Answer:
The average power dissipated is 72 W.
Explanation:
Given;
peak voltage of the AC circuit, V₀ = 120 V
resistance of the resistor, R = 100 -ohm
The average power dissipated by the resistor is given by;
[tex]P_{avg} = \frac{1}{2} I_oV_o= I_{rms}V_{rms} = \frac{V_{rms}^2}{R}[/tex]
where;
[tex]V_{rms}[/tex] is the root-mean-square-voltage
[tex]V_{rms} = \frac{V_o}{\sqrt{2}} \\\\V_{rms} = \frac{120}{\sqrt{2}}\\\\V_{rms} = 84.853 \ V[/tex]
The average power dissipated by the resistor is calculated as;
[tex]P_{avg} = \frac{V_{rms}^2}{R}\\\\P_{avg} = \frac{84.853^2}{100}\\\\P_{avg} = 72 \ W[/tex]
Therefore, the average power dissipated is 72 W.
A plano-convex glass lens of radius of curvature 1.4 m rests on an optically flat glass plate. The arrangement is illuminated from above with monochromatic light of 520-nm wavelength. The indexes of refraction of the lens and plate are 1.6. Determine the radii of the first and second bright fringes in the reflected light.
Given that,
Radius of curvature = 1.4 m
Wavelength = 520 nm
Refraction indexes = 1.6
We know tha,
The condition for constructive interference as,
[tex]t=(m+\dfrac{1}{2})\dfrac{\lambda}{2}[/tex]
Where, [tex]\lambda=wavelength[/tex]
We need to calculate the radius of first bright fringes
Using formula of radius
[tex]r_{1}=\sqrt{2tR}[/tex]
Put the value of t
[tex]r_{1}=\sqrt{2\times(m+\dfrac{1}{2})\dfrac{\lambda}{2}\times R}[/tex]
Put the value into the formula
[tex]r_{1}=\sqrt{2\times(0+\dfrac{1}{2})\dfrac{520\times10^{-9}}{2}\times1.4}[/tex]
[tex]r_{1}=0.603\ mm[/tex]
We need to calculate the radius of second bright fringes
Using formula of radius
[tex]r_{2}=\sqrt{2\times(m+\dfrac{1}{2})\dfrac{\lambda}{2}\times R}[/tex]
Put the value into the formula
[tex]r_{1}=\sqrt{2\times(1+\dfrac{1}{2})\dfrac{520\times10^{-9}}{2}\times1.4}[/tex]
[tex]r_{1}=1.04\ mm[/tex]
Hence, The radius of first bright fringe is 0.603 mm
The radius of second bright fringe is 1.04 mm.
what is defect of vision
Answer:
The vision becomes blurred due to the refractive defects of the eye. There are mainly three common refractive defects of vision. These are (i) myopia or near-sightedness, (ii) Hypermetropia or far – sightedness, and (iii) Presbyopia. These defects can be corrected by the use of suitable spherical lenses.
Three ideal polarizing filters are stacked, with the polarizing axis of the second and third filters at 29.0and 58.0, respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity 110 after it passes through the stack.
If the incident intensity is kept constant, what is the intensity of the light after it has passed through the stack if the second polarizer is removed?
Answer:
I₂ = 143.79
Explanation:
To solve this problem, work them in two parts. A first one where we look for the intensity of the incident light in the set and a second one where we silence the light transmuted by the other set,
Let's start with the set of three curling irons
Beautiful light falls on the first polarized is not polarized, therefore only half the radiation passes
I₁ = I₀ / 2
this light reaches the second polarized and must comply with the Mule law
I₂ = I₁ cos² tea
The angle between the first polarized and the second is Tea = 29.0º
I₂ = I / 2 cos² 29
The light that comes out of the third polarized is
I₃ = I₂ cos² tea
the angle between the third - second polarizer is
tea = 58-29
tea = 29th
I3 = (I₀ / 2 cos² 29) cos² 29
indicate the output intensity
I3 = 110
we clear
I₀ = 2I3 / cos4 29
I₀ = 2 110 / cos4 29
I₀ = 375.96 W / cm²
Now we have the incident intensity in the new set of three polarizers
back to the for the first polarizer
I₁ = I₀ / 2
when passing the second polarizer
I₂ = I1 cos² 29
I2 = IO /2 cos²29
let's calculate
I₂ = 375.96 / 2 cos² 29
I₂ = 143.79
Which object forms when a supergiant explodes? a red giant a black hole a white dwarf a neutron star
Answer:
a neutron star
Explanation:
Answer:
d
Explanation:
Each proton-proton cycle generates 26.7 MeV of energy. If 9.9 Watts are generated via by the proton-proton cycle, how many billion neutrinos are produced
Answer:
4.635 *10^12 Neutrinos
Explanation:
Here in this question, we are to determine the number of neutrinos in billions produced, given the power generated by the proton-proton cycle.
