Answer:
An estuary is the area where a river meets the sea or ocean, where fresh water from the river meets salt water from the sea.
Answer:
during the last interglacial period, the retreating of glaciers created massive valleys. When these glaciers melted the water filled up the valleys and thus created the first estuaries
Explanation:
In an electric motor, periodically changing the direction of current in the electromagnet can cause the axle to spin because
A. the electromagnet loses its magnetism.
B. mechanical energy is converted to electric energy.
C. the force is constant.
D. the magnetic field reverses direction.
Answer:
The magnetic field reverses direction.
Explanation:
Answer:
D The magnetic field reverses direction.
Explanation:
An electric motor works based on the principle of electromagnetic induction. It is the interaction of electric current and the magnetic field that makes a motor function.
An electric motor is a machine that will convert the electric energy to mechanical energy. In this a commutator is used to change the direction of current.
When the direction of flow of current is made to change, the magnetic field also reverses the direction.
There are different types of motors like AC motor,DC motor, Induction motor etc.
PLEASE HELP!
Find the angle of the resultant vector for the vectors shown below. (nearest whole number and angles measured from the positive x-axis)
vector
A) 39 degrees
B) 51 degrees
C) 70 degrees
Answer:
[tex]38.6^{\circ}[/tex]
Explanation:
In order to find the resultant of the two vectors, we need to find the components of each vector along the x- and y- axis.
For the horizontal vector, we have:
x-component: [tex]A_x = 15[/tex]
y-component: [tex]A_y = 0[/tex]
For the vectors of 18 units:
x-component: [tex]B_x = 18 cos 70^{\circ}=6.16[/tex]
y-component: [tex]B_y = 18 sin 70^{\circ}=16.91[/tex]
So the components of the resultant vector are
[tex]R_x=A_x + B_x = 15 +6.16 = 21.16[/tex]
[tex]R_y=A_y + B_y = 0 +16.91 = 16.91[/tex]
And so the direction is given by
[tex]\theta = tan^{-1} (\frac{R_y}{R_x})=tan^{-1} (\frac{16.91}{21.16})=38.6^{\circ}[/tex]
How are the planets sizes related to their surface gravity
Answer:
The surface gravity is inversely proportional to the square of the radius of the planet
Explanation:
The gravity at the surface of a planet is given by:
[tex]g=\frac{GM}{R^2}[/tex]
where
G is the gravitational constant
M is the mass of the planet
R is the radius of the planet
We see from the formula that the surface gravity is inversely proportional to the square of the radius of the planet, R.
At the Earth's surface, the value of the surface gravity is approximately 9.81 m/s^2.
A cheetah can run at 105 feet per second, but only for 7 seconds, at which time the animal must stop and rest. A fully rested cheetah at (0, 0) notices a nearby antelope, which is moving according to the parametric equation (x, y) = (−39 + 40t, 228 + 30t), where t is measured in seconds and x and y are measured in feet. If it started to run at t = 0, the cheetah could catch the antelope. For how many more seconds can the cheetah afford to wait before starting? Assume that the cheetah does not change direction when it runs.
Answer:
5 seconds
Explanation:
The straight line distance between (0, 0) and the antelope's position (x, y) at time t can be found using distance formula:
d² = x² + y²
d² = (-39 + 40t)² + (228 + 30t)²
d² = 1521 - 3120t + 1600t² + 51984 + 13680t + 900t²
d² = 53505 + 10560t + 2500t²
The cheetah can run a total distance of:
105 * 7 = 735
The time t at this distance is:
735² = 53505 + 10560t + 2500t²
540225 = 53505 + 10560t + 2500t²
0 = -486720 + 10560t + 2500t²
0 = -24336 + 528t + 125t²
t = 12, -16.224
t can't be negative, so t = 12.
Therefore, the cheetah can wait 5 seconds before it has to start running.
