A. Alex Morgan would need to kick the ball at an angle of approximately 29.5 degrees.
B. Alex Morgan should kick the ball with an initial speed of approximately 16.5 m/s to hit the top of the goal when kicked at an angle of 40.0 degrees.
A. To determine the angle at which Alex Morgan needs to kick the ball so that it just reaches the goal without touching the ground, we can use the equations of projectile motion. We'll assume the goal is at the same height as the ground.
To find the angle of projection (θ), we can use the equation for the horizontal range of a projectile:
Range = \((v0^2 * sin(2\theta)) / g\)
Since we want the ball to just reach the goal without touching the ground, the range should be equal to the initial distance from the goal:
50.0 m = \((19.7^2 * sin(2\theta)) / 9.8\)
Now, we can solve this equation to find the angle θ:
sin(2θ) =\((50.0 m * 9.8) / (19.7 m/s)^2\)
sin(2θ) = 0.4987
2θ = arcsin(0.4987)
θ ≈ 29.5 degrees
B. Now, let's determine the initial speed at which Alex Morgan should kick the ball at an angle of 40.0 degrees to hit the top of the goal.
Given:
Initial angle of projection (θ) = 40.0 degrees
Height of the top of the goal (y) = 2.44 m
Acceleration due to gravity (g) = \(9.8 m/s^2\)
To find the initial speed (v0), we can use the equation for the maximum height of a projectile:
Maximum height =\((v0^2 * sin^2(\theta)) / (2g)\)
Since we want the ball to reach the top of the goal, the maximum height should be equal to the height of the top of the goal:
2.44 m =\((v0^2 * sin^2(40.0 degrees)) / (2 * 9.8 m/s^2)\)
Now, we can solve this equation to find the initial speed v0:
\(v0^2 = (2 * 9.8 m/s^2 * 2.44 m) / sin^2(40.0 degrees)\)
v0 ≈ 16.5 m/s
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According to Newton's 2nd law of motion, if you hit a baseball with a bat it will
-hurt your hand from the reaction force
-accelerate according to the applied force
-fly in a straight line unless an outside force changes its course
-fall to the ground because of gravitational pull
Answer:
Newton's second law states that force is directly proportional to the product of mass and acceleration.
so if you hit a baseball with a bat it will accelerate according to the applied force.
Why are the voice of men women and children different??
We each have a unique voice because so many factors work together to produce that voice. As air passes over them, the vocal cords vibrate very quickly to produce sounds. The higher the rate of vibration, called frequency, the higher the pitch will be.
the best way to study warm (1000 k) young stars forming behind an interstellar dust cloud would be to use a. blue light b. ultraviolet light c. x-rays d. infrared light
The best way to study warm (1000 K) young stars forming behind an interstellar dust cloud would be to use infrared light. So option d is correct.
Interstellar dust clouds can block or scatter shorter-wavelength light, such as blue light and ultraviolet light, making it difficult to observe objects behind them. However, longer-wavelength infrared light can penetrate through the dust cloud with less scattering and absorption, allowing us to study the objects hidden behind the dust.
Infrared light is particularly effective for studying warm objects, as they emit most of their radiation in the infrared range. By using infrared telescopes and detectors, astronomers can observe the thermal radiation emitted by the young stars and study their formation and evolution processes.Therefore option d is correct.
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Where the h e l l did physics come from!?
Answer:
Physics is the natural science that studies matter, its motion and behavior through space and time, and the related entities of energy and force.
Ancient history. Elements of what became physics were drawn primarily from the fields of astronomy, optics, and mechanics, which were methodologically united through the study of geometry. These mathematical disciplines began in antiquity with the Babylonians and with writers such as Archimedes and Ptolemy.
Answer:
I don't know but It should exist or else reality would not exist
Explanation:
A 70 kg human sprinter can accelerate from rest to 10 m/s in 3.0 s. During the same time interval, a 30 kg greyhound can accelerate from rest to 20 m/s.
Part A: What is the specific power for the sprinter?
Part B: What is the specific power for the greyhound?
The specific power for the sprinter is 16.67 WS-1kg-1 and for the greyhound is 66.67 WS-1kg-1.
Specific Power is defined as the power of an object divided by its mass. The units of specific power are W/kg.
