Answer:
Nasopharynx
Explanation:
The nasopharynx is posterior to the nasal cavity and serves only as a passageway for air.
This 200-kg horse ran the track at a speed of 5 m/s. What was the average kinetic energy?
Answer:
2500 JExplanation:
The average kinetic energy can be found by using the formula
[tex]k = \frac{1}{2} m {v}^{2} \\ [/tex]
m is the mass
v is the velocity
From the question we have
[tex]k = \frac{1}{2} \times 200 \times {5}^{2} \\ = 100 \times 25[/tex]
We have the final answer is
2500 JHope this helps you
Two sacks contain the same number of identical apples and are separated by a distance r. The two
sacks exert a gravitational orce on each other that is opposite in direction but with the same
F. Half the apples are removed from one sack and placed in the second sack. What is the magnitude
the gravitational force between the two sacks in terms of the original force, F?
Answer:
The appropriate response will be "[tex]F_2=\frac{3}{4}F[/tex]". A further explanation is given below.
Explanation:
According to the question,
⇒ [tex]F_1=\frac{G(m_1 m_2)}{r^2}[/tex] ....(equation 1)
and,
⇒ [tex]F_2=\frac{G(m_1 m_2)}{r^2}[/tex] ....(equation 2)
Now,
On dividing both the equations, we get
⇒ [tex]\frac{F_1}{F_2}=\frac{\frac{G(2)(2)}{(1)^2}}{\frac{G(1)(3)}{(1)^2}}[/tex]
⇒ [tex]\frac{F_1}{F_2}= \frac{4}{3}[/tex]
⇒ [tex]F_2=\frac{3}{4}F[/tex]
The magnitude of gravitational force is different due to difference in masses of two sacks.
The magnitude of gravitational force between the two sacks in terms of the original force is different because the mass of the two objects are different from each other. There is direct relationship between gravitational force and mass of an object. Higher the mass of an object higher will be the gravitational force of attraction and vice versa.
So that sack which gains more weight have more force of gravitation as compared to the other sack which has less weight so we can conclude that the magnitude of gravitational force is different due to difference in masses of two sacks.
Learn more about gravitational force here: https://brainly.com/question/24783651
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During the contraction of the heart, 65 cm3 blood is ejected from the left ventricle into the aorta with a velocity of approximately 103 cm/s. The blood volume traverses the aortic arch, exiting with the same speed but opposite direction. Assume the mass density of the blood is 1060 kg/m3 blood, the aortic arch remains stationary, and that the heart rate is 59 bpm. What is the average force exerted by the blood on the wall of the aorta.
Answer:
The value [tex]F = 0.1396 \ N [/tex]
Explanation:
From the question we are told that
The volume blood ejected is [tex]V = 65 \ cm^3 = 65*10^{-6} \ m^3[/tex]
The velocity of the blood ejected is [tex]v = 103 \ cm/s = \frac{103}{100} = 1.03 \ m/s[/tex]
The density of blood is [tex]\rho = 1060 \ kg/m^3[/tex]
The heart beat is [tex]R = 59 \ bpm(beats \ per \ minute) = \frac{59}{60}= 0.9833\ bps[/tex]
The average force exerted by the blood on the wall of the aorta is mathematically represented as
[tex]F = 2 * \rho * V * R * v[/tex]
=> [tex]F = 2 * 1060 * 65*10^{-6} * 0.9833 * 1.03[/tex]
=> [tex]F = 0.1396 \ N [/tex]
An automobile travels to the right, with the center Aof the wheel moving at a constant speed of 48 mi/h. If the diameter of a wheel is 22in.,determine the velocities of points B, C, D, and E on the rim of the wheelassuming there is no slipping. [Hint: at any given instant the velocity of point C, which is in contact with the ground must be zero]. Please introduce axes and give your answers in vector form.
