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The angular diameter of Mars in radians and in arc minutes and the evaluation of the capability of human eyes to resolve Mars of diameter 6.8 × 10³ km, located 5.5 × 10⁷ km away are as follows;
(d) The angular diameter of Mars is 1.23[tex]\overline{63}[/tex] × 10⁻⁴ rad
(e) The angular diameter in arc minutes is about 0.425 arc minute.
Optical aid is required for humans to resolve Mars.What is an angular diameter?The angular diameter is an apparent dimension used to describe the size of a circular object, observed from a specified point of view or location.
The diameter of Mars = 6,800 km
The closest distance between Mars and Earth when Mars gets closest to Earth = 55,000,000 km
(d) The angular diameter of Mars can be obtained by finding the vertex angle formed by the diameter of Mars and the ray from the observer on Earth to the left and right extremities of Mars using the trigonometric ratio of tangent as follows;
Angular diameter = 2 × arctan((6,800/2)/55,000,000) = 0.000123636363 radians
The angular diameter of Mars as observed from Earth is 1.23[tex]\overline{63}[/tex] × 10⁻⁴ radians
(e) 1 radians = 3437.75 arc minute
0.000123636363 radians = 0.000123636363 × 3437.75 arc minute
0.000123636363 × 3437.75 ≈ 0.425
Therefore;
0.000123636363 radians ≈ 0.425 arc minute
The specified level of detail that the human eye can resolve is one arc minute (1')
The apparent angular diameter of Mars, which is about 0.425 arc minute is lesser than the angular limit of detail of one arc minute that the eye can resolve, therefore, humans can not resolve Mars without optical aid.
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Related Questions
which of these four ellipses has the greatest eccentricity? view available hint(s)for part a four ellipses of different elongation are shown. the first ellipse is almost a circle. the second ellipse has the length to width ratio of approximately 2 to 1. the third ellipse has the length-to-width ratio of approximately 1.5 to 1. the fourth ellipse has the length-to-width ratio of approximately 3 to 1. which of these four ellipses has the greatest eccentricity? 2 4 3 1
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The fourth ellipse, with the length-to-width ratio of approximately 3 to 1, has the greatest eccentricity.
Eccentricity of the ellipse: The eccentricity of an ellipse is a measure of its "oblateness" or how much it deviates from being a circle. An ellipse has an eccentricity between 0 and 1, with 0 representing a circle and values closer to 1 representing more elongated ellipses. So, in this case, the fourth ellipse with the highest length-to-width ratio would have the highest eccentricity value.
The first ellipse is a circle, it means its length-to-width ratio is 1. Second one is more closer to a circle than the third one. Similarly third ellipse is more closer to the circle than the fourth one.
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a 60 g tennis ball with an initial speed of 39 m/s hits a wall and rebounds with the same speed. (figure 1) shows the force of the wall on the ball during the collision.
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Fmax is calculated from Fmax = (pulse change) / peak time.
The maximum contact force Fmax on impact can be calculated using the impulse-impulse theorem.
Momentum - The momentum theorem states that the momentum (change in momentum) of an object is equal to the force on the object multiplied by the time the force is applied. In this case, the momentum of the ball is equal to the wall force on the ball multiplied by the time of the collision.
Momentum is also equal to the ball's momentum change, which is the final momentum minus the initial momentum.
Since the ball has a known mass (60 g) and a constant velocity, the momentum of the ball is equal to the mass multiplied by the velocity (60 g) (37 m/s).
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The question is -
A 60 g tennis ball with an initial speed of 37 m/s hits a wall and rebounds with the same speed. Shows the force of the wall on the ball during the collision.
What is the value of Fmax, the maximum value of the contact force during the collision?
Two conductors have the following initial charges: conductor A
has a negative charge QA = - 39.8 x 10-16 C and conductor B has a
positive charge qB = + 10.4 x 10-16 C. The two conductors are
brought in contact with one another (i.e., they touch) until they
reach electrostatic equilibrium (equal charges) and then
separated. Each conductor has now one-half of the sum of the
initial charges. How many excess electrons does conductor A has
after the equilibrium (after separation)? Please round your answer
to the nearest whole number (integer).
Equation: n=
Inet
e
where qnet is the absolute value of the net charge on conductor
A after separation and
e = 1.6 x 10-19 C.
Answers
The excess electrons that the conductor A has
after the equilibrium (after separation) is n = |qA + qB|/e = (39.8 + 10.4) x 10-16 C/1.6 x 10-19 C = 3000 electrons.
How do you calculate the excess electrons on a conductor after the electrostatic balance?The number of excess electrons on a conductor after the electrostatic balance can be calculated using the equation n=|Qnet|/e, where Qnet is the absolute value of the net charge on the conductor after the separation and e is the elemental charge (1.6 x 10-19 C). By using the formula and plugging in the values, we realize the value 3000 electrons
Therefore, conductor A has 3000 excess electrons after balance. It can then be concluded that the one the correct answer is as given.
