The peak value of the associated magnetic field is approximately 1.19×[tex]10^{6}[/tex] Tesla.
To find the peak value of the associated magnetic field, we can use the formula:
Peak magnetic field (B) = √(2P/μ0c)
Where P is the average power per unit area, μ0 is the permeability of free space, and c is the speed of light.
Substituting the given values, we get: B = √(2(2.12)/4π×[tex]10^{7}[/tex]×3×[tex]10^{8}[/tex])
Simplifying the expression, we get: B = √(1.41×[tex]10^{11}[/tex])
Therefore, the peak magnetic field is: B = 1.19×[tex]10^{6}[/tex] T
So the peak value of the associated magnetic field is approximately 1.19×[tex]10^{6}[/tex] Tesla.
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A particle is moving up an inclined plane. Its velocity changes from 15m/s to 10m/s in two
seconds. What is its acceleration?
Answer:
Explanation:
We can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
Plugging in the values given in the problem, we get:
acceleration = (10 m/s - 15 m/s) / 2 s
Simplifying this expression, we get:
acceleration = -5 m/s / 2 s
Therefore, the acceleration of the particle is -2.5 m/s^2.
Note that the negative sign indicates that the particle is decelerating or slowing down.
3.5g of liquid in 4mins with a pressure gradient of 10cm is how many m/s
To calculate the velocity of liquid flow, we need to use the equation Q = A*v, where Q is the volumetric flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the liquid.
Given that 3.5g of liquid flows in 4mins, we need to convert it into volumetric flow rate. 1g of water is equal to 1mL, therefore 3.5g is equal to 3.5mL. Since 4mins is equal to 240s, the volumetric flow rate is 3.5/240 = 0.0146mL/s.
To calculate the velocity of the liquid, we need to use the pressure gradient of 10cm. The pressure gradient is the change in pressure per unit distance along the pipe. 1cm of water column is equal to 0.098kPa, therefore the pressure gradient is 0.098*10 = 0.98kPa/m.
Using the equation ΔP = ρgh, where ΔP is the pressure difference, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the pressure gradient, we can calculate the velocity of the liquid. Rearranging the equation to solve for v, we get v = √(2ΔP/ρ), where ΔP is the pressure difference across the pipe.
Assuming the density of water is 1000kg/m³, the velocity of the liquid is v = √(2*0.98/1000) = 0.044m/s.
Therefore, the velocity of liquid flow is 0.044m/s, given that 3.5g of liquid flows in 4mins with a pressure gradient of 10cm.
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Car A and Car B are driving towards each other. Car A's speedometer shows that it is going 60 mph. Car B's speedometer shows that it is going 70 mph. How fast is Car A going relative to a passenger in Car B?
The speed of Car A going relative to a passenger in Car B is 10mph
Speed calculation.
The relative speed of Car A and Car B since they are driving towards each other is given by;
V = 60+70=130mph
In order to find the speed of Car A going relative to a passenger in Car B we need to subract speed of car B.
vA/vB= va-vB
60-70= -10mph
The negative sign indicate that car A is travelling in opposite direction relative to car B.
Therefore, The speed of Car A going relative to a passenger in Car B is 10mph
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A mass of 100 kg is 100 m away from a mass of 50 kg. Calculate the force of attraction between the masses. Show your work
The force of attraction between the two masses is [tex]3.335 \times 10^{-8} N[/tex].
The force of attraction between two masses is given by the gravitational force equation, which is expressed as:
[tex]$F = G \cdot \frac{m_1 \cdot m_2}{r^2}$[/tex]
where F is the force of attraction, G is the gravitational constant ([tex]$6.67 \times 10^{-11} , \text{N}\cdot\text{m}^2/\text{kg}^2$[/tex]), [tex]m_1[/tex]1 and [tex]m_2[/tex] are the masses of the two objects, and r is the distance between the centers of the two masses.
In this case, [tex]m_1[/tex] = 100 kg, [tex]m_2[/tex] = 50 kg, and r = 100 m. Substituting these values into the equation, we get:
[tex]$F = 6.67 \times 10^{-11} , \text{N}\cdot\text{m}^2/\text{kg}^2 \cdot \frac{(100 , \text{kg}) \cdot (50 , \text{kg})}{(100 , \text{m})^2}$[/tex]
[tex]F = 3.335 \times 10^{-8} N[/tex]
It is worth noting that the force of attraction between the two masses is very small, which is due to the large distance between them. The gravitational force decreases rapidly with distance, so as the distance between the two masses increases, the force of attraction decreases as well.
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A two-pole AC motor operates on a three-phase, 60 Hz, 240 Vrms line-to-line supply. What is its synchronous speed?a.1000 rpmb.1800 rpmc.2400 rpmd.3600 rpm
A two-pole AC motor operates on a three-phase, 60 Hz, 240 Vrms line-to-line supply.The answer is option B, 1800 rpm.
This is because the synchronous speed of a two-pole AC motor is given by the formula:
Synchronous speed (in RPM) = (120 x Frequency) / Number of poles
In this case, the frequency is 60 Hz and the number of poles is 2.
Synchronous speed = (120 x 60) / 2 = 3600 rpm
However, this is the theoretical speed that the motor would operate at if there was no load or slip. In reality, the motor will experience some slip, which means that its actual operating speed will be slightly less than the synchronous speed.
Therefore, the correct answer is option B, 1800 rpm, which is slightly less than the synchronous speed of 3600 rpm.
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PLEASE I NEED THIS TODAY!!!
What happens to the amount of carbon in a closed ecosystem? Explain by giving examples and evidence from the article.
Scientists around the world who study Earth’s atmosphere have discovered something dramatic and alarming: an increase in the amount of carbon dioxide in our atmosphere. They are finding that the increase in carbon dioxide in our atmosphere may have worldwide effects on our climate and our oceans, which can threaten life all over the planet.
