The surface area of the Earth is [tex]5.14\times 10^{14}\ m^2[/tex]
According to the question:
The surface area of the earth[tex](S) = 4\pi r^2[/tex] ...(i)
The radius of the earth [tex]r = 6400\ km[/tex]
To find:
The surface area of the earth in [tex]m^2[/tex].
[tex]r = 6400\ km[/tex], therefore in meters:
[tex]r = 6400\times 1000\ m = 6400000\ m\\r = 6.4\times 10^{6}\ m[/tex]
Substitute this value in equation (i), and let [tex]\pi = 3.1415[/tex], we get:
[tex]S = 4\times 3.1415\times (6.4 \times 10^{6})^2\ m^2[/tex]
[tex]S = 5.14\times 10^{14}\ m^2[/tex]
Therefore, the surface area of the Earth is [tex]5.14\times 10^{14}\ m^2[/tex].
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An object of mass 1.00 kg is attached to a vertical spring with spring constant 100 N/m. The object is held at rest in a position such that the spring is stretched upward a distance 1.00 cm beyond its undisturbed length. If the object is released, how far will it drop before coming to rest
The object will drop 5 cm if released before coming to rest.
How far will the object fall?We know from Hooke's law that the work that is done when the spring is stretched is given by the formula;
W = 1/2 kx^2
k= 100 N/m
x = 1.00 cm or 0.01 m
W = 0.5 * 100 * 0.01
W = 0.5 J
Now;
W = mgh
h = W/mg
m = 1.00 kg
g = 9.8 m/s^2
h = 0.5 J/1.00 kg * 9.8 m/s^2
h = 0.05 m or 5 cm
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The international Space Station (ISS) orbits the Earth once every 90 mins at an altitude of 409 km. How high would it have to be in order to be to be in geosynchronous orbit
It would have to be 36,719 Km high in order to be to be in geosynchronous orbit.
To find the answer, we need to know about the third law of Kepler.
What's the Kepler's third law?It states that the square of the time period of orbiting planet or satellite is directly proportional to the cube of the radius of the orbit.Mathematically, T²∝a³What's the radius of geosynchronous orbit, if the time period and altitude of ISS are 90 minutes and 409 km respectively?The time period of geosynchronous orbit is 24 hours or 1440 minutes.As the Earth's radius is 6371 Km, so radius of the ISS orbit= 6371km + 409 km = 6780km. If T1 and T2 are time period of geosynchronous orbit and ISS orbit respectively, a1 and a2 are radius of geosynchronous orbit and ISS orbit, as per third law of Kepler, (T1/T2)² = (a1/a2)³a1= (T1/T2)⅔×a2= (1440/90)⅔×6780
= 43,090 km
Altitude of geosynchronous orbit = 43,090 - 6371= 36,719 kmThus, we can conclude that the altitude of geosynchronous orbit is 36,719km.
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You are looking down on a 20 kg beam resting on a horizontal, frictionless surface. The beam is 2 m long and can pivot about one end. A small 0.1 kg rock slides across the surface at 400 m/s and hits the middle of the beam, embedding itself inside. What is the angular speed of the rod after the impact (in rad/s)
The angular speed of the rod after the impact is 1.49 rad/s
What is angular speed?
The rate of change of angular displacements is known as angular speed.
Angular speed is a scalar measure of the rotating object.
What is Angular momentum?
It is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object.
Angular momentum is expressed as follows:
L=m*v*r
Here,
mass of beam, M =20 kg
mass of rock, m =0.1 kg
length of the beam, L =2 m
length where rock slides, l = (L / 2), l = 1 m
velocity of rock, v =400 m/s
As here the Torque on which the system is zero implies that the angular momentum is conserved.
