To find the distances and times at which the two cars pass each other, we can use equations of motion. The car passes the Porsche at 20 meters and 2 seconds after the light turns green. The Porsche passes the car at 60 meters and 5 seconds after the light turns green.
Explanation:To solve this problem, we will use equations of motion to find the distances and times at which the two cars pass each other. Given that the Porsche starts from rest and accelerates at 3 m/s², we can use the equation x = xo + vot + ½at² to find the distance it travels before the other car reaches it. Similarly, for the other car which is traveling at a constant speed of 10 m/s, we can use the equation x = Ut. By solving these equations simultaneously, we can find the distances and times at which the two cars pass each other.
a. The distance at which you pass the Porsche can be found by setting the distances traveled by both cars equal to each other: 10t = 15 + 0.5(3)(t²). By solving this equation, we find that you pass the Porsche at a distance of 20 m from the stop line and at a time of 2 seconds after the light turns green.
b. To find the distance at which the Porsche passes you, we need to find the time at which the Porsche catches up to you. We can do this by setting the equation for the Porsche's distance equal to your distance: 15 + 0.5(3)(t²) = 10t. Solving this equation gives us a time of 5 seconds after the light turns green. Plugging this time into the equation for your distance, we find that the Porsche passes you at a distance of 60 meters from the stop line.
c. To determine if either of you will be pulled over for speeding, we need to compare your speeds to the speed limit of 50 km/h. Your speed is given as 36 km/h (10 m/s), which is less than the speed limit. The Porsche's speed can be found by taking the derivative of its distance equation with respect to time: v = at. Plugging in the time at which it passes you, we find that its speed is 30 m/s, which is also less than the speed limit. Therefore, neither of you will be pulled over for speeding.
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You pass the Porsche 16.65 meters beyond the stop line at 3.33 seconds, while the Porsche catches up 66.7 meters from the stop line at 6.67 seconds. Only the Porsche would be pulled over for speeding. The primary topic is the analysis of two moving vehicles using physics.
Part (a): When Do You Pass the Porsche?Your car's constant speed is [tex]36 km/h[/tex] or [tex]10 m/s[/tex] . The Porsche accelerates from rest at [tex]3 m/s^2[/tex].
Calculate the time it takes for the Porsche to reach your speed:
Using the equation: [tex]v = u + at[/tex],
where[tex]v = 10 m/s[/tex],[tex]u = 0[/tex], and[tex]a = 3 m/s^2[/tex], we get [tex]t = v/a = 10/3 \approx 3.33 seconds[/tex].
Now, find the distance the Porsche covers in this time with the equation: [tex]s = ut + 0.5at^2[/tex], where[tex]u = 0[/tex], [tex]a = 3 m/s^2[/tex] and [tex]t = 3.33 seconds[/tex],
thus [tex]s = 0.5 \times 3 \times 3.332 \approx 16.65 meters[/tex].
Your car covers [tex]3.33 \times 10 = 33.3 meters[/tex] in this same time.
Hence, you pass the Porsche [tex]33.3 - 16.65 = 16.65 meters[/tex] beyond the stop line.
Part (b): When Does the Porsche Pass You Again?To find when the Porsche catches up, consider the distance equations for both vehicles:
Your distance: [tex]d_{you}(t) = 10t[/tex].
Porsche’s distance: dporsche(t) = 0.5 * 3 * t2.
Set the distances equal to solve for [tex]t: 10t = 1.5t2[/tex], leading to [tex]t = 0[/tex] or [tex]t = 10/1.5 = 6.67 seconds[/tex].
The Porsche catches up [tex]0.5 \times 3 \times 6.672 = 66.7[/tex]meters from the stop line.
Part (c): Speeding CheckDetermine both cars' speeds when the Porsche passes you again:
Your speed:[tex]10 m/s = 36 km/h[/tex], under the limit.
Porsche’s speed: [tex]v = u + at = 3 \times 6.67 = 20.01 m/s \approx 72 km/h[/tex], over the limit.
Thus, only the Porsche would be pulled over for speeding.
Use the following half-life graph to answer the following question:
A graph titled half-life graph of a radioactive isotope is shown with mass remaining on the y axis from 0 to 60 grams and time on the x axis from o to 6 minutes. A curve connects the points 0, 50 and 1, 25 and 2, 12.5 and 3, 6.25 and 4, 3.125 and 5, 1.5625.
The graph is attached.
What is the half-life of the isotope? (5 points)
A. 1.0 min
B. 3.0 min
C. 5.0 min
D. 6.0 min
Answer:
A 1.0 min
Explanation:
The half-life of a radioisotope is defined as the time it takes for the mass of the isotope to halve compared to the initial value.
From the graph in the problem, we see that the initial mass of the isotope at time t=0 is
[tex]m_0 = 50.0 g[/tex]
The half-life of the isotope is the time it takes for half the mass of the sample to decay, so it is the time t at which the mass will be halved:
[tex]m'=\frac{50.0 g}{2}=25.0 g[/tex]
We see that this occurs at t = 1.0 min, so the half-life of the isotope is exactly 1.0 min.