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Introduction to forces. Identify the situations that have an unbalanced force. Check all that apply.
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The situations that have an unbalanced force are:
A. A baseball speeds up as it falls through the air D. A bumper car hit by another car moves off at an angleE. A balloon flies across the room when the air is released What are the forces about?These situations have an unbalanced force because in all of them an object is either accelerating (speeding up or changing direction) or moving with a force acting on it. In the first one, the baseball is accelerating due to gravity. In the second one, the bumper car is hit by another car and moves off at an angle. In the third one, the balloon flies across the room when the air is released, which is a force acting on it.
On the other hand, a soccer ball at rest on the ground and an ice skater gliding in a straight line at a constant speed, are both examples of balanced forces, as there is no net force acting on the objects and they are not accelerating.
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See full question below
Identify the situations that have an unbalanced force. Check all that apply. A baseball speeds up as it falls through the air. A soccer ball is at rest on the ground. An ice skater glides in a straight line at a constant speed. A bumper car hit by another car moves off at an angle. A balloon flies across the room when the air is released.
instructor problem 2: the mega 2560 has a built in 10 bit a/d, typically mapped with the input range 0-5 volt. sketch a curve similar to the curve below that relates input voltage (bottom axis) to output bits (vertical axis). show quantization levels etc.. you may want to search the internet for some ideas.
Answers
The Mega 2560 has a 10-bit A/D converter built-in. This means that analog input voltages can be converted to digital values with a resolution of 10 bits. Typically, a range of 0 to 5 volts is used to map the input voltage range.
With input voltage on the lower axis and output bit on the vertical axis, a graph representing the relationship between the two variables can be created. The A/D converter's quantization levels are represented by the curve. These discrete steps are used to turn the input voltage into a digital value.
The quantization levels within the input voltage range of a 10-bit A/D converter are evenly distributed. The minimum input voltage is equivalent to a digital value of 0, and the maximum input voltage is equivalent to a digital value of 1023. Each quantization level has a corresponding digital value.
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The question is -
The mega 2560 has a built-in 10-bit a/d, typically mapped with the input range of 0-5 volts. sketch a curve similar to the curve below that relates input voltage (bottom axis) to output bits (vertical axis). show quantization levels. So connect your LED and your 220 W resistor to pin 9 and ground. In your code you can get rid of the serial monitor code, and define what pin the LED is connected to int ledPin = 9; under setup add pinMode(ledPin, OUTPUT); Next, define a new integer variable called val and set it equal to the value of the sense in (use analogRead(sensePin)).
question an object of mass 0.5 kg experiences a force that is associated with the potential energy function u(x)
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a. The sketch graph of U(x) versus x is in the attachment.
b. The force function that associate with the potential energy function is F(x) = 8.0 (2.0 + x)⁻²
c. The speed of the particle at x = 2 is 2 m/s.
The full question is in the attachment. To create a graph, substitute some values of x into the equation of the function to determine the pair of point coordinates.
a. Graph of U(x) = 4.0/(2.0 + x) versus x making a curve because the function is a fraction function and the curve will not intersect the x-axis.
If x = 0U(0) = 4.0/(2.0 + x) = 4.0/(2.0 + 0) = 4.0/2.0 = 2.0
(0 , 2.0) If x = 2
U(2) = 4.0/(2.0 + x) = 4.0/(2.0 + 2) = 4.0/4.0 = 1.0
(2 , 1.0)If x = 3
U(3) = 4.0/(2.0 + x) = 4.0/(2.0 + 3) = 4.0/5.0 = 0.8
(3 , 0.8)
From these coordinates a graph is created in the image.