Initial angular momentum for rock: I(ri) = m*v*r
Final angular momentum for rock: I(rf) = m*w*r^2
Final angular momentum for beam: I(bf) = 1/3 (M*L^2w)
Now, According to the conservation of momentum:
m*v*r = m*w*r^2 + 1/3 (ML^2w)
w = m*v*r / ( mr^2 + 1/3 ML^2 )
w = 0.1 *400*1 / ( (0.1 * 1) + 1/3 20* 2^2 )
w = 1.49 rad / s
The angular speed of the rod after the impact is 1.49 rad/s
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How do astronomers explain the energetic jets that come out of quasars and active galactic nuclei in opposite directions
Astronomers explain the energetic jets that come out of quasars and active galactic nuclei(AGN) in opposite directions in a way that the supermassive black holes' chaotic accretion discs "spit out" jets in directions perpendicular to the disc.
Quasar : A supermassive black hole with a mass between millions and tens of billions of solar masses that is fueled by an extraordinarily bright active galactic nucleus (AGN) and encircled by a gaseous accretion disc is known as a quasar.
An active galactic nucleus (AGN) is a compact area at the Centre of a galaxy that exhibits features that indicate the luminosity is not coming from stars and is substantially brighter than usual over at least some of the electromagnetic spectrum.
Hence, astronomers propose that the chaotic accretion discs of supermassive black holes "spit out" jets in directions perpendicular to the disc, explaining the intense jets that emerge from quasars and active galactic nuclei in different directions.
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Water flows through a pipe with a cross-sectional area of 0.002 m^2 at a mass flow rate of 4 kg/s. the density of water is 1 000 kg/m^3. Determine its average velocity
Water flows through a pipe with a cross-sectional area of 0.002 m^2 at a mass flow rate of 4 kg/s. The density of water is 1 000 kg/m^3 . The average velocity will be 2m/s
The flow rate of a liquid is how much fluid passes through an area in a particular time. Flow rate can be articulated in either in terms of velocity and cross-sectional area, or time and volume.
Flow rate = Volume of fluid / time
= (Area * distance) / time
= Area * average velocity (distance / time = average velocity)
Given
Cross-sectional area = 0.002 [tex]m^{2}[/tex]
Flow rate = 4 kg/s
Average velocity = Flow rate / (Area * density)
= 4 / (0.002 * 1000)
= 2m/s
hence , the average velocity will be 2 m/s
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An object falls from the top of a building that is 25 m high. Air resistance is negligible.
What is the speed of the object when it hits the ground?
The velocity of the object s calculated as 22.1 m/s.
What is the speed of the object?Given that we can write that;
v^2 = u^2 + 2gh
Now u = 0 m/s because the object was dropped from a height
v^2 = 2gh
v = √2 * 9.8 * 25
v = 22.1 m/s
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According to max weber, flaunting of one’s wealth to show one’s status is called?
Status refers to a person's prestige, social honor, or reputation in society. Weber stated that political strength become now not rooted entirely in capital fees, but additionally in a single's individual popularity. Poets or saints, for example, can own a massive impact on society, often with little monetary worth.
The German sociologist Max Weber formulated a three-component theory of stratification that defines a status group (additionally status class and status estate) as a group of humans within a society who can be differentiated by means of non-financial characteristics along with honor, prestige, ethnicity, race, and religion.
Social stratification entails society as a system of hierarchical categories. Max Weber defined stratification because the division of a society into distinct communities, that have varying assignments of “status honor” or status.
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step by step process please
I know the ans but not the process
pic attached
Answer:
[tex]\huge\boxed{\sf F= 350 \ N}[/tex]
Explanation:
Considering pivot as the central point,
Key:
Torque = Force F × radius rAnticlockwise torque = Clockwise torque[tex]F_1r_1=F_2r_2[/tex]
Here,
Anticlockwise force is FClockwise force is 600 N[tex]r_1=70+50= 120 \ cm = 1.2 \ m[/tex][tex]r_2=70 \ cm = 0.7 \ m[/tex]Solution:Substitute the givens in the above formula.
[tex]F(1.2)=600(0.7)\\\\F(1.2)=420\\\\Divide \ 1.2 \ to \ both \ sides\\\\F=420/1.2\\\\F= 350 \ N\\\\\rule[225]{225}{2}[/tex]
A mass m is attached to an ideal massless spring. When this system is set in motion with amplitude a, it has a period t. What is the period if the amplitude of the motion is increased to 2a?.
