =\int_0^1(40 t+6) d t \\[/tex]
[tex]& =\left(\frac{40 t^2}{2}+6 t\right)_0^1 \\[/tex]
[tex]& =\left(20 t^2+6 t\right)_0^1 \\[/tex]
[tex]& =26[/tex]
Hence, work done over the particle is 26
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Calculate the total no. of electrons drifting through a circuit in 20 min 40 sec if a current of 40 mA flows through the circuit (charge of one electron = 1.6 x 10^-19)
The number of electrons drifting through the circuit is 3×10¹⁹.
What is an electron?An electron is a negatively charged subatomic particle that together with protons and neutrons form an atom's nucleus.
To calculate the total number of electrons drifting through the circuit, we use the formula below.
Formula:
n = It/q'.............................. Equation 1Where:
n = Number of electronsI = Currentt = Timeq' = Charge on one electronFrom the question,
Given:
I = 40 mA = 0.04 At = 20 min 40 sec = (20×60)+40 = 120+40 = 160 sq = 1.6×10⁻¹⁹ CSubstitute these values into equation 1
n = (0.04×120)/(1.6×10⁻¹⁹)n = 3×10¹⁹ ElectronHence, the number of electrons is 3×10¹⁹.
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find the work required to move an object in the force field f along the straight line from a(0,0,0) to b(,,). check to see whether the force is conservative.
Answer:
0.099
Explanation:
The CERN super collider built in Geneva has a radius of 30 km. It bombards protons together near the speed of light. If the speed of light is 3 x 10^8 m/s, how much centripetal acceleration would the atoms have when they were close to the speed of light? (ans 3x10¹2 m/s²)
The centripetal acceleration would the atoms have when they are close to the speed of light is 3 * 10¹² m/s².
What is centripetal acceleration?Centripetal acceleration is the acceleration of a body that is traveling in a circular path.
Centripetal acceleration is directed toward the center of the circular path. The centripetal acceleration of a body is equal and opposite to the centrifugal acceleration of a body which is directed outwards from the center of the circular path the object is traveling in.
The formula for calculating centripetal acceleration is given below as follows:
a = v² / r
where;
a is the centripetal accelerationv is velocityr is radiusCalculating the centripetal acceleration of the proton:
v = 3.0 * 10⁸ m/s
r = 30 km = 30000 m
a = (3.0 * 10⁸)² / 30000
a = 3 * 10¹² m/s²
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Khan academy need help asap
The correct expression of the acceleration of the object is given as; a = F/m. Option B.
What is the acceleration?We know that the acceleration has to do with the ratio of the force and the mass. The Newton second law can lead us to the definition of the force that acts on an object that does involve the acceleration of the object.
We then have;
F = ma
F = force on the object
m = mass of the object
a = acceleration of the object
Then we have;
a = F/m
This is the acceleration of the woman.
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two rollerbladers face each other and stand at rest on a flat parking lot. tracey has a mass of 32 kg, and jonas has a mass of 45 kg. when they push off against one another, jonas acquires a speed of 0.35 m/s .what is tracey's speed?
Since the momentum remains same before and after push-off, therefore Tracey's speed will be 0.492 m/s.
Momentum is a product of mass and the velocity of a body.
The SI unit for momentum is kg-m/sIt is a vector quantity and has the direction same as that of the velocity of the object.It is represented by M and mathematically, M = Mass * VelocityThe initial momentum is always equal to the final momentum during collisions between two bodies.
Therefore; M₁U₁ +M₂U₂ = M₁V₁+ M₂V₂,
where M₁ is the mass of Tracey
M₂ is the mass of Jonas,
U is the initial velocity
V is the final velocity.
(32 ×0)+ (45×0) = (32 × V₁) + (45 × 0.35)
0 = 32V₁ + 15.75
32 V₁ = - 15.75
V₁ = - 0.492 ( negative sign indicates difference in direction)
There, Tracey's speed will be 0.492 m/s.
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Collisions in Saturn’s Rings : Each of the particles in the densest part of Saturn’s rings collides with another particle about every 5 hours. If a ring particle survived for the age of the solar system, how many collisions would it undergo ?
The ring particle would undergo roughly 8.3 trillion collisions over that period of time.
