The source of errors in this experiment could occur from the improper measuring technique. While measuring the magnetic field in the solenoid, the magnetic field sensor might not be held properly perpendicular to the table on which the solenoid was resting.
What are the factors affecting the magnetic field of a solenoid?The factors that can affect the strength of a magnetic field at a point are the magnitude of the electric current and the perpendicular distance between the point and the conductor.
Can solenoids be a source of the magnetic field?The term solenoid refers to a long, thin loop of wire, often wrapped around a metallic core. Solenoids produce a magnetic field when an electric current is passed through them. Solenoids are significant because they can create and regulate magnetic fields and can be used as electromagnets.
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In its own reference frame, a box has the shape of a cube 1.5 m on a side. This box is loaded onto the flat floor of a spaceship and the spaceship then flies past us with a horizontal speed of 0.90 c.
Volume of the box observed at the given speed is 7.89 m³
Given:
Length of side of box = 1.5 m
horizontal speed = 0.90 c
To Find:
Volume of box
Solution: The amount of space occupied by a three-dimensional figure as measured in cubic units (as inches, quarts, or centimeters)
The edge length of the cube according to the stationary observer is calculated as
a' = a x √ 1 - v^2/c^2
a' = 1.5 x √ 1 - (0.9c)^2/c^2
a' = 1.5 x 0.19
a' = 0.285 m
The volume of the cube is calculated as follows;
V = A x a'
V = (a)^2 x a'
V = (1.5)^2 x 0.285
V = 7.89 m³
Thus, the volume of the box observed at the given speed is 7.89 m³
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A wire coil inside a generator has 150 square loops and an area equal to 0.042 m2.
The coil rotates one-quarter turn in 1.7 ms. If a 0.86 T magnetic field surrounds the
coil, what is the maximum electromotive force induced in the coil
a. 3.2 V
b. 130 V
c. 1600 V
d. 3200 V
D. The maximum electromotive force induced in the coil is determined as 3,200 V.
Maximum electromotive force induced in the coilemf(max) = NAB/t
where;
N is number of turnsB is magnetic fieldA is area of the coilt is timeSubstitute the given parameters and solve for emf
emf(max) = (150 x 0.042 x 0.86) / (1.7 x 10⁻³)
emf(max) = 3,187.1 V
emf(max) ≈ 3,200 V
Thus, the maximum electromotive force induced in the coil is determined as 3,200 V.
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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 will have moved a distance of 6 m.
Displacement of the 40 kg boy
The displacement of the 40 kg boy is calculated from the principle of center mass.
X(40 kg) = (60 x 10 m + 40 x 0)/(40 kg + 60 kg)
X(40 kg) = (600)/(100) = 6 m
X(60 kg) = (60 x 0 + 40 x 10 m)/(40 kg + 60 kg)
X(60 kg) = (400)/(100) = 4 m
Thus, when they meet the 40-kg boy will have moved a distance of 6 m.
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How can you determine where the wavelength released from a transition will fall in the electromagnetic spectrum?
You can change the wavelength into scientific notation and the electromagnetic spectrum will then tell you where it falls.
In physics, the wavelength is the spatial period of a periodic wave—the space over which the wave's shape repeats. It's miles the distance among consecutive corresponding points of the same section on the wave, together with two adjacent crests, troughs, or zero crossings, and is a function of each traveling wave and status wave, in addition to other spatial wave styles.
The inverse of the wavelength is referred to as the spatial frequency. Wavelength is normally designated through the Greek letter lambda (λ). The time period wavelength is also every now and then implemented to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed via interference of numerous sinusoids.
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Black smokers are hot volcanic vents that emit smoke deep in the ocean floor. Many of them teem with exotic creatures, and some biologists think that life on earth may have begun around such vents. The vents range in depth from about 1500 m to 3200 m below the surface. What is the gauge pressure at a 2452-m deep vent, assuming that the density of water does not vary
If the density of water does not vary and the vents range in depth from about 1500 m to 3200 m below the surface, then the gauge pressure at a 2452-m deep vent is 224.268 atm.
Calculation:
Step-1:
It is given that the vents range in depth from about 1500 m to 3200 m below the surface. If we are assuming that the density of water does not vary. Then it is required to calculate the gauge pressure at a 2452-m deep vent.