The period will be the same if the amplitude of the motion is increased to 2a
What is an Amplitude?
Amplitude refers to the maximum extent of a vibration or oscillation, measured from the position of equilibrium.
Here,
mass m is attached to the spring.
mass attached = m
time period = t
We know that,
The time period for the spring is calculated with the equation:
[tex]T = 2\pi \sqrt{\frac{m}{k} }[/tex]
Where k is the spring constant
Now if the amplitude is doubled, it means that the distance from the equilibrium position to the displacement is doubled.
From the equation, we can say,
Time period of the spring is independent of the amplitude.
Hence,
Increasing the amplitude does not affect the period of the mass and spring system.
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a charged partocle produces an electric field with a magnitude of 2.0 N/C at a point that is 50cm away from the particle
The charge on the particle is 5.6 × 10⁻¹¹ C.
Calculation:The magnitude of an electric field produced by a charge is given by:
E = q/ 4πε₀r²
where,
E = electric field
q = charge
r = distance
1/4πε₀ = 8.99 × 10⁹ Nm²/C²
Given,
E = 2.0 N/C
r = 50 cm = 0.5 m
To find,
q =?
Put the values in the above equation:
E = q/ 4πε₀r²
q = E (4πε₀r²)
q = 2.0 × (0.50²)/ 8.99 × 10⁹
q = 5.6 × 10⁻¹¹ C
Therefore, the particle has a charge of 5.6 × 10⁻¹¹ C.
What is an electric field?The physical field that surrounds each electric charge and acts to either attract or repel all other charges in the field is known as an electric field. Electric charges or magnetic fields with different amplitudes are the sources of electric fields.
I understand the question you are looking for is this:
A charged particle produces an electric field with a magnitude of 2.0 N/C at a point that is 50 cm away from the particle. What is the magnitude of the particle's charge?
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One method of getting a tight fit, say of a metal peg in a hole in a metal block, is to manufacture the peg slightly larger than the hole. The peg is then inserted when at a different temperature than the block. Should the block be hotter or colder than the peg during insertion
The block should be colder than the peg during insertion.
To find the answer, we have to know more about the thermal expansion of metal.
What is thermal expansion of metal?Metals' Thermal Expansion The phenomenon of material expanding on heating and contracting on cooling is now well-known. An object changes in size when heated. Depending on the body's form. It is known as linear expansion if the expansion takes place linearly.The peg should be warmer than the metal block. Since the metal peg is made larger, the temperature of the metal block should be lower than that of the peg in order for the metal block's thermal expansion to provide a tight fit when the peg is inserted into the hole and the temperature rises.Due to the metal's tendency to expand as temperature rises, the hole's size decreases. As a result, at the time of insertion, the metal block's temperature should be lower than the peg's temperature.Thus, we can conclude that, the block should be colder than the peg during insertion.
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Provided following are four different ranges of stellar masses. Rank the stellar mass ranges based on how many stars in each range you would expect to be born in a star cluster, from highest number to lowest number.
Highest to lowest number:
-less than 1 solar mass
-between 1 and 10 solar masses
-between 10 and 30 solar masses
-between 30 and 60 solar masses
What is Stellar masses ?Stellar mass is a phrase that is used by astronomers to describe the mass of a star. It is usually enumerated in terms of the Sun's mass as a proportion of a solar mass (M☉).
Hence, the bright star Sirius has around 2.02 M☉.A star's mass will vary over its lifetime as mass is lost with the stellar wind or ejected via pulsational behavior, or if additional mass is accreted, such as from a companion star.Learn more about Stellar masses here:
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A 52–newton bird feeder is tied to a rope, which is attached to a tree branch. Describe the tension force of the rope.
A 52-newton tension force pulls down on the branch, and a 52-newton tension force pulls up on the bird feeder.