Answer:
Explanation:
From the question we are told that
Constant speed =48mile/hr
Diameter of a wheel = 22inch therefore [tex]r=\frac{22}{2} =>11[/tex]
Generally Convert from mile/hr to inches/sec
The length in inches is equal to the miles multiplied by 63,360.
an hour is 3600seconds
[tex]\frac{48*63360}{3600}[/tex]
48miles/h = 849.8 inch/sec
[tex]V_a =844.8 inch/sec[/tex]
therefore
[tex]\omega= \frac{v}{r}[/tex]
[tex]\omega= \frac{844,8}{11}[/tex] =>[tex]76.8 sec ^-^1[/tex]
a)Considering the velocity of Vb in inches per seconds
Generally the formula is stated as
[tex]V_b= V_a + V_b_/_a[/tex]
[tex]V_b = 844.8 + \omega r[/tex]
[tex]V_b= 1639.6in/s[/tex]
b)Considering the velocity of Vc in inches per seconds
Since the tire doesn't slip as earlier stated in the question
Therefore [tex]V_c = 844.8 -w(r) =0[/tex]
c)Considering the velocity of Ve in inches per seconds
Generally the formula is stated as
[tex]V_e=V_a + V_e_/_a[/tex]
[tex]V_e = 844.8 \uparrow \theta -844.8 \uparrow = 844.8\sqrt{2}[/tex]
Expressing result with vector
[tex]V_e =844.54 + 20.85j[/tex]
d)Considering the velocity of Vd in inches per seconds
Generally the formula is stated as
[tex]V_d= V_a + V_d_/_a[/tex]
Mathematically
[tex]V_d =844.8 \uparrow +( 844.8\frac{\sqrt{3} }{2} \uparrow + \frac{844.8}{2} \uparrow)[/tex]
[tex]V_d= (1576.4 \uparrow + 422.4\uparrow)[/tex]
[tex]V_d= 1632.028in/s[/tex]
psychology: Echoic sensory memory is used when a lightning bolt flashes across the sky. Please select the best answer from the choices provided T F
Answer:
The answer is False
Explanation:
Echoic sensory memory is used when a lightning bolt flashes across the sky. This is false statement.
What is echoic sensory memory?Echoic memory is a type of sensory memory that registers and stores auditory information (sounds) until it is processed and understood (Carlson, 2010). This sensory store can hold a large amount of auditory information for 3 to 4 seconds (Clark, 1987).
Echoic Memory Examples:
While listening to music: When we listen to music, our brains recall each note briefly and connect it to the next note. As a result, the brain recognizes the note sequences as a song.Conversation: When we hear spoken language, our echoic memories retain every individual syllable. Our brains understand words by associating each syllable with the one before it.Learn more about echoic memory here:
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For a scene in a movie, a stunt driver drives a 1700 kg pickup truck with a length of 4.45 m around a circular curve with a radius 0f 0.355 km. The truck is to complete a semicircle, jump across a gully, and land on the other side 3.00 m below and 10.5 m away. What is the minimum centripetal acceleration the truck must have going around the circular curve so that the entire truck will clear the gully and land on the other side
Answer:
[tex]0.51\ \text{m/s}^2[/tex]
Explanation:
t = Time taken
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
r = Radius of track = 0.355 km
Displacement in [tex]y[/tex] direction is 3 m
[tex]y=ut+\dfrac{1}{2}gt^2\\\Rightarrow 3=0+\dfrac{1}{2}\times 9.81 t^2\\\Rightarrow t=\sqrt{\dfrac{3\times 2}{9.81}}\\\Rightarrow t=0.782\ \text{s}[/tex]
Displacement in [tex]x[/tex] direction
[tex]x=10.5\ \text{m}[/tex]
[tex]v=\dfrac{x}{t}\\\Rightarrow v=\dfrac{10.5}{0.782}\\\Rightarrow v=13.43\ \text{m/s}[/tex]
Centripetal acceleration is given by
[tex]a_c=\dfrac{v^2}{r}\\\Rightarrow a_c=\dfrac{13.43^2}{355}\\\Rightarrow a_c=0.51\ \text{m/s}^2[/tex]
The minimum centripetal acceleration the truck must have is [tex]0.51\ \text{m/s}^2[/tex]
Please help! What kind of energy is produce by filament light?