The gauge pressure at a particular depth of ocean water is calculated as:
[tex]$$P=\rho g h$$[/tex]
Here [tex]\rho[/tex] is the density of water, P is the required pressure, h is the depth of water, and g is the gravitational acceleration.
Step-2:
Now we are substituting the values to calculate the pressure at the depth of 2452-m.
[tex]$$\\\begin{aligned}\\P&=\rho gh\\&=1030 (\text{ kg/m}^3)\times 9.8 (\text{ m/s}^2)\times 2452 \text{ m}\\&=24.75\times 10^6 \text{ Pa}\times\frac{1 \text{ atm}}{10.1325 \times10^4 \text{ Pa}}\\&=224.268 \text{ atm}\\\end{aligned}\\$$[/tex]
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The diagram below shows a pendulum at two different positions in its path. The pendulum started from rest in position 1.
Pendulum with two different positions. Position 1 is higher and to the left compared to position 2
Which best describes the energy change as the pendulum moves from position 1 to position 2?
Group of answer choices
a. The total energy is decreasing.
b. The kinetic energy is increasing.
c. The thermal energy is decreasing.
d. The potential energy is increasing.
From position 1 to position 2, the kinetic energy is increasing.
Kinetic of a pendulum in simple harmonic motion
The kinetic energy of a pendulum undergoing simple harmonic motion decreases as the displacement of the pendulum increases and increases as the displacement of the pendulum decreases.
From position 1 to position 2, the kinetic energy is increasing while the potential energy is decreasing.
Thus, from position 1 to position 2, the kinetic energy is increasing.
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Velocity can best be described by which of the following statements?
OA. The speed of gravity
O B. How far you have traveled
C. Speed in a given direction.
о D. Miles per second
Answer: Velocity can best be described as, the speed in a given direction.
Explanation: To find the answer, we need to know more about the Velocity of a body.
What is Velocity of a body?Velocity is the rate of change of displacement.It's a vector quantity and is measured in m/s.It can be positive, negative or zero.A body is said to be in uniform motion, then its velocity remains constant.Change in velocity can be a change in speed.The magnitude of velocity is less than or equal to speed.Thus, we can conclude that, the option C is best describing velocity.
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The speed in a certain direction is the best way to define velocity.
We need to learn more about a body's velocity in order to locate the solution.
What does a body's velocity mean?The rate of change of displacement is known as velocity.It has a vector value and is expressed in m/s.It may be zero, negative, or positive.When a body is moving uniformly, its velocity is said to be constant.Speed might alter depending on the change in velocity.Speed and the magnitude of velocity are not comparable.As a result, we can say that choice C best captures velocity.
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Potentiometric measurements are based on galvanic electrochemical cells. these types of cells consist of:_______
Two-electron or metallic conducting electrodes that are connected by an electrolyte solution that conducts ions.
What are potentiometric measurements?An electrochemical measurement method is potentiometry. The phrase was first used in relation to possible electrochemical measurement chain determinations. Potentiometer is a tool that measures an electrochemical cell's potential without drawing current or changing the makeup of the cell.
Potentiometric measurement is done to detect the difference in potential between a working (an indicator) electrode and a counter (a reference), using a potentiometer. The working/indicator electrode is called the cathode (right half-cell) and the counter/reference electrode is called an anode(half of a left cell).
A basic galvanic cell may just have one electrolyte isolated from it by a semi-permeable membrane, but a more complex one has two independent half-cells linked together by a salt bridge. An inert electrolyte like potassium sulfate is included in the salt bridge, and its ions will diffuse into each of the individual half-cells to balance the charges that are building up at the electrodes.
I understand the question you are looking for is this:
Potentiometric measurements are based on galvanic electrochemical cells. These types of cells consist of:
two inert metal electrodes to which an electrical potential is applied.two-electron or metallic conducting electrodes that are connected by an electrolyte solution that conducts ions.a biological recognition element and a physicochemical transducer, often an electrochemical or optical device.a polarizable working electrode to which an external voltage is applied with the resulting cathodic or anodic current of the cell being monitored.Learn more about galvanic electrochemical cells here:
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The mass of the earth is 6x10^24 kg and that of the moon is 7.4x10^22 kg. If the radius of the moon is 1740 km, then find the value of g if the earth is compressed into the size of moon.
Answer:
In the surface of the moon, gravitational acceleration is 1.63 m/s*2.
Explanation:
An object of mass M will accelerate gravitationally at a distance R if it is at the following distance:
g = G*M/R^2
Where the gravitational constant is G.