Answer:
Wait time = 5 s
Explanation:
As we know that the position vector of the antelope is given as
[tex]x = -39 + 40 t[/tex]
[tex]y = 228 + 30 t[/tex]
so here at any instant of time its distance from origin is given as
[tex]d^2 = x^2 + y^2[/tex]
so we have
[tex]d^2 = (-39 + 40t)^2 + (228 + 30t)^2[/tex]
[tex]d^2 = 53505 + 2500 t^2 + 10560 t[/tex]
now when cheetah catch the antelope then distance of cheetah and antelope from origin must be same
so distance covered by cheetah in 7 s is given as
[tex]d = 105 \times 7[/tex]
[tex]d = 735 ft[/tex]
now from the above two equation
[tex]735^2 = 53505 + 2500 t^2 + 10560t[/tex]
by solving above equation we got
t = 12 s
so Cheetah must have to waith for
[tex]\Delta t = 12 - 7 = 5 s[/tex]
How might an intense solar storm affect people on Earth?
A. It could disrupt communications and damage the power grid.
B. It would cause an intensely hot summer.
C. It could cause the Van Allen belts to expand.
D. It would not affect people on the surface of Earth, only astronauts.
An intense solar storm COULD disrupt communications and damage the power grid. (A)
An intense solar storm may disrupt communications and damage the power grid, affecting technology-reliant services such as GPS and wireless communication, as well as increasing radiation exposure for astronauts and aircraft passengers on polar routes. Advanced warnings would allow for preventative measures to protect infrastructure and people.
An intense solar storm can have significant impacts on Earth, affecting various aspects of our technology-dependent civilization. The most accurate answer to how a solar storm might affect people on Earth is A. It could disrupt communications and damage the power grid. These storms can cause geomagnetic disturbances that induce currents capable of damaging power systems, leading to widespread outages. Furthermore, the high-energy particles and radiation from solar storms can severely affect satellites and spacecraft, leading to malfunctions in navigation, communication, and other satellite-based services. Moreover, increased radiation poses risks for astronauts and could lead to higher levels of radiation for aircraft passengers on polar routes.
A planet moves fastest in its orbit around the sun when it is at which position?
Answer:
When it's closest to the sun.
Explanation:
The force of gravity acting on a planet is equal to its mass times its centripetal acceleration.
Fg = m v^2 / r
The force of gravity is defined by Newton's law of universal gravitation as:
Fg = mMG / r^2
Therefore:
mMG / r^2 = m v^2 / r
MG / r = v^2
v increases as r decreases. So the planet is moving fastest when it's closest to the sun, also known as the perihelion.
The force of gravity acting on a planet is equal to its mass times its centripetal acceleration.
Fg = m v² / r
The force of gravity is defined by Newton's law of universal gravitation as:
Fg = mMG / r²
Therefore:
mMG / r² = m v² / r
MG / r = v²
v increases as r decreases. So the planet is moving fastest when it's closest to the sun, also known as the perihelion.
perihelion
The fastest a planet moves is at perihelion (closest) and the slowest is at aphelion (farthest). Law 3. The square of the total time period (T) of the orbit is proportional to the cube of the average distance of the planet to the Sun (R)
What is the Earth's perihelion?The Earth is closest to the Sun, at its perihelion, about two weeks after the December solstice and farthest from the Sun, or at its aphelion, about two weeks after the June solstice. Earth is farthest from the Sun when it is summer in the Northern Hemisphere.
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In baseball, a home run means the batter has hit the baseball into the stands, beyond the baseball field. Compare the force of the batter when bunting the ball into the in-field versus hitting a grand slam.
A) There is no way to estimate the batter's force.
B) The force is much less when bunting into the in-field.
C) The force of the batters in each case is about the same.
D) The force of the batter is much less when hitting the ball out of the park.
Answer:
B
Explanation:
"Bunting" is when the batter lets the ball hit the bat without swinging it.
Force is mass times acceleration. The mass of the ball is the same in both scenarios, but the acceleration is much lower when bunting than it is when hitting a grand slam, so the force is much lower.
Therefore, the answer is B.
Answer: The force is much less when bunting into the in-field.
Explanation: usually, a home run is more a technique thing than a force thing.
an example can be that, two swings with the same force, but one hits the ball with the border of the bat, and the other hits the ball with the middle, in the second case more force will be transmitted to the ball, and it will go further away (increasing in this way the probability of a home run).
Assuming that in both cases the ball is hit exactly in the same way, now the force matters. Then a ball that goes out of the field is hit with more force than one that does not go out of the field.