Where is the carbon that makes up all that carbon dioxide coming from? Carbon is an element that makes up a lot of the matter on Earth. New carbon can’t be created, so the extra carbon in our atmosphere had to come from somewhere—it must have decreased in some other part of the Earth system. But where? Humans put carbon into the atmosphere when we burn fuels like coal, oil, and gas that are found deep underground. These are called fossil fuels.
These fossil fuels make the modern human lifestyle possible. Most of the time, when we use a cell phone, drive a car, heat our homes, or turn on the lights, we are using energy that comes from burning fossil fuels. We currently depend on these fuels to power our lives, but burning them releases large amounts of carbon dioxide into the air—and that increase in carbon dioxide might jeopardize life as we know it.
Fossil Fuels
Coal, oil, and gas are called “fossil fuels” for a reason: they are the carbon-rich matter left behind by plants and animals that died millions of years ago. These plants and animals were buried deep underground before they could decompose, so decomposers never broke down the dead matter. Over millions of years, the remains of the plants and animals turned into carbon-rich fossil fuels—coal, oil, and gas. The carbon that was in the plants and animals when they died is still there; it’s just part of the fossil fuels. When we burn fossil fuels in cars, factories, or power plants, carbon that has been stored in the ground for millions of years is released into the air as carbon dioxide.
An illustration of ancient organisms.
Fossil fuels are the remains of animals and plants that died millions of years ago and were buried before they could decompose.
The Carbon Cycle
Earth is a closed ecosystem.
Earth is a closed ecosystem. There are many different regional ecosystems on Earth, but they all share one atmosphere and one ocean. Very little matter escapes from Earth into space, and almost none enters. Since almost no carbon enters or leaves Earth’s system, and carbon isn’t being produced or used up, the amount of carbon in the system does not change. If carbon is increasing in one part of Earth’s system, it must be decreasing somewhere else.
Although carbon rarely leaves Earth’s system, carbon moves in a cycle within Earth’s ecosystem. This cycle is powered by energy. Carbon cycles from biotic matter to abiotic matter and back again. This means that carbon spends time in the air, in the ocean, in the soil, and in organisms as it moves continuously through the ecosystem. Powered by energy from sunlight, photosynthesis moves carbon from the air and water into living things. At the same time, cellular respiration moves carbon from living things to the air and water. This continuous, consistent pattern of movement is called the carbon cycle, and it is essential to the survival of life on Earth. However, human activities are altering the way carbon moves through the global ecosystem.
A diagram depicting the carbon cycle.
The Carbon Cycle: The arrows in this diagram show the pathways that carbon follows as it moves around the ecosystem. The black arrows show the pathways that exist naturally in the ecosystem. The large red arrow shows how humans can increase the amount of carbon in the atmosphere by burning dead matter like fossil fuels.
As people around the world burn more and more fossil fuels, a great deal of carbon from deep underground is moving into the atmosphere. Carbon in one part of the system (abiotic matter) is increasing, and as a result, carbon in another part of the system is decreasing—in this case, biotic matter, which includes dead matter. Since the entire Earth shares the same atmosphere, changes in levels of carbon dioxide affect ecosystems all over the planet.
All the extra carbon dioxide in the atmosphere is having many negative effects on the global ecosystem, and especially on the climate of our planet. Adding carbon dioxide to the atmosphere changes climate and weather patterns around the globe in ways that make it harder for many organisms to survive. Increased carbon dioxide causes global temperatures to rise, makes ocean water more acidic, and changes weather patterns. These changes may increase the chances of extreme weather events like hurricanes and droughts, which affect humans directly as well as the ecosystems and farms we depend on. By increasing the amount of carbon dioxide in the atmosphere, we are gambling with our very way of life.
Answer: What is the main cause of the increase in carbon dioxide in our atmosphere?
The main cause of the increase in carbon dioxide in our atmosphere is the burning of fossil fuels, such as coal, oil, and gas. When these fuels are burned, carbon dioxide is released into the atmosphere, which can have negative effects on our climate and oceans. This increase in carbon dioxide is caused by human activities, and it may jeopardize life on the planet if we do not take action to reduce our reliance on fossil fuels.
Explanation: very long /:
A lamp is connected to the power supply.
The lamp requires an input potential difference of 5. 0V
The alternator generates a potential difference of 1. 5V
The primary coil of the transformer has 150 turns.
Calculate the number of turns needed on the secondary coil
Number of turns on the secondary coil = ?
The number of turns needed on the secondary coil is 45. The transformer is a device that transfers electrical energy from one circuit to another through electromagnetic induction.
In order to determine the number of turns needed on the secondary coil of the transformer, we need to use the equation:
Vp/Vs = Np/Ns
Where Vp is the potential difference on the primary coil, Vs is the potential difference on the secondary coil, Np is the number of turns on the primary coil, and Ns is the number of turns on the secondary coil.
We know that Vp is 1.5V and Vs is 5.0V. We also know that Np is 150. So, we can rearrange the equation to solve for Ns:
Ns = (Vp/Vs) x Np
Ns = (1.5V/5.0V) x 150
Ns = 45
Therefore, the number of turns needed on the secondary coil is 45. The transformer is a device that transfers electrical energy from one circuit to another through electromagnetic induction. The voltage ratio between the primary and secondary coils is determined by the ratio of the number of turns in each coil.
In this case, we are given the input and output voltages and the number of turns on the primary coil, and we use this information to calculate the number of turns needed on the secondary coil.
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By how much is each post compressed by the weight of the aquarium?.
The weight of the aquarium affects the amount of compression of each post. The heavier the aquarium, the more force it exerts on the posts, causing them to compress.