G = 6.67*10^(-11) m^3/(kg*s^2)
At the surface of a moon, the distance between its surface and its center will be equal to its radius, since a moon's mass is concentrated at its center, thus:
R = 1740 km
It's important to remember that we need meters in order to work:
1 km = 1000 m
so:
1740 km = (1740)*1000 m = 1740000 m
R = 1740000 m
Basically, the mass consists of:
M = 7.4x10^22 kg
Incorporating all that into the gravitational acceleration equation, we get:
g = (6.67*10^(-11) m^3 / (kg*s^2))*(7.4x10^22 kg) / ( 1740000 m)^2
g = 1.63 m / s^2
In the surface of the moon, gravitational acceleration is 1.63 m / s*2.
What kind of physics is used to describe the interaction of matter and energy from the beginning of the cosmic singularity to the Planck time
Cosmology physics is used to describe the interaction of matter and energy from the beginning of the cosmic singularity to the Planck time.
Astronomy's field of cosmology examines the beginnings and development of the universe, from the Big Bang through the present and into the future. The current cosmological model for the development of the universe is the Big Bang theory, which relies on the validity of general relativity. There is a singularity there as well.
According to the Big Bang theory, the cosmos was once compressed into an infinitely small point 13.77 billion years ago. Prior to 10-43 seconds after the Big Bang, during the Planck Era, gravity, nuclear strong, nuclear weak, and electromagnetic forces are thought to have been merged into a single "super" force.
Therefore, cosmology physics is used to describe the interaction of matter and energy from the beginning of the cosmic singularity to the Planck time.
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A person riding a Ferris wheel moves through positions at (1) the top, (2) the bottom, and (3) mid-
height. If the wheel rotates at a constant rate, rank these three positions according to
(a)the magnitude of the person’s centripetal acceleration,
(b) the magnitude of the net centripetal force on the person, and
(c) the magnitude of the normal force on the person from the bottom, and
(d) the weight the person feels, greatest first.
A person riding a Ferris wheel moves through positions at
(1) the top,
(2) the bottom, and
(3) mid-height. If the wheel rotates at a constant rate, rank these three positions according to
(a)the magnitude of the person’s centripetal acceleration, is same in all cases.
(b) the magnitude of the net centripetal force on the person, is same in all three cases.
(c) the magnitude of the normal force on the person from the bottom,
2<3<1
(d) the weight the person feels, greatest first is at the bottom.
What is the relation between force and acceleration?The centripetal acceleration [tex]a_{c}[/tex] exists provided by : a= [tex]v^{2} /r[/tex] , therefore the magnitude depends upon the speed and the radius. This represents that in the case of the Ferris wheel the centripetal acceleration includes a constant magnitude so its value exists the same in all cases.From Newton's second law the force is provided by F=ma and since a exists constant in magnitude , F is also constant in magnitude. and its value exists the same in all three cases.At the top [tex]a_{c}[/tex] stands directed downward so the normal force exist given by [tex]F_{N}[/tex]=[tex]mg[/tex]- [tex]ma_{c}[/tex]While at the bottom [tex]a_{c}[/tex] exist directed upward and the normal force is provided by [tex]F_{N}[/tex]=mg +m[tex]a_{c}[/tex]Meanwhile,at mid -height [tex]a_{c}[/tex] stands directed horizontally to the inside so it doesn't have a vertical component so its normal force is provided by [tex]F_{N}[/tex]=mgThe normal force exists greatest at the bottom than at mid-height than at the top.To learn more about centripetal force , refer :
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This simulation has three parts: Intro, Compare, & Mystery.I. Explore the Intro section of this simulation.1. Based on your exploration how will you define the density D, of a substance? Writedown an algebraic expression relating D to the mass and volume of a substance.2. Does the density of a substance change with its mass? If yes, how? If no, why not?
a) Density is mass of a unit volume of a material substance
b) Algebraic expression relating Density = m / v
c) Density is an intensive property, which means the density does not change as the amount of the substance present changes
a) Density is mass of a unit volume of a material substance. The formula for density is d = M/V, where d is density, M is mass, and V is volume. Density is the measurement of how tightly a material is packed together.
The more closely packed particles are, the more dense the object. The amount of mass in a particular space or volume. The more particles (or mass) in a given space, the more dense it is.
b) Algebraic expression relating Density = mass / volume or m/v
where d is density, M is mass, and V is volume.
c) Density (ρ) is the amount of mass (m) per unit volume (V) of a substance. Density is an intensive property, which means the density does not change as the amount of the substance present changes.