We proceed as follows;
In proton-proton cycle generates 26.7 MeV of energy and in this cycle two neutrinos are produced.
From the question, we are given that
Power P = 9.9 watts = 9.9 J/s
Watts is same as J/s
The number of proton-proton cycles required to generate E energy is N = E / E '
Where E ' = Energy generated in proton-proton cycle which is given as 26.7 Mev in the question
Converting Mev to J, we have
= 26.7 x1.6 x10 -13 J
To get the number N which is the number of proton-proton cycle required, we have;
N = 9.9 /(26.7 x1.6 x10^-13) = 2.32 * 10^12
Since we have two proton cycles( proton-proton), it automatically means 2 neutrinos will be produced.
Therefore number of neutrions produced = 2 x Number of proton-proton cycles = 2 * 2.32 * 10^12 = 4.635 * 10^12 neutrinos
One long wire carries a current of 30 A along the entire x axis. A second long wire carries a current of 40 A perpendicular to the xy plane and passes through the point (0, 4, 0) m. What is the magnitude of the resultant magnetic field at the point y
Complete question is;
One long wire carries a current of 30 A along the entire x axis. A second long wire carries a current of 40 A perpendicular to the xy plane and passes through the point (0, 4, 0) m. What is the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis?
Answer:
B_net = 50 × 10^(-7) T
Explanation:
We are told that the 30 A wire lies on the x-plane while the 40 A wire is perpendicular to the xy plane and passes through the point (0,4,0).
This means that the second wire is 4 m in length on the positive y-axis.
Now, we are told to find the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis.
This means that the position we want to find is half the length of the second wire.
Thus, at this point the net magnetic field is given by;
B_net = √[(B1)² + (B2)²]
Where B1 is the magnetic field due to the first wire and B2 is the magnetic field due to the second wire.
Now, formula for magnetic field due to very long wire is;
B = (μ_o•I)/(2πR)
Thus;
B1 = (μ_o•I_1)/(2πR_1)
Also, B2 = (μ_o•I_2)/(2πR_2)
Now, putting the equation of B1 and B2 into the B_net equation, we have;
B_net = √[((μ_o•I_1)/(2πR_1))² + ((μ_o•I_2)/(2πR_2))²]
Now, factorizing out some common terms, we have;
B_net = (μ_o/2π)√[((I_1)/R_1))² + ((I_2)/R_2))²]
Now,
μ_o is a constant and has a value of 4π × 10^(−7) H/m
I_1 = 30 A
I_2 = 40 A
Now, as earlier stated, the point we are looking for is 2 metres each from wire 2 end and wire 1.
Thus;
R_1 = 2 m
R_2 = 2 m
So, let's calculate B_net.
B_net = ((4π × 10^(−7))/2π)√[(30/2)² + (40/2)²]
B_net = 50 × 10^(-7) T
In a velocity selector having electric field E and magnetic field B, the velocity selected for positively charged particles is v= E/B. The formula is the same for a negatively charged particles.
a. True
b. False
Answer:
True or False
Explanation:
Because.....
easy 50% chance you are right
Two parallel metal plates, each of area A, are separatedby a distance 3d. Both are connected to ground and each plate carries no charge. A third plate carrying charge Qis inserted between the two plates, located a distance dfrom the upper plate. As a result, negative charge is induced on each of the two original plates. a) In terms of Q, find the amount of charge on the upper plate, Q1, and the lower plate, Q2. (Hint: it must be true that Q
Answer:
Upper plate Q/3
Lower plate 2Q/3
Explanation:
See attached file
A train is approaching you at very high speed as you stand next to the tracks. Just as an observer on the train passes you, you both begin to play the same recorded version of a Beethoven symphony on identical MP3 players. (a) According to you, whose MP3 player finishes the symphony first?
A. your player,
B. the observer's player,
C. both finish at the same time. (b) According to the observer on the train, whose MP3 player finishes the symphony first?