The amount of compression of each post depends on the weight of the aquarium, the size of the posts, and the type of material the posts are made from. For example, a heavier aquarium will compress wood posts more than metal posts of the same size.
Generally, the amount of compression of each post should be calculated by the weight of the aquarium divided by the number of posts. This number can then be used to determine the amount of compression of each post.
To ensure the posts remain secure, it is important to ensure the amount of compression does not exceed the post's maximum compression capacity.
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A 500g trolley is placed on a runway that is tilted so that it makes an angle of 30° to a horizontal table
2.4N is the magnitude of the tension T in the string
Define tension force.
It is also possible to refer to tension as the action-reaction pair of forces acting at each end of the aforementioned elements. Tension is defined as the pulling force transmitted axially by a string, rope, chain, or other similar object, or by each end of a rod, truss member, or other comparable three-dimensional object.
When an object is compressed or stretched, spring forces come into play. The degree of compression or stretching has a direct relationship to the force a spring produces. In other words, the force a spring produces increases with the amount it is compressed or stretched.
T=Mgsin30−Ff +mg
T=(0.5)(9.8)sin30−1.5+(0.15)(9.8)
T=2.4 N
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Complete question:
A 500g trolly is placed on a runway that is tilted so that it makes an angle of 30 degrees to a horizontal table.A light inextensible string is attached to 150g mass piece.the trolly accelerates down the slope as a result of the force applied by the hanging mass piece.the frictional force between the trolly and the runway is 1.5N, what is the magnitude of the tension T in the string?
Show that 1Kwh is equal to 3.6MJ of energy.
Answer:
3.6 MJ
Explanation:
1 kWh = 1 MJ
Remember that this is the same as the equation Power×time = Energy
Step 1: Convert kWh (kiloWatt×hour) to Ws (Watt×second)
1 kW = 1000 Watt
1 h = 60 min×60 sec = 3600 seconds
1000 W×3600s = 3600000 Joules
Divide 3600000 J by 10^6 to get 3.6 Mega Joules
As an object moves from point a to point b only two forces act on it: one force is nonconservative and does −30 j of work, the other force is conservative and does +50 j of work. between a and b,
Between point A and point B, the net work done on the object is: +20 joules, indicating that the system has gained energy overall, likely in the form of kinetic or potential energy.
As the object moves from point A to point B, it experiences both conservative and nonconservative forces. Conservative forces, such as gravity and spring forces, have the ability to store energy in the form of potential energy, and the work done by these forces can be recovered. Nonconservative forces, like friction or air resistance, dissipate energy as heat, and the work done by these forces cannot be recovered.
In this specific case, the nonconservative force does -30 joules of work, which implies that energy is being removed from the system as heat. On the other hand, the conservative force does +50 joules of work, meaning energy is being stored as potential energy in the system.
To find the net work done on the object as it moves from point A to point B, you can simply add the work done by both forces. In this case, the net work is -30 joules (nonconservative force) + 50 joules (conservative force) = +20 joules.
So, between point A and point B, the net work done on the object is +20 joules, indicating that the system has gained energy overall, likely in the form of kinetic or potential energy.
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The maximum number of tension forces that can act on an object is
a) there is no limit
b) 2
c) more than 2
d) 1
The correct answer is d) 1.
An object can only have one maximum tension force acting on it at a given time. Tension is a force that occurs when a material is pulled in opposite directions, creating a stretching or elongating effect. If there were multiple tension forces acting on an object, it would create a net force and cause the object to move in different directions, which is not physically possible. Therefore, an object can only have one maximum tension force acting on it.
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Why does an increase in P. D of a thermistor decrease the resistance and increase the temperature???
An increase in potential difference (P.D.) across a thermistor leads to an: increase in current flow, which generates heat and raises the temperature of the thermistor.
A thermistor is a temperature-sensitive resistor whose resistance varies with temperature changes. When the potential difference (P.D.) across a thermistor increases, more electric current flows through it. As the electric current increases, the electrons in the thermistor gain more kinetic energy and collide more frequently with the lattice structure of the material, which generates heat.
The increased heat raises the temperature of the thermistor. In a negative temperature coefficient (NTC) thermistor, the resistance decreases as the temperature rises. This is because, as the thermistor heats up, the lattice structure of the material expands, allowing more electrons to move more freely and conduct electricity more efficiently. Consequently, the resistance decreases with an increase in temperature.
So, to summarize, an increase in potential difference (P.D.) across a thermistor leads to an increase in current flow, which generates heat and raises the temperature of the thermistor. In an NTC thermistor, this increased temperature causes a decrease in resistance due to the expansion of the lattice structure, which allows electrons to move more freely and conduct electricity more efficiently.
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A ball of mass 0.2kg travelling in the x direction at a speed of 0.5m/s collides with a ball of mass 0.3kg travelling in the y direction at a speed of 0.4m/s. the two balls stick together after the collision travelling at an tita to the x direction. what is the value of tita
The value of tita is approximately 32.4 degrees.
The momentum in the x direction before the collision is 0.2 kg * 0.5 m/s = 0.1 kgm/s. The momentum in the y direction before the collision is 0.3 kg * 0.4 m/s = 0.12 kgm/s. The total momentum before the collision is the vector sum of the momenta in the x and y direction, which is √(0.1^2 + 0.12^2) = 0.16 kg*m/s.
After the collision, the two balls stick together and move at an angle tita to the x direction. Let's call the velocity of the combined mass v. The total momentum after the collision is the mass of the combined balls multiplied by the velocity, which is (0.2 kg + 0.3 kg) * v = 0.5 kg * v.