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What will be the pressure exerted by the object if 5,000 N of force
area of 200 cm²?
Answer:
[tex]250000 \frac{n}{m {}^{2} } [/tex]
Explanation:
pressure is the force applied perpendicular to the surface area of an object per unit area.
for the question,
Force (F) = 5000N
[tex]Area = 200cm {}^{2} = 0.02m {}^{2} \\ Pressure = \frac{force}{area} \\ Pressure = \frac{5000}{0.02} \\ Pressure = 250000 \frac{n}{m {}^{2} } [/tex]
(a) What is the resistance of a lightbulb that uses an average power of 120 W when connected to a 60.0-Hz power source having a maximum voltage of 170 V
Resistance of a lightbulb is 240.8 ohm
Given:
Power = 120 W
Frequency = 60.0-Hz
Voltage = 170 V
To Find:
Resistance of a lightbulb
Solution: The electrical resistance of a circuit is the ratio between the voltage applied to the current flowing through it. Rearranging the above relation, R = V I. The unit of electrical resistance is ohms.
The resistance of the light bulb is given by the formula, R=V²/P
R = (170)^2/120
R = 240.8 ohm
Hence, the resistance of light bulb is R = 240.8 ohm
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Give an example of q eqluibrium in a linear motion
Answer:
What type of equilibrium? There are more types, lol.
If you want a mechanical equilibrium, then just take in consideration the uniform linear motion. The resultant of the forces is null.
The second step in converting between the mass of a compound and moles of a compound is to:________
The second step would be to divide the mass of the compound by the molar mass of the compound.
Converting mass to moleIn converting the mass of a compound to the number of moles of the same compound, one needs to divide the mass by the molar mass of the compound.
Mathematically, this is expressed as:
Number of moles of a compound = mass of the compound/molar mass of the compound.
Thus, the first step would be to calculate the molar mass of the compound from the molar weight of the atoms of elements that constitute the compound.
The second step would then be to divide the mass by the calculated molar mass in order to obtain the number of moles.
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What is the purpose of nucleophilic substitution reactions of akyly halides experiment?
The purpose of nucleophilic substitution reactions of alkyl halides experiment is to demonstrate in the laboratory setting Nucleophilic substitution reactions of alkyl halides.
In this it is been aimed to observe nucleophilic substitution reactions, SN1 and SN2 will by the addition of a solvent to mixtures of alkyl halides. In order to make this experiment effective a standard procedure is being used and noted observations while each reaction occurred.
Nucleophilic substitution reactions are an important class of reactions that allow the interconversion of functional groups. For alcohols, the range of substitution reactions possible can be increased by utilizing the tosylates (R-OTs), an alternative method of converting the -OH to a better leaving group.
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Work is best described as?
Answer:
Explanation:
In physics, work can be described as force multiplied by the displacement of the object (distance caused by the force acted on the object).
Work is a form of energy, therefore, it is measured in joules.
If Alex pushed on an object with 10N of force, and the object moved 2 meters, the work of Alex will be equal to:
W = Ft
W = 10N * 2m
W = 20 Joules
But, if we have John, that pushed on an object with 2N of force, but, since the object was way smaller, therefore it had way less inertia, the object moved a distance equal to 10 meters. Let's also calculate his work.
W = Ft
W = 2N * 10m
W = 20 Joules
And we got the same result.
Work can also be used to calculate power.
Power is equal to P = Work / time
It can also be written as P = delta Work / delta time
Power is measured in joules per second.
With power you can make the difference between someone that got a 2 kg object up in 2 second, and someone that got a 2 kg object up in 5 second.
The more powerful one would be the one who managed to make the same work in less time.
Hope it Helped!
Work is described as: the measure of energy transfer resulting from the application of force over a displacement.
What is Work?In the field of physics, work is most accurately defined as the outcome of multiplying the force exerted on an object by the distance the object is displaced in the same direction as the force.
This calculation serves to quantify the energy transferred to or from the object. For instance, if an individual applies a 50 Newton force to push a box across a 5-meter distance in the force's direction, the work done on the box would equal 250 Joules (50 N × 5 m).
