The electric potential energy of a system of two point charges is inversely proportional of the distance between the two charges.
Electric potential energy is a implicit energy( measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may be said to have electric implicit energy by virtue of either its own electric charge or its relative position to other electrically charged objects.
The term" electric implicit energy" is used to describe the implicit energy in systems with time- variant electric fields, while the term" electrostatic implicit energy" is used to describe the implicit energy in systems with time- steady electric fields.
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12. Viking 1, the first spacecraft to land on Mars, traveled 7.00x10 km in 303 d. Calculate its average
speed in kilometers per second
Answer:
Viking 1 had reached a top speed of over 4 kilometers per second, or almost 9000 miles per hour. This is a fair bit over 10 times the speed of sound (in air), making it well over supersonic speeds.
What is the difference between precession and nutation in terms of the earth's rotation?
Precession is the change in direction of axis without change in tilt. Whereas nutation is the rocking, swaying, or nodding motion in the axis of rotation.
What is the difference between precession and nutation?Precession and nutation are due to gravity of nearer Earth and farther Sun on the Earth that varies with changing distance. The inclination 5 deg of orbital plane of Moon to the Earth's orbital plane and the inclination of equatorial bulge of the Earth at 23.4 deg to ecliptic are also contributors.
Period of long-term precession motion is about 260 centuries. In this motion, poles trace small circle of radius almost 2530 km, about normal to ecliptic. The short-term nutation (nodding) of polar axis is having compounded period of almost 18.6 years from oscillations with smaller periods up to as low as some days.
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A spring of k=500 N/m that is initially compressed 2m is used to launch a 100N load of bricks up a 2 m tall
hill. Find the speed of the bricks at the top of the hill.
a. Qualitatively complete the energy flow diagram and the energy bar graphs.
c. Determine the speed
e. What would the speed at the top of the hill be with 2m of initial compression if 15% of the energy is
dissipated through friction?
d. What is the minimum compression of the spring necessary to get to the top of the hill? (v=0 at top, no
friction)
Speed of the bricks at the top of hill is 6.26 m/s. c.)speed of the bricks at the top of hill is 14.14 m/s. d)minimum compression of spring necessary to get to the top of hill is 6.26 m. e) speed of the bricks at the top of hill with 2 m of initial compression and 15% energy dissipation is 13.04 m/s.
What is energy?The capacity or power to do work, such as the capacity to move an object by application of force is called energy.
Initial potential energy of compressed spring is:
Ep = 1/2 kx^2 = 1/2 * 500 N/m * (2 m)^2 = 1000 J
k is spring constant, x is compression of the spring, and J is unit of energy in joules.
Final potential energy of the bricks is:
Ep = mgh = 100 N * 9.81 m/s^2 * 2 m = 1962 J
Ep = Ep
1/2 kx^2 = mgh
v = sqrt(2gh) = sqrt(2 * 9.81 m/s^2 * 2 m) = 6.26 m/s
Therefore, the speed of the bricks at the top of the hill is 6.26 m/s.
c. Initial potential energy of compressed spring is: 1000 J
Ek = Ep = 1000 J
Kinetic energy of the bricks is given by:
Ek = 1/2 mv^2
1000 J = 1/2 * 100 N * v^2
v = sqrt(200 / 1) = 14.14 m/s
Therefore, the speed of the bricks at the top of the hill is 14.14 m/s.
d. As, Ep = m g h
where m is mass of the bricks, g is acceleration due to gravity, and h is height of the hill.
Ep = 100 N * 9.81 m/s^2 * 2 m = 1962 J
Ep = 1/2 kx^2 = 1962 J
1/2 * 500 N/m * x^2 = 1962 J
x = sqrt(2 * 1962 J / 500 N/m) = 6.26 m
Therefore, the minimum compression of the spring necessary to get to the top of the hill is 6.26 m.
e. If 15% of the energy is dissipated through friction, final kinetic energy of the bricks at the top of the hill will be 85% of initial potential energy of the compressed spring. Therefore,
0.85 * 1000 J = 1/2 mv^2
v = sqrt(170 / 1) = 13.04 m/s
Therefore, the speed of the bricks at the top of the hill with 2 m of initial compression and 15% energy dissipation is 13.04 m/s.
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What is kinetic-molecular theory in solids?
Kinetic molecular theory states that gas particles are in constant motion and exhibit perfectly elastic collisions.
The assumption that matter is made up of microscopic particles that are always in motion is the foundation of the kinetic-molecular theory, a theory that describes the states of matter.