The age of the solar system is estimated to be 4.6 billion years. This means that a ring particle would undergo roughly 8.3 trillion collisions over that period of time. To calculate this number, we can use the following formula:
Number of collisions = Time (in hours) / Time between collisions (in hours) x Number of years
Number of collisions = 4.6 x 109 (years) x 24 (hours/day) x 365.25 (days/year) / 5 (hours)
Number of collisions = [tex]8.3 * 10^{12}[/tex] (collisions)
Therefore, the number of collisions in the ring are
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A 70.0 kg person leaps from a bridge in with a bungee cord attached and falls 120 meters. If the bungee cord stretches 2.5 meters during the stopping process, what’s its force constant (k)?
The force constant of the bungee cord when a person of mass 70 kg leaps on a bridge with it is 219.52 N/m.
What is force constant?The force constant or spring constant is a measure of the stiffness of a spring. It is the force per unit deformation of the spring. Its SI unit is N/m.
To calculate the force constant of the bungee cord, we use the formula below.
Formula:
K = 2mgh/e²............. Equation 1Where:
K = Force contant of the bungee cordm = Mass of the persong = Acceleration due to gravityh = Height at which the person falle = extensionFrom the question,
Given:
m = 70 kgg = 9.8 m/s²h = 120 me = 2.5 mSubstitute these values into equation 1
K = (2×70×9.8/2.5²)K = 219.52 N/mHence, the force constant of the bungee cord is 219.52 N/m.
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Stars begin burning helium to carbon when the temperature rises in the core. This temperature increase is caused by a. gravitational collapse. b. fusing hydrogen into helium in the core. c. fusing hydrogen into helium in a shell around the core. d. degenerate-electron pressure.
When the core temperature rises, stars start burning helium to carbon. Hydrogen and helium are fused in a shell surrounding the core, raising the temperature.
The most prevalent method of generating energy in the cosmos is hydrogen fusion. The gravitational force is utilised to fuse hydrogen at the centres of our Sun and other stars, where it has a density more than 70 times greater than that of steel. Thus, all of the heat and light on earth comes from fusion. Helium is a chemical element with the atomic number 2 and the symbol He. The first member of the noble gas group in the periodic table, it is a colourless, odourless, tasteless, inert, monatomic gas that is not harmful.
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how many wavelengths of the radio waves are there between the transmitter and radio receiver if the woman is listening to an am radio station broadcasting at 1540 khz?
Wavelengths of the radio waves between the transmitter and radio receiver if the woman is listening to an am radio station broadcasting at 1540 Khz is 194 m.
We can deduce three important relationships from the wave equation:
Speed is directly proportional to wavelengthSpeed is directly proportional to frequencyWavelength is inversely proportional to frequencySo the relation is : v = λf
where, v = speed of wavelength
λ = wavelength
f = frequency
Given, frequency (f) = 1540Khz = 1540000hz
v = speed of light = [tex]3 * 10^{8} m/s[/tex]
Putting these values in above equation we get λ = 194m
So Wavelengths of the radio waves between the transmitter and radio receiver if the woman is listening to an am radio station broadcasting at 1540 Khz is 194 m.
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PLEASE HELP 50 POINTS!!
An unknown material bolt with a mass of .43 kg is heated to a temperature of 100 oC, then it is placed in 1 kg of water at a temperature of 20oC, a simple calorimeter and the top is sealed. Time is allowed to go by and the equilibrium temperature is 23.059oC. What is the energy gained by the water during this process?
4186 J
96523.80 J
It doesn't gain any energy
12804.974 J
Answer:
Explanation:
The energy gained by the water can be calculated using the formula for the heat capacity of water, which is: q = mc * Delta T, where q is the energy gained by the water, m is the mass of the water, c is the heat capacity of water, and Delta T is the change in temperature of the water. In this case, m = 1 kg, c = 4.184 J/g * oC, and Delta T = 23.059 - 20 = 3.059 oC. Substituting these values into the formula, we find that the energy gained by the water is approximately 52.3 J.
The heat gained by water will be equal to the heat lost by the material bolt and it can be calculated using calorimetric equation. The heat energy gained by water is equal to 12800 J.
What is calorimetry?Calorimetry is an analytical technique used to determine the heat energy absorbed or released by a reaction system. The calorimetric equation connecting the heat energy q with the mass m, temperature difference ΔT and specific heat capacity c is written as:
q = m c ΔT.