Since momentum is conserved, the total momentum before the collision is equal to the total momentum after the collision: 0.16 kg*m/s = 0.5 kg * v. Solving for v, we get v = 0.32 m/s. We can find the angle tita using trigonometry. The x component of the velocity is v_x = v * cos(tita) and the y component of the velocity is v_y = v * sin(tita). So we have v_x / v_y = tan(tita). Plugging in the values, we get tan(tita) = (0.32 m/s) / 0.5 m/s, or tita = arctan(0.64) = 32.4 degrees.
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The idea of "visible" and "invisible" work is related to other hierarchical dichotomies in our culture about work, including "valuable" and "unvalued" work
The statement "The idea of 'visible' and 'invisible' work is related to other hierarchical dichotomies in our culture about work, including 'valuable' and 'unvalued' work" is true.
Visible work refers to tasks that are easily seen and recognized, such as high-profile jobs in fields like business, law, or medicine. Invisible work, on the other hand, refers to tasks that are often unseen and undervalued, such as caregiving, domestic work, or service industry jobs.
This dichotomy is further perpetuated by the gendered division of labor, where women are often expected to perform invisible work while men are expected to perform visible work. This results in a devaluation of traditionally feminine jobs and reinforces gender inequalities in the workforce.
Furthermore, the value placed on certain types of work is often linked to the economic rewards and social status that accompany them. This creates a hierarchy of jobs where those in visible, high-status positions are paid more and afforded more respect than those in invisible, low-status positions.
In summary, the idea of visible and invisible work is related to other hierarchical dichotomies in our culture about work, including valuable and unvalued work. This perpetuates gender inequalities and creates a hierarchy of jobs based on economic rewards and social status.
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Complete Question:
The idea of "visible" and "invisible" work is related to other hierarchical dichotomies in our culture about work, including "valuable" and "unvalued" work. True or False.
suppose you stand on a swing instead of sitting on it will your frequency of oscillation increase or decrease
If you stand on a swing instead of sitting on it, the frequency of oscillation will decrease.
Frequency of oscillationsThe frequency of oscillation of a swing depends on its length and acceleration due to gravity. The longer the swing, the slower it oscillates, and the shorter the swing, the faster it oscillates. The acceleration due to gravity provides the restoring force that pulls the swing back toward its equilibrium position.
When you stand on a swing instead of sitting on it, you effectively shorten the length of the swing. This is because your center of mass is higher up on the swing, which reduces the length of the pendulum from the pivot point to your center of mass. A shorter pendulum has a higher frequency of oscillation than a longer pendulum, so the frequency of oscillation of the swing will increase.
However, when you stand on a swing, you also make it harder for the swing to move. This is because your legs are now acting as shock absorbers, and they absorb some of the energy that would otherwise be used to swing the swing. This makes it harder for the swing to oscillate, which reduces the frequency of oscillation.
The net effect of these two factors is that the frequency of oscillation of the swing decreases when you stand on it instead of sitting on it.
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Your lawn is twice as large as your neighbor’s lawn. You both start cutting your lawn with the same model, self-propelled lawn mower (requiring the same force) beginning at 9:00am on a Saturday morning. You finish cutting your lawn at 11:00 am. What time will your neighbor finish cutting her lawn if you are equally powerful?
Your neighbor will finish cutting her lawn at 10:00 am, which is one hour after both of you started.
Since your lawn is twice as large as your neighbor's lawn, it takes you a certain amount of time to cut it, which we can analyze to determine when your neighbor will finish cutting her lawn.
You started cutting your lawn at 9:00 am and finished at 11:00 am. This means it took you 2 hours to complete the task. Since your neighbor's lawn is half the size of yours, it will take her half the amount of time to finish cutting her lawn, assuming you both exert the same force using the same self-propelled lawn mower.
To calculate the time it will take your neighbor to cut her lawn, simply divide your time (2 hours) by 2. This gives us 1 hour. Your neighbor started cutting her lawn at the same time you did, 9:00 am, and will take 1 hour to complete the task.
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in an rlc series circuit as shown, there is a phase angle between the instantaneous current through the circuit and the instantaneous voltage vad across the entire circuit. for what value of the phase angle is the greatest power delivered to the resistor? group of answer choices 900 2700 zero 1800
The phase angle that maximizes the power delivered to the resistor is zero degrees. So, correct option is C.
In an RLC series circuit, the impedance Z is given by the equation Z = R + j(XL - XC), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance. The current in the circuit is given by the equation I = V/Z, where V is the voltage across the circuit.
The power delivered to the resistor in the circuit is given by the equation P = I^2R. To maximize this power, we need to maximize the current I in the circuit.
The phase angle between the current and voltage is given by the equation tan(phi) = (XL - XC)/R, where phi is the phase angle. This means that the phase angle is zero when XL = XC, or when the reactances cancel out.
At this point, the impedance of the circuit is purely resistive and is equal to R. This means that the current is at its maximum value, which maximizes the power delivered to the resistor.
Therefore, correct option is C.
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Complete question is:
in an rlc series circuit , there is a phase angle between the instantaneous current through the circuit and the instantaneous voltage vad across the entire circuit. for what value of the phase angle is the greatest power delivered to the resistor? group of answer choices
A)90
B)270
C) zero
D) 180
Object A is traveling at half the speed of light colliding with object B that is stationary. How does object A experience time in comparison to object B and how does object B experience time in comparison to object A before there collision?
Object A will experience time passing slower than Object B due to its velocity, while Object B will experience time passing at its normal rate. As the objects approach each other, their perception of time will start to converge.
According to the theory of relativity, time appears to be different for two observers in relative motion. In this scenario, Object A is traveling at half the speed of light, while Object B is stationary.
From Object A's perspective, time appears to be moving slower for Object B, while for Object B, time appears to be moving at its normal rate. This is due to the time dilation effect, which is a consequence of special relativity.