However, the theory is most simply understood when it is applied to gases, therefore this is where our in-depth study will start. The theory especially pertains to the ideal gas model of a gas. An ideal gas is a hypothetical gas whose behaviour exactly matches all of the kinetic-molecular theory's presumptions. Although they are not perfect in actuality, gases come extremely close to being perfect in most real-world situations.
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Three objects having the same mass begin at the same height, and all move down the same vertical distance h. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of of a string.
The work completed should be comparable in all three circumstances.
The body's work is equal to mgH. (Gravitational potential energy).
Gravity and the normal force are both at work on a body descending a frictionless inclined plane. It won't make a difference to the gravitational potential energy.
The purpose of distance calculationWe can find out an object's actual size by knowing how far away it is. The area an object occupies in space above us can be measured. Once we know how far away it is, we can calculate its true size.
What is a distance?Length is an item's general motion in a purposeless fashion. Distance can be thought of as the amount of space a thing has traveled since it first appeared.
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How big is the Sun's radius compared to Earth?
The Sun is tons large than the Earth, with a radius of about 695,700 kilometers, while the earth has a radius of around 6,371 kilometers.
Because of this, the Sun's radius is greater than one hundred times larger than the earth's. The size difference between the Sun and the earth is quite massive.
In fact, if you have been to compare the sizes of the 2 items visually, the sun might appear as a huge, sparkling ball in the sky, while the earth might be just a tiny dot in contrast.
The sun's gigantic size performs a crucial position in the formation and renovation of our sun machine. Its gravity is chargeable for keeping all the planets in orbit, inclusive of the earth.
Additionally, the sun's excessive warmth and radiation provide the electricity important for existence to exist in the world. Standard, the sun's radius is an awful lot larger than earth's, and this size distinction has essential implications for the structure and behavior of our solar gadget.
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Only two forces act on an object (mass = 3. 00 kg), as in the drawing. Find the magnitude and direction (relative to the x axis) of the acceleration of the object.
The magnitude of the acceleration of the object is 17.6 m/s2 and the direction is 30.2° relative to the x axis.
What is accelaration?Acceleration is the rate if we object increases speed velocity of rate and change it is the change of the position of an object is relation can be either positive when the speed of an object increasing a negative in the speed of the object is decreasing.
The magnitude and direction of the acceleration of the object can be found by using Newton's Second Law of Motion. Newton's Second Law states that the net force on an object is equal to the mass of the object multiplied by its acceleration. Therefore, the net force of the two forces acting on the object (F1 and F2) can be found using the equation: Fnet = ma.
For this problem, we can assume that the mass of the object is 3.00 kg, so the equation becomes: Fnet = 3.00 kg × a.
We can now solve for the acceleration by substituting the values of the two forces (F1 and F2) into the equation. The two forces can be found by using the equation for the magnitude of a force: F = ma.
For force F1, we can assume that its magnitude is 10 N and its direction is 45° relative to the x axis. Therefore, the equation for F1 becomes: F1 = (3.00 kg) × (10 N) × cos(45°).
For force F2, we can assume that its magnitude is 8 N and its direction is -30° relative to the x axis. Therefore, the equation for F2 becomes: F2 = (3.00 kg) × (8 N) × cos(-30°).
Substituting these two equations into the equation for net force (Fnet = ma), we get:
Fnet = (3.00 kg) × (10 N × cos(45°) + 8 N × cos(-30°)).
Solving for the acceleration, we get: a = (10 N × cos(45°) + 8 N × cos(-30°))/3.00 kg.
Therefore, the magnitude of the acceleration of the object is 17.6 m/s2 and the direction is 30.2° relative to the x axis.
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4. Find someone in the class that has a wire hoop with a different number of loops in it. When you put your magnet near their hoop, does it rotate at the same rate, at a greater rate, or at a lower rate? Explain why you think this is relative to their number of loops.
When you put your magnet near a wire hoop with a different number of loops, the rate of rotation will depend on the number of loops in the wire hoop.
How does wire hoop experiment work?The greater the number of loops, the greater the induced current and the stronger the magnetic field. This results in a greater torque on the wire hoop and a faster rate of rotation. On the other hand, a wire hoop with a smaller number of loops will have a weaker induced current and magnetic field, resulting in a slower rate of rotation.
Therefore, the rate of rotation of the wire hoop will depend on the number of loops in the wire hoop, with more loops resulting in a greater rate of rotation and fewer loops resulting in a slower rate of rotation.
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early february is halfway between what two seasonal events. t/f
True.
Early February is halfway between the winter solstice and the spring equinox in the Northern Hemisphere.