The specific heat capacity of water = 4.18 J/ g °C
mass = 1 kg = 1000 g
temperature difference from 20 to 23. 059 °C.
The heat energy gained by water from the material bolt is then calculated as follows:
q = 4.18 J/ g °C × 1000 g × (23. 059 0 - 20 °C )
= 12800 J.
Therefore, the energy gained by water during the process is 12800 J.
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in an oscillator consisting of a spring and a block, the amount of elastic potential energy is at its maximum when:
For 1/4 value of r is the potential energy equal to the total energy.
What is potential energy?Potential energy is the form of energy that a object gain.
first want to find the value of our, what value of R is the potential energy equal to the total energy? So you are is equal to negative 1/4 pi epsilon naught E squared over R. Which is the potential energy. And E. This is a total energy. So we just set these two values equal to each other. So negative 1/4 pi epsilon naught E squared over R. Is equal to negative M. E. To the fourth divided by eight E squared and squared each squared and R is equal to two. So we can go ahead and solve this. We get R. Is equal to two. Absolutely not H squared divided by pi M. R. E squared. And actually this is just two times A. So the radius is to a. Now part B. We want to find the probability of electron being found in this classically forbidden forbidden region are greater than the classical turning point. So we need, so first of all let's look at the ground state wave function which is one over squared pi a cubed times E. To the negative are over A. This is what will be needed to integrate to find the probability. So the probability goes from R. is equal to two way to sigh.
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ou hold a picture motionless against a wall by pressing on it, as shown in the figure.You hold a picture motionless against a wall by pressing on it. draw a free body diagram.
The picture of free body diagram drawn below:
What is free body diagram?A free-body diagram (FBD; sometimes known as a force diagram) is a graphical representation used in physics and engineering to illustrate the applied forces, moments, and consequent reactions on a body under a particular state.
The object of interest, the forces acting on it, and the resolution of each force vector into its x- and y-components are all shown in a free-body diagram. Each item in the issue requires a distinct free-body diagram.
Forces are depicted as arrows heading away from the object, which is depicted as a dot. Occasionally known as force diagrams.
The picture of free body diagram drawn below:
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The complete question is as follows:
how much excess charge must be placed on a copper sphere 25.0 cmcm in diameter so that the potential of its center is 3.75 kvkv ?
Excess charge must be placed on a copper sphere = 4.167 x 10^(-8) C
The potential is the same within and equal to the potential outside, as if the charge were concentrated in the center, at all places. At infinity, there is no potential.
From the question, we have
kq/r = 1.5 x 1000
q = 1500r/k
= 1500*(0.25)/9x10^9 C
= 4.167 x 10^(-8) C
Electric potential :
The amount of work required to convey a unit of electric charge from a reference point to a given place in an electric field is known as the electric potential (also known as the electric field potential, potential drop, or the electrostatic potential).
Complete question:
How much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its center, relative to infinity, is 3.75 kv?
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Which of the following is the half life of first order reaction
A. t1/2 = A0/2k
B. t1/2 = 0.693/2k
C. t1/2 = 2k
D. t1/2 = 0.693/k
A first order reaction has a half-life of t1/2 = 0.693/k. When the rate and reactant concentration are inversely correlated, a reaction is referred to as a first-order reaction.
Give an illustration of first order answer:
First-order reactions frequently happen. Aspirin hydrolysis and the interaction of t-butyl bromide with water to form t-butanol are examples of first-order reactions. Another process with apparent first-order kinetics is the hydrolysis of the antitumor drug cisplatin.
First and second order reactions: what do they signify?
The rate of a first-order reaction is influenced by the concentration of one of the reactants. The second-order reaction rate is determined by the square of the concentration of a reactant or by the product of the concentrations of two reactants.
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a person, sunbathing on a warm day, is lying horizontally on the deck of a boat. her mass is 59.5 kg, and the coefficient of static friction between the deck and her is 0.566. assume that she is moving horizontally, and that the static frictional force is the only force acting on her in this direction. (a) what is the magnitude of the static frictional force when the boat moves with a constant velocity of 8.16 m/s? (b) the boat speeds up with an acceleration of 1.00 m/s2, and she does not slip with respect to the deck. what is the magnitude of the static frictional force that acts on her? (c) what is the magnitude of the maximum acceleration the boat can have before she begins to slip relative to the deck?
a) since a=0 therefore, friction force =0
b) friction = 59.5 × 1 =59.5 N.
c)maximum acceleration = 0.566 × g =5.54 m/s².