What is tension ?
The tension force is defined as the force that is transmitted through a rope, string or wire when pulled by forces acting from opposite sides. The tension force is directed over the length of the wire and pulls energy equally on the bodies at the ends.
Tension is the opposite of compression force. All the objects that are present in contact with each other exert a force on each other. The best example of a tension force can be seen while pulling a rope. When a pull force is applied to the rope, a significant amount of tension gets built.
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In nineteenth century, physical science was divided into discipline. .
Answer:
Here! Try this Website!: www.britannica.com › science › physical-science physical science | Definition, History, & Topics | Britannica. So you will learn a lot more about science, history, and topics about it!
Answer:i have no idea
Explanation:
please help me to find out my mistake
From the calculation, the speed of sound at 10 K is 63.5 m/s.
What is the speed of sound?We know that the speed of sound is directly proportional to the temperature of the body thus we can write;
V1/V2 = √T1/T2
Then;
T1 = 0 degrees or 273 K
T2 = 10 K
V1 = 330 m/s
V2 = ?
330/T2 = √273/10
330/T2 = 5.2
330 = 5.2T2
V2 = 330/5.2
V2 = 63.5 m/s
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A piece of copper of mass 150g at temperature of mass 70g containing 60g of water at temperature of 20°C. Ignoring heat losses, what would be the final steady temperature of the mixture? [Specific of heat capacity of copper = 4.0× 10²J/kg-1/K ^-1. Please any Physics student can help or if you have any idea, you can help me out. Thanks.✨✨
Answer:
The final temperature is [tex]29.6^oC[/tex].
Explanation:
When the two masses come in contact, one releases heat and the other absorbs it. The former can be modelled with the equation [tex]HeatLost = (Mass1 (kg))(c1)(T1-T)[/tex], and the latter by [tex]HeatGained=(Mass2(kg))(c2)(T-T2)[/tex]
m1=0.15 kg
m2=0.06 kg
T1 = 70 degrees Celsius = 343 K
T2 = 20 degrees Celsius = 293 K
T= Final temperature
c1 = Specific heat capacity of copper
c2 = Specific heat capacity of water
Because there is no heat lost into the surroundings, the heat removed from one substance is the same as the heat gained in the other. Therefore:
[tex](Mass1)(c1)(T1-T)=(Mass2)(c2)(T-T2)[/tex]
[tex](0.150)(400)(343-T)=(0.06)(4184)(T-293)[/tex]
[tex](60)(343-T)=(251.04)(T-293)[/tex]
[tex]20580-60T=251.04T-73554.72[/tex]
[tex]-311.04T=-94134.72[/tex]
[tex]T=302.6 K[/tex]
[tex]T=29.6^oC[/tex]
Hope this helps! (My apologies if the answer is wrong, it has been a while since I've done this)
Which of these is most likely to create a boating hazard around river bridges?
a) boats slowing as they approach the bridge
b) cars crossing the bridge
c) debris collecting around pilings
d) bridges swaying due to wind and waves
Debris collecting around pilings is most likely to create a boating hazard around river bridges.
The option (c) is the correct option.
Boating Hazards:
Dams, submerged items, freezing water, rapidly changing weather, sunstroke, and current are just a few of the dangers that boaters may encounter. It's not always easy to see these risks. These risks must be recognized by boaters, and they must always be prepared to prevent hazards.
Operator negligence is the most frequent reason for boating accidents, according to US Coast Guard (USCG) recreational boating statistics from 2019. Inattentiveness on the part of the operator can result in crashes, people falling overboard, and slip-and-fall incidents on board, all of which can result in life-threatening injuries.
The greatest places to find more about any potential local risks are marinas and local boaters. Check any nearby marine charts as well to learn about potential dangers and how to avoid them.
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Two boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 40-kg boy will have moved what distance?.
When they meet the 40-kg boy would have moved a distance of 6 m.