Given:
Mass of the sprinter, m1 = 70 kg
Mass of the greyhound, m2 = 30 kg
Acceleration of the sprinter, a1 = (10 m/s) / 3 s = 3.33 m/s²
Acceleration of the greyhound, a2 = (20 m/s) / 3 s = 6.67 m/s²
A):
The power of the sprinter is given by:
P1 = (1/2) × m1 × v² / t
where v = 10 m/s P1 = (1/2) × 70 × 10² / 3P1 = 1166.67 WS-1
Specific power is given by:
P1 / m1 = 1166.67 / 70 = 16.67 WS-1kg-1
Specific power for the sprinter is 16.67 WS-1kg-1.
B):
The power of the greyhound is given by:
P2 = (1/2) × m2 × v² / t
where v = 20 m/sP2 = (1/2) × 30 × 20² / 3P2 = 2000 W
Specific power is given by:
P2 / m2 = 2000 / 30 = 66.67 WS-1kg-1.
Specific power for the greyhound is 66.67 WS-1kg-1.
Therefore, the specific power for the sprinter is 16.67 WS-1kg-1 and for the greyhound is 66.67 WS-1kg-1.
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The role of the critical theorist in the emancipation process is similar to the role of a A. mediator.
B. freedom fighter.
C. detective.
D. psychoanalyst.
The role of the critical theorist in the emancipation process is similar to the role of a (B) freedom fighter.
Critical theorists aim to challenge and critique existing power structures and social norms to promote social justice and liberation. They analyze and question societal systems of oppression and seek to empower marginalized groups by exposing injustices and advocating for change.
Similar to freedom fighters who actively resist and fight against oppressive systems, critical theorists engage in intellectual activism, advocating for the liberation and empowerment of individuals and communities.
While other options like mediator, detective, and psychoanalyst may play important roles in various contexts, they do not capture the active and transformative nature of critical theory in the pursuit of emancipation and social transformation.
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Which of the following would produce the most power?
a
A mass of 5 kilograms lifted 5 meters in 10 seconds
b
A mass of 5 kilograms lifted 10 meters in 5 seconds
c
A mass of 10 kilograms lifted 10 meters in 5 seconds
d
A mass of 10 kilograms lifted 10 meters in 10 seconds
Answer:
A
Explanation:
The answer option which would produce the most power is: C. A mass of 10 kilograms lifted 10 meters in 5 seconds
Power can be defined as the capacity to do work.
Mathematically, power is given by the formula;
\(Power = \frac{Work \; done}{time} \\\\But, \;Work \; done = mgh\\\\Power = \frac{mgh}{time}\)
Where:
m is the mass of object. g is the acceleration due to gravity. h is the height of an object.Note: Acceleration due to gravity is equal to 10 \(m/s^2\).
For option A:
\(Work\; done = 5(10)(5)\)
Work done = 250 Joules
\(Power = \frac{250}{10}\)
Power = 25 Watts.
For option B:
\(Work\; done = 5(10)(10)\)
Work done = 500 Joules
\(Power = \frac{500}{10}\)
Power = 50 Watts.
For option C:
\(Work\; done = 10(10)(10)\)
Work done = 1,00 Joules
\(Power = \frac{1000}{5}\)
Power = 200 Watts.
For option D:
\(Work\; done = 10(10)(10)\)
Work done = 1,00 Joules
\(Power = \frac{1000}{10}\)
Power = 100 Watts.
Therefore, a mass of 10 kilograms lifted 10 meters in 5 seconds would produce the most power.
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the lowest level of drinking water constituent that can be measured reliably in an approved laboratory is the
The lowest stage of ingesting water constituent that may be reliably measured in an permitted laboratory is called the method detection limit (MDL).
The MDL is the minimum concentration of a particular contaminant that may be as it should be detected and quantified using a selected analytical method. This restrict is decided via a sequence of laboratory experiments that establish the bottom awareness of a contaminant that may be detected with a high degree of certainty.
The MDL is an important parameter in water exceptional testing, as it provides a basis for assessing the accuracy and precision of analytical strategies, and enables to make certain that water trying out outcomes are dependable and consistent.
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The word _____ is defined as either of two points when the sun's rays strike the earth at the equator.
Answer:
Equinox.
Explanation:
It is Equinox because Equinox is defined as the time when the sun rays passes through the Earth's equator. This happen twice in the year around 21 March and 23 September. It is the time when the center of the sun is directly above the equator.
This normally occur when the Earth axis is either tilted toward or away from the sun which lead to equal amount of daylight and darkness.
Which object has potential energy?(1 point)
Responses
unlit lightbulb
unlit lightbulb
rock on the ground
rock on the ground
stereo speaker
stereo speaker
can of gasoline
The object that has potential energy is the can of gasoline.