What is Friction force?The force preventing sliding against one another of solid surfaces, fluid layers, and material components is known as friction. There are various kinds of friction: Two solid surfaces in touch are opposed to one another's a relative lateral motion by dry friction.
What is acceleration?Acceleration is the rate at which an object's velocity with respect to time changes. They are vector quantities. The direction of the net force acting on an object determines the direction of its acceleration.
Hence, (a) since a=0 therefore, friction force =0, (b) friction = 59.5 × 1 =59.5 N, (c)maximum acceleration = 0.566 × g =5.54 m/s².
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the specific heat capacity of aluminum is about twice that of iron. Consider two blocksof equal mass, onemade of aluminum and the other one made of iron, initially in thermal equillibrium. when the two materials have reached thermal equilibrium, the block of aluminum is cut in half in equal quantities of heat are added to the iron block and to each portion of the aluminum block. which of the following statements is true? a)the three block are no longer in thermal equilibrium, the iron block is warmer b)the three blocks are no longer in thermal equilibrium, both aluminum blocks are warmer c)the three blocks remain in thermal equilibrium
The statement which is true for three blocks is c)the three blocks remain in thermal equilibrium. So, correct option is c.
Specific heat capacity or warm limit is an actual property of issue, characterized as how much intensity to be provided to an item to deliver a unit change in its structure. The SI unit of intensity limit is joule per kelvin (J/K).
Two actual frameworks are in thermal equilibrium in the event that there is no net progression of nuclear power between them when they are associated by a way penetrable to warm. Warm harmony submits to the zeroth law of thermodynamics. A framework is supposed to be in warm harmony with itself on the off chance that the temperature inside the framework is spatially uniform and transiently consistent.
The reason behind of being in thermal equilibrium state is because specific heat capacity depends on the type of material or we can it depends on the property of the material by which it is made, but not on orientation of the material how it is placed.
Hence, option c is correct.
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determine which integers in the set s:(-32 -8 16 32) will make the inequailty
The number m has the ability to make the inequality true = -8
What is an inequality ?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
Inequalities which are commonly used are as follows :
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
The integer that will make the inequality true is m = -8
(1/4)(m - 4) ≤ (1/8)(m - 16)
1/4 x -12 ≤ 1/8 x -24
-3 ≤ -3
According to the given information
We have,
One-fourth times the difference between m and four is less than or equal to one-eighth times the difference between m and sixteen
This can be written as,
(1/4)(m - 4) ≤ (1/8)(m - 16)
The value at which the inequality will be true.
S = {−32, −8, 16, 32}
We will check each value.
m = -32
1/4 x -36 ≤ 1/8 x -48
-9 ≤ -4
Not true
m= -8
1/4 x -12 ≤ 1/8 x -24
-3 ≤ -3
True
m = 16
1/4 x 12 ≤ 1/8 x 0
3 ≤ 0
Not true
m = 32
1/4 x 28 ≤ 1/8 x 16
7 ≤ 2
Not true
Thus,
The number m has the ability to make the inequality true = -8
(1/4)(m - 4) ≤ (1/8)(m - 16)
1/4 x -12 ≤ 1/8 x -24
-3 ≤ -3
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The net force exerted on a car traveling in a circular path at constant speed i A) directed toward the center of the curve. B) zero because the car is not accelerating. C) directed forward, in the direction of travel. D) none of the above
The net force exerted on a car traveling in a circular path at constant speed is A) directed toward the center of the curve. So, correct option is A.
The force which is acted on the car and responsible to move a car towards the center of the curve is called as centripetal force. A centripetal force is a force that causes a body to follow a bended way. Its course is dependably symmetrical to the movement of the body and towards the decent place of the quick focus of shape of the way. Isaac Newton portrayed it as "a force by which bodies are drawn or prompted, or in any capacity tend, towards a point regarding a center". In Newtonian mechanics, gravity gives the centripetal force causing galactic circles.
Hence, correct option is A.