Distance moved by the 40 kg boyApply the principle of center mass;
Take the 40 kg mass as the reference point;
X(40 kg) = (40kg x 0 + 60kg x 10 m)/(40 kg + 60 kg)
X(40 kg) = (600)/(100)
X(40 kg) = 6 m
Thus, when they meet the 40-kg boy would have moved a distance of 6 m.
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The resistance, r, to electricity of a cylindrical-shaped wire is given by the equation r = startfraction p l over pi d squared endfraction, where p represents the resistivity of the wire’s material, l represents the length of the wire, and d represents the diameter of the wire. what happens to the resistance of the wire as the diameter approaches 0?
As the diameter of the wire approaches to zero, the resisitance approaches infinity.
What is resistance?Electrical resistance is the physical capacity of any body to oppose the flow of electric current even when there is an applied potential difference, capacity calculated by Ohm's First Law, and, according to the International System of Units (IS), is measured in ohms.
With that being said, and knonwing that:
R = Resistance; p = Resistivity; L = Length; d = Diameter
It is possible to calculate the resistance of the wire by:
[tex]R = p\frac{L}{A}[/tex]
Where A is calculated by:
[tex]A = \frac{\pi d^{2} }{4}[/tex]
Changing in the first formula:
[tex]R = p\frac{L}{\pi d^{2} } \\\\R = p\frac{4L}{\pi d^{2} }[/tex]
Knowing that when the diameter tends to zero resistance tends to infinity, it is possible to say that resistance of the wire will tend to infinity when the diameter approaches zero.
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Answer:
The resistance approaches infinity.
Explanation:
100% Correct
When the absolute value of the price elasticity of demand falls in the range 0 to 1, demand is said to be _____.
When the absolute value of the price elasticity of demand falls in the range 0 to 1, demand is said to be inelastic.
A good or service that has an income elasticity of demand between zero and 1 is considered a normal good and income inelastic. If a good or service has an income elasticity of demand below zero, it is considered an inferior good and has negative income elasticity.
Inelastic is an economic term referring to the static quantity of a good or service when its price changes. Inelastic means that when the price goes up, consumers' buying habits stay about the same, and when the price goes down, consumers' buying habits also remain unchanged.
Price elasticity of demand is a measurement of the change in consumption of a product in relation to a change in its price. A good is elastic if a price change causes a substantial change in demand or supply.
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the question is down below
The speed of the airplane, v is 144.2 m/s
The height, H of the roof above the head of the man is 66.4 m.
What is the speed of the airplane?The speed of the airplane is determined using the Pythagoras theorem.
The speed of the airplane, v is calculated as follows:
v = √(80² + 120²0
v = 144.2 m/s
The height, H of the roof above the head of the man is calculated as follows:
tan 38° = H/85
H = tan 38° * 85 m
H = 66.4 m
In conclusion, the tangent ratio is used to find the height of the roof above the head of the man.
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Mindspore accelerates model convergence through automatic parallelism and second-order optimization.
a. True
b. False
Mindspore accelerates model convergence through automatic parallelism and second-order optimization.
The statement is a)true.
Mind Expression, MindSpore frontend, which is used to compile duties from user source code to computational graphs, control execution at some point of schooling, preserve contexts (in non-sink mode), and dynamically generate graphs (in PyNative mode).
Using a distributed structure, MindSpore leverages a local differentiable programming paradigm and new AI local execution modes to attain higher aid performance, safety, and trustworthiness.
It consists of the Ascend collection chips, Atlas series hardware, CANN chip enablement, MindSpore AI framework, ModelArts, and MindX utility enablement.
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The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2.00 103 N with an effective perpendicular lever arm of 3.40 cm, producing an angular acceleration of the forearm of 165 rad/s2. What is the moment of inertia of the boxer's forearm
Answer: The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2.00 103 N with an effective perpendicular lever arm of 3.40 cm, producing an angular acceleration of the forearm of 165 rad/s2. Then, the moment of inertia of the boxer's forearm will be 0.412Nm/rad/sec2.
Explanation: To find the correct answer, we have to know more about the moment of force or torque.
