The equations for the camber and half thickness distributions are:
A. For 0 < (x/c) < 0.6 n = 0.3(x/c), t = 0.1(x/c)
B. For 0.6 < (x/c) < 1.0 n = 0.45 (1 - x/c), t = 0.15 (1 - x/c)
The camber and half thickness distributions can be found using the thin airfoil theory. According to this theory, the camber and half thickness distributions are given by:
n = (Y upper - Y lower ) / 2 (for camber)
t = (Y upper + Y lower ) / 2 (for half thickness)
For the given airfoil, we can find the camber and half thickness distributions by applying the above equations to each segment separately.
The theory simply states that flow around an airfoil is described as two-dimensional flow around a thin airfoil. It is possible to imagine it addressing an airfoil with zero thickness and infinite wingspan.
For 0 < (x/c) < 0.6
Y upper = 0.4(x/c), Y lower = 0.2(x/c)
Therefore,
n = (0.4(x/c) - 0.2(x/c)) / 2 = 0.3(x/c)
t = (0.4(x/c) + 0.2(x/c)) / 2 = 0.1(x/c)
For 0.6 < (x/c) < 1.0
Y upper = 0.6(1 - x/c), Y lower = 0.3(1 - x/c)
Therefore,
n = (0.6(1 - x/c) - 0.3(1 - x/c)) / 2 = 0.45 (1 - x/c)
t = (0.6(1 - x/c) + 0.3(1 - x/c)) / 2 = 0.15 (1 - x/c)
So, the equations for the camber and half thickness distributions are:
A. For 0 < (x/c) < 0.6 n = 0.3(x/c), t = 0.1(x/c)
B. For 0.6 < (x/c) < 1.0 n = 0.45 (1 - x/c), t = 0.15 (1 - x/c)
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Occurs when the type, degree, and duration of force employed was not necessary or appropriate.
The type, degree, and duration of force that is employed during the moment was not necessary.
in mechanics, any action that seeks to preserve, modify, or deform a body's motion. Isaac Newton's three laws of motion, which are outlined in his Principia Mathematica, are frequently used to illustrate the concept of force (1687).
Simple people with simple minds teach simple subjects, like physics. The first thing physicists do when they examine an object is to simplify it. A book is a box, not a collection of paper sheets attached with glue and string. A automobile is a box; it doesn't have rotating rubber tires, six-way adjustable seats, lots of cup holders, or a rear window defogger. A human is not formed of bone, muscle, skin, and hair; rather, they are a box with two arms, two legs, and a head. This is the start of a free body diagram, a style of drawing popular among engineers and physicists.
The foundation of physics is the logical process of analysis, which involves dissecting complex circumstances into a collection of smaller ones.
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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
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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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
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 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.
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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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?
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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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
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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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
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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the rigid bar efg is supported by the truss system shown. knowing that the member cg is a solid circular rod of 0.75-in. diameter, determine teh normal stress in cg
Normal stress in CG is 13.58 Ksi
When the deforming force is applied to an item, it deforms. The object will generate an opposing force from within to revert to its previous dimensions and shape. This restoring force will be applied in the opposite direction and have the same magnitude as the deforming force.Stress is a term used to describe how much of this restorative force is produced per unit area of the material. When the path of the deforming force is perpendicular to the body's cross-sectional area, stress is said to be normal stress. If the wire's length or the body's volume changes, the stress level will remain normal.
Using the portion EFCGB as a free body ,
∑[tex]F_{y} =0 :[/tex]
[tex]\frac{3}{5}F_{AE}[/tex]-3600=0
[tex]F_{AE}[/tex]=6000 lb
Using beam EFG as a free body ,
+[tex]M_{F} =[/tex]0 ,
-(4) [tex]\frac{3}{5}F_{AE}[/tex] + (4)[tex]\frac{3}{5}F_{cc}[/tex] = 0
[tex]F_{cc} =F_{AE} =[/tex]6000lb
cross section area of member CG :
[tex]A_{CG}=\frac{\pi}{4} d^{2}[/tex]= [tex]\frac{\pi}{4} (0.75)^{2}[/tex]
[tex]A_{CG}=0.44179 \:in^{2}[/tex]
Let the normal stress is 'B'
Normal stress in CG
[tex]B_{CG} =\frac{ F_{CG} }{ A_{CG} }[/tex] = [tex]\frac{6000 }{0.44179 }[/tex] = 13,580 psi
[tex]B_{CG} =[/tex] 13.58 Ksi
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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.