As Object A approaches Object B, both objects will experience a different perception of time. Object A will perceive time to be passing more slowly, while Object B will perceive time to be passing at its normal rate. However, this difference will be negligible due to the low relative velocity of the objects.
In summary, Object A will experience time passing slower than Object B due to its velocity, while Object B will experience time passing at its normal rate. As the objects approach each other, their perception of time will start to converge.
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Identify what is being described in each sentence
Conductor, solar energy, power, solid wire, nonconductor or insulator power supply unit, stranded, conductor, fuse, LED , switch, may being described in each sentence.
Material with resistance to electricity, heat and sound.Device that requires energy to operate.Energy generating object that cannot dissipate energy.Type of wire made up of a single piece of metal.Material that allows the flow of electrical current, heat and sound.Computer hardware responsible for supplying power.Conductor made up of multiple small strands.Safety device used to protect an electrical circuit from excessive current.Semiconductor that illuminates with electrical charge.Device used to interrupt and transfer electric current.The complete question is ,
Direction: Identify what is being described in each sentence. Write your answer on a separate sheet of paper. 1. It resists electricity, heat and sound. 2. It requires a source of energy for its operation.
3. It generates energy but can't dissipate energy.
4. It is a type of wire assembled in a single piece of metal.
5. It permits electrical current, heat and sound to flow freely.
6. It is a computer hardware responsible in supplying power.
7. It is made up of multiple small strands that make-up a single conductor
8. It is a safety device used to protect an electrical circuit from cxcessive current. 9. It is a semiconductor that illuminates when an electrical charge passes through it.
10. It is a device used to break an electric current and transfer it to another conductor.
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Suppose you were traveling in your family's car. imagine you are at a red light and the light turns green. when the driver puts their foot on the gas petal are they accelerating? help me and ithe next 24 hours, i will put you brainliest nd lots of stars
Yes, the driver is accelerating when they put their foot on the gas pedal. Acceleration is the rate of change of velocity, which means that any change in speed or direction of motion is considered acceleration.
In this case, when the driver presses on the gas pedal, the car's velocity increases, causing a change in speed.
Therefore, the car is accelerating.
It's important to note that acceleration doesn't only refer to an increase in speed but can also refer to a decrease in speed or a change in direction, such as turning a corner.
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1) Calculate the centripetal force acting on a 925 kg car as it rounds an unbanked curve with a radius of 75 m at a speed of 22 m/s.
2) A car with a mass of 833 kg rounds an unbanked curve in the road at a speed of 28. 0 m/s. If the radius of the curve is 105 m, what is the average centripetal force exerted on the car?
3) An amusement park ride has a radius of 2. 8 m. If the time of one revolution of a rider is 0. 98 s, what is the speed of the rider?
4) An electron (m=9. 11x10 -31kg) moves in a circle whose radius is 2. 00 x 10 -2m. If the force acting on the electron is 4. 60x10 -14N, what is its speed?
5) A 2. 7x10 3kg satellite orbits the Earth at a distance of 1. 8x10 7m from the Earth’s centre at a speed of 4. 7x10 3m/s. What force does the Earth exert on the satellite?
6) A string can withstand a force of 135 N before breaking. A 2. 0 kg mass is tied to the string and whirled in a horizontal circle with a radius of 1. 10 m. What is the maximum speed that the mass can be whirled at before the string breaks?
7) A motocross rider at the peak of his jump has a speed such that his centripetal acceleration is equal to g. As a result, he does not feel any supporting force from the seat of his bike, which is also accelerating at rate g. Therefore, he feels if there is ni force of gravity on him, a condition described as apparent weightlessness. If the radius of the approximately circular jump is 75. 0 m, what is the speed of the bike?
The centripetal force is 5,444.27 N, the average centripetal force exerted on a car is 6,988.31 N, the speed of the rider is 18.06 m/s, the speed of an electron is 1.73 x 10⁷ m/s, the force exerted by the Earth on a satellite is 1.84 x 10⁴ N, the maximum speed is 27.39 m/s and the speed of the bike is 27.39 m/s.
1. The centripetal force acting on a 925 kg car as it rounds an unbanked curve with a radius of 75 m at a speed of 22 m/s can be calculated using the formula [tex]Fc = (mv^{2} )/r[/tex]. Substituting the given values, we get [tex]Fc = (925 kg \times 22^{2} m^{2} / s^{2} ) / 75m[/tex] = 5,444.27 N.
2. To find the average centripetal force exerted on a car with a mass of 833 kg rounding an unbanked curve with a radius of 105 m at a speed of 28.0 m/s, we can use the same formula [tex]Fc = (mv^{2} )/r[/tex]. Substituting the given values, we get [tex]Fc = (833 kg \times 28.0^{2} m^{2} /s^{2} ) / 105 m[/tex] = 6,988.31 N.
3. The speed of the rider in an amusement park ride with a radius of 2.8 m and a time of one revolution of 0.98 s can be calculated using the formula [tex]v = 2\pi r / t[/tex]. Substituting the given values, we get[tex]v = (2 \times 3.14 \times 2.8 m) / 0.98 s[/tex] = 18.06 m/s.