b. A conservative force is a force that works on an object depends only on the initial and final position of the object and not on the path of the object. The total work from a conservative energy is always the same with the changes in potential energy
W = - ΔU
F × Δx = - ΔU
W = the total work (J)Δx = the distance (m)ΔU = the potential energy (J)The conservative force acting on the object is the derivate of the potential energy function for the objects
F = - dU/dx
U(x) = 4.0/(2.0 + x) = 4.0 (2.0 + x)⁻¹
F = - 4.0 × - 2 (2.0 + x)⁻² × 1
F(x) = 8.0 (2.0 + x)⁻²
c. The kinetic energy Ke = 0.5 mv²
m = the massv = the speedKe = kinetic energyWhen the object is released from rest at the origin to x = 2
The initial speed = v₁ = 0Kinetic energy = Ke₁ = 0.5 mv₁² = 0 J
Potential energy = U(0) = 4.0/(2.0 + x) = 4.0/(2.0 + 0) = 4.0/2.0 = 2.0 JAt x = 2
Potential energy = U(2) = 4.0/(2.0 + x) = 4.0/(2.0 + 2) = 4.0/4.0 = 1.0 J
According to law of conservation of energy
Ke₁ + U(0) = Ke₂ + U(2)
0 + 2.0 = Ke₂ + 1.0
Ke₂ = 2.0 - 1.0
Ke₂ = 1.0 J
0.5 mv₂² = 1.0
0.5 × 0.5 × v₂² = 1.0
v₂² = 1.0 ÷ 0.25
v₂² = 4
[tex]v_2 \:=\: \sqrt{4}[/tex]
v₂ = 2 m/s
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the charge on a nonconducting rod increases linearly from end a to end b. the rod is bent in a circle so that ends a and b almost meet very near the top of the circle (figure 1). figure1 of 1 a positively charged rod a b is bent into a ring so that its ends almost meet at the top of the ring. end b is on the left, end a is on the right. the center of the ring is marked by a black dot. a dashed horizontal line passes through the black dot. part a what is the direction of the electric field at the center of the circle? (hint: consider contributions from diametrically opposite segments!)
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A uniformly charged ring has zero electric field at its center. Radially inwards toward negative point charge and outwards from positive charge is the electric field.
Which way does the electric field point in the center of a charged circular loop?Radially inwards toward negative point charge and outwards from positive charge is the electric field.A uniformly charged ring has zero electric field at its center.Both of the electric fields that are donated to the dipole are pointing in the same general direction—that is, toward the negative charge—in the middle of the dipole.The electric field's strength can be calculated using the equation E = k | Q | r 2 by using the formula. The charge's sign—negative in this instance—determines the direction of the electric field.To learn more about electric field refer to:
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charges on raindrops vary widely in both magnitude and sign. consider a case where the two drops on the x -axis are 2.18 mm apart and have charge q=-1.87miuC. Find the electric force on the upper drop.
Answers
The electrostatic force acting on the charge is Fe = 1.5 × 10^-3N The magn
Find the electric force on the upper drop?
We can use the equation E = k | Q | r 2 E = k | Q | r 2 to find the magnitude of the electric field. The direction of the electric field is determined by the sign of the charge, which is negative in this case. E = k | Q | r 2 = ( 8.99 × 10 9 N ⋅ m 2 /C 2 ) | − 1.5 × 10 − 9 C | ( 0.035 m ) 2 = 1.1 × 10 4 N/C.The repulsive or attractive interaction between any two charged bodies is called as electric force. Similar to any force, its impact and effects on the given body are described by Newton's laws of motion. The electric force is one of the various forces that act on objects.Coulomb's law calculates the magnitude of the force F between two point charges, q1 and q2, separated by a distance r. F=k|q1q2|r2.To learn more about electric force refers to:
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in fig. 22-51, two curved plastic rods, one of charge q and the other of charge iq, form a circle of radius r i 8.50 cm in an xy plane. the x axis passes through both of the connecting points, and the charge is distributed uniformly on both rods. if q i 15.0 pc, what are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the electric field e produced at p, the center of the circle?
Answers
The answer is 23.8 N/C.
From symmetry, we see that the net field at
P is twice the field caused by the upper semicircular charge
+q=λ(πR)
What is electric field?The physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them, is known as an electric field (also known as an E-field[1]). [2] It can also refer to a system of charged particles' physical field. [3] Electric charges and time-varying electric currents are the building blocks of electric fields. The electromagnetic field, one of the four fundamental interactions (also known as forces) of nature, manifests itself in both electric and magnetic fields.
Electrical technology makes use of electric fields, which are significant in many branches of physics. For instance, in atomic physics and chemistry, the electric field acts as an attracting force to hold atoms' atomic nuclei and electrons together. Additionally, it is the force that causes atoms to connect chemically.
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a light ray propagating in vacuum contains both 600nm light and 400 nm light and is incident on top of a glass cube. compare how the two types of light travel through the block. select all that apply
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A light ray having 600 nm light will travel faster than 400 nm light.
Other names for "refractive index" are index of refraction and refraction index. The properties of the medium have an impact on the speed of light there. The medium's optical density has an impact on the electromagnetic waves' speed. Optical density is the propensity of the atoms in a substance to recover the captured electromagnetic energy. How quickly light moves through a substance depends on its optical density. One such indicator of a medium's optical density is its refractive index. Refraction is expressed mathematically as follows.
This suggests that the relationship between the velocity and refractive index is inverse. Therefore, light ray at 600 mm with a refractive index of 1.5 will move more quickly than light at 400 mm with a refractive index of 1.6.
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the 50-kg passenger in a car moving at 10 m/s crashes into a tree and stops in 0.2 seconds. the average force exerted on the passenger to bring her to a stop is
Answers
The passenger experiences a 2500 Newton force on average to stop the vehicle.