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An explorer in Antarctica leaves his shelter during a whiteout. He takes 40 steps northeast, next 80 steps at 60$^{\circ}$ north of west, and then 50 steps due south. Assume all of his steps are equal in length. (a) Sketch, roughly to scale, the three vectors and their resultant. (b) Save the explorer from becoming hopelessly lost by giving him the displacement, calculated by using the method of components, that will return him to his shelter.
a) R= Resultant vector R=A+B+C ,D=12 steps i^−48 steps j^
A resultant vector is what?The resultant vector is described as a single vector with the same consequence as several other vectors taken together.
How do you locate the outcome vector?R = A + B.Formula 2: To obtain the resultant, opposing vectors are subtracted from one another.Here, a vector B is pointing in the opposite direction of the vector A, as well as the resulting vector is called R.
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you are at a furniture store and notice that a grandfather clock has its time regulated by a physical pendulum that consists of a rod with a movable weight on it. when the weight is moved downward, the pendulum slows down; when it is moved upward, the pendulum swings faster. if the rod has a mass of 1.23 kg and a length of 1.25 m and the weight has a mass of 0.50 kg located a distance of 1.00 meters from the top of the pendulum, what will the period be?
The separates the attached mass from the pendulum's peak.
The moment of inertia of an item is the opposite of its angular acceleration. Moment of inertia is influenced by mass and gyrating radius, respectively. The moment of inertia can be altered by modifying the rotational axis.
Moment of inertia: The phrase "moment of inertia" refers to a physical quantity that measures how resistant a body is to having the direction of a torque change the speed at which it rotates along an axis (turning force).
Complete question:
You are at a furniture store and notice that a Grandfather clock has its time regulated by a physical pendulum that consists of a rod with a movable weight on it. When the weight is moved downward, the pendulum slows down; when it is moved upward, the pendulum swings faster. If the rod has a mass of 1.23kg and a length of 1.25m and the weight has a mass of 1.36kg, where should the mass be placed to give the pendulum a period of 2.00 seconds? Measure the distance in meters from the top of the pendulum.
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the period of a mass-spring oscillator is 2.84 s. every time the oscillator completes a full period, the amplitude of the oscillation gets reduced to 93.6 percent of the previous amplitude. how much time does it take for the amplitude to decay to 43.2 percent of its original initial value?\
30.05 sec much time it takes for the amplitude to decay to 43.2 percent of its original initial value
What is amplitude?The greatest displacement or distance that a point on a wave or vibrating body may travel in relation to its equilibrium position It is equivalent to the vibration path's half-length.
Given data
Time period (T) = 2.84 sec
Reduction = 93.6 %
We know that logarithmic decrement is given by:
a₁ = a₀ [tex]e^-{bt}[/tex]
where b = constant
As a₁ = 0.936 a₀
or, 0.936 a₀ = a₀ [tex]e^-{b*2.84}[/tex]
or, b = 0.002
Now a₁ = 0.432 a₀
or, 0.432 a₀ = a₀ [tex]e^-{0.002*t}[/tex]
or, t = 30.05 sec
So, it will take 30.05 sec to decay 43.2 %.
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a thick copper wire connected to a voltmeter surrounds a region of time-varying magnetic flux, and the voltmeter reads 5 volts. if instead of a single wire we use a coil of thick copper wire containing 24 turns, what does the voltmeter read?
If instead of a single wire we use a coil of thick copper wire containing 24 turns, then the voltmeter reads 120 V.
What is voltmeter?A voltmeter is also known as a voltage meter. It is an instrument used for measuring the potential difference or voltage between two points in an electrical circuit.
Emf of a solenoid is given by formula:
E= - N (dФ/dt)
Where,
N is Number of turns;
Ф is Magnetic flux and t is time taken
The negative sign indicates the direction of flow or polarity.
It can be seen clearly that the induced emf is directly proportional to the number of turns.
So, if the initial voltage is given 5 volts at a set number of 24 turns, the voltmeter reads:
= E *N
= 5 * 24
Voltmeter reads = 120 volts.
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9. 2076 Set B Q.No. 9b Two galvanometers, which are otherwise identical; are fitted with different coils. One has coil of 50 turns and resistance 1022 while the other has 500 turns and a resistance of 6002. What is the ratio of the deflection when each is connected in turns to a cell of e.m. 25 V and internal resistance 50 ohms?
The ratio of the deflection when each is connected in turns to a cell of e.m.f 25 V and internal resistance 50 ohms is 13: 12
What is internal resistance?Internal resistance can be described as the resistance within a battery, or other voltage source, that causes a drop in the source voltage when there is a current.