Answer:a
Explanation:test
Which characteristic is common to microwave radar, waves ,and television waves? A they are different types of waves with frequencies higher than radio waves B they are all radio waves with frequencies lower than visible light C they are all radio waves with wavelength shorter than visible light
Answer:
B they are all radio waves with frequencies lower than visible light
Explanation:
The electromagnetic spectrum classifies all the electromagnetic waves according to their frequency. In order from highest to lowest frequency, we have:
Gamma rays
X-rays
Ultraviolet
Visible light
Infrared
Microwaves
Radio waves
In particular, radio waves are the electromagnetic waves with lowest frequency (and longest wavelength), usually less than 300 GHz ([tex]300\cdot 10^9 Hz[/tex]).
Microwaves radar, radio waves and television waves are all examples of radio waves, which have frequencies lower than visible light. Radio waves are generally used for long-range communications, because given their long wavelength they are able to "bypass" huge obstacles like mountains or building, without being absorbed.
Answer:
B they are all radio waves with frequencies lower than visible light
Explanation:
Please help on this one?
the object distance of both lenses are positive.
A night lamp uses a 30 W bulb. If it is left on continuously for 8 hours, how much energy will it use?
_____ kWh
The answer was 0.24!
Answer:
Explanation:
[tex] 30W * 8 h = 240 Wh = 0.240 kWh[/tex]
Answer:
0.24 kWh
Explanation:
When humans look at the sky, it appears blue, but the Sun appears yellow. What causes this phenomenon?
Light behaves like a wave, and the different colors we perceive are the result of light hitting our eyes at different wavelengths. The air molecules in our atmosphere scatter this visible light, with a "preference" towards light of shorter wavelengths -- blue and violet light. Light of longer wavelengths (green, yellow, orange, red), doesn't pass through to us as visibly until later in the day, when the sun's light has more atmosphere to pass through before it reaches our eyes. The blue light becomes so scattered by the air molecules in its way at this point that we're finally able to see those yellows and reds coming through on our end.
Why is the answer B for this problem?
Answer:
B
Explanation:
This looks like a momentum question. It also looks like there is no horizontal acceleration.
Momentum before Momentum after
m1vo (m1 + m2)*vo/3 multiply through by 3
3 m1*vo m1* vo + m2*vo subtract m1*vo from both sides
3m1*vo - m1*vo m2*vo
2m1*vo m2*vo Divide by vo
2m1 = m2
Conclusion: It takes 2 m1's to equal 1 m2.
B is the answer.
Planets in our solar system do not revolve around the sun in perfect circles. Their orbits are more like ovals. Which term do scientist use to describe these orbits
Answer:
It is most likely the word elliptical.
Explanation:
Usually the term elliptical refers to the oval-like shape of a substance or path of an object. The question states, "Planets in our solar system do not revolve around the sun in perfect circles. Their orbits are more like ovals." Because the planets orbit around the sun in an oval-like path, those orbits can be described as elliptical. Scientists also normally use this word to describe the same thing; Therefore, your answer is elliptical.
Planets in our solar system do not revolve around the sun in perfect circles. They revolve in the elliptical orbits.
What is the solar system?The solar system consists of the planet's satellites, as well as numerous comets, asteroids, and meteoroids, as well as the interplanetary medium.
Planets in our solar system do not revolve around the sun in perfect circles. They revolve in the elliptical orbits.
Hence, option D is correct.
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Which of the following is the best paraphrasing of the Heisenberg uncertainty principle?
(a) Only if you know the exact position of a particle can you know the exact momentum of the particle.
(b) The larger the momentum of a particle, the smaller the position of the particle.
(c) The more precisely you know the position of a particle, the less well you can know the momentum of the particle.
(d) The better you know the position of a particle, the better you can know the momentum of the particle.
(e) How well you can determine the position and momentum of a particle depends on the particle’s quantum numbers.
The Heisenberg uncertainty principle was enunciated in 1927. It postulates that the fact that each particle has a wave associated with it, imposes restrictions on the ability to determine its position and speed at the same time.
In other words:
It is impossible to measure simultaneously (according to quantum physics), and with absolute precision, the value of the position and the momentum (linear momentum) of a particle.
So, the greater certainty is seeked in determining the position of a particle, the less is known its linear momentum and, therefore, its mass and velocity.In fact, even with the most precise devices, the uncertainty in the measurement continues to exist. Thus, in general, the greater the precision in the measurement of one of these magnitudes, the greater the uncertainty in the measure of the other complementary variable.
Therefore the correct option is C.
Two identical metal bars are heated up until they are both glowing. One of them is "red hot" and the other is "blue hot." Which one is hotter, the one that glows red or the one that glows blue?A) the red oneB) the blue oneC) We cannot tell without knowing more about the two bars.