A. your player,
B. the observer's player,
C. both finish at the same time. (c) Whose MP3 player actually finishes the symphony first?
A. your player,
B. the observer's player,
C. each observer measures his symphony as finishing first,
D. each observer measures the other's symphony as finishing first.
Answer:
a) Your player
b) Observer's player
c) Each measures their own first
Explanation:
Because given problem is having relative velocity to each other. The person sitting on the train is moving with a very high speed relative to the person standing next to the track.
In this case, the clock situated in the train will be running slow with respect to the stationary frame of reference
Which one of the following frequencies of a wave in the air can be heard as an audible sound by human ear
Answer:
1,000 Hz hope this helps.
Explanation:
The sound said to be audible if it comes in the range of audible sound range. The audible sound is the specific frequency range of sound, which can be heard by human ears. The audible sound frequency range is 20Hz−20,000H
You shine unpolarized light with intensity 52.0 W/m2 on an ideal polarizer, and then the light that emerges from this polarizer falls on a second ideal polarizer. The light that emerges from the second polarizer has intensity 15.0 W/m2. Find the intensity of the light that emerges from the first polarizer.
Answer:
The intensity of light from the first polarizer is [tex]I_1 = 26 W/m^2[/tex]
Explanation:
The intensity of the unpolarized light is [tex]I_o = 52.0 \ W/m^2[/tex]
Generally the intensity of light that emerges from the first polarized light is
[tex]I_1 = \frac{I_o}{2 }[/tex]
substituting values
[tex]I_1 = \frac{52. 0}{2 }[/tex]
[tex]I_1 = 26 W/m^2[/tex]
Two protons moving with same speed in same direction repel each other but what about two protons moving with different speed in the same direction?
Answer:In the case of two proton beams the protons repel one another because they have the same sign of electrical charge. There is also an attractive magnetic force between the protons, but in the proton frame of reference this force must be zero! Clearly then the attractive magnetic force that reduces the net force between protons in the two beams as seen in our frame of reference is relativistic. In particular the apparent magnetic forces or fields are relativistic modifications of the electrical forces or fields. As such modifications, they cannot be stronger than the electrical forces and fields that produce them. This follows from the fact that switching frames of reference can reduce forces, but it can’t turn what is attractive in one frame into a repulsive force in another frame.
In the case of wires the net charges in two wires are zero everywhere along the wires. That makes the net electrical forces between the wires very nearly zero. Yet the relativistic magnetic forces and fields will be of the same sort as in the case of two beams of charges of a single sign. This is true even in the frame of reference of what we think as the moving charges, that is, the electrons. In the frame of reference moving at the drift velocity of these current-carrying electrons, it is the protons or positively charged ions that are moving in the other direction. Consequently in any frame of reference for current-carrying wires in parallel, the net electrical force will be essentially zero, and there will be a net attractive magnetic force
Explanation:
Explanation:
Particles with similar charges (both positive or both negative) will always repel each other, regardless of their speed or direction.
Water has a specific heat capacity of 1.00 cal/g °C, and copper has a specific heat capacity of 0.092 cal/g °C. If both are heated to 100 °C, which takes longer to cool?
Answer:
The water takes longer, because it is the better insulator here.
Explanation:
Conductors and insulators work similarly in "reverse".
If something is a good heat conductor, then it's good at both absorbing heat energy and giving it away. Insulators are good at resisting temperature changes, but also take longer to cool down once they are heated up.
So because copper is the better conductor here, it will cool faster than the water at the same temperature.
Which statement about kinetic and static friction is accurate?
Static friction is greater than kinetic friction, and they both act in conjunction with the applied force.
Kinetic friction is greater than static friction, and they both act in conjunction with the applied force.
Kinetic friction is greater than static friction, but they both act opposite the applied force.
Static friction is greater than kinetic friction, but they both act opposite the applied forcr
Answer:
Static friction is greater than kinetic friction, but they both act opposite the applied force.
Explanation:
Newton's 3rd law states that every action has and equal but opposite reaction.
If an object has static friction, that means it stays in one spot, and it takes a great amount of force to get it moving.
Once the object is moving it has kinetic friction, but it's easier to keep it moving unless you are trying to stop it.
The equal but opposite reaction to something moving it is stopping it, and the equal but opposite reaction to stopping something is moving it.
The same amount of force used to move/stop something is used to stop/move it.
Static friction is greater than kinetic friction, but they both act opposite the applied force.