Then the correct option would be option B: The force is much less when bunting into the in-field.
Capacitor 2 has half the capacitance and twice the potential difference as capacitor 1. What is the ratio (U_{\rm C})_1/\,(U_{\rm C})_2.
Answer:
1/2
Explanation:
The energy stored in a capacitor is given by
[tex]U=\frac{1}{2}CV^2[/tex]
where
C is the capacitance
V is the potential difference
Calling [tex]C_1[/tex] the capacitance of capacitor 1 and [tex]V_1[/tex] its potential difference, the energy stored in capacitor 1 is
[tex]U=\frac{1}{2}C_1 V_1^2[/tex]
For capacitor 2, we have:
- The capacitance is half that of capacitor 1: [tex]C_2 = \frac{C_1}{2}[/tex]
- The voltage is twice the voltage of capacitor 1: [tex]V_2 = 2 V_1[/tex]
so the energy stored in capacitor 2 is
[tex]U_2 = \frac{1}{2}C_2 V_2^2 = \frac{1}{2}\frac{C_1}{2}(2V_1)^2 = C_1 V_1^2[/tex]
So the ratio between the two energies is
[tex]\frac{U_1}{U_2}=\frac{\frac{1}{2}C_1 V_1^2}{C_1 V_1^2}=\frac{1}{2}[/tex]
Color depends on what characteristic of light?a) wavelengthb) frequencyc) both of these ( frequency x wavelength = speed )d) neither of these
Answer:
a) Wavelength .
Explanation:
Visible light is comprised of all the seven colors Violet , Indigo , Blue , Green , Yellow and Red .
Color depends up on the wave length of the light .
For example a red ball appears red because it absorbs wavelengths of all the other colors and reflects only wavelengths corresponding to red color.
Color in terms of light is determined by both the wavelength and frequency, with different combinations producing all the colors we humanly perceive.
Explanation:In the context of light, color is dependent on both the wavelength and frequency of light. This is because the visible spectrum which represents the colors that can be seen by the human eye, is defined by varying wavelengths and frequencies. Shorter wavelengths (and correspondingly higher frequencies) are associated with cooler colors like blue and violet, while longer wavelengths (and correspondingly lower frequencies) are associated with warmer colors like red and orange. Therefore, the answer to this is option c) both frequency and wavelength determine the color of light.
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The Milky Way is often considered to be an intermediately wound,barred spiral, which would be type ________ according to Hubble.A) E4B) SaC) SBbD) SBVE) B2S
Answer: SBb
On 1930 the astronomer Edwin Hubble classified the galaxies based on their visual appearance into elliptical, spiral and irregular, being the first two classes the most frequent.
So, according to this classification, the Milky Way is a barred spiral galaxy (SBb in Hubble's notation system) because it has a central bar-shaped structure of bright stars that spans from one side of the galaxy to the other. In addition, its spiral arms seem to emerge from the end of this "bar".
Scientifics considered this, after measuring the the disk and central bulge region of the galaxy, and the conclusion is the Milky Way fulfills these conditions, because is a galaxy that orbits on its same axis and with this rotation its arms are twisted in opposite directions around the mentioned axis.
Therefore the correct answer is option C.
Are radio waves transverse or longitudinal
Answer:
Transverse
Explanation:
There are two types of waves, depending on the direction of the oscillation:
- Transverse wave: in a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave - examples of transverse waves are electromagnetic waves
- Longitudinal wave: in a longitudinal wave, the direction of the oscillation is parallel to the direction of motion of the wave - examples of longitudinal waves are sound waves
Radio waves are a type of electromagnetic waves - consisting of oscillations of electric and magnetic field that propagate in a vacuum at the speed of light - so they are an example of transverse wave.
In what order do the three types of seismic waves arrive at a seismograph
Answer: Seismic waves arrive at a seismograph in the order of fastest to slowest:primary waves, secondary waves, surface waves.
Explanation:
P-waves, S-waves, and surface waves arrive at a seismograph in a specific order.