Answer:
B) the blue one
Explanation:
We can assimilate each metal bar to a black body. The peak wavelength of the radiation emitted by a blackbody is given by Wien's displacement law:
[tex]\lambda = \frac{b}{T}[/tex] (1)
where
b is the Wien's displacement constant
T is the absolute temperature of the object
In this case, we have one object hotter and the other one colder. We see from (1) that the peak wavelength is inversely proportional to the temperature: therefore, the hotter object will have shorter peak wavelength, while the colder object will have longer peak wavelength.
Since red light has longer wavelength than blue light, we can conclude that the object that glows blue is hotter than the one that glows red.
Which type of tissue allows for cordination and control movement ?
The Nerve Tissue allows for coordination and control movement
Nervous tissue is used for coordination and control movement.
Explanation:
The group of organized cells that is in the nervous system, which is responsible in controlling the movements of the human body, sending and carrying signals to and from different body parts is called Nervous tissue. It is also responsible in controlling functions in the body like digestion.
This tissue is classified into categories such as neurons and neroglia. The electric impulses are transmitted by neurons and supporting and protecting neurons is done by neuroglia. The whole nervous system is comprised of neurons.
A 800 J
B -800 J
C 400 J
D -400 J
??
I think it will be 800j because right absorb mean getting more
The change in internal energy of the system is 400 joules. The correct answer is: C. 400 J
To determine the change in internal energy of a system that does 200 joules of work and absorbs 600 joules of heat, we can use the first law of thermodynamics. The first law of thermodynamics states:
[tex]\[ \Delta U = Q - W \][/tex]
[tex]\(\Delta U\)[/tex] is the change in internal energy,
Q is the heat added to the system,
W is the work done by the system.
In this problem:
Q = 600 joules (heat absorbed by the system),
W = 200 joules (work done by the system).
Substituting the given values into the equation:
[tex]\[ \Delta U = 600\, \text{J} - 200\, \text{J} \][/tex]
[tex]\[ \Delta U = 400\, \text{J} \][/tex]
The electrical force between two objects 36N. If the distance between the two objects is doubled the force between them will be
Answer:
The electrical force is 9N
Explanation:
For point loads, charged bodies very small compared to the distance r that separates them, Coulomb discovered that the electric force is proportional to [tex]\frac{1}{r^{2}}[/tex]. So, if the distance is doubled, the force will decrease a [tex]\frac{1}{4}[/tex] of its initial value.
[tex]F=\frac{36N}{4}=9N[/tex]
When the distance between two charged objects is doubled, the electrostatic force between them becomes one-fourth of the original force. Thus, if the original force is 36 N, the new force would be 9 N.
Explanation:The force between two charges is governed by Coulomb's Law, which states that the electrostatic force (F) between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance (r) between them. The law is mathematically expressed as F = k * (|q1*q2|) / r², where k is Coulomb's constant. If the distance between two charges is doubled, since the force is inversely proportional to the square of the distance, the new force will be one-fourth of the original force.
Thus, if the initial force is 36 N and the distance is doubled, the new force is calculated as:
Initial force: 36 N
New distance: 2r
New force (F') = F / (22) = 36 N / 4 = 9 N
Therefore, the new electrostatic force between the two objects when the distance is doubled would be 9 N.
What do we mean by the event horizon of a black hole?
A) It is the place where X rays are emitted from black holes.B) It is the very center of the black hole.C) It is the point beyond which neither light nor anything else can escape.D) It is the distance from the black hole at which stable orbits are possible.
The correct answer is: C. It is the point beyond which neither light nor anything else can escape.
The event horizon of a black hole is the boundary where the escape velocity is equal to the speed of light, making it impossible for anything, including light, to escape. It's defined by the Schwarzschild radius and increases in size with additional mass. The center is thought to contain a singularity, which is infinitely dense and small.
Explanation:The event horizon of a black hole is the boundary beyond which nothing, including light, can escape its gravitational pull. It corresponds to the distance at which the escape velocity equals the speed of light. This boundary is known as the Schwarzschild radius, which is directly proportional to the mass of the black hole. The event horizon is not visible because it does not emit any light; however, it can be inferred by observing the effects of its powerful gravity on nearby matter and radiation.
The size of the Schwarzschild radius (and therefore the event horizon) depends only on the mass of the black hole. If our Sun were to collapse into a black hole, which is purely a theoretical scenario since it lacks sufficient mass, its Schwarzschild radius would be approximately 3 kilometers. Any additional mass added to the black hole would increase the size of its event horizon proportionally.
Inside the event horizon, the center of the black hole is thought to contain a singularity, a point of infinite density and zero volume, which is not directly observable. As matter crosses the event horizon, it seems to freeze in position to an outside observer due to the extreme gravitational effects on lt's travel, but would, in reality, continue to fall inward toward the singularity.
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The diagram below illustrates the law of reflection.
Which is the angle of reflection?
A
B
C
D
C Is the angle of reflection. The reflected ray is consistently in the plane determined by the incident ray and perpendicular to the surface at the point of reference of the incident ray.