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The diagram shows the forces acting on a truck as it travels along a flat road:
A truck with a 500 N force pointing up, 500 N force pointing down and 100 N pointing at the back of the truck, and 60 N pointing at the front of the truck.
(a) Are the forces acting on the truck balanced? Which forces cancel out? Explain your answer.
(b) What is the resultant force acting on the truck? Define its magnitude and direction.
(c) What is the effect of the resultant force on the speed of the truck?
(a) The forces acting on the truck is not balanced.
(b) The resultant force acting on the truck is 40 N towards the right direction.
(c) As the resultant force increases, the speed of the truck increases.
net vertical force = 500 N - 500 N = 0
net horizontal force = 100 N - 60 N = 40 N
The forces acting on the truck is not balanced.
The resultant force acting on the truck is 40 N towards the right direction.
Thus, as the resultant force increases, the speed of the truck increases.
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What does oxygen deficit represent?
Answer: It represents a small amount of oxygen being taken into the body when the body consumes more oxygen than what is being intake
Explanation: to be deficit means the amount of something is too small and there for oxygen deficit is a too small amount of oxygen.
The length of a rectangular plot of land is 151.28 m, and its width is 72.35 m. What is the perimeter of this plot?
605.1 m
223.6 m
289.4 m
a.
b. 447.3 m
c.
d.
Please select the best answer from the choices provided
OA
OB
OC
OD
[tex] \large{ \boxed{ \tt{447.3 \: m}}}[/tex]
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A 220- resistor is connected across an ac voltage source v = (150 v) sin [2pi(60 hz)t]. what is the average power delivered to this circuit?
The average power delivered to this circuit is 51.1 W.
Average power delivered to this circuit
The average power delivered to this circuit is calculated as follows;
P = v²(rms)/R
v(rms) = 0.7071v₀
where;
v₀ is peak voltagev(rms) is the root mean voltageR is resistance of the circuitSubstitute the given parameters and solve for average power
v(rms) = 0.7071v₀
v(rms) = 0.7071(150 V)
v(rms) = 106.1 V
Power = (106.1²) / (220)
Power = 51.2 W
Thus, the average power delivered to this circuit is 51.1 W.
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Which of newton's three laws is the hardest to describe or explain when viewing common occurrences?
Newton's second law is the hardest to describe as it is about momentum (F = ma), and a lot of people don't know the concept of momentum.
Newton's first law of motion:- every object moves in a straight line unless acted upon by a force.
Newton's 2nd law of motion:-the acceleration of an object is directly proportional to the net force exerted and inversely proportional to the item's mass. Newton's 2nd law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it.
Newton's 3rd law of motion:- For every action, there's an equal and opposite reaction.
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Earth orbits the sun at an average circular radius of about 149.60 million kilometers every 365.26 Earth days.
a) Determine the Earth’s average orbital speed expressed in kilometers per hours.
b) Based on the information given in this question, calculate the approximate mass of the Sun.
The Earth’s average orbital speed expressed in kilometers per hours is 107225.5 Km/hr and the mass of the sun is 2.58 x [tex]10^{24}[/tex] Kg
Relationship between Linear and angular speedLinear speed is the product of angular speed and the maximum displacement of the particle. That is,
V = Wr
Where
V = Linear speedW = Angular speedr = RadiusGiven that the earth orbits the sun at an average circular radius of about 149.60 million kilometers every 365.26 Earth days.
a) To determine the Earth’s average orbital speed, we will make use of the below formula to calculate angular speed
W = 2[tex]\pi[/tex]/T
W = (2 x 3.143) / (365.26 x 24)
W = 6.283 / 876624
W = 7.2 x [tex]10^{-4}[/tex] Rad/hr
The Earth’s average orbital speed V = Wr
V = 7.2 x [tex]10^{-4}[/tex] x 149.6 x [tex]10^{6}[/tex]
V = 107225.5 kilometers per hours.
b) Based on the information given in this question, to calculate the approximate mass of the Sun, we will use Kepler's 3rd law
M = (4[tex]\pi ^{2}[/tex][tex]r^{3}[/tex]) / G[tex]T^{2}[/tex]
M = (4 x 9.8696 x 3.35 x [tex]10^{24}[/tex]) / (6.67 x [tex]10^{-11}[/tex] x 7.68 x [tex]10^{11}[/tex])
M = 1.32 x [tex]10^{26}[/tex] / 51.226
M = 2.58 x [tex]10^{24}[/tex] Kg
Therefore, the Earth’s average orbital speed expressed in kilometers per hours is 107225.5 Km/hr and the mass of the sun is 2.58 x [tex]10^{24}[/tex] Kg
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The question is in the picture
Answer:
See below
Explanation:
Power = amps * volts = .27 * 12 = 3.24 watts
V= IR
R = V/I = 12/.27 = 44.44 ohms
What is the amount of charge a capacitor can store per volt of potential difference?