Explanation:The three types of seismic waves arrive at a seismograph in a specific order. First, P-waves (also known as pressure waves or longitudinal waves) arrive at the seismograph. These waves are compressional and travel faster than the other two types. Next, S-waves (also known as shear waves or transverse waves) arrive. These waves move the ground perpendicular to their path. Finally, surface waves arrive, which are similar to surface waves on water and cause the most damage during an earthquake.
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When an alpha particle is emitted from the nucleus of an atom?
Answer:
During an alpha decay
Explanation:
An alpha particle is a particle consisting of 2 protons and 2 neutrons - basically it is equivalent to a nucleus of helium.
Alpha particles are emitted during alpha decays, which are one of the three types of radioactive decays (the other two being beta decay and gamma decay) in which an unstable nucleus decays emitting an alpha particle:
[tex]X \rightarrow Y + \alpha[/tex]
In the process, the original nucleus X loses 2 protons and 2 neutrons, so:
- its atomic number decreases by 2 units: Z --> Z-2
- its mass number decreases by 4 units: A --> A-4
The energy of a photon is directly proportional to its
directly proportional to its frequency
A wooden block with mass 1.45 kg is placed against a compressed spring at the bottom of a slope inclined at an angle of 29.0 degrees (point A). When the spring is released, it projects the block up the incline. At point B, a distance of 4.60 m up the incline from A, the block is moving up the incline at a speed of 5.10 m/s and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is μk=0.45. The mass of the spring is negligible.A.Calculate the amount of potential energy that was initially stored in the spring.Take free fall acceleration to be 9.80 m/s2 .
Answer:
76.3 J
Explanation:
I'm assuming the distance of 4.60 m is along the incline, not the vertical distance from the bottom. I'll call this distance d, so h = d sin θ.
Initial energy = final energy
Energy in spring = gravitational energy + kinetic energy + work by friction
E = mgh + 1/2 mv² + Fd
We need to find the force of friction. To do that, draw a free body diagram.
Normal to the incline, we have the normal force pointing up and the normal component of weight (mg cos θ).
Sum of the forces in the normal direction:
∑F = ma
N - mg cos θ = 0
N = mg cos θ
Friction is defined as:
F = Nμ
Plugging in the expression for N:
F = mgμ cos θ
Substituting:
E = mgh + 1/2 mv² + (mgμ cos θ) d
E = mg (d sin θ) + 1/2 mv² + (mgμ cos θ) d
E = mgd (sin θ + μ cos θ) + 1/2 mv²
Given:
m = 1.45 kg
g = 9.90 m/s²
d = 4.60 m
θ = 29.0°
μ = 0.45
v = 5.10 m/s
Solving:
E = mgd (sin θ + μ cos θ) + 1/2 mv²
E = (1.45) (9.80) (4.60) (sin 29.0 + 0.45 cos 29.0) + 1/2 (1.45) (5.10)²
E = 76.3 J
The amount of potential energy initially stored in the spring is 49.3 J.
Explanation:To calculate the amount of potential energy initially stored in the spring, we need to consider the conservation of mechanical energy. At the bottom of the slope, the initial potential energy stored in the spring is converted to a combination of kinetic energy and gravitational potential energy as the block moves up the incline. We can use the equation:
PE(initial) = KE(final) + PE(final)
Substituting the given values and using the fact that the block is moving at a constant velocity up the incline, we can solve for the initial potential energy and find that it is 49.3 J.
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An object is located 5.0 cm from a concave mirror. The focal length is 15.0 cm. What is the image distance? Use the equation attached.
A.3.8 Cm
B.-3.8 Cm
C.-7.5 Cm
D.7.5 Cm
Answer:
-7.5 cm
Explanation:
OK so in the equation they're having you use the variables are:
[tex]d_o = 5.0 cm\\\\f = 15.0 cm\\\\d_i = ?[/tex]
So we simply plug in the variables:
[tex]d_i = \frac{d_of}{d_o-f} \\\\d_i = \frac{5.0 * 15.0}{5.0 - 15.0}\\\\d_i = \frac{75}{-10}\\\\d_i = -7.5 cm[/tex]
Answer:
C. -7.5 cm
Explanation:
got it right, trust
What is the source of energy across the entire spectrum
The answer to your question is Sun.
Which way does light bend when traveling from glass to air?