What is Winter Solstice & Spring Equinox?The winter solstice occurs around December 21st or 22nd and marks the shortest day and longest night of the year. The spring equinox occurs around March 20th or 21st and marks the start of spring, when the day and night are roughly equal in length. Halfway between these two events is approximately February 10th, marking the gradual shift from winter to spring.
The winter solstice marks the point when the sun is at its farthest point from the equator and the Northern Hemisphere is tilted away from the sun, causing the shortest day and longest night of the year. On the other hand, the spring equinox marks the point when the sun is directly over the equator and the day and night are approximately equal in length.
Halfway between the winter solstice and the spring equinox is a time when the days start to get noticeably longer and the sun rises higher in the sky, signaling the end of winter and the beginning of spring. This is a gradual transition and not a sudden change. In early February, the sun rises earlier and sets later, and the length of daylight continues to increase until the spring equinox.
In the Northern Hemisphere, early February is a time when the weather starts to warm up and the first signs of spring become visible, such as the emergence of buds on trees and the first crocus flowers in gardens. However, it is still winter and the weather can be cold and wintry.
In the Southern Hemisphere, early February is the height of summer, with warm temperatures and longer daylight hours. This is the opposite of the Northern Hemisphere, where it is the height of winter.
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What does the change in the period with respect to the semimajor axis tell you about the dependence of the period on the semimajor axis?
The change in the period with respect to the semi major axis tells that as the semi major axis of an object's orbit increases, its period will increase as well. (Kepler's Third Law of Planetary Motion)
What is Kepler's Third Law of Planetary Motion?Kepler's Third Law of Planetary Motion, also known as the "Harmonic Law," states that the square of the period of an object in orbit around a central body is proportional to the cube of its semi major axis. In other words, the longer the average distance of an object from the central body, the longer its orbital period will be.
This law applies to all objects in orbit around a central body, including planets, moons, asteroids, and comets. It is based on the laws of gravitation and provides important information about the dynamics of objects in orbit. By using this law, we can calculate the average distance of an object from a central body, its orbital period, and other orbital characteristics.
The relationship can be expressed as:
[tex]T^2 = k * a^3[/tex]
where T is the period of the object, a is its semi major axis, and k is a constant of proportionality.
Therefore, a change in the period with respect to the semi major axis can provide information about the dependence of the period on the semi major axis, specifically that the period increases as the semi major axis increases. This relationship is a direct result of Kepler's Third Law and the laws of gravitation, and provides important insights into the behaviour of objects in orbit.
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During a race, the 48 kg runner accelerates from 5.1 m/s to 8.7 m/s to take the lead. What is the runner's change
in momentum?
Answer: the runner's change in momentum is 172.8 kg·m/s.
Explanation:
To find the change in momentum of the runner, we can use the equation:
change in momentum = mass x change in velocity
The mass of the runner is given as 48 kg, and the change in velocity can be calculated as:
change in velocity = final velocity - initial velocity
change in velocity = 8.7 m/s - 5.1 m/s
change in velocity = 3.6 m/s
Therefore, the change in momentum of the runner is:
change in momentum = mass x change in velocity
change in momentum = 48 kg x 3.6 m/s
change in momentum = 172.8 kg·m/s
So the runner's change in momentum is 172.8 kg·m/s.
two coherent sources of radio waves, a and b, are 5.00 meters apart. each source emits waves with wavelength 6.00 meters. consider points along the line connecting the two sources.
At points along the line connecting the two sources, the two sources of radio waves interfere with each other. This interference can result in constructive or destructive interference, depending on the relative phase of the waves at the point of interest.
If the two waves have the same phase, they will reinforce each other, resulting in constructive interference and a maximum in the total amplitude of the waves. If the two waves have a phase difference of 180 degrees, they will cancel each other out, resulting in destructive interference and a minimum in the total amplitude of the waves.
The phase difference between the two waves at a given point along the line connecting the two sources can be calculated using the difference in the path lengths from the two sources to the point. The path difference is given by:
d = (2n + 1) λ/2
where n is an integer, λ is the wavelength of the radio waves, and d is the path difference. For constructive interference, the path difference must be an integer multiple of λ, while for destructive interference, it must be an odd multiple of λ/2.
So, considering the two sources of radio waves a and b are 5.00 meters apart and each source emits waves with wavelength 6.00 meters, the path difference between the two waves at a given point along the line connecting the two sources can be calculated as d = 5.00 meters. Based on the equation above, this corresponds to a phase difference of approximately 150 degrees, resulting in destructive interference at that point.