What is the law of reflection?The law of reflection specifies that upon reflection from a downy surface, the slope of the reflected ray is similar to the slope of the incident ray.
When the light rays descend on the smooth surface, the angle of reflection is similar to the angle of incidence, also the incident ray, the reflected ray, and the normal to the surface all lie in a similar plane.
Hence,C Is the angle of reflection.
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In an isobaric compression of an ideal gas
a. no heat flows into gas.
b. the internal energy of the gas remains constant
c. no work is done on the gas
d. work is done on the gas
e. work is done by the gas
Answer:
d. Work is done on the gas
Explanation:
We are considering an isobaric compression, which means:
- Isobaric: the pressure of the gas is constant
- Compression: the volume of the gas is decreasing
For an isobaric compression, the volume done BY the gas is
[tex]W=p \Delta V= p (V_f -V_i)[/tex]
where
p is the gas pressure
[tex]V_f[/tex] is the final volume of the gas
[tex]V_i[/tex] is the initial volume of the gas
If the sign of W is positive, it means that the gas is doing work on the surrounding; if the sign of W is negative, it means that the surrounding is doing worn ON the gas.
In this case, since it is a compression, we have that the final volume is smaller than the initial volume:
[tex]V_f < V_i[/tex]
Therefore, the sign of W is negative, and therefore work is done ON the gas by the surroundings.
Final answer:
In an isobaric compression, work is done on the gas by the force exerted on the movable piston.
Explanation:
In an isobaric compression of an ideal gas,(option d) work is done on the gas. This means that energy is transferred to the gas through mechanical work. To understand this, let's consider a piston-cylinder system.
During an isobaric compression, the gas is compressed while the pressure remains constant. The gas particles push against the piston, causing it to move, and thus work is done on the gas.
This work is done by the force exerted on the movable piston, which causes a displacement. As a result, the volume and temperature of the gas decrease, indicating that the gas's internal energy has been decreased by doing work.
What is the element with the lowest electronegativity value?
Let's start by explaining that electronegativity is a term coined by Linus Pauling and is determined by the ability of an atom of a certain element to attract electrons when chemically combined with another atom.
So, the more electronegative an element is, the more electrons it will attract.
It should be noted that this value can not be measured directly by experiments, but it can be determined indirectly by means of calculations from other atomic or molecular properties of the element. That is why the scale created by Pauling is an arbitrary scale, where the maximum value of electronegativity is 4, assigned to Fluorine (F) and the lowest is 0.7, assigned to Francium (Fr).
Francium is the element with the lowest electronegativity value, which is determined by factors such as atomic number, distance from the nucleus to the valence electrons, and effective nuclear charge. Fluorine, on the other hand, has the highest electronegativity value. While electron-electron repulsion and electron affinity can influence electronegativity, they are different atomic properties.
Explanation:The element with the lowest electronegativity value is francium. Electronegativity, which describes how tightly an atom attracts electrons in a bond, is a dimensionless quantity that is calculated rather than measured. It depends on several factors, including the atomic number and the distance from the nucleus to the valence electrons.
Francium has the lowest electronegativity value mostly due to its large size and its single valence electron which is located very far from the nucleus. Hence, the electron is not strongly attracted to the nucleus, resulting in a low electronegativity. Comparably, Fluorine is given the highest electronegativity value of 4 on the Pauling scale, due to its small size and high effective nuclear charge.
Various other factors such as electron-electron repulsion, electron affinity, and formal charge can also influence electronegativity. Please remember that these factors should not be confused with electronegativity itself as they correspond to different atomic properties.
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During a solar eclipse, the Moon, Earth, and Sun all lie on the same line, with the Moon between the Earth and the Sun. Answer all questions to 3 significant figures. (a) What force is exerted by the Sun on the Moon? WebAssign will check your answer for the correct number of significant figures. Incorrect: Your answer is incorrect. Enter a number. (b) What force is exerted by the Earth on the Moon? WebAssign will check your answer for the correct number of significant figures. (c) What force is exerted by the Sun on the Earth? WebAssign will check your answer for the correct number of significant figures.