4. The speed of an electron in a circle with a radius of [tex]2.00 \times 10^{-2} m[/tex] and a force [tex]4.60 \times 10^{-14} N[/tex] acting on it can be calculated using the formula [tex]v = \sqrt{(Fcr / m)}[/tex]. Substituting the given values, we get
[tex]v = \sqrt{[(4.60 \times 10^{-14} N \times 2.00 x 10^{-2} m) / 9.11 \times 10^{-31} kg]}[/tex]
[tex]= 1.73 \times 10^7 m/s.[/tex]
5. The force exerted by the Earth on a satellite with a mass of [tex]2.7 \times 10^3[/tex] kg orbiting at a distance of [tex]1.8 \times 10^7[/tex] m and a speed of [tex]4.7 \times 10^3\;m/s[/tex] can be calculated using the formula [tex]Fg = (Gm_{1} m_{2}) / r^{2}[/tex]. Substituting the given values, we get
[tex]Fg = (6.67 \times 10^{-11} N(m/kg)^2 \times 5.97 \times 10^{24} kg \times 2.7 \times 10^3 kg) / (1.8 \times 10^7 m)^{2}[/tex]
[tex]= 1.84 \times 10^4 N.[/tex]
6. The maximum speed at that a 2.0 kg mass can be whirled in a horizontal circle with a radius of 1.10 m before the string breaks, given a maximum force of 135 N that the string can withstand, can be calculated using the formula[tex]v = \sqrt(Fr / m)[/tex]. Substituting the given values, we get
[tex]v = \sqrt{[(135 N \times 1.10 m) / 2.0 kg]}[/tex]
= 16.47 m/s.
7. The speed of the bike in a motocross jump with a radius of 75.0 m, where the rider experiences apparent weightlessness due to the acceleration of the bike, can be calculated using the formula [tex]v = \sqrt{(rg)[/tex]. Substituting the given values, we get
[tex]v = \sqrt{(75.0\;m \times 9.81 m/s^{2} )}[/tex]
= 27.39 m/s.
In summary, these problems involve calculating various aspects of circular motion, including centripetal force, speed, and radius, using different formulas. The calculations involve substituting the
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A pendulum is constructed from a thin, rigid, and uniform rod with a small sphere attached to the end opposite the pivot. This arrangement is a good approximation to a simple pendulum (period = 0. 65 s), because the mass of the sphere (lead) is much greater than the mass of the rod (aluminum). When the sphere is removed, the pendulum no longer is a simple pendulum, but is then a physical pendulum. What is the period of the physical pendulum?
The period of a physical pendulum depends on its mass distribution and can be calculated using the moment of inertia. The equation for the period takes into account the mass, length, radius, and distance between the pivot and center of mass.
A physical pendulum is a type of pendulum in which the mass is distributed along the length of the pendulum, and its period depends on the distribution of the mass.
To find the period of the physical pendulum, we need to consider the moment of inertia of the system, which is given by the sum of the moment of inertia of the rod and the moment of inertia of the sphere about the pivot.
Assuming that the length of the rod is much greater than the radius of the sphere, we can approximate the moment of inertia of the rod as [tex](1/3)ml^2[/tex], where m is the mass of the rod and l is its length. The moment of inertia of the sphere about the pivot is [tex](2/5)mR^2[/tex], where R is the radius of the sphere.
Using the parallel axis theorem, we can find the moment of inertia of the system about the pivot as [tex](1/3)ml^2 + (2/5)mR^2 + md^2[/tex], where d is the distance between the pivot and the center of mass of the system.
The period of the physical pendulum is given by [tex]T = 2\pi \sqrt{(I/mgd)}[/tex], where g is the acceleration due to gravity.
Thus, the period of the physical pendulum depends on the distribution of the mass, and it cannot be determined without knowing the values of m, l, R, and d.
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Andrew was running late for class and could only find a parking space next to the golf course. His new truck was hit by a 0. 300 kg golf ball which left a 0. 400 cm dent in the hood. The golf ball was falling with a velocity of 8. 00 m/s.
a) What is the initial momentum of the golf ball? b) what average force did the hood of the truck exert on the ball to stop it? c) how long did it take for the hood to stop the ball?
The initial momentum of the golf ball is 2.40 kg⋅m/s. The average force exerted by the hood of the truck on the ball to stop it is [tex]-2.40 \times 10^4 N[/tex] and the time taken for the hood to stop the ball is [tex]1.00 \times 10^{-4} s[/tex]
a) The initial momentum of the golf ball can be calculated by using the formula:
p = mv
where m is the mass of the ball and v is the velocity of the ball. Plugging in the given values, we get:
p = (0.300 kg)(8.00 m/s) = 2.40 kg⋅m/s
Therefore, the initial momentum of the golf ball is 2.40 kg⋅m/s.
b) The average force exerted by the hood of the truck on the ball to stop it can be calculated using the formula:
[tex]F = \Delta p/ \Delta t[/tex]
where Δp is the change in momentum of the ball and Δt is the time taken for the ball to come to rest. Since the ball comes to rest, the final momentum of the ball is zero. So the change in momentum is:
[tex]\Delta p[/tex] = 0 - 2.40 kg⋅m/s = -2.40 kg⋅m/s
To find the time taken, we need to use the formula for distance traveled during a uniform deceleration:
[tex]d = (1/2)at^2[/tex]
where d is the distance traveled, a is the deceleration, and t is the time taken. The distance traveled by the ball can be taken as the dent made by the ball on the hood, which is 0.400 cm or 0.00400 m. The deceleration of the ball can be found by using the formula:
[tex]v^2 = u^2 + 2ad[/tex]
where u is the initial velocity (8.00 m/s), v is the final velocity (0 m/s), and d is the distance traveled (0.00400 m). Solving for a, we get:
[tex]a = (v^2 - u^2)/2d = -80,000 \;m/s^2[/tex]
(Note that the negative sign indicates that the ball is decelerating.)
Now we can find the time taken:
[tex]t = \sqrt{(2d/a)}[/tex]
[tex]t = \sqrt{(2 \times 0.00400\; m/80,000 \;m/s^2) }[/tex]
[tex]t = 1.00 \times 10^{-4} s[/tex]
So the average force exerted by the hood of the truck on the ball to stop it is:
[tex]F = \Delta p/ \Delta t[/tex]
[tex]F = (-2.40\; kg\;m/s)/(1.00 \times 10^{-4} s)[/tex]
[tex]F = -2.40 \times 10^4 N[/tex]
(Note that the negative sign indicates that the force is in the opposite direction to the motion of the ball.)
c) The time taken for the hood to stop the ball is [tex]1.00 \times 10^{-4} s[/tex], as found in part (b).