Friction is the force that opposes motion. Frictional force always acts in opposition to the direction of motion.
There are two kinds of friction;
Static frictionDynamic frictionSince more forces tend to act on a body at rest and prevent it from getting into motion than the forces that tend to stop an already moving body, it follows that static friction is greater than kinetic friction. Both act in opposite direction to the applied force.
Learn more: https://brainly.com/question/18754989
Charge of uniform density (0.30 nC/m2) is distributed over the xy plane, and charge of uniform density (−0.40 nC/m2) is distributed over the yz plane. What is the magnitude of the resulting electric field at any point not in either of the two charged planes?
Answer: E = 39.54 N/C
Explanation: Electric field can be determined using surface charge density:
[tex]E = \frac{\sigma}{2\epsilon_{0}}[/tex]
where:
σ is surface charge density
[tex]\epsilon_{0}[/tex] is permitivitty of free space ([tex]\epsilon_{0} = 8.85.10^{-12}[/tex][tex]C^{2}/N.m^{2}[/tex])
Calculating resulting electric field:
[tex]E=E_{1} - E_{2}[/tex]
[tex]E = \frac{\sigma_{1}-\sigma_{2}}{2\epsilon_{0}}[/tex]
[tex]E = \frac{[0.3-(-0.4)].10^{-9}}{2.8.85.10^{-12}}[/tex]
[tex]E=0.03954.10^{3}[/tex]
E = 39.54
The resulting Electric Field at any point is 39.54N/C.
The magnitude of the resulting electric field at any point should be 28.2 N/C.
Calculation of the magnitude:Since the Charge of uniform density (0.30 nC/m2) should be allocated over the xy plane, and charge of uniform density (−0.40 nC/m2)should be allocated over the yz plane.
So,
E1
= σ1/2ε0
= 0.30e-9/(2*8.85e-12)
= 16.949 N/C
So, direction of E1 is +z
Now
E2 = σ2/2ε0
= 0.40e-9/(2*8.85e-12)
= 22.6 N/C
So, direction of E2 is -x
Now
E = √(E1*E1+E2*E2)
= √(16.949*16.949+22.6*22.6)
= 28.2 N/C
Learn more about magnitude here: https://brainly.com/question/14576767
a 2.0 kg block slides on the horizontal, frictionless surface until it counters a spring force constant with
Complete question:
a 2.0 kg block slides on the horizontal, frictionless surface until it counters a spring with force constant of 955 N/m. The block comes to rest after compressing the spring a distance of 4.6 cm. Find the initial speed (in m/s) of the block.
Answer:
The initial speed of the block is 1.422 m/s
Explanation:
Given;
mass of the block, m = 2.0 kg
force constant of the spring, K = 955 N/m
compression of the spring, x = 4.6 cm = 0.046 m
Apply Hook's law to determine applied force on the spring;
F = Kx
F = (955 N/m)(0.046 m)
F = 43.93 N
Apply Newton's 2nd law to determine the magnitude of deceleration of the block when it encounters the spring;
F = ma
a = F / m
a = 43.93 / 2
a = 21.965 m/s²
Apply kinematic equation to determine the initial speed of the block;
v² = u² + 2ax
where;
v is the final speed of the block = 0
u is the initial speed of the block
x is the distance traveled by the block = compression of the spring
a is the block deceleration = -21.965 m/s²
0 = u² + 2(-21.965 )(0.046)
0 = u² - 2.021
u² = 2.021
u = √2.021
u = 1.422 m/s
Therefore, the initial speed of the block is 1.422 m/s
A goldfish bowl is spherical, 8.0 cm in radius. A goldfish is swimming 3.0 cm from the wall of the bowl. Where does the fish appear to be to an observer outside? The index of refraction of water is 1.33. Neglect the effect of the glass wall of the bowl.
Answer:
41.5 cm to the left of the observer
Explanation:
See attached file
which category would a person who has an IQ of 84 belong ?
The hot glowing surfaces of stars emit energy in the form of electromagnetic radiation. It is a good approximation to assume that the emissivity eee is equal to 1 for these surfaces.
Required:
a. Find the radius RRigel of the star Rigel, the bright blue star in the constellation Orion that radiates energy at a rate of 2.7 x 10^31 W and has a surface temperature of 11,000 K.
b. Find the radius RProcyonB of the star Procyon B, which radiates energy at a rate of 2.1 x 10^23 W and has a surface temperature of 10,000 K. Assume both stars are spherical. Use σ=5.67 x 10−8^ W/m^2*K^4 for the Stefan-Boltzmann constant.