Answer:
electrical to thermal and light
(may wanna change the answers)
and the one before that should be electrical to electrical i think
Explanation:
The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. A single lap should be completed each time you hear this sound. Remember to run in a straight line, and run as long as possible.
3. If a net horizontal force of 49 N is applied to a box whose mass is 5 kg what acceleration
is produced?
Answer:
9.8 m/s²Explanation:
The acceleration of an object given it's mass and the force acting on it can be found by using the formula
[tex]a = \frac{f}{m} \\ [/tex]
f is the force
m is the mass
From the question we have
[tex]a = \frac{49}{5} \\ [/tex]
We have the final answer as
9.8 m/s²Hope this helps you
A force of 100 N acts on a body and moves at a distance of 2 m in the direction of the force. How much work has been done?
Answer:
200 joules
Explanation:
work=force×distance
2. Fossil fuel has been used more in the
existing world
Answer: fossil fuels are using more in the existing world because fossil fuels are of great importance because they can burned producing significant amount of energy prr unit mass the use of coal as a fuel prefates recorded history
Explanation:
Answer:
A fossil fuel is a fuel formed by natural processes, such as anaerobic decomposition of buried dead organisms, containing organic molecules originating in ancient photosynthesis[1] that release energy in combustion.[2] Such organisms and their resulting fossil fuels typically have an age of millions of years, and sometimes more than 650 million years.[3] Fossil fuels contain high percentages of carbon and include petroleum, coal, and natural gas.[4] Peat is also sometimes considered a fossil fuel.[5] Commonly used derivatives of fossil fuels include kerosene and propane. Fossil fuels range from volatile materials with low carbon-to-hydrogen ratios (like methane), to liquids (like petroleum), to nonvolatile materials composed of almost pure carbon, like anthracite coal. Methane can be found in hydrocarbon fields alone, associated with oil, or in the form of methane clathrates.
Coal, a fossil fuel
As of 2018, the world's main primary energy sources consisted of petroleum (34%), coal (27%), and natural gas (24%), amounting to an 85% share for fossil fuels in primary energy consumption in the world. Non-fossil sources included nuclear (4.4%), hydroelectric (6.8%), and other renewables (4.0%, including geothermal, solar, tidal, wind, wood, and waste).[6] The share of renewables (including traditional biomass) in the world's total final energy consumption was 18% in 2018.[7] Compared with 2017, world energy-consumption grew at a rate of 2.9%, almost double its 10-year average of 1.5% per year, and the fastest since 2010.[8]
Although fossil fuels are continually formed by natural processes, they are generally classified as non-renewable resources because they take millions of years to form and known viable reserves are being depleted much faster than new ones are generated.[9][10]
Most air pollution deaths are due to fossil fuel combustion products, it is estimated to cost over 3% of global GDP,[11] and fossil fuel phase-out would save 3.6 million lives each year.[12]
The use of fossil fuels raises serious environmental concerns. The burning of fossil fuels produces around 35 billion tonnes (35 gigatonnes) of carbon dioxide (CO2) per year.[13] It is estimated that natural processes can only absorb a small part of that amount, so there is a net increase of many billion tonnes of atmospheric carbon dioxide per year.[14] CO2 is a greenhouse gas that increases radiative forcing and contributes to global warming and ocean acidification. A global movement towards the generation of low-carbon renewable energy is underway to help reduce global greenhouse-gas emissions.
Describe the Rutherford model
Answer:
The Rutherford model was devised by the New Zealand-born physicist Ernest Rutherford to describe an atom. Rutherford directed the Geiger–Marsden experiment in 1909, which suggested, upon Rutherford's 1911 analysis, that J. J. Thomson's plum pudding model of the atom was incorrect.
Atomic theory year: 1911
Explanation:
Hope this helps, Merry Christmas, and have a good day
Which wave has a longer wavelength?