A. Toward the normal
B. Away from the normal
C. It does not bend
I think its B. Away from the normal because light speeds up going into a less dense substance, and the ray bends away from the normal.
Option B is the right answer!
Explanation :
When light rays travel from air into glass or from air into water, it bends towards normal. This is because the speed of light rays decrease while travelling from air into glass or water .
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If the voltage across a circuit of constant resistance is doubled, the power dissipated by that circuit will
Answer:
The voltage will quadruple
Explanation:
The power dissipated in a circuit is given by
[tex]P=\frac{V^2}{R}[/tex]
where
V is the voltage
R is the resistance
In this problem, the voltage across the circuit is doubled:
V' = 2V
So the new power dissipated is
[tex]P'=\frac{V'^2}{R}=\frac{(2V)^2}{R}=4\frac{V^2}{R}=4 P[/tex]
so, the power dissipated will quadruple.
When the voltage across a circuit of constant resistance is doubled, the current doubles and the power dissipated increases by a factor of four.
To understand what happens when the voltage across a circuit of constant resistance is doubled, we need to refer to Ohm's Law and the formula for electrical power dissipation.
Ohm's Law states that the current through a resistor is directly proportional to the voltage across it and inversely proportional to the resistance
I = V / R
Therefore, if the voltage is doubled, the current will also double, assuming the resistance remains constant.
The power dissipated by a resistor can be calculated using the formula:
[tex]P = V^2 / R[/tex]
When the voltage is doubled, the expression for power becomes:
[tex]P = (2V)^2 / R \\= 4V^2 / R[/tex]
This means that doubling the voltage will result in the power being multiplied by a factor of four.
Thus,when the voltage across a circuit of constant resistance is doubled, the current will double, and the power dissipated by the circuit will increase by a factor of four.
What is the most common fuel used in nuclear power plants
Answer:
uranium
Explanation:
it is radioactive
Answer:
UraniumExplanation:
uranium is the most common fuel used in a nuclear power because actinides produced by neutron captureA clay pot at room temperature is placed in a kiln, and the pot\'s temperature doubles. how much more heat per second is the pot radiating when hot compared to when cool?
Answer:
16
Explanation:
If we treat the pot as a black body, then:
q = σ T⁴ A,
where q is the heat per second radiated,
σ is the Stefan-Boltzmann Constant,
T is the absolute temperature,
and A is the surface area.
If the absolute temperature doubles, then q increases by a factor of 2⁴ = 16.
What can Lisa do to increase the strength of the electromagnet?
She can use a nail with weaker magnetic properties.
She can change the direction of the nail.
She can move the wire loops closer together.
She can reduce the number of wire loops.
Answer:
move the wire loops closer
Explanation:
because the closer t they are the more concentrated the energy is in that specific area
Lisa can move the wire loops closer together to increase the strength of the electromagnet. Option C is correct.
What is electromagnet?An electromagnet is a magnet whose magnetic field is generated by an electric current. Wire coiled into a coil is used to make electromagnets.
A current flowing through the wire produces a magnetic field that is focused in the hole.
The strength of the electromagnet is increased by;
Adding further twists to the coil by wrapping it around a piece of iron and increasing the amount of electricity that flows through the coil.
Hence, option C is correct.
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The gravitational force between two objects is 1600 N what will be the gravitational force if they double
Final answer:
The new gravitational force between the two objects will be 6400 N.
Explanation:
The gravitational force between two objects can be calculated using Newton's law of gravitation, which states that the gravitational force (F) is directly proportional to the product of the masses of the objects (M1 and M2) and inversely proportional to the square of the distance between their centers (r).
So, if the gravitational force between two objects is initially 1600 N and the masses of the objects are doubled, the new gravitational force (F') can be calculated using the equation:
F' = (2M1)(2M2)G / (r^2)
Substituting the values into the equation and simplifying, we get:
F' = 4F
Therefore, the new gravitational force will be 4 times the initial force, which is 4 * 1600 N = 6400 N.
Why you cannot use an elastic measuring tape to measure distance. What problem you may face if you use it
The problem you would encounter is measuring the height of two different people, a tall one and a short one, and getting the same answer for both of them.