What is Torque?Torque is the measure of turning effect of a force.If the object rotates about an axis, then the perpendicular distance from the axis to the line of action of the force is called the lever arm.Torque is measured by the product of force and the lever arm.If r is the position vector of the point of application of force, then torque T is,[tex]T=rFsin\alpha[/tex], where, [tex]\alpha[/tex] will be the angle between r and F.
Torque in terms of moment of inertia [tex]I[/tex] and the angular acceleration [tex]\beta[/tex] will be,[tex]T=I\beta[/tex]
Where, [tex]I=r[/tex]×m
How to solve the problem?Given that,[tex]F=2*10^3N\\r=3.40*10^-2m\\\beta =165 rad/sec^2[/tex]
From the above equation of T, we can produce the equation of moment of inertia as,[tex]I=\frac{T}{\beta } =\frac{rFsin\alpha }{\beta } \\where, sin\alpha =1.\\Thus,\\T=\frac{rF}{\beta } =\frac{68}{165} =0.412Nm/rad/s^2.[/tex]
Thus, we can conclude that, moment of inertia of the boxer's forearm will be, 0.412Nm/rad/sec².
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In 2020, UMass Amherst professors Jun Yao and Derek Lovley invented a generator to create electricity from:
moisture in the air
Electrical engineer Jun Yao and microbiologist Derek Lovley have developed a device that uses a natural protein to create electricity from moisture in the air, a new technology they say could have significant implications for the future of renewable energy, climate change, and the future of medicine.
What is electricity from moisture in the air ?Air Generator," or “Air-Gen,” with electrically conductive protein nanowires produced by the microbe Geobacter, discovered by Lovley some years ago.
The Air-Gen connects electrodes to the protein nanowires in such a way that electrical current is generated from the water vapor naturally present in the atmosphere.Learn more about Air Generator here:
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17% Part (a) Calculate the x-component of the electric field at point P due to charge Q1. Write your answer in units of N/C.
The x component would be Ex = 412 x cos 49° = 270 N/C
Assume there is a small positive charge located at point P. By definition the magnitude of the electric field at point P due to charge Q1 is
E = kQ1/d2
where k is the coulomb constant and d is the straight line distance from Q1 to P.
The distance is the hypotenuse of the triangle formed by Q1, Q2, and P.
d = √0.065^2 + 0.075^2 = 0.099 m at an angle of θ = arctan 7.5/6.5 = 49°.
|E| = 8.99 x 10^9 Nm^2 C^-2 x 0.45 x 10^-9 C/ 0.099^2 m^2 = 412 n/C
The x component would be Ex = 412 x cos 49° = 270 N/C
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What is the safest method to determine electrical current
airs of conductors carrying current into or out of the power-supply components of electronic equipment are sometimes twisted together to reduce magnetic-field effects. Why does this help
Answer: Pairs of conductors carrying current into or out of the power-supply components of electronic equipment are sometimes twisted together to reduce magnetic-field effects. This is for reducing the area of the loop and hence reducing the inductance and suffer less interference or improving electromagnetic compatibility.
Explanation: To find the answer, we need to know more about Twisted pairs.
What is twisted pairs?Twisted pairs are simply conductors carrying current into and out of the power supply components of the electronic equipment, which are sometimes twisted together to reduce magnetic field effects.It can be able to minimize the area of the loop around the circuit. thus, the magnetic field from each wire will cancels each other.This will reduce the inductance as well as interference caused by the nearest fields.Twisting them will defines a transmission line impedance.Thus, we can conclude that, the twisted pairs are used for reducing the area of the loop and hence reducing the inductance and suffer less interference or improving electromagnetic compatibility.
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Find the work done when a constant force f = 13 lbs moves a chair from x = 2.4 to x = 4.1 ft. along the x -axis.