Given that,
Energy [tex]H=2.7\times10^{31}\ W[/tex]
Surface temperature = 11000 K
Emissivity e =1
(a). We need to calculate the radius of the star
Using formula of energy
[tex]H=Ae\sigma T^4[/tex]
[tex]A=\dfrac{H}{e\sigma T^4}[/tex]
[tex]4\pi R^2=\dfrac{H}{e\sigma T^4}[/tex]
[tex]R^2=\dfrac{H}{e\sigma T^4\times4\pi}[/tex]
Put the value into the formula
[tex]R=\sqrt{\dfrac{2.7\times10^{31}}{1\times5.67\times10^{-8}\times(11000)^4\times 4\pi}}[/tex]
[tex]R=5.0\times10^{10}\ m[/tex]
(b). Given that,
Radiates energy [tex] H=2.1\times10^{23}\ W[/tex]
Temperature T = 10000 K
We need to calculate the radius of the star
Using formula of radius
[tex]R^2=\dfrac{H}{e\sigma T^4\times4\pi}[/tex]
Put the value into the formula
[tex]R=\sqrt{\dfrac{2.1\times10^{23}}{1\times5.67\times10^{-8}\times(10000)^4\times4\pi}}[/tex]
[tex]R=5.42\times10^{6}\ m[/tex]
Hence, (a). The radius of the star is [tex]5.0\times10^{10}\ m[/tex]
(b). The radius of the star is [tex]5.42\times10^{6}\ m[/tex]
The roller coaster car reaches point A of the loop with speed of 20 m/s, which is increasing at the rate of 5 m/s2. Determine the magnitude of the acceleration at A if pA
Answer and Explanation:
Data provided as per the question is as follows
Speed at point A = 20 m/s
Acceleration at point C = [tex]5 m/s^2[/tex]
[tex]r_A = 25 m[/tex]
The calculation of the magnitude of the acceleration at A is shown below:-
Centripetal acceleration is
[tex]a_c = \frac{v^2}{r}[/tex]
now we will put the values into the above formula
= [tex]\frac{20^2}{25}[/tex]
After solving the above equation we will get
[tex]= 16 m/s^2[/tex]
Tangential acceleration is
[tex]= \sqrt{ac^2 + at^2} \\\\ = \sqrt{16^2 + 5^2}\\\\ = 16.703 m/s^2[/tex]
A point source emits sound waves with a power output of 100 watts. What is the sound level (in dB) at a distance of 10 m
Answer:
[tex]L = 109.01 db[/tex]
Explanation:
Given
Power, P = 100 W
Distance, d = 10 m
Required
Determine the Sound Level
First, the sound intensity as to be calculated; This is done, as follows;
[tex]I = \frac{P}{4\pi d^2}[/tex]
Substitute for P, d and take π as 3.14
[tex]I = \frac{100}{4 * 3.14 * 10^2}[/tex]
[tex]I = \frac{100}{4 * 3.14 * 100}[/tex]
[tex]I = \frac{100}{1256}[/tex]
[tex]I = 0.0796Wm^{-2}[/tex] --- Approximated
Next is to calculate the Sound Level, as follows
[tex]L = 10 * Log(\frac{I}{I_o})[/tex]
Where [tex]I_o = 10^{-12} Wm^{-2}[/tex]
Substitute for I and Io
[tex]L = 10 * Log(\frac{0.0796}{10^{-12}})[/tex]
[tex]L = 10 * Log(0.0796*10^{12)[/tex]
[tex]L = 10 * Log(0.0796*10^{12)[/tex]
[tex]L = 10 * 10.901[/tex]
[tex]L = 109.01 db[/tex]
Hence, the sound level is 109.01 decibels
If you stood on a planet having a mass four times higher than Earth's mass, and a radius two times 70) lon longer than Earth's radius, you would weigh:________
A) four times more than you do on Earth.
B) two times less than you do on Earth.
C) the same as you do on Earth
D) two times more than you do on Earth.
CHECK COMPLETE QUESTION BELOW
you stood on a planet having a mass four times that of earth mass and a radius two times of earth radius , you would weigh?
A) four times more than you do on Earth.
B) two times less than you do on Earth.