(a) [tex]4.40\cdot 10^{20}N[/tex]
The distance between the Sun and the Earth is
[tex]d_{SE}=1.496 \cdot 10^11 m[/tex]
The distance between the Earth and the Moon is
[tex]d_{EM} = 3.84\cdot 10^8 m[/tex]
So, the distance between the Sun and the Moon, when the Moon is between the Earth and the Sun, is
[tex]d_SM = 1.496\cdot 10^{11}m -3.84\cdot 10^8 m=1.492\cdot 10^{11} m[/tex]
So the gravitational force between the Sun and the Moon is
[tex]F_{SM} = G \frac{M_S M_M}{d_{SM}^2}[/tex]
where
G is the gravitational constant
[tex]M_S = 1.988 \cdot 10^{30}kg[/tex] is the mass of the Sun
[tex]M_M = 7.384\cdot 10^{22}kg[/tex] is the mass of the Moon
[tex]d_{SM}=1.492\cdot 10^{11} m[/tex] is their distance
Substituting,
[tex]F_{SM} = (6.67\cdot 10^{-11}) \frac{(1.988\cdot 10^{30} kg)(7.384\cdot 10^{22}kg)}{(1.492\cdot 10^{11} m)^2}=4.40\cdot 10^{20}N[/tex]
(b) [tex]2.00\cdot 10^{20}N[/tex]
The gravitational force between the Earth and the Moon is
[tex]F_{EM} = G \frac{M_E M_M}{d_{EM}^2}[/tex]
where
G is the gravitational constant
[tex]M_E = 5.972 \cdot 10^{24}kg[/tex] is the mass of the Earth
[tex]M_M = 7.384\cdot 10^{22}kg[/tex] is the mass of the Moon
[tex]d_{EM}=3.84\cdot 10^{8} m[/tex] is their distance
Substituting,
[tex]F_{EM} = (6.67\cdot 10^{-11}) \frac{(5.972\cdot 10^{24} kg)(7.384\cdot 10^{22}kg)}{(3.84 \cdot 10^{8} m)^2}=2.00\cdot 10^{20}N[/tex]
(c) [tex]3.54\cdot 10^{22}N[/tex]
The gravitational force between the Earth and the Sun is
[tex]F_{ES} = G \frac{M_E M_S}{d_{ES}^2}[/tex]
where
G is the gravitational constant
[tex]M_E = 5.972 \cdot 10^{24}kg[/tex] is the mass of the Earth
[tex]M_S = 1.988 \cdot 10^{30}kg[/tex] is the mass of the Sun
[tex]d_{SE}=1.496 \cdot 10^{11} m[/tex] is their distance
Substituting,
[tex]F_{ES} = (6.67\cdot 10^{-11}) \frac{(5.972\cdot 10^{24} kg)(1.988\cdot 10^{30}kg)}{(1.496 \cdot 10^{11} m)^2}=3.54\cdot 10^{22}N[/tex]
To derive the force exerted by the Sun on the Moon the Earth on the Moon and the Sun on the Earth during a solar eclipse, you apply Newton's law of universal gravitation taking into account the respective masses of the Sun, Earth, and Moon as well as their distances from each other.
Explanation:Determining the force exerted between celestial bodies during a solar eclipse involves understanding the gravitational relationship between them; primarily the gravitational forces between the Earth, Moon, and the Sun, and the principles of celestial mechanics.
Firstly, we know that the force of gravity follows Newton's law of universal gravitation: F = G (m1m2/r^2),where F is the force of gravity, m1 and m2 are the masses of the two bodies involved, r is the distance between the centers of the two bodies, and G is the gravitational constant.
For any of the specific forces asked in the question (i.e., the force exerted by the Sun on the Moon force exerted by the Earth on the Moon, and the force exerted by the Sun on the Earth), we would need specific values for the masses of the Sun, Earth, and Moon as well as their respective distances. Once those values are known, you can substitute into the above equation to obtain the force.
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Which planet is named after the roman god of the sea
The answer is: Neptune
Answer:
Explanation:
the answer is Neptune
Tim adds salt as he starts to heat a pot of water to cook pasta. When the water is boiling, he notices the salt has dissolved
Answer:
The salt is dissolved by the water and heat. If the pot isn't boiling, the salt wouldn't dissolve, it would stay undissolved.
Seyed made a chart to compare Einstein's and Newton's ideas about time and space.
Which best completes the chart?
The speed of light is absolute.
The speed of light varies.
Space is three-dimensional.
Space is four-dimensional.
Answer:
space is three dimensional
Answer: Space is three-dimensional
Explanation: For Newton, space time forms a three-dimensional universe, with the characteristic of an absolute void that determines the order of the things that compose it.
This is a map that shows hot spots around the world.
Which phrases describe the formation of the Hawaiian Islands? Check all that apply.
formed due to subduction
formed in the middle of a plate
formed at a divergent boundary
formed at a convergent boundary.
formed where mantle erupts through crust
Answer:
formed in the middle of a plate
formed where mantle erupts through crust
Explanation:
The Hawaiian Islands are Volcanoes that formed right in the middle of the Pacific plate which is moving North-westward.
Lithospheric plates lies on the weak and plastic asthenosphere. Such is the Pacific plate too. The weak asthenosphere can erupt on the surface if it gets access through faulting or other geologic conduits. When these mantle magma reaches the surface, they form hotpots on the crust.
The Hawaiian island is a series of these hotspot as it forms when mantle materials upwells to the surface. The hotspot from which the magma is sourced is relatively fixed. The moving plate is what leads to the eruption of the magma at several other parts in the crust.
Vector A has a magnitude of 50 units and points in the positive x direction. A second vector, B , has a magnitude of 120 units and points at an angle of 70 degrees below the x axis.
Part A
Which vector has the greater x component.