We may use the formula force = mass x acceleration to get the average force applied on the passenger. The passenger's deceleration in this scenario is the acceleration, which can be computed by dividing the velocity change by the time change.
The passenger's velocity in this instance decreases from 10 m/s to 0 m/s in 0.2 seconds, hence the deceleration is as follows:
deceleration = (change in velocity) / (change in time)
Substitute the value in above equation we get,
deceleration = (0 m/s - 10 m/s) / 0.2 seconds
deceleration = -50 m/s²
Remember that the acceleration is moving in the opposite direction of the velocity when the sign is negative. In this instance, the passenger is originally travelling forward at a positive velocity, but the deceleration is negative, demonstrating that the force is pushing on the passenger from the opposite direction and slowing her down.
Thus, the passenger is subjected to the following force:
mass times acceleration equals force.
Substitute the value in above equation we get,
force = 50 x -50 = 2500 N.
force = 2500 Newton
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three objects are brought close to one another, two at a time. when objects a and b are brought together, they attract. when objects b and c are brought together, they repel. which one of the following choices is necessarily true of object a?
Answers
The choice is necessarily true of object A is that objects A and C posses charges of of opposite sign.
A force can reason an item with mass to alternate its velocity, i.e., to accelerate. Force also can be defined intuitively as a push or a pull. A pressure has each importance and direction, making it a vector quantity. the word 'pressure' has a specific meaning. At this level, it's miles absolutely suitable to explain a pressure as a push or a pull. A pressure isn't some thing that an item includes or 'has in it'. A pressure is exerted on one item with the aid of using another. The concept of a pressure isn't restricted to dwelling matters or non-dwelling matters. The objects A and C posses charges of of opposite sign. It is because A attracts B and B repels C so A and C also attract each other.
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Complete question:
Three objects are brought close to one another, two at a time. When objects A and B are brought together, they attract. When objects B and Care brought together, they repel. Which of the following are necessarily true? (Select all that apply.) One object is neutral. Objects A and C possess charges of opposite sign. Objects A and C possess charges of the same sign. All three objects possess charges of the same sign. Additional experiments must be performed to determine information about the charges on the objects. Three objects are brought close to each other, two at a time. When objects A and B are brought together, they repel. When objects B and C are brought together, they also repel. Which of the following are true? (Select all that apply.) All three objects possess charges of the same sign. Objects A and C possess charges of opposite sign. One object is neutral. Additional experiments must be performed to determine the signs of the charges. Objects A and C possess charges of the same sign.
assuming the earth is a perfect sphere, determine the difference in the weight of a 100.0 kg object between the poles and the equator
Answers
Suppose Earth were perfectly spherical. At the equator, the centripetal acceleration, given by the equation a = v^2/r, comes out to 460^2 / 6371000 = 0.033 .
Determine the difference in the weight of a 100.0 kg object between the poles and the equator?
The effective acceleration of gravity at the poles is 980.665 cm/sec/sec while at the equator it is 3.39 cm/sec/sec less due to the centrifugal force. If you weighed 100 pounds at the north pole on a spring scale, at the equator you would weigh 99.65 pounds, or 5.5 ounces less.The difference is small, but still measurable. A person who weighed exactly 100 kg at the pole would weigh about 99.3 kg at the equator. The difference is made up of about 0.7 kg from the greater distance from the center of mass at the equator, and about 0.0007 kg from the 'centrifugal' force at the equator.Since there is more centrifugal force at the equator to cancel gravity, your overall weight at the equator versus at the poles is even less. The centrifugal force on your body at the equator is 0.034 m/s2 times the mass of your body. The centrifugal force at the poles is zero.To learn more about poles refers to:
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in the following scenarios, the driver of a car has a cup of coffee set in a drink holder. identify how the coffee in the cup would be affected when the car is at constant velocity, speeding up, and slowing down.
Answers
The coffee in the cup would be affected differently. At constant velocity, the coffee remains still, when speeding up it is pushed forward, and when slowing down, it is pushed backward.
When the car is at constant velocity, the coffee in the cup would remain still and not spill. However, when the car is speeding up, the coffee in the cup would be pushed forward, and if the car is slowing down, the coffee would be pushed backward.
This is due to the principle of inertia, which states that an object in motion will remain in motion and an object at rest will remain at rest unless acted upon by an unbalanced force.
As the car accelerates or decelerates, the coffee in the cup will experience the force of the car's motion and be pushed in the opposite direction. The amount of force and the resulting movement of the coffee will depend on the acceleration of the car and the size of the cup.
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a block slides down a smooth ramp , starting from rest at a heigh h. when it reaches the bottom it's moving at speed v. it then contiunes to slide up a second smooth ramp.