Which of the following cars have the most kinetic energy
[tex]\huge\boxed{OptionA}[/tex]
_____________________________________DATA:Blue Car:mass = 4 kg
velocity = 5 m/s^2
Orange truck:Mass= 2kg
Velocity = 7m/s^2
Grey Car:mass = 6 kg
velocity = 4m/s^2
Green Car:Mass = 8 kg
Velocity = 3 m/s^2
_____________________________________SOLUTION:By the equation of kinetic energy,
K.E = [tex]\frac{1}{2} mv^2[/tex]
Where,
K.E is kinetic energy
m is mass
v is velocity
_____________________________________Kinetic energy of Blue car:
Directly substitute the variables in the equation,
K.E = [tex]\frac{1}{2}x4x5^2[/tex]
Simplify the equation,
K.E = 50 J
_____________________________________Kinetic Energy of Silver Car:
Directly substitude the variable in the equation,
K.E = [tex]\frac{1}{2}x6x4^2[/tex]
Simplify the equation,
K.E = 48J
_____________________________________Kinetic Energy of Green Car:Substitute the variables in the equation,
K.E = [tex]\frac{1}{2}x8x3^2[/tex]
Simplify the Equation,
K.E = 36J
_____________________________________Kinetic Energy of Orange Truck:Substitute the variable,
K.E = [tex]\frac{1}{2}x 2x7^2[/tex]
Simplify the equation,
K.E = 49J
_____________________________________As you can see that the highest value of kinetic energy is of Blue SUV thus it will be out answer.
_____________________________________Best Regards,'Borz'How do the permanent magnets in an electric generator induce a current in a loop of wire that is moving between them?
A. The magnets cause charged particles within the wire to move as the poles of the magnets switch.
B. The moving electrons flow from the permanent magnets into the loop of wire.
C. The magnetic field of each magnet attracts the metal in the moving loop of wire.
D. The magnetic field between the magnets causes the charged particles within the wire to move.
Correct answer is D
The magnetic field between the magnets causes the charged particles within the wire to move.
According Faraday's law of electromagnetic induction, whenever their is a relative motion of a conductor is magnetic field, an emf will be induced in the conductor and the strength of the induced emf is directly proportional to the rate of change of magnetic flux linking the circuit.
The motion of the electrons is due to magnetic field created by the permanent magnet of the electric generator.
Thus, the magnetic field between the magnets causes the charged particles within the wire to move.
Learn more about about Faraday's law here: https://brainly.com/question/4418412
In specific heat capacity experiment, the ammeter in circuit is connected in
Answer:
In series
Explanation:
In such experiment, the ammeter is connected in series with the heater, in order to measure the circulating current.
By the way, ammeters are always connected in series in circuits to measure the running current in it.
1. Derive the equation of the trajectory of a projectile.
(3mks)
2. A ball is thrown with an initial speed uof 30 m/s at an angle & above thehorizontal, where
sin 0 = 4/5 and cos 0 = 3/5.
(5mks)
(a) decompose the vector u into itsx and y components.
(b) When t= 2 s, find the position of the ball andthe magnitude and direction of its
velocityu.
(c) Determine
the value
of the highest point of the ball's trajectory.
(d) calculate how much time has elapsed forthe ball to reach the highest point.
(e) Calculate the values of the total time of theball's flight T and the horizontal range R.
ASAN
3. In the model of the hydrogen atom proposed by Niels Bohr an electron circulatesa
stationary proton in a circle of radius 7' = 5.28 x 10-11 m with a speedı= 2.18 x 106m's
(a) Find the magnitude of the electron sradial acceleration in this model.
(1mk)
(b) Determine the period of the motion,
(Imk)
Look at this model of an atom. Using a periodic table, which element does it represent?
Answer:
Nitrogen
Explanation:
What speed should a satellite with a mass of 1500 kg at 8,500 km above the center of the earth be traveling at in order to stay in orbit (remember the mass of the earth is 5.97×10 to the 24th kg ) (in m/s , G= 6.67×10 to the -11 n (m/kg) ^2)
Answer:
6844.5 m/s.
Explanation:
To get the speed of the satellite, the centripetal force on it must be enough to change its direction. This therefore means that the centripetal force must be equal to the gravitational force.
Formula for centripetal force is;
F_c = mv²/r
Formula for gravitational force is:
F_g = GmM/r²
Thus;
mv²/r = GmM/r²
m is the mass of the satellite and M is mass of the earth.