Part B
Which vector has the greater y component?
Vector A has the greater x-component, while vector B has the greater y-component.
Explanation:The x-component of a vector can be calculated by multiplying its magnitude by the cosine of the angle it makes with the x-axis. For vector A, the x-component is 50 units (since it lies entirely on the x-axis). For vector B, the x-component equals 120 units * cos(70 degrees) = 40.96 units. So, vector A has the greater x-component.
The y-component of a vector can be calculated by multiplying its magnitude by the sine of the angle it makes with the x-axis. For vector A, the y-component is 0 (since it lies completely on the x-axis). For vector B, the y-component equals 120 units * sin(70 degrees) = 112.90 units. So, vector B has the greater y-component.
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A motor attached to a 120 V/60 Hz power line draws an 8.40 A current. Its average energy dissipation is 850 W. How much series capacitance needs to be added to increase the power factor to 1.0?
To increase the power factor to 1.0 in a motor circuit, a capacitor should be added. The capacitance value of the capacitor can be calculated by knowing the real and apparent power of the motor circuit before and after the capacitor addition. The introduction of the capacitor provides reactive power that neutralizes the inductiveness of the motor coil, making the circuit purely resistive.
Explanation:The subject matter pertains to understanding power factor, power dissipation and the effects of adding capacitance in a motor circuit. Now, the question mentions that the motor draws 8.40 A current at 120 V giving us a power apparent = V*I = 120 * 8.40 VA. However, the average power dissipated (Real power, P) is 850 W. The power factor is the ratio of real power to apparent power. However, to achieve a power factor of 1 (i.e., make the circuit purely resistive), we must add a capacitor (reactive power component) that will counteract the inductiveness of the motor coil.
The power factor before the capacitor is added is P/S = 850/(120*8.4) = 0.84. The reactive power Q before the capacitor is added can be calculated by the formula Q = sqrt[(S^2)-(P^2)] = sqrt[((120*8.4)^2)-(850^2)] VAR. After the capacitor is added, the power factor is 1 (as per the question), which means the reactive power Q' = 0. Therefore, reactive power supplied by the capacitor C = Q - Q' = Q = sqrt[((120*8.4)^2)-(850^2)].
Using Q = sqrt[(S^2)-(P^2)], we can find the current supplied by the capacitor as Ic = Q/V. From this current, we can find the capacitance using the formula C = Ic / (2*π*f.*V) where f = frequency = 60 Hz.
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To improve the power factor of a 120 V motor that draws 8.40 A to unity, we need to add a 94.6 µF series capacitance. This helps cancel out the reactive power, thereby achieving a power factor of 1.0.
Calculating Series Capacitance to Improve Power Factor
To increase the power factor to 1.0 for a motor attached to a 120 V/60 Hz power line that draws an 8.40 A current and has an average energy dissipation of 850 W, follow these steps:
Step 1: Calculate Apparent Power (S)
we know , Apparent power S = V * I
Where:
V = 120 V
I = 8.40 A
So,
S = 120 V * 8.40 A = 1008 VA
Step 2: Calculate the Current Power Factor (pf)
The power factor is the ratio of real power (P) to apparent power (S). Therefore:
pf = P / S = 850 W / 1008 VA ≈ 0.843
Step 3: Calculate the Reactive Power (Q)
Reactive power can be determined using the Pythagorean theorem for the power triangle:
Q = √(S² - P²)
So,
Q = √(1008² - 850²) ≈ 512 VAR
Step 4: Calculate Required Capacitive Reactance (Xc)
For unity power factor, the reactive power provided by the capacitor should cancel out the Q value:
Xc = V² / Q
So,
Xc = 120² / 512 ≈ 28.125 ohms
Step 5: Calculate Series Capacitance (C)
Use the formula for capacitive reactance:
Xc = 1 / (2πfC)
Solve for C:
C = 1 / (2π * 60 Hz * 28.125 ohms) ≈ 94.6 µF
Adding a series capacitance of approximately 94.6 µF will increase the power factor to 1.0.
Which of the following statements are true regarding the electromagnetic spectrum?1. X rays and gamma rays have very long wavelengths and very low photon energies.2. Radio waves have wavelengths on the order of meters and very low photon energies.3. Ultraviolet radiation has long wavelengths and low photon energies.4. Visible light lies at the center of the electromagnetic spectrum.5. Infrared radiation has long wavelengths and low photon energies.
Answer:
2, 4, 5
Explanation:
The electromagnetic spectrum gives the classification of the electromagnetic waves according to their wavelength/frequency. In order from the shortest to the greatest wavelength, we have:
Gamma rays
X-rays
Ultraviolet
Visible light
Infrared
Microwaves
Radio waves
Moreover, the frequency of an electromagnetic wave is inversely proportional to its wavelength, according to:
[tex]f=\frac{c}{\lambda}[/tex]
where c is the speed of light.