A) permittivity
B) dielectric constant
C) capacitance
D) electric potential energy
Capacitance is the amount of charge a capacitor can store per volt of potential difference.
What is capacitance?Capacitance is defined as the capacitors ability to store an electrical charge on its plates. Capacitance is derived from capacity which means ability to store.
So we can conclude that Capacitance is the amount of charge a capacitor can store per volt of potential difference.
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The amount of charge a capacitor can store per volt of potential difference is called the capacitance of the capacitor.
What is the capacitance?The capacitance has to do with the amount of charge that is stored by a capacitor. We know that a capacitor is a device that can be used to store electric charges. We have in it, two capacitors separated by a dielectric material.
Hence, the amount of charge a capacitor can store per volt of potential difference is called the capacitance of the capacitor.
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How many people are allowed daily into the coyote buttes north area, which includes the wave?.
64 people are allowed daily into the coyote buttes north area, which includes the wave.
What can be seen in coyote buttes north?The Wave and other aesthetically stunning natural sandstone formations can be found in Coyote Buttes North.
Where is coyote butte north located?It is a small portion of the 112,500-acre Paria Canyon-Vermilion Cliffs Wilderness of Northern Arizona.
To enter Coyote Buttes North (The Wave) and Coyote Buttes South, you need a permission. There are only daytime permits available. Permits have a daily maximum. Coyote Buttes North (The Wave) permits are distributed via lottery.How was the wave in coyote buttes formed?
The Wave is a Navajo Sandstone formation found in the Paria Canyon-Vermilion Cliffs Wilderness of Northern Arizona. The amazing patterns in the rock here were created by the wind and erosion over millions of years.To learn more about coyote buttes north visit:
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64 people are allowed daily into the coyote buttes north area, which includes the wave.
What can be seen in coyote buttes north?The Wave and other aesthetically stunning natural sandstone formations can be found in Coyote Buttes North.
Where is coyote butte north located?
It is a small portion of the 112,500-acre Paria Canyon-Vermilion Cliffs Wilderness of Northern Arizona.
To enter Coyote Buttes North (The Wave) and Coyote Buttes South, you need a permission.
There are only daytime permits available.
Permits have a daily maximum.
Coyote Buttes North (The Wave) permits are distributed via lottery.
How was the wave in coyote buttes formed?The Wave is a Navajo Sandstone formation found in the Paria Canyon-Vermilion Cliffs Wilderness of Northern Arizona.
The amazing patterns in the rock here were created by the wind and erosion over millions of years.
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Josie ran at an average speed of 16 m/s. if her mass 10 kg, what was her kinetic energy as she crosses her finish line?
Answer: 1280 J
[tex]KE=\frac{1}{2}mv^{2} \\\\KE= \frac{1}{2} (10 kg)(16 m/s)^2\\=1280 J[/tex]
I have to be honest with you . . . It's not possible to determine the answer with only the information given in the question.
Kinetic energy = (1/2) (mass) (speed squared).
Josie's Kinetic energy as she crosses the finish line is
(1/2) (her mass) (her speed as she crosses the finish line)².
That's (5 kg) x (her speed as she crosses the finish line)² .
But read the question again.
WE DON'T know her speed as she crosses the finish line.
The question only tells us her average speed for the whole race.
We can be confident that her Average Kinetic Energy was
(5 kg) (16 m/s)² = 1,280 Joules.
But we can't tell what her kinetic energy was as she crossed the finish line, beause we don't know what her speed was at that instant.
A 0.41 kg particle moves in an xy plane according to x(t) = - 11 + 1 t - 5 t3 and y(t) = 19 + 3 t - 9 t2, with x and y in meters and t in seconds. At t = 1.4 s, what are (a) the magnitude and (b) the angle (within (-180°, 180°] interval relative to the positive direction of the x axis) of the net force on the particle, and (c) what is the angle of the particle's direction of travel?