The parameters given are :
Coil 1 = 50 turns
Coil 2 = 500 turns
Resistance 1 = 1022
Resistance 2 = 6002
Internal resistance = 50 ohms
Emf = 25v
I = 25/ 50+ 10
I = 25/60
I = 5/ 12 A
[tex]I_{2}[/tex] = 25/50+ 600
= 25/ 650
= 5/ 130 A
The ratio of the deflection when each is connected in turns to a cell of e.m. 25 V and internal resistance 50 ohms =
Q1/ Q2
Q1 = N1 x B x [tex]I_{1}[/tex] / c
Q2 = N2 x B x [tex]I_{2}[/tex] / c
therefore Q/ Q2 = (50 x 5/12 )/ (500 x 5/130)
Q1 / Q2 = 12/ 13 which 13: 12
Therefore, The ratio of the deflection when each is connected in turns to a cell of e.m. 25 V and internal resistance 50 ohms is 13: 12.
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what is the angular-momentum quantum number, ℓ, for the orbital shown here?
The orbital form of an electron is generally described by the angular momentum quantum number, denoted by the letter l. The value of the main quantum number, n, determines the value of l.
How can the orbital angular momentum L be determined?The sum of the orbital angular momenta from each electron creates the total orbital angular momentum, which has a magnitude of square root of L(L + 1) (L), where L is an integer.
How is the angular quantum number L calculated?Therefore, using the equation l=n1 l = n 1 and knowing the main quantum number, it is easy to determine the angular momentum quantum number. According to this statement, the primary quantum number will never be greater than the azimuthal quantum number.
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a 0.50-kg mass is attached to a spring of spring constant 20 n/m along a horizontal, frictionless surface. the object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. what is the amplitude of vibration?
The vibration amplitude of a spring with a constant of 20 N/m which has a speed of 1.5 m/s with a mass of 0.50 kg which is associated = 0.237 m.
Oscillation EnergyWhen an object oscillates on a spring, the kinetic energy and potential energy of the mass-spring system change with time.
The total energy (the kinetic energy + potential energy) is constant.
The kinetic energy of an object moving with speed v is:
½ mv².
The potential energy of a spring with a constant k is:
= ½ kx².
The total energy = ½ kx² + ½ mv² = ½ kA².
The total energy equation gives the general property of simple harmonic oscillations which is directly proportional to the square of the amplitude.
And, we have:
m = 0.50 kg
k = 20 N/m
v = 1.5 m/s
Remember, the total energy = ½ kA².
So,
A² = (m)(v)² / k
= (0.50) (1.5)² / 20
= 0.05625
A = [tex]\sqrt{0.05625}[/tex]
= 0.237 m
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what is a wave frequency? a. the loudness of a wave as it travels though the air b. the speed that a wave is passed from particle to particle through a medium c. the height of a wave between peak and trough d. the number of waves that pass a fixed point in a fixed period of time
The quantity of waves that pass a set location in a predetermined period of time is known as frequency. Therefore, if a wave passes through in half a second, the frequency is 2 per second. The frequency is 100 times per hour if it takes 1/100 of an hour.
This quiz asks, "What is the frequency of a wave?
The quantity of waves emitted by a source per second is known as the frequency of a wave. It is also the quantity of waves per second that pass a specific spot.
In a nutshell, what is the frequency of a sound wave?
The frequency of the wave is the total number of waves generated in one second. Frequency refers to the number of vibrations measured each second. Here is an easy illustration: The frequency of the waves will be 5 hertz (Hz), or 5 cycles per second, if five full waves are created in one second.
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Matt decides to stage dive into the mosh pit. If the stage is 2.5 m above the crowd and he jumps with a horizontal velocity of 2m / s how far from the stage will he land in the crowd
Distance Matt will land 1 m away from the stage.
What is Distance?Distance is a numerical measurement of how far apart two objects or points are in space. It is usually measured in linear units such as meters, miles, or kilometers. Distance can also be measured in angular units such as degrees or radians. Distance can be measured in both two-dimensional and three-dimensional space. In two-dimensional space, distance is measured along the x-axis and y-axis. In three-dimensional space, distance is measured along the x-axis, y-axis, and z-axis.
The horizontal distance traveled by Matt can be calculated using the equation:
d = v * t
where d is the distance, v is the velocity, and t is the time.