Making v the subject, we have;
v = √(GM/r)
We are given;
G = 6.67 × 10^(-11) m/kg²
M = 5.97 × 10^(24) kg
r = 8500 km = 8500000
Thus;
v = √((6.67 × 10^(-11) × (5.97 × 10^(24)) /8500000) = 6844.5 m/s.
Answer:
6.8 × 10³ m/s
Explanation:
for those using CK12, the answer, (6.78 × 10³ m/s), rounds to 6.8 × 10³ m/s
A thyristor (SCR) is a
Answer:
A thyristor (/θaɪˈrɪstər/) is a solid-state semiconductor device with four layers of alternating P- and N-type materials. It acts exclusively as a bistable switch, conducting when the gate receives a current trigger, and continuing to conduct until the voltage across the device is reversed biased, or until the voltage is removed (by some other means).
Explanation:
Correct me if im wrong
What are the factors affect the Electric forces between two charges and What is the relationship between each factor and the Electric force ?
Explanation:
If the two charges are point charges - i.e., they don't have a size - the force between these charges depends on the
• Magnitude if each charge, q1 and q2
• Sign of each charge (+ or -)
• Distance between the charges, r
This is essentially Coulomb’s Law:
FE = (kq1q2)/r2
For collections of charges, you need to find the electric field E, and then use this fields to find a force on a small test charge q in the field. The test charge is always small to help you map the electric field, but not disturb it.
I NEED BY JAN 4!!!!!!
Research what is known about Earth’s magnetic field. Begin by looking for images and credible sites on the Internet or refer to some books in a library. Answer the following questions:
What is the approximate size of Earth’s magnetic field?
Where are Earth’s magnetic poles?
Where is the magnet that causes Earth’s magnetic field located? What is this magnet made of?
Does Earth’s magnetic field move?
The earth has a magnetic field. It is much like a bar magnet. Imagine a gigantic bar magnet inside the Earth. But there is no giant magnet inside it.
To have a pretty good idea what earth's magnetic field is shaped like we imagine a bar magnet inside the earth.
The magnetic field is made by the motion of molten iron in earth's outer core. The swirling motion of molten iron changes all the time. Therefore, the magnetic fields will also get change. Then, the magnet poles also move.
The North pole and the south pole are two geographic poles of earth. These poles are the places on the earth's surface that earth's imaginary spin axis passes through.
There are two magnetic poles of the earth: North magnetic pole and South magnetic pole.
Earth's magnetic field is tilted a little bit. If we imagine that earth's magnetic field is made by a giant bar magnet. Then, the bar magnet would make an with earth's spin axis.
The geographic poles and the magnetic poles are not in the same place.
If we are standing at one magnetic poles then the magnetic field lines would be straight up and down.
Earth's magnetic field is a complex and dynamic phenomenon that is generated by the motion of molten iron in its outer core. The magnetic field extends far beyond the planet and is responsible for protecting Earth from harmful solar radiation and cosmic rays.
What is the approximate size of Earth's magnetic field?Earth's magnetic field is roughly dipolar in shape, meaning it has two main magnetic poles - north and south - and the field lines emerge from the north and re-enter at the south pole. The magnetic field has a strength of about 25-65 microteslas (μT) at the Earth's surface, and it extends for several tens of thousands of kilometers into space.
2. Where are Earth's magnetic poles?
Earth's magnetic poles are not fixed and are constantly moving due to the complex and dynamic nature of the planet's magnetic field. Currently, the north magnetic pole is located in the Arctic Ocean, close to Canada's Ellesmere Island, and the south magnetic pole is located in the Antarctic Ocean, near the coast of Antarctica.
3. Where is the magnet that causes Earth's magnetic field located? What is this magnet made of?
The magnet that causes Earth's magnetic field is not a physical magnet but rather a result of the motion of molten iron in the Earth's outer core. The outer core is a layer of liquid iron and nickel that surrounds the solid inner core. The motion of this molten iron generates electrical currents, which in turn create a magnetic field.