What is potential energy?Potential energy is described as the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
The forms of potential energy includes:
Elastic Potential Energy.Electrical (Electromagnetic) Potential Energy.Gravitational Potential Energy.Nuclear Potential Energy.Potential energy is described as the energy a system has due to position, shape, or configuration.
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A vertical spring has a spring constant k=32 N/m with a 2 kg mass connected to it. The spring is initially at rest and hanging at its equilibrium position. At t=0, a force is applied to the spring given by: F=128sin(4t). Neglecting air resistance or other damping forces, find the position of the mass as a function of time.
The position of the mass as a function of time is x(t) = 5 * sin(4t).
To find the position of the mass as a function of time, we can use Newton's second law of motion, which states that the sum of the forces acting on an object is equal to the mass of the object multiplied by its acceleration.
The equation of motion for a mass-spring system is given by:
m * d^2x/dt^2 + k * x = F(t)
Where:
m is the mass connected to the spring,
x is the position of the mass,
t is time,
k is the spring constant,
F(t) is the applied force as a function of time.
In this case, the mass m is 2 kg, the spring constant k is 32 N/m, and the applied force is given by F(t) = 128sin(4t).
Plugging these values into the equation of motion, we get:
2 * d^2x/dt^2 + 32 * x = 128sin(4t)
Rearranging the equation, we have:
d^2x/dt^2 + 16 * x = 64sin(4t)
This is a second-order linear ordinary differential equation with constant coefficients. To solve this equation, we can assume a solution of the form x(t) = A * sin(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle.
Differentiating x(t) twice with respect to time, we have:
dx/dt = A * ω * cos(ωt + φ)
d^2x/dt^2 = -A * ω^2 * sin(ωt + φ)
Substituting these derivatives into the equation of motion, we get:
-A * ω^2 * sin(ωt + φ) + 16 * A * sin(ωt + φ) = 64sin(4t)
Equating the terms with sin(ωt + φ) on both sides, we have:
-A * ω^2 + 16 * A = 64
Simplifying the equation, we get:
16A - Aω^2 = 64
We know that the angular frequency ω is related to the spring constant k and the mass m as ω = √(k/m). Substituting the given values, we have:
ω = √(32 N/m / 2 kg) = √(16) = 4
Plugging ω = 4 into the equation, we get:
16A - 16 = 64
Solving for A, we have:
16A = 80
A = 5
Therefore, the amplitude A is 5.
Now, we can write the position function as:
x(t) = 5 * sin(4t + φ)
To find the phase angle φ, we can use the initial conditions. At t = 0, the spring is initially at rest and hanging at its equilibrium position, which means x(0) = 0.
Plugging this into the position function, we have:
0 = 5 * sin(0 + φ)
Since sin(0) = 0, we get:
0 = 0 + φ
φ = 0
Therefore, the phase angle φ is 0.
Finally, the position of the mass as a function of time is:
x(t) = 5 * sin(4t)
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Select the correct answer. If the resistance remains constant and the voltage doubles, what effect will that have on the power? A. The power will remain the same. B. The power will decrease by a factor of 2. C. The power will decrease by a factor of 4. D. The power will increase by a factor of 2. E. The power will increase by a factor of 4.
If the resistance remains constant and the voltage doubles, the power will increase by a factor of 4 (option E)
How do i determine the new power?The following data were obtained from the question:
Initial power (P₁) = PInitial voltage (V₁) = VResistance = ConstantNew voltage (V₂) = 2VNew power (P₂) =?P = V² / R
Resistance is constant, we have
V₁² / P₁ = V₂² / P₂
V² / P = (2V)² / P₂
V² / P = 4V² / P₂
Cross multiply
V² × P₂ = P × 4V²
Divide both side by V²
P₂ = P × 4V² / V²
P₂ = P × 4
From the above, we can conclude that the power will increase by a factor of 4 (option E)
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Which of these questions is the best example of elasticity?
Answer:
Elastic goods and services generally have plenty of substitutes. As an elastic service/good's price increases, the quantity demanded of that good can drop fast. Example of elastic goods and services include furniture, motor vehicles, instrument engineering products, professional services, and transportation services.
Explanation:
elasticity of supply measures the responsiveness to the supply of a good or service after a change in its market price. According to basic economic theory, the supply of a good will increase when its price rises. Conversely, the supply of a good will decrease when its price decreases.