Finally, the energy of a photon of an electromagnetic wave is directly proportional to the frequency, and inversely proportional to the wavelength:
[tex]E=hf = \frac{hc}{\lambda}[/tex]
where h is the Planck constant.
Keeping in mind these facts, let's now analyze each statement:
1. X rays and gamma rays have very long wavelengths and very low photon energies. --> FALSE: X-rays and gamma rays have the shortest wavelength, so they have the highest frequency and very high energy.
2. Radio waves have wavelengths on the order of meters and very low photon energies. --> TRUE. Radio wave wavelengths are on the order of meters, so very long; consequently, their frequency is very low, and so their energy is also very low.
3. Ultraviolet radiation has long wavelengths and low photon energies. --> FALSE. Ultraviolet has short wavelength, so high frequency and high photon energy.
4. Visible light lies at the center of the electromagnetic spectrum. --> TRUE: visible light photons have wavelength between 380 and 750 nm, and lie at the center of the electromagnetic spectrum.
5. Infrared radiation has long wavelengths and low photon energies. --> TRUE: infrared radiation has longer wavelengths (if compared to the visible light), and therefore lower frequency and lower energy.
X-rays and gamma rays have high photon energies and short wavelengths, radio waves have long wavelengths and low photon energies, visible light lies in the middle of the electromagnetic spectrum.
Explanation:Among the statements, the correct ones regarding the electromagnetic spectrum are:
X rays and gamma rays have very high photon energies and very short wavelengths. This is because they have high frequencies and carry a lot of energy.Radio waves have long wavelengths on the order of meters and low photon energies. They have low frequencies and carry less energy compared to other types of radiation in the electromagnetic spectrum.Visible light lies at the middle of the electromagnetic spectrum. It has wavelengths that are longer than X-rays but shorter than infrared and ultraviolet radiation.Based on the information about the characteristics and properties of electromagnetic radiation, these statements accurately reflect the nature of X-rays, gamma rays, radio waves, and visible light.
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Determine which type of property each statement describes by typing "physical" or "chemical" in the blank. Hydrogen is a colorless, tasteless, and odorless gas. Hydrogen is very combustible in the presence of oxygen. Hydrogen is very reactive with most elements. Hydrogen is the least dense of all elements.
physical:1.Hydrogen is a colorless,tasteless and odourless gas.2.Hydrogen is the least dense of all elements.
chemical:1.hydrogen is very combustible in the presence of oxygen.2.hydrogen is very reactive with most elements.
Answer: Hydrogen is a colorless, tasteless, and odorless gas : Physical property
Hydrogen is very combustible in the presence of oxygen: Chemical property
Hydrogen is very reactive with most elements : Chemical property
Hydrogen is the least dense of all elements: Physical property
Explanation:
Chemical property is defined as the property of a substance which is observed during a reaction where the chemical composition identity of the substance gets changed.
Physical property is defined as the property which can be measured and whose value describes the state of physical system. For Example: State, density etc.
Hydrogen is a colorless, tasteless, and odorless gas is a physical property.
Hydrogen is very combustible in the presence of oxygen is a chemical property.
Hydrogen is very reactive with most elements is a chemical property.
Hydrogen is the least dense of all elements is a physical property.
How many potassium ions pass through if the ion channel opens for 1.0 ms?
answer:
1.8E-15C/1.6E-19=11,250
Explanation:
The biochemistry that takes place inside cells depends on various elements, such as sodium, potassium, and calcium, that are dissolved in water as ions. These ions enter cells through narrow pores in the cell membrane known as ion channels. Each ion channel, which is formed from a specialized protein molecule, is selective for one type of ion. Measurements with microelectrodes have shown that a 0.30-nm-diameter potassium ion ({\rm{{\rm K}}}^{\rm{ + }} ) channel carries a current of 1.8 {\rm pA}.
The number of potassium ions that will pass through the ion channel is 11250.
What are potassium ions?Potassium ions, possibly the most often constituted electrolyte.
Calculating the number of potassium ions that passes through the ion channel
Given that the channel opens for 1.0 ms
Step1: determine the value of charge ( Q )
[tex]Q = I \times \Delta t = ( 1.8 \times 10^-^1^0 A )\times (1.0 \times 10^1^3 s ) = 1.8 \times 10^-^1^5 C[/tex]
where ; I = 1.8 × 10⁻¹² A
[tex]\Delta t = 1.0 \times 10^-^3 s[/tex]
Step2: determine number of K⁺ ions passing through
[tex]NK^+ = Q \times e = ( 1.8 \times 10^-^1^5 C )\times ( 1.60 \times 10^-^1^9 C) = 11250[/tex]
Thus, the potassium ions pass through the channel is 11250.
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A 15.75-g piece of iron absorbs 1086.75 joules of heat energy, and its temperature changes from 25°C to 175°C. Calculate the specific heat capacity of iron.