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In a recent movie, a car and a truck had a head on collision. The car was moving to the right with a constant speed of 21 m/s. A parked truck that was 310 m in front of the car began moving to the left and speeding up at a rate of 1.2 m/s/s. Position 0 m is the car's initial position.
What is the position of the car after 4 seconds?
What is the position of the truck after 4 seconds?
What is the velocity of the truck upon impact with the car?
How much time passes before the collision happens?
Where do the car and truck collide?
Answer:To solve this problem, we need to use the equations of motion and kinematics.
1. What is the position of the car after 4 seconds?
The position of the car after 4 seconds can be found using the equation:
position = initial position + (initial velocity x time) + (1/2 x acceleration x time^2)
Plugging in the values, we get:
position = 0 + (21 x 4) + (1/2 x 0 x 4^2) = 84 meters
Therefore, the position of the car after 4 seconds is 84 meters.
2. What is the position of the truck after 4 seconds?
The position of the truck after 4 seconds can be found using the equation of motion for uniform acceleration:
position = initial position + (initial velocity x time) + (1/2 x acceleration x time^2)
Initial velocity of the truck is zero, and the acceleration is 1.2 m/s^2. The initial position of the truck is 310 meters ahead of the car.
Plugging in the values, we get:
position = 310 + (0 x 4) + (1/2 x 1.2 x 4^2) = 326.4 meters
Therefore, the position of the truck after 4 seconds is 326.4 meters.
3. What is the velocity of the truck upon impact with the car?
To find the velocity of the truck upon impact with the car, we need to use the equation:
final velocity = initial velocity + acceleration x time
The initial velocity of the truck is zero, the acceleration is 1.2 m/s^2, and the time is the time it takes for the collision to happen.
4. How much time passes before the collision happens?
To find the time it takes for the collision to happen, we need to use the equations of motion and kinematics.
The position of the car at the time of the collision is the same as the position of the truck at the time of the collision. Let's call this position "x".
Using the equation of motion for the car, we have:
x = 0 + (21 x t) + (1/2 x 0 x t^2) = 21t
Using the equation of motion for the truck, we have:
x = 310 + (0 x t) + (1/2 x 1.2 x t^2) = 0.6t^2 + 310
Setting these two equations equal to each other, we get:
21t = 0.6t^2 + 310
Simplifying and solving for t, we get:
t = 23.98 seconds
Therefore, the time it takes for the collision to happen is approximately 24 seconds.
5. Where do the car and truck collide?
The position of the collision can be found by plugging the time into either the equation of motion for the car or the equation of motion for the truck.
Using the equation of motion for the car:
position = 21 x 23.98 = 503.58 meters
Using the equation of motion for the truck:
position = 0.6 x (23.98)^2 + 310 = 503.58 meters
Therefore, the car and truck collide at a position of 503.58 meters.
Explanation:
M. bouc believes the italian is the murderer because
a. ) ratchett stole a car from him
b. ) ratchett insulted him
c. ) he must be a member of the mafia
d. ) he has been seen lurking around the safe
e. ) he has a hot temper
M. Bouc suspects Gino Foscarelli as the murderer due to Ratchett stealing Foscarelli's car, insults, hot temper, and possible mafia connections. The correct options are A, B, C, and E.
In Agatha Christie's "Murder on the Orient Express," M. Bouc believes that the Italian, Gino Foscarelli, is the murderer based on several reasons. Firstly, Ratchett had stolen a car from Foscarelli, indicating a possible motive for revenge.
Secondly, Ratchett had insulted Foscarelli, which could have provoked him to commit the crime. Additionally, Foscarelli's hot temper made him a likely suspect. Furthermore, M. Bouc believes that Foscarelli is a member of the mafia, which implies that he has the capability to carry out such a crime.
However, these reasons are not enough to make a conclusive argument for Foscarelli's guilt. The evidence against Foscarelli is based on assumptions, and Poirot highlights that the clues and motives are too obvious and simple.
Ultimately, the real motive and identity of the murderer are much more complex than initially anticipated. Therefore, M. Bouc's belief that Foscarelli is the murderer may not be entirely accurate.
In summary, M. Bouc believes that Foscarelli is the murderer due to several reasons, such as a possible motive for revenge and a hot temper. However, these reasons are not enough to make a conclusive argument for Foscarelli's guilt, and the real motive and identity of the murderer are much more complex. Therefore, the correct options are A, B, C, and E.
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A 0. 41 kg spike is hammered into a railroad
tie. The initial speed of the spike is equal to
1. 4 m/s. If the tie and spike together absorb 40. 4
percent of the spikeâs initial kinetic energy
as internal energy, calculate the increase in
internal energy of the tie and spike.
Answer in units of J.
please and thank you
A 0.41 kg spike is hammered into a railroad tie with 1.4 m/s initial speed. They absorb 40.4% of its initial kinetic energy as internal energy, resulting in an increase of 0.164 J in their internal energy.
To solve this problem, we need to use the conservation of energy principle, which states that the total energy in a closed system remains constant. In this case, the initial kinetic energy of the spike is converted into internal energy of the spike and tie.
The initial kinetic energy of the spike is given by:
[tex]KEi = (1/2) \times m \times v^2[/tex]
[tex]KEi = (1/2) \times 0.41 kg \times (1.4 m/s)^2[/tex]
KEi = 0.4054 J
The internal energy gained by the spike and tie is given by:
[tex]\Delta E = KEi \times 40.4\%[/tex]
[tex]\Delta E = 0.4054 J \times 0.404[/tex]
ΔE = 0.164 J
Therefore, the increase in internal energy of the spike and tie is 0.164 J.