It looks like you're given
[tex]x(t) = -11\,\mathrm m + \left(1\dfrac{\rm m}{\rm s}\right) t - \left(5\dfrac{\rm m}{\mathrm s^3}\right) t^3[/tex]
[tex]y(t) = 19\,\mathrm m + \left(3\dfrac{\rm m}{\rm s}\right) t - \left(9\dfrac{\rm m}{\mathrm s^2}\right) t^2[/tex]
The particle's position vector at time [tex]t[/tex] is given by
[tex]\vec r(t) = x(t)\,\vec\imath + y(t)\,\vec\jmath[/tex]
Differentiate [tex]\vec r[/tex] twice to recover the velocity and acceleration vectors.
[tex]\vec a(t) = \dfrac{d\vec v(t)}{dt} = \dfrac{d^2\vec r}{dt^2} = x''(t)\,\vec\imath + y''(t)\,\vec\jmath \\\\ \implies \vec v(t) = \left(1\dfrac{\rm m}{\rm s} - \left(15\dfrac{\rm m}{\mathrm s^3}\right) t^2\right)\,\vec\imath + \left(3\dfrac{\rm m}{\rm s} - \left(18\dfrac{\rm m}{\mathrm s^2}\right) t\right) \,\vec\jmath \\\\ \implies \vec a(t) = -\left(30\dfrac{\rm m}{\mathrm s^3}\right)t \, \vec\imath - \left(18\dfrac{\rm m}{\mathrm s^2}\right) \,\vec\jmath[/tex]
At [tex]t=1.4\,\rm s[/tex], the particle has acceleration
[tex]\vec a(1.4\,\mathrm s) = \left(-42\,\vec\imath - 18\,\vec\jmath) \dfrac{\rm m}{\mathrm s^2}[/tex]
with magnitude
[tex]\|\vec a(1.4\,\mathrm s)\| = \sqrt{\left(-42\dfrac{\rm m}{\mathrm s^2}\right)^2 + \left(-18\dfrac{\rm m}{\mathrm s^2}\right)^2} \approx 45.695\dfrac{\rm m}{\mathrm s^2}[/tex]
and making an angle [tex]\theta[/tex] relative to the positive [tex]x[/tex]-axis such that
[tex]\tan(\theta) = \dfrac{-18}{-42} = \dfrac37[/tex]
Since both components of the acceleration vector have negative sign, the acceleration points into the third quadrant, so that we add a multiple of 180° after taking the inverse tangent of both sides, namely
[tex]\theta = \tan^{-1}\left(\dfrac37\right) - 180^\circ \approx -156.801^\circ[/tex]
Now, (a) the magnitude of the net force acting on the particle is, by Newton's second law,
[tex]F = (0.41\,\mathrm{kg})\|\vec a(1.4\,\mathrm s)\| \approx \boxed{18.735\,\mathrm N}[/tex]
and (b) makes the same angle as the acceleration vector, [tex]\theta \approx \boxed{-156.801^\circ}[/tex].
At this moment, its velocity vector is
[tex]\vec v(1.4\,\mathrm s) = \left(-28.4\vec\imath - 22.2\,\vec\jmath\right) \dfrac{\rm m}{\rm s}[/tex]
which (c) makes an angle [tex]\theta[/tex] such that
[tex]\tan(\theta) = \dfrac{-22.2}{-28.4} = \dfrac{111}{142}[/tex]
This vector also points in the third quadrant, so
[tex]\theta = \tan^{-1}\left(\dfrac{111}{142}\right) -180^\circ \approx \boxed{-142.986^\circ}[/tex]
Tina is singing a song. At a certain point in the song, she forces a large volume of air out of the glottis and at the same time increases the tension on her vocal cords. The sound that she produces is
The sound that Tina produces while singing is loud and high-pitched.
How is a sound produced?
Vibrations that travel through the air or another medium and can be heard by an observer are called sounds. Sound is produced by the following cycle:
A column of air in the lungs leads to the opening of the bottom section of vocal folds. It then continues to move upwards towards the top of the vocal folds and escapes out. This causes Bernoulli's effect, that is as low pressure gets created behind the fast-moving air column, the bottom section of the vocal folds closes, followed by the top. The air gets cut off due to the closure of the vocal folds which releases a pulse of air and the cycle continues.Therefore, when Tina sings larger vibrations are created, and the tension within her vocal cords increases producing a very high-pitched loud sound.
Learn more about the sound here:
https://brainly.com/question/20999521
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