Answer:
0.46 J/gC
Explanation:
The specific heat capacity of a material is given by:
[tex]C_s = \frac{Q}{m \Delta T}[/tex]
where
Q is the amount of heat absorbed
m is the mass
[tex]\Delta T[/tex] is the variation of temperature
For the piece of iron in the problem:
[tex]m = 15.75 g[/tex]
[tex]Q=1086.75 J[/tex]
[tex]\Delta T=175 C-25 C=150^{\circ}[/tex]
Substituting into the equation,
[tex]C_s = \frac{1086.75 J}{(15.75 g)(150^{\circ}C)}=0.46 J/gC[/tex]
Answer:
0.46 J/gC
Explanation:
The specific heat capacity of a material is given by:
where
Q is the amount of heat absorbed
m is the mass
is the variation of temperature
For the piece of iron in the problem:
Substituting into the equation,
Explanation:
You observe two stars in the sky and measure their angular distance as 60 degrees. How many arc seconds is this angular distance?
(60 degrees) x (60 arcminutes/degree) x (60 arcseconds/arcminute) =
(60 degrees) x (3600 arcseconds/degree) =
216,000 arc seconds
(60 degrees) x (60 arcminutes/degree) x (60 arcseconds/arcminute) = (60 degrees) x (3600 arcseconds/degree) = 216,000 arc seconds.
What is Angular distance?
The angular distance is a measurement of how far apart two points appear to be from the viewpoint of the observer. From each point to the observer, straight lines extended and intersected.
The angular distance, which is commonly stated in degrees or radians, is the angle at which these two lines intersect. This angle can be used in trigonometry to determine heights and distances.
Astronomers frequently refer to the angle instead of the actual distance between celestial bodies when describing the apparent gap between them.
Therefore, (60 degrees) x (60 arcminutes/degree) x (60 arcseconds/arcminute) = (60 degrees) x (3600 arcseconds/degree) = 216,000 arc seconds.
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When a guitar is tuned to adjust it pitch what is it that is changed?
A) its wavelength
B) Its frequency
C) Its amplitude
D) its linear density
Answer:
B) Its frequency
Explanation:
The pitch of sound heard depends on its frequency of the sound wave. Frequency refers to how fast the sound wave is oscillating. A high frequency sound wave has a high pitch while a low frequency sound wave has a low pitch.The faster the sound wave oscillates the higher the pitch. For instance, a guitar with a big heavy string will vibrate slowly and thus create a low pitch.When a guitar is tuned to adjust its pitch, B) its frequency is changed.
The frequency determines how high or low we perceive the sound (or pitch) to be. This adjustment is achieved by tightening or loosening the tension on the strings, which alters the rate at which the string vibrates.
Frequency is the number of vibrations per second of the string and is measured in Hertz (Hz). Higher tension on the string increases the vibration rate, leading to a higher pitch, while lower tension decreases the vibration rate, resulting in a lower pitch.
So, the frequency is key in changing the pitch of the guitar string, not the wavelength, amplitude, or linear density. The correct answer is B.
Electrons in a photoelectric-effect experiment emerge from a copper surface with a maximum kinetic energy of 1.10 eV. What is the wavelength of the light?
The photoelectric effect consists of the emission of electrons (electric current) that occurs when light falls on a metal surface under certain conditions.
If the light is a stream of photons and each of them has energy, this energy is able to pull an electron out of the crystalline lattice of the metal and communicate, in addition, a kinetic energy.
This is what Einstein proposed:
Light behaves like a stream of particles called photons with an energy
[tex]E=h.f[/tex] (1)
So, the energy [tex]E[/tex] of the incident photon must be equal to the sum of the Work function [tex]\Phi[/tex] of the metal and the kinetic energy [tex]K[/tex] of the photoelectron:
[tex]E=\Phi+K[/tex] (2)
Where [tex]\Phi[/tex] is the minimum amount of energy required to induce the photoemission of electrons from the surface of a metal, and its value depends on the metal.
In the case of Copper [tex]\Phi=4.7eV[/tex]
Now, applying equation (2) in this problem:
[tex]E=4.7eV+1.10eV[/tex] (3)
[tex]E=5.8eV[/tex] (4)
Now, substituting (1) in (4):
[tex]h.f=5.8eV[/tex] (5)
Where:
[tex]h=4.136(10)^{-15}eV.s[/tex] is the Planck constant
[tex]f[/tex] is the frequency
Now, the frequency has an inverse relation with the wavelength [tex]\lambda[/tex]:
[tex]f=\frac{c}{\lambda}[/tex] (6)
Where [tex]c=3(10)^{8}m/s[/tex] is the speed of light in vacuum
Substituting (6) in (5):
[tex]\frac{hc}{\lambda}=5.8eV[/tex] (7)
Then finding [tex]\lambda[/tex]:
[tex]\lambda=\frac{hc}{5.8eV } [/tex] (8)
[tex]\lambda=\frac{(4.136(10)^{-15} eV.s)(3(10)^{8}m/s)}{5.8eV }[/tex]
We finally obtain the wavelength:
[tex]\lambda=213^{-9}m=213nm[/tex]