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
A beachgoer in Florida notices the waves crashing ashore are spaced 13 meters apart and hit the shore every 6 s. How fast (in m/s) are the waves traveling?
The speed of the waves at the beach in Florida is 2.167 m.s.
What is the wavelength of the wave?The wavelength of a wave is the distance between successive points in a wave.
The wavelength of the given wave is obtained as follows:
Wavelenegh of the wave = 13 meters
The frequency of the wave is 1/6 per second
The wavelength, speed, and frequency of the wave is related as follows;
The velocity of a wave = wavelength * frequency
The speed or velocity of the wave = 13 * 1/6
The speed or velocity of the wave = 2.176 m/s
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water flows with speed v through a horizontal, cylindrical pipe. which of the following changes in the geometry of the pipe will double the speed of the water in the pipe?
Halving the area of the pipe will double the speed of the water in the pipe. Therefore, option(c) is the correct answer.
Given,
initial flow speed, V₁ = v
let's area, A₁ = A
Now, to double the speed of the water flow
V₂ = 2v
we know that,
using continuity equation of flow:
A₁V₁ = A₂V₂
or A x v = A₂ x 2v
A₂ = A/2 or A₁/2
Therefore, By Halving the area of the pipe will double the speed of the water in the pipe.
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The complete question is:
water flows with speed v through a horizontal, cylindrical pipe. which of the following changes in the geometry of the pipe will double the speed of the water in the pipe?
(a) Doubling the area of the pipe
(b) Doubling the radius of the pipe
(c) Halving the area of the pipe
(d) Halving the radius of the pipe
examine the graphs below, which show salinity, temperature, and density with depth from the atlantic ocean. which letter on the graphs represents the halocline?
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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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!)
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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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.
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)).
A 500 kg roller coaster car starts from rest at point A and moves down the curved track._ The speed of the car at the point C is 10 m/s. Calculate the energy loss due to friction from A to C
The appropriate values into the equation: E = (500 kg) (9.81 m/s2) (change in height between A and C).
What is equation?An equation is a mathematical statement that expresses the relationship between two or more variables. It is composed of algebraic expressions, including constants, coefficients, variables, and operators, arranged in a particular order.
The energy loss due to friction from A to C can be calculated using the equation E = mgh, where m is the mass of the car (500 kg), g is the acceleration due to gravity (9.81 m/s2), and h is the change in height between points A and C.
Assuming that the track is level between A and C,
then the change in height is zero and the energy loss due to friction is also zero. If, however,
the track is not level and there is a change in height between A and C,
then the energy loss due to friction can be calculated by plugging in the appropriate values into the equation: E = (500 kg) (9.81 m/s2) (change in height between A and C).
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a person wants to transmit an audio file from a device to a second device. which of the following scenarios best demonstrates the use of lossless compression of the original file? What is the speed of the block immediately after the bullet exits?
The answer is that A device compresses the audio file before transmitting it to a second device. The second device restores the compressed file to its original version.
What is an compresses an audio file?To compresses an audio file is a term that connote the act of making an audio file to be smaller in size so as to fit into a given device or app. Note that the option that best demonstrates the use of lossless compression of the original file is that A device compresses the audio file before transmitting it to a second device. The second device restores the compressed file to its original version before playing it and as such, option A is correct.
Here,
The solution is that before sending the audio file to a second device, A compresses it. The second device converts the compressed file back to its original state.
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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?
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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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
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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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?
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.
If 240 million people in the United States jumped up into the air simultaneously pushing off the earth with an average force of 800 N each for 0.10 s, what would happen to the 5.98x10^24 kg earth?
when 270 million people jump at the same time the Earth will move at 1.3 m/s.