Answers
At the height of 3/4h, the speed of the block will be v/2 when it continues to slide up a second smooth ramp. When it is released from rest at the top.
As we know the total energy of the system remains conserved so the kinetic energy that it possesses will be converted to potential energy after juping back.
So 1/2mv^2 = mgh => v^2 = 2gh
and as given velocity remains v/2 So
1/2mv2^2 = 1/8mv1^2
So 1/2 mv2^2 +mgh2 = mgh1 => 1/8mv1^2 + mgh2 = mgh
1/8m(2gh)+mgh2=mgh
1/4mgh+mgh2=mgh. ⇒ h2=3/4h.
The speed of the block is v1/2
at a height of 3/4h.
So by the rule of energy changes, and its forms we can conclude that at the height of 3/4h, the velocity of the block will be v/2.
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during the spin cycle, a clothes washer, with a radius of 1.5 feet, rotates at a rate of four revolutions per second when at maximum speed. if the velocity of the outside wall of the washer follows the function ft/s when starting from rest, determine the time it takes to get the washer to maximum speed. also, find the magnitude of the acceleration of the outside wall the instant before it reaches maximum speed. (7.54 s, 948 ft/s^2)
Answers
The magnitude of the acceleration of the outside wall the instant before it reaches maximum speed is 948 ft/s^2.
What is acceleration?Acceleration is the rate of change of velocity over time. It is the increase in speed or the decrease in the time taken to cover a particular distance.
The equation describing the velocity of the outside wall of the washer is a linear one, given by the equation:
v(t) = at
where a is the acceleration of the wall and t is the time.
We know that the velocity of the wall when it reaches maximum speed is 4 revolutions per second. We can convert this to linear velocity by multiplying it by the circumference of the washer, 2πr, where r is the radius of the washer (1.5 feet). This gives us a final velocity of 9π ft/s
We can now solve for the acceleration of the wall. We know the final velocity and we can set the initial velocity to 0 due to the fact that the washer is starting from rest. So we can solve for the acceleration using the equation:
a = v(t) / t
Plugging in our values, we get:
a = 9π ft/s / t
Now we can solve for the time it takes to get the washer to maximum speed. We know that the final velocity is 9π ft/s and the acceleration is a. So we can solve for the time by rearranging the equation to get:
t = v(t) / a
Plugging in our values, we get:
t = 9π ft/s / a
Solving for t, we get:
t = 9π ft/s / 948 ft/s^2
Simplifying, we get:
t = 7.54 s
Therefore, it takes 7.54 seconds for the washer to reach its maximum speed. The magnitude of the acceleration of the outside wall the instant before it reaches maximum speed is 948 ft/s^2.
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We know that the velocity (v(t)) is the derivative of position (x(t)) with respect to time, meaning v(t) = d. Given that, what do we get if we integrate the velocity of an object from t=1 to t=4, meaning Stu(t)dt?
Answers
In other words, the integral of the velocity from t=1 to t=4 is the difference between the object's position at t=4 and its position at t=1.
What is velocity?Velocity is a vector quantity that measures the rate of change in an object’s position. It is the rate of displacement (change in position) with respect to time. Velocity is a combination of speed and direction and is typically denoted as v or u in an equation. It is measured in meters per second (m/s) or kilometers per hour (km/h).
The integral of the velocity of an object from t=1 to t=4 is the change in position (x(t)) of the object from t=1 to t=4. This is represented mathematically as:
Stu(t)dt = x(4) - x(1)
In other words, the integral of the velocity from t=1 to t=4 is the difference between the object's position at t=4 and its position at t=1.
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a conducting bar moves to the left at a constant speed v on two conducting rails joined at the left as shown. as a result of the bar moving through a constant magnetic field, a current i is induced in the indicated direction. which one of the following directions is that of the magnetic field?
Answers
As a result of the bar moving through a constant magnetic field, a current i is induced in the indicated direction. The field is pointing downwards as a result of this.
Option E is correct.
How does a magnetic field work?A moving electric charge or an electric current can produce a magnetic field, which is a physical phenomenon. It is a field of force that is hard to see that surrounds an object and has the power to attract or repel other magnets. Tesla or Gauss units are used to measure magnetic field strength. Magnetic resonance imaging (MRI), electricity generation, and navigation are just a few examples of the many applications for magnetic fields.
The magnetic field is oriented out of the plane of the page and is perpendicular to the plane of the conducting rails. The field is pointing downwards as a result of this. If a compass needle were placed in the field, its north-seeking pole would point in the same direction as the current that was induced in the rails because of the field's direction.
Question incomplete:a conducting bar moves to the left at a constant speed v on two conducting rails joined at the left as shown. as a result of the bar moving through a constant magnetic field, a current i is induced in the indicated direction. which one of the following directions is that of the magnetic field?