How high up is a cliff with 45 kg boulder if the boulder has a potential energy of 90,000 j
The height of the cliff is 200 meter where potential energy of the boulder is measured.
What is potential energy?Potential energy in physics is the energy that an item retains as a result of its position in relation to other objects, internal tensions, electric charge, or other elements.
The gravitational potential energy of an item, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field are examples of common types of potential energy.
The height of the cliff is = 90,000 ÷ (45 ×10) meter = 200 meter.
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Why does a person feel weightlessness during freefall
It is because the weight W = 0, due to g = a, the person falling during the free fall will therefore experience weightlessness.
FREE FALLA free fall is a situation where a body or an object fall solely under the influence of gravity.
Why does a person feel weightlessness during freefall ?
The weight of a body = mg
When a person is falling, the person will be falling with a certain acceleration. The weight W of the person will be;
W = m( a - g )
During free fall, acceleration a will be equal to acceleration due to gravity g. That is, a = g
W = m( a - a )
W = m( 0 )
W = 0
Since the weight W = 0, the person falling during the free fall will therefore experience weightlessness.
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3. We consider a conducting sphere of radius R consisting of two hemispheres. The upper hemisphere is kept at the potential V while the lower hemisphere is kept at the potential −V. We can use the Green function method to calculate the scalar potential ϕ. The Dirichlet Green function G p
(r,r ∗
) is given as follows: G D
(r,r ′
)= r 2
+r ′2
−2rr ′
cosγ
1
− r 2
r ′2
/R 2
+R 2
−2rr ′
cosγ
1
The r vector denotes the position of observation and the r ′
vector denotes the position of charges where γ is the angle between r and r ∗
. Using the above Green function. calculate the potential along the positive z-axis.
By integrating the given equation, we can find the potential ϕ as a function of z.
Let's consider a point P along the positive z-axis with coordinates (0, 0, z). To find the potential at point P, we integrate the Green function G_D(r, r') with respect to the charge distribution over the surface of the conducting sphere.
The potential ϕ at point P can be calculated using the following integral:
ϕ(P) = ∫∫ G_D(r, r') σ(r') dS
Here, σ(r') represents the charge density on the surface of the sphere, and dS represents the differential surface element.
Since we are interested in the potential along the positive z-axis, we can simplify the integral by considering the symmetry of the problem. Due to symmetry, the potential ϕ will only depend on the radial distance r from the z-axis. Thus, we can rewrite the integral as:
ϕ(P) = 2π∫ G_D(r, r') σ(r') r' dr'
Now, we need to express the charge density σ(r') in terms of the potential difference V and the radius R. The charge density on the upper hemisphere is V/(4πR^2), and on the lower hemisphere, it is -V/(4πR^2). Therefore, we can write:
ϕ(P) = (V/R^2) ∫ (r^2 + r'^2 - 2rr')/(r-r')^2 r' dr'
This integral can be evaluated using appropriate techniques of integration.
By integrating the above equation, we can find the potential ϕ as a function of z.
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Explain Kepler's Third Law of Planetary Motion
Answer:
The squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.
Explanation:
When humans pollute lakes, rivers, and streams,
Answer:
when waterways are polluted it affects all forms of life in the area - including us
expression:
for example when Lakes streams and ponds are polluted it can kill or harsh fish and other Wildlife that lives there!
hope that helps !
The speed of sound in air is 340 m/s. The length of the shortest pipe, closed at one end that
will respond to a 512 Hz tuning fork is approximately:
A. 8.30 cm
B. 33.2 cm
C. 16.6 cm
D. 66.4 cm
the length of the shortest pipe, closed at one end that will respond to a 512 Hz tuning fork is approximately 16.6 cm (option C).
The speed of sound in air is 340 m/s, and we need to find the length of the shortest pipe closed at one end that will respond to a 512 Hz tuning fork. To do this, we can use the formula for the fundamental frequency of a closed pipe:
f = (2n-1)(v / 4L),
where f is the frequency, n is the harmonic number, v is the speed of sound, and L is the length of the pipe.
For the shortest pipe, we will consider the first harmonic (n=1):
f = (2(1)-1)(v / 4L)
512 Hz = (1)(340 m/s / 4L)
Now, we can solve for L:
L = (340 m/s) / (4 * 512 Hz)
L ≈ 0.166015625 m
Converting to centimeters:
L ≈ 16.6 cm
Therefore, the length of the shortest pipe, closed at one end that will respond to a 512 Hz tuning fork is approximately 16.6 cm.