4. Does Earth's magnetic field move?
Yes, Earth's magnetic field is not static and is constantly changing due to the complex nature of the planet's interior. The magnetic poles are constantly moving and the strength of the magnetic field can vary over time. The magnetic field can also be influenced by external factors such as solar storms and changes in the solar wind. Scientists continue to study Earth's magnetic field to better understand its behavior and how it affects the planet.
Therefore, The magnetic field of the Earth is a complex and dynamic phenomenon caused by the movement of molten iron in its outer core. The magnetic field extends far beyond the planet and is in charge of shielding the planet from harmful solar radiation and cosmic rays.
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how do you determine half life
Answer:
T= In(2)/___ =__ In(2)
Explanation:
the equation pices arnt on the keyboard so i put the blanks
sorry
jope it helps some. Have a good day ir night! :)
the maximum intensity levels of a trumpet, trombone, and a bass drum, each at a distance of 3m are 94 dB, 107dB, and 113dB respectively. What is the intensity level of the three different instruments when played simultaneously, again at 3m?
Answer:
β = 114 db
Explanation:
The intensity of sound in decibles is
β = 10 log [tex]\frac{I}{I_{o}}[/tex]
in most cases Io is the hearing threshold 1 10-12 W / cm²
let's calculate the intensity of each instrument
I / I₀ = 10 (β / 10)
I = I₀ 10 (β / 10)
trumpet
I1 = 1 10⁻¹² 10 (94/10)
I1 = 2.51 10⁻³ / cm²
Thrombus
I2 = 1 10⁻¹² 10 (107/10)
I2 = 5.01 10-2 W / cm²
low
I3 =1 1-12 (113/10) W/cm²
I3 = 1,995 10-1 W / cm²
when we place the three instruments together their sounds reinforce
I_total = I₁ + I₂ + I₃
I_ttoal = 2.51 10-3 + 5.01 10-2 + 1.995 10-1
I_total = 0.00251 + 0.0501 + 0.1995
I_total = 0.25211 W / cm²
let's bring this amount to the SI system
β = 10 log (0.25211 / 1 10⁻¹²)
β = 114 db
A piece of copper wire with thin insulation, 200 m long and 1.00 mm in diameter, is wound onto a plastic tube to form a long solenoid. This coil has a circular cross section and consists of tightly wound turns in one layer. If the current in the solenoid drops linearly from 1.60 A to zero in 0.120 seconds, an emf of 80.0 mV is induced in the coil. What is the length of the solenoid, measured along its axis
Answer:
N= 3
Explanation:
For this exercise we must use Faraday's law
E = - dФ / dt
Ф = B . A = B Acos θ
tje bold indicate vectors. As it indicates that the variation of the field is linear, we can approximate the derivatives
E = - A cos θ (B - B₀) / t
The angle enters the magnetic field and the normal to the area is zero
cos 0 = 1
A = π r²
In the length of the wire there are N turns each with a length L₀ = 2π r
L = N (2π r)
r = L / 2π N
we substitute
A = L² / (4π N²)
The magnetic field produced by a solenoid is
B = μ₀ N/L I
for which
B₀ = μ₀ N/L I
The final field is zero, because the current is zero
B = 0
We substitute
E = - (L² / 4π N²) (0 - μ₀ N/L I) / t
E = μ₀ L I / (4π N t)
N = μ₀ L I / (4π t E)
The electromotive force is E = 0.80 mV = 0.8 10⁻³ V
let's calculate
N = 4π 10⁻⁷ 200 1.60 / (4π 0.120 0.8 10⁻³)]
N = 320 10⁻⁷ / 9.6 10⁻⁶
N = 33.3 10⁻¹
N= 3
Help!!!!
A car has an oil drip. As the car moves, it drips oil at a regular rate, leaving a trail of spots on the road. Which diagram shows the spots
of car that is continuously slowing down?
The light given off by an object based only on its temperature supports the
particle model of light. Which term applies to this light?
A. Blackbody radiation
B. Photoelectric effect
C. Ultraviolet
D. Constructive interference
SUBM
Answer:
A.Blackbody Radiation
Explanation:
Answer:
A. Blackbody radiation
Explanation:
Please help! What kind of energy is produce when solar panel to lightbulb filament?