A. towards the right
B. towards the left
C.parallel along the axis
D. into the page
E. out the page
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3) for the following measurements, underline the digits that are known with certainty and highlight in color the digits that are estimated. if a number is ambiguous, that is, the number of significant figures is uncertain, state so. in each case, explain your reasoning.
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Measurements with precise numbers underlined and estimated numbers highlighted are a) 4.35 m, b) 0.009340 g, c) 3400 km, and d) 1.38 x 103 m/s. An extrapolation using scientific notation is used to create the final figure in d).
A) 4.35 m - Since they can be measured directly or read from a meter, the numbers 4, 3, and 5 are well-known.
B) 0.009340 g - The numbers 0, 0, 9, 3, 4, and 0 are known for sure because they can be measured or read from a scale.
C) 3400 km - The numbers 3, 4, 0, and 0 can be read directly from a measuring device, so they are known for sure.
D) 1.38 x 103 m/s - Numbers 1, 3, and 8 can be measured or read directly from the instrument, so they are known for sure. Since the number "3" is written in scientific notation, it qualifies as an estimate and thus approximates the true value.
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The question is -
For the following measurements, underline the digits that are known with certainty and highlight in color the digits that are estimated. If a number is ambiguous, that is, the number of significant figures is uncertain, state so. In each case, explain your reasoning. 3) a) 4.35 m b) 0.009340 g c) 3400 km d) 1.38 x 103 m/s
let v be the center of mass of a system of point masses located at v1, . . . , vk in r 3 . is v in span{v1, . . . , vk}? explain.
Answers
No, v is not in span{v1, . . . , vk}, because the center of mass of a system of point masses is a vector that lies outside of the span of any of the individual point masses.
What is vector?A vector is a mathematical object used in computer programming and other fields. It is a collection of elements, usually numbers or other data points, represented by a single line segment and denoted by an arrow. Vector elements are often used to represent physical quantities such as velocity, acceleration, force, or position. In computer programming, vectors are used to store data in a structured way.
The center of mass is calculated by taking the weighted average of the positions of the individual point masses, thus it is a vector that lies in between the points of the system rather than being one of the points itself.
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examine the graphs below, which show salinity, temperature, and density with depth from the atlantic ocean. which letter on the graphs represents the halocline?
Answers
Of the five oceans, the Atlantic Ocean has the highest salinity. Near the equator and at both poles, salinity clearly decreases.
The amount of dissolved salts in water is known as salinity. This explains not just sodium chloride but all salts (table salt). Because salinity interferes with nitrate uptake, stunts development, and prevents plant reproduction, it has an impact on the production of pastures, trees, and crops. Some ions, most notably chloride, are poisonous to plants, and when their concentration rises, the plant becomes poisoned and perishes.
Due to changes in solar radiation and the physical characteristics of water, the temperature of ocean water fluctuates depending on location, both in terms of latitude and depth. The majority of the lightest water in the Pacific has densities under 26.0, while the majority of the densest water in the Atlantic has densities between 27.5 and 28.0.
A halocline is a layer that separates two water masses by difference in density, albeit it does not occur because of temperature this time. When two bodies of water—one containing freshwater and the other saltwater—converge, it happens.
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an object of mass initially at rest on a surface has both kinetic and potential energies equal to zero. it is then lifted under the influence of both nonconservative forces and the conservative force of gravity. the nonconservative forces do of work on the object. the conservative force does of work. 25. the potential energy of the object after the motion is
Answers
Speed of the object after motion is finished will be 3.0 m/s if surface has kinetic and potential energy as zero.
The speed of the object at the end of the motion can be calculated using the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
First, we need to calculate the final kinetic energy of the object. The work done by non-conservative forces is positive, so it increases the kinetic energy of the object. The work done by the conservative force of gravity is negative, so it decreases the kinetic energy of the object.
Final kinetic energy = initial kinetic energy + work done by nonconservative forces + work done by conservative forces
Final kinetic energy = 0 + 40 J - 22 J
Final kinetic energy = 18 J
Next, we can use the formula for kinetic energy (1/2mv^2) to calculate the final velocity of the object.
Final kinetic energy = 1/2mv^2
18 J = 1/2 (4 kg) v^2
v^2 = 18 J / (1/2)(4 kg)
v^2 = 72 J/kg
v = √(72 J/kg)
v = √(72 J/kg)
v ≈ 3.0 m/s
Therefore, the speed of the object at the end of the motion is most nearly 3.0 m/s.
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Answer:
+ 22 J
Explanation:
This one is quite short.
We are told that -22 J of conservative work was done. Thus, the work by gravity was - 22J.
Since we know energy is conserved, that energy would now be positive as it is now stored.
Thus, we would have +22J stored as potential energy (gravity) after the motion.