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crystal clear, crystal yellow, and crystal orange are driven by which factors?
The appearance of crystal clear, crystal yellow, and crystal orange can be influenced by a wide range of factors, and each crystal or gemstone is unique in terms of its specific coloration and underlying properties.
Crystal clear, crystal yellow, and crystal orange are all colors that can be found in various natural crystals and gemstones. The factors that drive the appearance of these colors can vary depending on the specific crystal or gemstone.
In general, the color of a crystal or gemstone is determined by the presence of trace elements or impurities within the crystal lattice structure. For example, the vibrant yellow color in citrine crystals is caused by the presence of iron impurities, while orange sapphire can get its color from the presence of titanium and iron.
Other factors that can affect the color of a crystal or gemstone include the lighting conditions, the angle at which the crystal is viewed, and any treatments or enhancements that have been applied to the stone.
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What is competition?
Answer:
two team in a conflict
Explanation:
Competition arises whenever two or more parties strive for a common goal which cannot be shared: where one's gain is the other's loss. Competition includes rivalry between entities such as organisms, individuals, economic and social groups, etc.
I WILL MARK U HELP PLZ
The free body diagram for an object is projected. Calculate the net force acting on the object. If this object is 10 kg, how/where will it accelerate?
Explanation:
By the end of the section, you will be able to:
Apply problem-solving techniques to solve for quantities in more complex systems of forces
Use concepts from kinematics to solve problems using Newton’s laws of motion
Solve more complex equilibrium problems
Solve more complex acceleration problems
Apply calculus to more advanced dynamics problems
through this steps you will get the answer.thank youA healthy mind and body is important. The decisions you make can have a serious effect on your health and the health of those around you. Think about what you have learned in the module. Use the information from your milestone 1 and milestone 2 projects to help you complete your final project.
Your project should be about the diseases that can be caused by hereditary traits.
Choose a healthy behavior and develop a positive health media message.
TV commercial
Radio commercial
Magazine ad
Internet popup ad
Teacher approved idea
Examples of hereditary diseases include heart disease, Type 1 Diabetes, or many other diseases you may have learned about in your interviews.
You will present a message that tries to get people to make health choices that will help them reduce the impact of hereditary disease. Your message can be presented as a video or by using a Web 2.0 tool such as Weebly or Jing.
Your presentation will focus on:
Making people aware of hereditary traits.
Getting people to make good health choices to help lessen the risk of hereditary disease.
Answer the following questions to help you get started on your project:
What is the purpose of your media message? (to inform or persuade)
What type of medium is it? (commercial, advertisement, or teacher approved)
Who is your intended audience?
What is the message? (main idea or main points)
What information can be omitted?
What techniques are you going to use to get attention?
(Please put an actual answer please.)
PLEASE HELPPPP You have a oxygen atom that is looking to bond. How many atoms of one element from column 1 would need to bond with that oxygen to form an ionic bond? Why?
Answer:
Two atoms from column 1. Each would give 1 electron to the Oxygen. Oxygen will be 2- and each group 1 ion will be 1+
Explanation:
Sorry if Im wrong
Advanced Wireless Services (AWS) is a wireless telecommunications spectrum band used for mobile voice and data services, video, and messaging. The AWS band uses frequencies in several segments: from 1695 to 2200 MHz. a) Determine the corresponding range of wavelengths used by the AWS mobile devices. b) To what region/band of electromagnetic spectrum does the range belong
Given data
*The given frequency is
\(f_1_{}=1695\text{ MHz}=1695\times10^6\text{ Hz}\)*The another given frequency is
\(f_2=2200\text{ MHz=}2200\times10^6\text{ Hz}\)*The given speed of light is c = 3.0 × 10^8 m/s
(a)
The formula for the wavelength is given as
\(\lambda_1=\frac{c}{f_1}\)Substitute the known values in the above expression as
\(\begin{gathered} \lambda_1=\frac{(3\times10^8)}{(1695\times10^6)^{}} \\ =0.176\text{ m} \end{gathered}\)The another wavelength for the another frequency is calculated as
\(\begin{gathered} \lambda_2=\frac{c}{f_2} \\ =\frac{(3.0\times10^8)}{(2200\times10^6)} \\ =0.136\text{ m} \end{gathered}\)(b)
Radio spectrum is an electromagnetic spectrum where the frequency range belongs of wireless telecommunication.
we know that galaxies farther away from us are moving faster than nearby galaxies because we measure the
Galaxies farther away from us exhibit higher rates of motion compared to nearby galaxies.