C) the same as you do on Earth
D) two times more than you do on Earth
Answer:
OPTION C is correct
The same as you do on Earth
Explanation :
According to law of gravitation :
F=GMm/R^2......(a)
F= mg.....(b)
M= mass of earth
m = mass of the person
R = radius of the earth
From law of motion
Put equation b into equation a
mg=GMm/R^2
g=GMm/R^2
g=GM/R^2
We know from question a planet having a mass four times that of earth mass and a radius two times of earth radius if we substitute we have
m= 4M
r=(2R)^2=4R^2
g= G4M/4R^2
Then, 4in the denominator will cancel out the numerator we have
g= GM/R^2
Therefore, g remain the same
Which is produced around a wire when an electrical current is in the wire? magnetic field solenoid electron flow electromagnet
Answer:
A. magnetic field
Explanation:
The magnetic field is produced around a wire when an electrical current is in the wire because of the magnetic effect of the electric current therefore the correct answer is option A .
What is a magnetic field ?A magnetic field could be understood as an area around a magnet, magnetic material, or an electric charge in which magnetic force is exerted.
As given in the problem statement we have to find out what is produced around a wire when an electrical current is in the wire.
The magnetic field is produced as a result when an electrical current is passed through the conducting wire .
Option A is the appropriate response because a wire's magnetic field is created when an electrical current flows through it due to the magnetic influence of the electric current .
Learn more about the magnetic fields here, refer to the link given below;
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A person is being pulled by gravity with a force of 500 N. What is the force with which the person pulls Earth?
1,000 N
O100 N
500 N
0 250 N
Answer:
The correct answer is 500 N
Explanation:
This is an exercise in Newton's third law or law of action and reaction
The Earth exerts a force on the person, which we call a weight of 500 N directed downwards, we can call this action and the person exerts a force on the Earth of equal magnitude 500N and in the opposite direction, that is directed upwards.
Which force we call action does not matter, the analysis and conclusions are the same
The correct answer is 500N
g Assume you are a farsighted person who has a near point distance of 40 (cm). If you use a converging contact lens with focal length of 10 (cm). What is nearest distance you can vision with you contacts now?
Answer:
object distance p = 13.33 cm
Explanation:
For this problem of finding the image of an object we must use the constructor equation
1 / f = 1 / p + 1 / q
where f is the focal length, p and q are the distances to the object and the image, respectively.
In this case they indicate the focal length f = 10 cm, since the person has hyperopia, the image must be formed q = 40 cm, let's find where the object is (p)
1 / p = 1 / f - 1 / q
1 / p = 1/10 - 1/40
1 / p = 0.075
p = 13.33 cm
The place you get your hair cut has two nearly parallel mirrors 6.5 m apart. As you sit in the chair, your head is
Complete question is;
The place you get your hair cut has two nearly parallel mirrors 6.50 m apart. As you sit in the chair, your head is 3.00 m from the nearer mirror. Looking toward this mirror, you first see your face and then, farther away, the back of your head. (The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem.) How far away does the back of your head appear to be?
Answer:
13 m
Explanation:
We are given;
Distance between two nearly parallel mirrors; d = 6.5 m
Distance between the face and the nearer mirror; x = 3 m
Thus, the distance between the back-head and the mirror = 6.5 - 3 = 3.5m
Now, From the given values above and using the law of reflection, we can find the distance of the first reflection of the back of the head of the person in the rear mirror.
Thus;
Distance of the first reflection of the back of the head in the rear mirror from the object head is;
y' = 2y
y' = 2 × 3.5
y' = 7
The total distance of this image from the front mirror would be calculated as;
z = y' + x
z = 7 + 3
z = 10
Finally, the second reflection of this image will be 10 meters inside in the front mirror.
Thus, the total distance of the image of the back of the head in the front mirror from the person will be:
T.D = x + z
T.D = 3 + 10
T.D = 13m
Can you come up with a mathematical relationship, based on your data that shows the relationship between distance from the charges and electric field strength?
Answer:
Explanation:
This question appears incomplete because of the absence of the data been talked about in the question. However, there is a general ruling here and it can be applied to the data at hand.
If an increase in the distance of charges (let's denote with "d") causes the electric field strength (let's denote with"E") to increase, then the mathematical representation can be illustrated as d ∝ E (meaning distance of charge is directly proportional to electric field strength).
But if an increase in the distance of the charges causes the electric field strength to decrease, then the mathematical representation can be illustrated as d ∝ 1/E (meaning distance of charge is inversely proportional to electric field strength).