What is average force?The vector quantity of a force. It is a quantity with both magnitude and direction, hence.
We must specify both the size and the direction of the force operating on an object in order to adequately understand it. The average force is the force applied by an item traveling over a specific period of time at a defined rate of speed, or velocity.
This velocity is not instantaneous or precisely calculated, as the word "average" indicates. As a result, the average force is determined by multiplying the body's mass by the object's average velocity during the specified period of time.
Therefore, when 270 million people jump at the same time the Earth will move at 1.3 m/s.
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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.
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 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.
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 systemE₂ 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.b. At x = 0.15 m
Look at picture b
The direction E₂ from x = 0.15 to the origin.c. At y = 0.15 m
Look at picture c
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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.
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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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.
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.
a cup of hot tea initially at 95*c, cools to 75*c, in 5.0 minutes when sittinf in 25*c surroundings. use newton's law of cooling to determine how long it will take to cool to 35*c
According to Newton's law of cooling, the rate of cooling is inversely related to the temperature differential between the object and its surroundings. For this, the equation is:
dT/dt = k (T - Ts) (T - Ts)
where T is the object's temperature, Ts is the environment's temperature, and k is the cooling constant. where dT/dt is the rate of change in temperature.
This equation can be used to calculate the cooling constant k for the cup of tea. We know that the temperature started off at 95 degrees Celsius, dropped to 75 degrees Celsius, and took 5 minutes to cool down.
95 - 75 = 20, dT/dt = k (20), dT/dt = k (20) *(1/5), and dT/dt = 4k.
Then, we can determine how long it will take for the temperature to cool to the desired level by using this cooling constant and the target temperature (35°C).
35 - 75 = -40\s-40 = 4k(t) (t)
t = -40 / 4k
We are unable to solve for t since we lack the value for k. But if we assume that the cooling rate is comparable to the rate we currently know, we can come up with an estimate. If we assume that the rate of cooling is constant, we can calculate how long it will take for the tea to cool from 75 to 35 degrees by using the rate of cooling from 95 to 75 degrees.
t = -40/20 equals 2 minutes.
It would take around 2 minutes to cool the tea from 75c to 35c under the assumption of similar cooling rate.
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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
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.
Hope this helped :)
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.
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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how can a simple fixed pulley make a job easier
a. by decreasing the work done
b. by changing the direction at which the force needs to be applied
c. by decreasing the distance that the force needs to be applied
d. by decreasing the force required to lift the object
It is considerably easier for us to move objects thanks to simple machinery called pulleys that can shift the direction of force. The amount of force necessary to lift something up is reduced by this procedure. Option d
What does a scientific force mean?A clear meaning is attached to the word "force." The terms "push" and "pull" are perfectly acceptable at this level to describe forces. An object does not have a force inside of it or within it.
Who or what is force?A massed item changes its velocity in response to a push or pull. A body can change its state of rest or motion when an external force acts on it. It is directed and has a magnitude.
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what is the direction of the acceleration of the object at moment 5? enter the letter of the arrow with this direction from the compass rose in the figure. type z if the acceleration vector has zero length.
The direction of the acceleration of the pendulum at moment 5 is towards A (center), which is perpendicular to the direction of motion of the bob.
There is no any component of force acting along the tangent direction, when the bob is at the equilibrium mid-position as the string is completely vertical. Restoring force is momentarily absent in the bob when it is moving through the equilibrium position. The restoring force is only required when the pendulum bob has been slightly displaced away from the equilibrium position.
In the equilibrium position, the tension force is greater than the perpendicular component of gravity when the bob moves through this equilibrium position. As the bob continues its motion along a circular arc, so there must be a net centripetal force towards the center. So the direction will be towards A.
--The given question is incomplete, the complete question is:
"what is the direction of the acceleration of the object at moment 5? enter the letter of the arrow with this direction from the compass rose in the figure. type z if the acceleration vector has zero length."
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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?
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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