This phenomenon is known as the cosmological redshift and is attributed to the expansion of the universe. According to Hubble's Law, the recessional velocity (v) of a galaxy is proportional to its distance (d) from us: v = H₀ × d, where H₀ is the Hubble constant.
As space itself expands, it carries galaxies along with it, causing their wavelengths to stretch and shift towards longer (red) wavelengths. This shift is observed as a redshift in the light emitted by distant galaxies.
Thus, by measuring the redshift of galaxies, astronomers can determine their recessional velocities and infer their distances from us. The greater the distance, the faster the apparent motion due to the expanding universe.
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A current loop in a motor has an area of 1.55 cm2 . It carries a 240 mA current in a uniform field of 0.62 T. Part A What is the magnitude of the maximum torque on the current loop
The magnitude of the maximum torque on the current loop can be calculated using the formula τ = NIAB, where N is the number of turns in the loop, I is the current flowing through the loop, A is the area of the loop, and B is the magnetic field strength.
In this case, the current loop has an area of 1.55 cm² and carries a current of 240 mA (0.24 A) in a uniform magnetic field of 0.62 T.
To calculate the torque, we need to determine the number of turns in the loop. However, this information is not provided in the question. Assuming the current loop consists of only one turn, we can calculate the torque using the formula τ = NIAB:
τ = (1)(0.24 A)(1.55 cm²)(0.62 T) = 0.22744 N·m
Therefore, the magnitude of the maximum torque on the current loop is approximately 0.22744 N·m. It's worth noting that if the current loop consists of multiple turns, the torque value will be multiplied by the number of turns.
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can Somebody Explain Please
Introduction to Newton's law of gravitation
Answer: so basically, Newtons Law states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Explanation: newtons law simplified in my opinion is a physical law that describes the attraction between two objects with mass.
hope this helps.
Answer:
Explanation:
she rieat
A system has the input-output relation given by y[n] = T{x[n]} = nx[n] (1.113) Determine whether the system is (a) memoryless, (b) causal, (c) linear, (d) time-invariant, or (e) stable.
The system whose input-output relation is y[n] = T{x[n]} = nx[n] is a)memoryless, b)causal, and d)time-invariant but not linear or stable.
Below are the reasons why the system is classified as such.
Memoryless: A system is memoryless if its output is exclusively based on its input at the present time t = n. The system given has its output y[n] that solely depends on x[n] at that time.
Thus, the system is memoryless
Causal: A system is causal if its output relies solely on the values of its input at present and past time. The output of the system given depends on x[n], which is present time and n, which is past time. Hence, the system is causal.
Linear: The system is not linear. For a system to be linear, it should satisfy the properties of homogeneity and additivity.
In this case, if we consider two inputs x1[n] and x2[n], the corresponding output should satisfy the following equation,
T{x1[n] + x2[n]} = T{x1[n]} + T{x2[n]} = nx1[n] + nx2[n].
However, the output of the system will be,
y1[n] = n x1[n] + n x2[n] = n(x1[n] + x2[n]) ≠ T{(x1[n] + x2[n])}.
Hence, the system is not linear.
Time-invariant: The system is time-invariant. A system is said to be time-invariant if a time shift in the input signal causes the output to shift by the same amount of time. In this case, if we shift the input signal x[n] to x[n - k], the output signal will also shift to
y[n - k] = (n - k) x[n - k].
Therefore, the system is time-invariant.
Stable: The system is not stable. A system is stable if its output remains bounded for any finite input signal. The output signal of this system is,
y[n] = n x[n]
Thus, the system output will be unbounded whenever the input signal grows or decreases without bound. Hence, the system is not stable.
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A 0.68 kg squirrel is resting on a branch 8 meters above the ground. What is the gravitational potential energy of a squirrel? A: 2.27 J. B :5.44 J. C :21.76 J. D :53.312 J
Answer:
The gravitational potential energy of a squirrel is 53.312 J.
Explanation:
We have,
Mass of a squirrel is 0.68 kg
It is placed at a height of 8 m above the ground.
It is required to find the gravitational potential energy of a squirrel. It is possessed by an object due to its position. Its formula is given by :
\(E=mgh\\\\E=0.68\times 9.8\times 8\\\\E=53.312\ J\)
So, the gravitational potential energy of a squirrel is 53.312 J.