In summary, a 0.41 kg spike is hammered into a railroad tie with an initial speed of 1.4 m/s. The tie and spike absorb 40.4% of the spike's initial kinetic energy as internal energy. Using the conservation of energy principle, we calculate that the increase in internal energy of the tie and spike is 0.164 J.
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c. To what height can a 400w engine lift a 100kg mass in 3s?
We need to use the formula for work done, which is :
W = F x D
P = W / T
In this case, the force (F) is equal to the weight of the mass, which is :
F = m x g
where m is the mass (100kg) and g is the acceleration due to gravity (9.81 m/s²).
F = 100kg x 9.81 m/s² = 981 N
The power (P) of the engine is 400 W, and the time (T) is 3 seconds.
P = W / T, therefore W = P x T = 400 W x 3 s = 1200 J
Now we can use the work formula to find the distance (D) that the engine can lift the mass :
D = W / F = 1200 J / 981 N = 1.22 m
Therefore, the 400W engine can lift a 100kg mass to a height of 1.22 meters in 3 seconds.
Coherent light of frequency 6. 32 x 1014 Hz passes through two thin slits and falls on a screen 85. 0 cm away. You observe that the third bright fringe occurs at ±3. 11 cm on either side of the central bright fringe.
(a) How far apart are the two slits?
(b) At what distance from the central bright fringe will the third dark fringe occur?
The distance among the two slits is 1.73 x 10⁻³ cm.
The third black fringe will appear 0.627 cm from the center of the dazzling fringe.
(a) The distance between the central bright fringe and the third bright fringe is given by:
Δy = (nλD) / d
where Δy is the distance between the central fringe and the nth bright fringe, λ is the wavelength of the light, D is the distance between the slits and the screen, and d is the distance between the slits.
Substituting the given values, we get:
3.11 cm = (1 x 632.8 nm x 85.0 cm) / d
Solving for d, we get:
d = (1 x 632.8 nm x 85.0 cm) / 3.11 cm = 1.73 x 10⁻³ cm
Therefore, the distance between the two slits is 1.73 x 10⁻³ cm.
(b) The distance between the central bright fringe and the nth dark fringe is given by:
Δy = [(2n - 1)λD] / (2d)
where Δy is the distance between the central fringe and the nth dark fringe, λ is the wavelength of the light, D is the distance between the slits and the screen, and d is the distance between the slits.
Substituting the given values and n=3, we get:
Δy = [(2 x 3 - 1) x 632.8 nm x 85.0 cm] / (2 x 1.73 x 10⁻³ cm) = 0.627 cm
Therefore, the third dark fringe will occur 0.627 cm away from the central bright fringe.
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A. the distance between the two slits is approximately 12.8 micrometers. B. the third dark fringe will occur at a distance of approximately 0.557 cm from the central bright fringe.
What is slit?Slit is a term used to refer to a long, narrow opening or gap. It is most commonly used to describe a thin cut in a piece of material or a surface. Slits are used in a variety of fields, including engineering, manufacturing, and architecture.
A. The distance between the two slits can be calculated using the equation:
d sinθ = mλ
First, we need to calculate the wavelength of the light using the frequency:
[tex]\lambda = c/f = (3.00 \times 10^8 m/s) / (6.32 \times 10^{14} Hz) = 4.74 \times 10^{-7} m[/tex]
[tex]tan \theta = (3.11 cm) / (85.0 cm)[/tex]
[tex]\theta = tan^{-1} (3.11 cm / 85.0 cm) = 2.10^{\circ}[/tex]
Finally, we can substitute the values into the equation and solve for d:
[tex]d = m\lambda / sin\theta = (3)(4.74 \times 10^{-7} m) / sin(2.10^{\circ}) \approx 1.28 \times 10^-5 m = 12.8 \mu m[/tex]
Therefore, the distance between the two slits is approximately 12.8 micrometers.
B. The distance from the central bright fringe to the third dark fringe can be calculated using the equation:
[tex]y = (m + 1/2) (\lambda d)\\y = (m + 1/2) (\lambda D/d) = (3 + 1/2) (4.74 \times 10^{-7} m) (85.0 cm) / (12.8 \times 10^{-6} m) \approx 0.557 cm[/tex]
Therefore, the third dark fringe will occur at a distance of approximately 0.557 cm from the central bright fringe.
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The various possible standing waves on a string are called theNodesAntinodesHarmonics (or resonant modes)incident waves
Answer: The various possible standing waves on a string are called Harmonics (or resonant modes). Harmonics are the frequencies of the standing waves that are produced when a string is plucked or struck. The harmonics are also sometimes referred to as overtones or partials. The nodes and antinodes are the points on the string where there is no displacement and maximum displacement respectively. The incident waves are the initial waves that are set up on the string before any reflections occur.
Explanation:
The various possible standing waves on a string are called Harmonics (or resonant modes).
Standing waves occur when two waves with the same frequency, amplitude, and wavelength travel in opposite directions and interfere with each other. This interference creates a unique pattern with specific points called Nodes and Antinodes.
Nodes are points on the string where the displacement is always zero, meaning they do not move. These points occur when the two waves perfectly cancel each other out.
Antinodes, on the other hand, are points on the string where the displacement is maximum. These points occur when the two waves perfectly reinforce each other, resulting in the greatest possible amplitude.
Harmonics (or resonant modes) are the different frequencies at which a string can support standing waves. The fundamental frequency, or first harmonic, is the lowest frequency at which a standing wave can form. Higher harmonics, or overtones, are multiples of the fundamental frequency and create more complex standing wave patterns.
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