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Name and describe one type of evidence that the Earth has been through colder conditions
One type of evidence that the Earth has been through colder conditions is the presence of glacial deposits, such as till, striations, and moraines.
What is glacial deposits?Glacial deposit refers to the material that has been deposited by a glacier, either through direct contact or through the action of meltwater.
This material can include rock fragments of various sizes, ranging from fine-grained clay to large boulders, as well as sand and gravel. In some cases, the material may be sorted into distinctive layers, depending on the size and type of the particles.
Glacial deposits can be found in areas that were covered by ice during the last ice age, as well as in areas that are currently covered by glaciers. They provide important clues about the movement and behavior of glaciers and can also be valuable resources for construction and other industries.
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When heating this reaction mixture at reflux, the reaction temperature will be maintained at approximatelyA. 25CB. 65CC. 100CD. 125C
The reaction temperature will be maintained at approximately 100°C when heating the reaction mixture at reflux.
What is Reflux?Reflux is a common technique in organic chemistry where a reaction mixture is heated at a temperature near its boiling point, with the vapor generated by the reaction being condensed and returned to the reaction flask. This maintains the temperature of the reaction mixture at a constant value, typically near the boiling point of the solvent used in the reaction.
In general, the temperature of a reflux reaction will depend on the boiling point of the solvent used. If the solvent has a boiling point of 100°C, for example, then the reaction temperature will be maintained at approximately 100°C when the reaction mixture is heated at reflux.
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rank the types of radiation in order of their energy, from least to greatest.
The types of radiation, ranked in order of their energy from least to greatest are:
Radio WavesMicrowavesInfrared RadiationVisible LightUltraviolet RadiationX-raysGamma RaysWhat is radiation?It's important to note that these types of radiation form a continuous spectrum, with the boundaries between each type of radiation being somewhat arbitrary. The amount of energy in a particular type of radiation depends on its frequency or wavelength. In general, radiation with higher frequency or shorter wavelength has more energy than radiation with lower frequency or longer wavelength.
Radiation refers to the emission of energy as electromagnetic waves or as moving subatomic particles, especially high-energy particles that cause ionization.
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what is theory of change lewin?
The theory of change Lewin is a framework used to analyze and understand how a certain change can be achieved in a given situation.
The theory of change Lewin was developed by Kurt Lewin, a social psychologist who studied how to bring about change in organizations and communities. The theory explains that any change process involves three main stages: unfreezing, changing, and refreezing.
Unfreezing is when people become aware that change is necessary and are willing to let go of old habits and beliefs. Changing is the actual implementation of new behaviors and practices. Refreezing is when the new behaviors become the norm and are reinforced to ensure sustainability.
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what did newton do in an attempt to separate the visible light spectrum?
Answer:
He used a prism.
Explanation:
Newton set up a prism near his window, and projected a beautiful color spectrum 22 feet onto the far wall.
what theory was written by copernicus, and it placed the sun in the middle of the solar system?
Copernicus proposed the heliocentric theory of the solar system, in which the sun is positioned at the system's centre.
In his heliocentric theory, Copernicus predicted the arrangement of all known planets and calculated their average orbital periods around the sun.He was also effective in explaining the everyday motions of heavenly bodies, such as the sun's rising and setting, with this idea.He said that the sun is fixed and situated at the centre of the solar system under this hypothesis.This model provided a mathematical explanation for the apparent daily motion of the stars and planets, and it also allowed for better predictions of their positions in the sky.
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What is spring-mass-damper system formula?
The formula of a spring-mass-damper system is given by md2x/dt2 + cdx/dt + kx = F(t).
The spring-mass-damper system is a common model used in physics and engineering to describe the behavior of various mechanical systems, such as a car suspension system or a building during an earthquake. The equation of motion for a spring-mass-damper system is typically given by:
md2x/dt2 + cdx/dt + kx = F(t)
where m is the mass of the object attached to the spring and damper, x is the displacement of the mass from its equilibrium position, t is time, c is the damping coefficient, k is the spring constant, and F(t) is an external force applied to the system at time t.
The term md2x/dt2 represents the acceleration of the mass, while cdx/dt represents the damping force (i.e. resistance to motion) caused by the damper, and kx represents the force exerted by the spring. The external force F(t) can be any force applied to the system, such as an oscillating force or a constant force.
The solution to this differential equation depends on the initial conditions (i.e. the initial position and velocity of the mass) and the specific values of the parameters m, c, and k. The behavior of the system can be analyzed using various techniques, such as finding the natural frequency of the system or using numerical simulations to model the motion over time.