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A uniform electric field exists everywhere in the x, y plane. This electric field has a magnitude of 4500 N/C and is directed in the positive x direction. A point charge -8.0 x 10-9 C is placed at the origin. �Determine the magnitude of the net electric field at (a) x = -0.15 m, (b) x = +0.15 m, and (c) y = +0.15 m.
Answers
The magnitude of the net electric field
At x = - 0.15 m is 7,700 N/C and is directed in the positive x direction.At x = 0.15 m is 1,300 N/C and is directed in the positive x direction.At y = 0.15 m is 5,521.78 N/C and is directed in 324.58° from the positive x direction.The direction of the net electric field from a point to a negative charge is from the point to the charge. The magnitude of the electric field from the point to a point charge
E = kq ÷ r²
k = an electrostatic constant = 9 × 10⁹ Nm²/C² q = point charge = - 8.0 × 10⁻⁹ C r = Distant between point and point charge (m)E = The magnitude of electric fields (N/C) Electric fields in the systemE₁ = 4,500 N/C in the positive x-axis direction
E₂ is the electric fields from a point charge to r = 0.15 m
E₂ = 9 × 10⁹ × 8.0 × 10⁻⁹ ÷ 0.15²
E₂ = 72.0 ÷ 0.0225
E₂ = 3,200 N/C
a. At x = - 0.15 m
Look at picture a
The direction E₂ from x = - 0.15 to the origin.To the positive x direction. The net electric fields
E = E₁ + E₂
E = 4,500 + 3,200
E = 7,700 N/C
in the positive x direction
b. At x = 0.15 m
Look at picture b
The direction E₂ from x = 0.15 to the origin.To the negative x direction. The net electric fields
E = E₁ + E₂
E = 4,500 - 3,200
E = 1,300 N/C
in the positive x direction
c. At y = 0.15 m
Look at picture c
The direction E₂ from y = 0.15 to the origin.To the negative y direction. The net electric fields
Using Pythagorean theorem
E² = E₁² + E₂²
E² = 4,500² + 3,200²
E² = 20,250,000 + 10,240,000
E² = 30,490,000
E = 5,521.78 N/CThe direction
E₂ = - 3,200 N/C because of the negative y direction.
tan θ = E₂/E₁
tan θ = - 3,200/4,500
tan θ = - 0.711
θ = tan⁻¹ (- 0.711)
θ = - 35.42°
θ = 360° + (- 35.42°)
θ = 324.58° from the positive x direction
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a simply supported beam has a concentrated moment ma applied at the left support and a concentrated force f applied at the free end of the overhang on the right. using superposition, determine the deflection equations in the regions ab and bc.
Answers
To determine the deflection equations in the regions AB and BC of the simply supported beam using superposition, we first need to find the deflection equations for the beam under each load separately and then add them together.
Deflection due to the concentrated moment M_A at the left support:
The deflection equation for this case can be found using the equation:
δ(x) = (M_A * x²) / (6 * E * I)
Where δ(x) is the deflection at a distance x from the left support, M_A is the concentrated moment at the left support, E is the modulus of elasticity, and I is the moment of inertia.
Deflection due to the concentrated force F at the free end of the overhang on the right:
The deflection equation for this case can be found using the equation:
δ(x) = (F * (L - x)³) / (3 * E * I)
Where δ(x) is the deflection at a distance x from the right support, F is the concentrated force at the free end of the overhang, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.
SuperpositionBy the principle of superposition, the total deflection at any point is the sum of the deflections caused by each load.
Therefore,
δ(x) = (M_A * x²) / (6 * E * I) + (F * (L - x)³) / (3 * E * I)
Where x is the distance from the left support (AB) and
δ(x) is the total deflection in AB
And,
δ(x) = (F * (L-x)³) / (3 * E * I)
Where x is the distance from the right support (BC) and
δ(x) is the total deflection in BC
Note: The concentrated moment M_A has no effect on deflection in BC as it is on the left side of the support.
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A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 3.0 s for
the boat to travel from its highest point to its lowest, a total distance of
0.69 m. The fisherman sees that the wave crests are spaced 8.0 m apart.
(a) How fast are the waves traveling
Answers
Longitudinal waves takes the boat 2.5 seconds to move from the highest point to the lowest point and the total distance is 0.62 m. A fisherman confirms that the summit he is 6.0 off.