No matter WHAT we're hearing out of the White House these days, you CAN'T bend and stretch your standard measuring devices, or any other 'facts', to make them fit the thing that you're measuring. This does not work. You're always entitled to your own opinions, but you're not entitled to your own facts.
An elastic measuring tape should not be used to measure distance because its stretchability can lead to inaccurate and unreliable measurements.
Explanation:You cannot use an elastic measuring tape to measure distance accurately because it can stretch, which would result in an unreliable measurement. The problem you may face if you use an elastic measuring tape is that the stretching of the tape will lead to incorrect measurements, especially if the distances being measured require precise and firm measurement tools. Measuring tapes are typically flexible but maintain their length without stretching to ensure that measurements are consistent. For accurate measurement of length or distance, you should select a measuring tool that is suited to the size you are trying to measure, ranging from a ruler for small items to a yardstick or a non-elastic measuring tape for larger distances.
The magnetic field about a straight length of current-carrying wire is _________.
a. similar to the shape of an electric field about a charged wire
b. circular in shape
c. aligned from north to south poles in the wire
d. in accord with the inverse-square law
Answer:
b. circular in shape
Explanation:
The magnetic field around a current-carrying wire forms concentric circles around the axis of the wire. In particular, the direction of the field lines can be found by using the right hand rule:
- the thumb must be placed along the direction of the current in the wire
- the other fingers, wrapped around the wire, give the direction of the magnetic field lines
The strenght of the magnetic field around the wire decreases linearly with the distance from the wire, according to the equation:
[tex]B=\frac{\mu_0 I}{2\pi r}[/tex]
where
[tex]\mu_0[/tex] is the vacuum permeability
I is the current in the wire
r is the distance from the wire
B. In the vicinity of Earth’s orbit around the Sun, the energy intensity of sunlight is about 1600 W/m2 . What is the approximate magnitude of the electric field in the sunlight?
Answer:
1097.8 V/m
Explanation:
The equation that relates the intensity of an electromagnetic wave with the magnitude of the electric field is:
[tex]I=\frac{1}{2}c\epsilon_0 E^2[/tex]
where
c is the speed of light
[tex]\epsilon_0[/tex] is the vacuum permittivity
E is the peak magnitude of the electric field
In this problem, we know the intensity:
I = 1600 W/m^2
So we can rearrange the formula to find E:
[tex]E=\sqrt{\frac{2I}{c\epsilon_0}}=\sqrt{\frac{2(1600 W/m^2)}{(3\cdot 10^8 m/s)(8.85\cdot 10^{-12} F/m)}}=1097.8 V/m[/tex]
Who was the first american to orbit the earth?
Answer:
John Glenn
Explanation:
Answer:
John Glenn was the first American to orbit the Earth. The first human in space was the Soviet cosmonaut Yuri Gagarin.
Explanation:
Hope this helps. Feel free to let me know if you need any more help :)
If we use 1 millimeter to represent 1 light-year, how large in diameter is the Milky Way Galaxy?
a.100 millimeters
b.100 kilometers
c.1 kilometer
d.100 meters
e.1 million millimeters
Answer:
d.100 meters
Explanation:
The diameter of the Milky Way Galaxy is approximately 100,000 light years.
Here we are using 1 millimiter (1 mm) to represent 1 light-year (1 ly). So, we can set the following proportion:
[tex]1 mm : 1 ly = x : 100,000 ly[/tex]
and by finding x, we find the diameter of the Milky Way Galaxy in the scale used:
[tex]x=\frac{(1mm )(100,000 ly)}{1 ly}=100,000 mm = 100 m[/tex]
so the correct answer is
d. 100 meters
Final answer:
Using a scale where 1 millimeter represents 1 light-year, the diameter of the Milky Way Galaxy at 100,000 light-years translates to 100,000 millimeters, which is equivalent to 100 meters. The correct answer is (d) 100 meters.
Explanation:
The Milky Way Galaxy has a diameter of approximately 100,000 light-years. To convert light-years to millimeters, we use a scale where 1 millimeter represents 1 light-year. Therefore, the Milky Way Galaxy's diameter would be 100,000 millimeters, which can be converted to meters by dividing by 1,000 (since there are 1,000 millimeters in a meter).