Answer:
electrical energy
Explanation:
sorry I'm really tired but trust me on this one
Answer:
electrical to thermal and light
Explanation:
The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. A single lap should be completed each time you hear this sound. Remember to run in a straight line, and run as long as possible.
Power lines often carry high voltages. For example, a single power line may carry 100,000 volts. An outlet in a home only carries 120-240 volts. What accounts for this difference in voltage?
- Voltage is decreased due to traveling long distances.
- Voltage is decreased by local transformers.
- Voltage is decreased as it is lost to the environment.
Answer: The second one? C.
Answer:
B. - Voltage is decreased by local transformers.
Explanation:
edge 2021 beep boop
The space shuttle releases a satellite into a circular orbit 630 km above the Earth.
How fast must the shuttle be moving (relative to Earth's center) when the release occurs?
Answer:
7,539 m/s
Explanation:
Let's use this equation to find the gravitational acceleration of this space shuttle:
[tex]\displaystyle g=\frac{GM}{r^2}[/tex]We know that G is the gravitational constant: 6.67 * 10^(-11) Nm²/kg².
M is the mass of the planet, which is Earth in this case: 5.972 * 10^24 kg.
r is the distance from the center of Earth to the space shuttle: radius of Earth (6.3781 * 10^6 m) + distance above the Earth (630 km → 630,000 m).
Plug these values into the equation:
[tex]\displaystyle g=\frac{(6.67\cdot 10^-^1^1 \ Nm^2kg^-^2)(5.972\cdot 10^2^4 \ kg)}{[(6.3781\cdot 10^6 \ m)+(630000 \ m)]^2}[/tex]Remove units to make the equation easier to read.
[tex]\displaystyle g=\frac{(6.67\cdot 10^-^1^1 )(5.972\cdot 10^2^4 )}{[(6.3781\cdot 10^6)+(630000 )]^2}[/tex]Multiply the numerator out.
[tex]\displaystyle g=\frac{(3.983324\cdot 10^1^4)}{[(6.3781\cdot 10^6)+(630000 )]^2}[/tex]Add the terms in the denominator.
[tex]\displaystyle g=\frac{(3.983324\cdot 10^1^4)}{[(7008100)]^2}[/tex]Simplify this equation.
[tex]\displaystyle g=8.11045189 \ \frac{m}{s^2}[/tex]The acceleration due to gravity g = 8.11045189 m/s². Now we use the equation for acceleration for an object in circular motion which contains v and r.
[tex]\displaystyle a = \frac{v^2}{r}[/tex]a = g, v is the velocity that the space shuttle should be moving (what we are trying to solve for), and r is the radius we had in the previous equation when solving for g.
Plug these values into the equation and solve for v.
[tex]\displaystyle 8.11045189 \ \frac{m}{s^2} = \frac{v^2}{7008100 \ m}[/tex]Remove units to make the equation easier to read.
[tex]\displaystyle 8.11045189 = \frac{v^2}{7008100}[/tex]Multiply both sides by 7,008,100.
[tex]56838857.89=v^2[/tex]Take the square root of both sides.
[tex]v=7539.154985[/tex]The shuttle should be moving at a velocity of about 7,539 m/s when it is released into the circular orbit above Earth.
A runner starts from rest and accelerates at a rate of 1.5 m/s2 and covers 375 m. How long did it take the runner to cover this distance?
Answer:
it takes him 22.36 seconds to cover that distance
Explanation:
We can solve this problem using the kinematic equation for uniformly accelerated motion:
[tex]x_f-x_i=v_0*t\,+\,\frac{1}{2} a\,*\,t^2[/tex]
which replacing the values given for our case becomes:
[tex]375=0*t\,+\,\frac{1}{2} (1.5)\,t^2\\375=\frac{1}{2} (1.5)\,t^2[/tex]
and which solving for t gives:
[tex]375=\frac{1}{2} (1.5)\,t^2\\t^2=2*375/1.5\\t^2=500\\t=\sqrt{500} \\t \approx 22.36\,\,sec[/tex]