What is longitudinal waves?In the deep waters far offshore, the slowest wave components with the shortest periods and the smallest wave-to-height intervals can travel at less than 5 miles per hour. The component with the longest period could be moving at 35 miles per hour or more. Longitudinal waves, like sound, travel through a medium at a velocity that depends on the density and elasticity of the material. The speed of sound is 0.33 km/sec (0.2 miles/sec) in air, 1.5 km/sec in water, and 5 km/sec in steel.Longitudinal waves, like sound, travel through a medium at a velocity that depends on the density and elasticity of the material. The speed of sound is 0.33 km/sec (0.2 miles/sec) in air, 1.5 km/sec in water, and 5 km/sec in steel.To learn more about longitudinal waves from the given link:
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if the current i is .6 a for an air gap length of 1 mm, calculate the magnetic field density in the air gap
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Magnetic field density in the air gap = mmf/area of air gap = 0.6/1 mm2 = 0.6 Tesla
What is Magnetic field?A magnetic field is an invisible force field created by an electric current or a permanent magnet. It is a vector field that surrounds a magnetically charged object and exerts a force on other objects in its vicinity. The strength of a magnetic field is measured in amperes per meter (A/m).
The magnetic field density in the air gap is equal to the magnetomotive force (mmf) divided by the area of the air gap.
mmf = i x (1 mm) = 0.6
Area of air gap = 1 mm x 1 mm = 1 mm2
Magnetic field density in the air gap = mmf/area of air gap = 0.6/1 mm2 = 0.6 Tesla
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sunlight reflects from a concave piece of broken glass, converging to a point 15 cm from the glass. part a what is the radius of curvature of the glass? express your answer using two significant figure
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The radius of curvature of the broken glass from a concave piece is calculated to be 30 cm.
As the Sun's light rays are parallel to one another, they focus into the concave piece of glass's focus, which is f = 15 cm, when it serves as a concave mirror and reflects them.
It is known that, the radius of curvature of a concave mirror is twice its focal length, so in this case it is,
Radius = 2 × Focal length = 2 × 15 = 30 cm.
Thus, the required radius of curvature of the broken glass from a concave piece is calculated to be 30 cm.
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Two vectors ⃗
and ⃗
are shown in the figure. Vector ⃗
has a magnitude of =24.5
and an angle of =33.5∘.
Vector ⃗
has a magnitude of =46.9
and an angle of =57.5∘.
The figure is not to scale.
Express each vector in the figure using
unit vector notation,
⃗ =+
⃗ =+
where ,
,
,
and
are the calculated values of the
‑ and
‑components of vectors ⃗
and ⃗ ,
respectively.
A x y coordinate system with the positive x axis pointing horizontally to the right and the positive y axis pointing vertically upwards. Vector A extends from the origin into the first quadrant, has length r subscript A, and makes an angle theta subscript a with the positive x axis. Vector B extends from the origin into the third quadrant, has length r subscript b, and makes an angle theta subscript b with the negative x axis.
Answers
Explanation:
To express each vector in the figure using unit vector notation, we can use the following equations:
⃗ =
⃗ =
where is the x-component of the vector and is the y-component of the vector.
For vector :
x = 24.5cos(33.5) = 20.8
y = 24.5sin(33.5) = 14.2
So
⃗ =
For vector :
x = -46.9cos(57.5) = -31.8
y = -46.9sin(57.5) = -38.4
So
⃗ =
Note that the negative sign on the x-component of vector is due to the fact that it is in the third quadrant.
It is important to take into account that the angle provided on the question is in degrees, and in this case trigonometric functions are used to calculate the x and y component of the vector.
The note A (the one just above the middle of the piano keyboard) has a frequency of 440 Hz (the so-called A-440). It is the standard pitch for tuning instruments. What is the frequency of a note TWO octaves lower than this?
Answers
The frequency of a note two octaves lower than note A (the one right above the center of the piano keyboard) is 110 Hz (the so-called A-440).
What is frequency?The frequency of a repeated event is the number of occurrences per unit of time. It is separate from angular frequency and is sometimes referred to as temporal frequency. The unit of frequency is hertz, which equals one occurrence every second. The number of waves that travel through a particular point in a given length of time is described by frequency. So, if a wave takes half a second to pass, the frequency is 2 per second. The frequency is 100 per hour if it takes 1/100 of an hour. Frequency is a measurement of how frequently a recurrent event, such as a wave, happens in a certain period of time. A cycle is one completion of the repeating pattern.
Here,
The frequency of a note two octaves lower than note A (the one just above the middle of the piano keyboard) has a frequency of 440 Hz (the so-called A-440) is 110 Hz.
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Air moves across a warm body of water and rises in the atmosphere. This heat is most likely transmitted by which of the following? • Convection only • Radiation only • Convection and conduction • Radiation and conduction
Answers
This heat is most likely transmitted by Convection only. The first option is the correct answer.
What is Convection?Convection is the transfer of heat by the movement of a fluid or gas. When air moves across a warm body of water, it is heated by the water through convection and rises in the atmosphere. This process is called a sea breeze.
Heat convention in materials can be calculated using the formula:
Q = h A ΔT
Where,
Q = heat transfer rate
h = convection heat-transfer coefficient
A = exposed surface area
ΔT = temperature difference
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