The work done in moving the chair from x = 2.4 to x = 4.1 ft using a force of F = 13 lbs is 29.98 J
What is work done?This is simply defined as the product of force and distance moved in the direction of the force. Mathematically, it can be expressed as
Workdone (Wd) = force (F) × distance (d)
Wd = Fd
How to convert lb to N1 lb = 4.45 N
Therefore,
13 lbs = 13 × 4.45
13 lbs = 57.85 N
How to determine the distance in mInitial distance = 2.4 ftFinal distance = 4.1 ftChange in distance = 4.1 -2.4 = 1.7 ft1 ft = 0.3048 m
Therefore,
1.7 ft = 1.7 × 0.3048
1.7 ft = 0.51816 m
How to determine the workdoneForce (F) = 57.85 NDistance (d) = 0.51816 mWorkdone (Wd) =?Wd = Fd
Wd = 57.85 × 0.51816
Workdone = 29.98 J
Thus, the workdone in moving the chair is 29.98 J
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Plane-polarized light is incident on a single polarizing disk with the direction of E0 parallel to the direction of the transmission axis. Through what angle should the disk be rotated so that the intensity in the transmitted beam is reduced by a factor of:
Answer: Plane-polarized light is incident on a single polarizing disk with the direction of E0 parallel to the direction of the transmission axis. Through angle [tex]\alpha=cos^-1(\sqrt{\frac{1}{n} })[/tex] should the disk be rotated so that the intensity in the transmitted beam is reduced by a factor of n .
Explanation: To find the correct answer, we need more clarifications about the Malu's law.
What is Malu's law?When a beam of plane polarized light is passed through an analyzer, the intensity I of the transmitted light varies directly as the square of the angle between the direction of polarizer and the analyzer.[tex]I=I_0cos^2\alpha[/tex]
where, [tex]I_0[/tex] is the maximum intensity of transmitted light.
Intensity of the light transmitted through the polarizer is half of the incident intensity.How to solve the problem?Here in the question ,let's take the factor at which the intensity of transmitted light is reduced by as n.we have the expression[tex]I=I_0cos^2\alpha[/tex]
we have to find the value of angle alpha, so that the intensity in the transmitted beam is reduced by a factor of n.[tex]\alpha =cos^-1\sqrt{(\frac{I}{I_0}} )=cos^-1\sqrt{\frac{I}{nI} } \\\alpha =cos^-1\sqrt{\frac{1}{n} }[/tex]
If we know the value of n, then we can easily find the angle.Thus, we can conclude that, the value of angle alpha, so that the intensity in the transmitted beam is reduced by a factor of n will be,
[tex]\alpha=cos^-1(\sqrt{\frac{1}{n} })[/tex] .
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A projectile is launched with initial velocity vo. If a second projectile is launched with half of the initial velocity of the first projectile. Compare the range of the second projectile with the first one:
Comparison of the range:
If a second projectile is launched with half of the initial velocity of the first projectile. The range of the second projectile is one-fourth of the first one.
Calculation:
Step-1:
It is given that the first particle has an initial velocity of [tex]v_0[/tex], and the second particle has an initial velocity of [tex]\frac{v_0}{2}[/tex]. It is required to compare the range of the second projectile with the first one.
It is known that the range of a projectile is calculated as,
[tex]R=\frac{u^{2} \sin 2 \theta}{g}[/tex]
Where u is the initial speed, g is the acceleration due to gravity, and [tex]\theta[/tex] is the angle at which the particle is thrown.
This problem [tex]\theta[/tex] is the same in both cases.
Step-2:
Therefore the range of the first projectile is,
[tex]R_1=\frac{v_0^{2} \sin 2 \theta}{g}[/tex]
The range of the second projectile is,
[tex]$$\begin{aligned}R_2&=\frac{(\frac{v_0}{2})^{2} \sin 2 \theta}{g}\\&=\frac{v_0^2\sin 2 \theta}{4g}\\\end{aligned}$$[/tex]
Therefore,
[tex]$$\begin{aligned}\\\frac{R_2}{R_1}&=\frac{1}{4}\\\Rightarrow R_2&=\frac{1}{4}R_1\\\end{aligned}\\$$[/tex]
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