In this case, v = 2 m/s and t = the time it takes for Matt to fall 2.5 m. This can be calculated using the equation:
d = g * t^2 / 2
where g is the acceleration due to gravity, which is 9.8 m/s^2.
Plugging in the values, we get:
t = sqrt(2*2.5/9.8) = 0.5 seconds
Therefore, the distance traveled horizontally can be calculated as:
d = 2 * 0.5 = 1 m
Therefore, Matt will land 1 m away from the stage.
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You make yourself and your friend a cup of hot chocolate and add vanilla ice cream. You quickly enjoy yours, but your friend takes a long time to come, so you get to observe theirs as a science experiment.
In what direction does the heat flow? (2 points)
Describe how the kinetic energy of the hot chocolate changes once you add the ice cream. (2 points)
How does the kinetic energy of the ice cream change once you put it in the hot chocolate? (2 points)
What happens to the temperature of each substance? Be specific. (2 points)
When will the temperature of the ice cream and the hot chocolate stop changing? (2 points)
The answers include the following;
The direction in which the heat flows is from hot chocolate to the vanilla ice cream. The kinetic energy of the hot chocolate decreases once you add the ice cream.The kinetic energy of the ice cream increases once you put it in the hot chocolate.The temperature of each substance will exchange heat till an equilibrium is reached.The temperature of the ice cream and the hot chocolate will stop changing when there is uniformity.What is Temperature?This is referred to as the degree of hotness or coldness of a substance and it is influenced by thermal energy.
The direction in which the heat flows is from hot chocolate to the vanilla ice cream and the kinetic energy of the hot chocolate decreases once you add the ice cream.
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two blocks of masses m and 3 m are placed on a horizontal, frictionless surface. a light spring is attached to one of them, and the blocks are pushed together with the spring between them. m 3m m 3m before after (a) (b) v a cord holding them together is burned, after which the block of mass 3 m moves to the right with a speed of 2.06 m/s. what is the speed of the block of mass m? answer in units of m/s
V1f= -6.75 m/s (left),original elastic potential energy = 12.7575 J,The original energy is in the Spring,In bursting-apart process, The conservation of momentum is Holds.
(a) Mass of the first block, M
Mass of the second block, 3M
final speed of the second block, V2f =2.25 m/s
Before the cord burns, both masses are in rest oposition,
Hence, initial speed of then m is 0,
They are V1i, V2i = 0 m/s
Hence, by conservation of momentum,
MV1i + 3MV2i = MV1f + MV2f
M(0) + 3M (0) = MV1f + 3M (2.25 m/s)
V1f= -6.75 m/s (left)
(b) Kinetic energy of the system,
K.E = 1/2 MV1f2 + 1/2 3M V2f2
=1/2 (0.420 kg)(6.75 m/s)2+1/2(1.26)(2.25 m/s)2 (given, M = 0.420 kg)
=9.568125 J + 3.189375 j
=12.7575 j
According to conservation of energy,
The loos of kinetic energy is used to gain in original elastic potential energy
Hence, original elastic potential energy = 12.7575 J
(c) Since the spring stores the potential energy,
The original energy is in the Spring
(d) In bursting-apart process, The conservation of momentum is Holds.
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the absolute value of the slope of the production possibility frontier at any point:
The absolute value of the slope of the production possibility frontier at any point gives the quantity of the good on the vertical axis that must be given up producing an additional unit of the good on the horizontal axis. (Option C)
The marginal rate of transformation (MRT) enables the economists to evaluate the opportunity costs to produce one extra unit of something. MRT refers to the absolute value of the slope of the production possibility frontier. The production possibility frontier (PPF) refers to a curve on a graph that demonstrates the possible quantities that can be produced of two products if both depend upon the same finite resource. For each point on the frontier displayed as a curved line, there is a different marginal rate of transformation, and this rate is based on the economics of producing the two goods. Hence, MRT is equal to the opportunity cost of an additional unit of the good on the horizontal axis.
Note: The question is incomplete as it is missing options which are A) gives the autarky price of the good on the vertical axis. B) is found by dividing the horizontal change by a vertical change. C) gives the quantity of the good on the vertical axis that must be given up to produce an additional unit of the good on the horizontal axis. D) gives the autarky price of the good on the horizontal axis relative to the autarky price of the good on the vertical axis.
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