100,000 millimeters / 1,000 = 100 meters. So, the diameter of the Milky Way Galaxy, when represented at a scale of 1 millimeter per light-year, is 100 meters. Hence, the correct answer is (d) 100 meters.
Which portion of the electromagnetic spectrum is used in a television?
a) infrared waves
b) X-rays
c) radio waves
d) gamma waves
Radio waves are a type of electromagnetic radiation with wavelengths between 10 m to 10,000 m. In the electromagnetic spectrum this wavelength is longer than infrared light and therefore, it goes beyond the visible spectrum.
This type of electromagnetic waves is very well reflected in the ionosphere, the layer of the atmosphere through which they travel directly or using repeaters.
In addition, they are very useful to transport information, being important in telecommunications. They are used not only for conventional radio transmissions but also in mobile telephony and TV.
It should be noted that since radio signals have large wavelengths, they can be diffracted around certain obstacles, such as hills and mountain ranges, preventing the signal from reaching its destination.
Therefore, the correct option is C.
Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 4.57 x 10^(-21) N?
Answer:
894 electrons
Explanation:
The electrostatic force between the two charges is given by:
[tex]F=\frac{k q_1 q_2}{r^2}[/tex]
where we have
[tex]F=4.57\cdot 10^{-21} N[/tex] is the force
k is the Coulomb's constant
q1 = q2 =q is the magnitude of the charge on each sphere
r = 20.0 cm = 0.20 m is the distance between the two spheres
Substituting and solving for q, we find the charge on each sphere:
[tex]q=\sqrt{\frac{Fr^2}{k}}=\sqrt{\frac{(4.57\cdot 10^{-21} N)(0.20 m)^2}{9\cdot 10^9 Nm^2C^{-2}}}=1.43\cdot 10^{-16} C[/tex]
And since each electron has a charge of
[tex]e=1.6\cdot 10^{-19}C[/tex]
the net charge on each sphere will be given by
[tex]q=Ne[/tex]
where N is the number of excess electrons; solving for N,
[tex]N=\frac{q}{e}=\frac{1.43\cdot 10^{-16}C}{1.6\cdot 10^{-19}C}=894[/tex]
Using Coulomb's Law and the given values, we find that each sphere must have approximately 891 excess electrons to produce a repulsive force of [tex]4.57 \times 10^{-21} N[/tex] at a distance of 20 cm.
To solve this problem, we will use Coulomb's Law, which is given by:
[tex]F = k_e \times (q_1 \times q_2) / r^2[/tex]
Where:
F is the force of repulsion between the charges.[tex]k_e[/tex] is Coulomb's constant ([tex]8.99 \times 10^9 N m^2/C^2[/tex]).q₁ and q₂ are the charges (since the charges are equal, we can use q²).r is the distance between the charges.Given data:
[tex]F = 4.57 \times 10^{-21} N[/tex][tex]r = 20.0\left cm = 0.20\left m[/tex]We can rearrange Coulomb's Law to solve for the charge:
[tex](q_1 \times q_2) = F \times r^2 / k_e[/tex]Since [tex]q_1 = q_2 = q[/tex], the equation becomes:
[tex]q^2 = F \times r^2 / k_e[/tex]Now, we can plug in the values:
[tex]q^2 = (4.57 \times 10^{-21} N) \times (0.20 m)^2 / (8.99 \times 10^9 N m^2/C^2)[/tex][tex]q^2 = 4.57 \times 10^{-21} \times 0.04 / 8.99 \times 10^9[/tex][tex]q^2 = 1.828 \times 10^{-22} / 8.99 \times 10^9[/tex][tex]q^2 \approx 2.034 \times 10^{-32}[/tex]Taking the square root of both sides, we get:
[tex]q \approx 1.426 \times 10^{-16} C[/tex]Since we need to find the number of excess electrons, we divide by the elementary charge ([tex]e = 1.6 \times 10^{-19} C[/tex]):
Number of excess electrons [tex]\approx 1.426 \times 10^{-16} C / 1.6 \times 10^{-19} C/electron[/tex]Number of excess electrons [tex]\approx 891\left electrons[/tex]So, each sphere must have approximately 891 excess electrons to produce the given force of repulsion.