A scatterplot can also be used to determine this. If there is a positive correlation (correlation value is greater than zero but less than or equal to 1) on the graph, then it is illustrated as "d ∝ E" BUT if there is a negative correlation (correlation value is less than zero but greater than or equal to -1), then it can be illustrated as "d ∝ 1/E".
A charge of uniform density (0.74 nC/m) is distributed along the x axis from the origin to the point x = 10 cm. What is the electric potential (relative to zero at infinity) at a point, x = 23 cm, on the x axis? Hint: Use Calculus to solve this problem.
Answer:
V = - 3.85 V
Explanation:
The electric potential of a continuous charge distribution is
V = k ∫ dq / r
to find charge differential let's use the concept of linear density
λ = dq / dx
dq = λ dx
the distance from a load element to the point of interest
x₀ = 23 cm = 0.23 m
r = √ (x-x₀)² = x - x₀
we substitute
v = k ∫ λ dx / (x-x₀)
we integrate and evaluate between x = 0 and x = l = 0.10 cm
V = k λ [ln (x-x₀) - ln (-x₀)]
V = k λ ln ((x-x₀) / x₀)
let's calculate
V = 9 10⁹ 0.74 10⁻⁹ ln ((0.23 - 0.10) / 0.23)
V = - 3.85 V
Suppose there are only two charged particles in a particular region. Particle 1 carries a charge of +q and is located on the positive x-axis a distance d from the origin. Particle 2 carries a charge of +2q and is located on the negative x-axis a distance d from the origin.
Required:
Where is it possible to have the net field caused by these two charges equal to zero?
1. At the origin.
2. Somewhere on the x-axis between the two charges, but not at the origin.
3. Somewhere on the x-axis to the right of q2.
4. Somewhere on the y-axis.
5. Somewhere on the x-axis to the left of q1.
Answer:
x₂ = 0.1715 d
1) false
2) True
3) True
4) false
5) True
Explanation:
The field electrifies a vector quantity, so we can add the creative field by these two charges
E₂-E₁ = 0
k q₂ / r₂² - k q₁ / r1₁²= 0
q₂ / r₂² = q₁ / r₁²
suppose the sum of the fields is zero at a place x to the right of zero
r₂ = d + x
r₁ = d -x
we substitute
q₂ / (d + x)² = q₁ / (d-x)²
we solve the equation
q₂ / q₁ (d-x)² = (d + x) ²
let's replace the value of the charges
q₂ / q₁ = + 2q / + q = 2
2 (d²- 2xd + x²) = d² + 2xd + x²
x² -6xd + d² = 0
we solve the quadratic equation
x = [6d ± √ (36d² - 4 d²)] / 2
x = [6d ± 5,657 d] / 2
x₁ = 5.8285 d
x₂ = 0.1715 d
with the total field value zero it is between the two loads the correct solution is x₂ = 0.1715 d
this value remains on the positive part of the x axis, that is, near charge 1
now let's examine the different proposed outcomes
1) false
2) True
3) True
4) false
5) True
3. A very light bamboo fishing rod 3.0 m long is secured to a boat at the bottom end. It is
held in equilibrium by an 18 N horizontal force while a fish pulls on a fishing line
attached to the rod shown below. How much force F does the fishing line exert on the
rod? (3)
18 N
pivot
30°
1.8 m
3.0 in
The image in the attachment describes the situation of the fishing rod.
Answer: F = 10.8 N
Explanation: The image shows a fishing rod attached to an axis. To stay in equilibrium, Torque must be equal for the force of magnitude 18N and for the unknow force.
Torque (τ) is a measure of a force's tendency to cause rotation and, in physics, defined as:
τ = F.r.sin(θ)
F is the force acting on the object;
r is distance between where the torque is measured to where the force is applied;
θ is the angle between F and r;
For the fishing rod:
[tex]\tau_{1} = \tau_{2}[/tex]
[tex]F_{1}.r_{1}.sin(\theta) = F_{2}.r_{2}.sin(\theta)[/tex]
Assuming part (1) is related to unknown force:
[tex]F = \frac{F_{2}.r_{2}.sin(\theta}{r_{1}.sin(\theta) }[/tex]
Replacing the corresponding values:
[tex]F = \frac{18*1.8*sin(30)}{3*sin(30)}[/tex]
[tex]F = \frac{18*1.8}{3}[/tex]
F = 10.8
The fishing line exert on the the rod a force of 10.8N.