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under electrostatic conditions, there is no electric field inside a solid conductor. True/False ?
False. Under electrostatic conditions, there is no electric field inside a solid conductor only if the conductor is in a state of electrostatic equilibrium. In other words, if the conductor is charged, there will be an electric field inside the conductor, but it will decrease rapidly as you move away from the surface of the conductor.
What is electric field?The electric field is a field that represents the force that would be exerted on a charged particle at a particular point in space. It is a measure of the intensity of the electric force that a charged object would experience if placed at that point in space.
The electric field can be represented mathematically as a vector field and is typically denoted by the symbol "E". It is a measure of the force per unit charge and has units of volts per meter (V/m). The direction of the electric field at a particular point is the direction of the force that would be exerted on a positive test charge placed at that point.
Electric fields are a fundamental concept in electricity and electromagnetism and play an important role in a wide range of applications, including electric motors, generators, and electronic devices. They are used to describe the behavior of charged particles and the interactions between charged particles, and are an essential tool for understanding and describing the behavior of electric and magnetic fields.
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In terms of the behaviour of molecules, describe what happens during the process of evaporation
Answer: Evaporation happens when a liquid substance becomes a gas. When water is heated, it evaporates. The molecules move and vibrate so quickly that they escape into the atmosphere as molecules of water vapor
Explanation: Evaporation is simply the heating of water to turn it to gas,like when you boil water in a kettle,that process is defined as evaporation
4. A roller coaster car of mass m = 200 kg is released from rest at the top of a 60
Im high hill (position A), and rolls with negligible friction down the hill,
through a circular loop of radius 20 m (positions B, C, and D), and along a
horizontal track (to position E).
A
b = 60m
r = 20m
B
D
C
a. What is the velocity of the car at position B?
The velocity of the car at position B would be 34.7 m/s.
What is potential energy?The energy of the body due to its position in relative to earth is called potential energy.
Given is that a roller coaster car of mass m = 200 kg is released from rest at the top of a 60m high hill (position A), and rolls with negligible friction down the hill, through a circular loop of radius 20 m (positions B, C, and D), and along a horizontal track (to position E).
From the energy conservation, we can write -
mgh = 1/2 mv²
60 x 10 x 200 = 1/2 x 200 x v²
v² = 1200
v = √1200
v = 34.7 m/s
Therefore, the velocity of the car at position B would be 34.7 m/s.
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An object is spun around in a circle of radius 1. 0 m with a period of 4. 0 s. What is the magnitude of the velocity?.
According to the question the magnitude of the velocity is 2π m/s.
What is magnitude?Magnitude is a measure of the size or intensity of something. It is often used to describe the size and intensity of physical phenomena such as earthquakes, floods, and hurricanes. Magnitude is usually measured in terms of a numerical scale, where a higher number indicates a higher level of intensity. Magnitude is a relative measure, meaning that it is measured in comparison to other phenomena of the same type. For example, a magnitude 5 earthquake is five times more intense than a magnitude 4 earthquake. The magnitude of some phenomena like wind speed, solar radiation, and temperature can also be measured in terms of their absolute values.
This can be calculated using the formula V = 2πr/T,
where V is the velocity,
r is the radius, and T is the period.
In this case, r is 1 m, and T is 4 s,
so V = 2π/4 = 2π m/s.
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A box sits on the horizontal bed of a truck accelerating to the left. Static friction between the box and the truck keeps the box from sliding around as the truck accelerates. The work done on the box by the static friction force as the accelerating truck moves a distance D to the left is:a. positiveb. zeroc. negatived. dependent on the speed of the truck
The work done on the box by the static friction force is zero.
What is work done ?Work is a measure of the energy transferred to or from an object by a force when the object is displaced. The amount of work done is defined as the product of the magnitude of the force and the distance over which the force is applied. It could be written as
Work (W) = Force (F) x Distance (d) x cos(theta)
where theta is the angle between the force and the displacement.
When a force is applied to an object, work is done if there is displacement in the direction of the force. If there is no displacement, no work is done. If the force is perpendicular to the displacement, no work is done, as the cosine of 90 degrees is zero.
Work is a scalar quantity and is measured in joules (J) in the SI system. One joule of work is done when a force of one newton (N) is applied over a distance of one meter (m) in the direction of the force.
Work can be either positive or negative, depending on the direction of the force and the displacement. When the force and displacement are in the same direction, the work is positive. When the force and displacement are in opposite directions, the work is negative.
The work done on the box by the static friction force is zero.
This is because the static friction force acts perpendicular to the displacement of the box. Therefore, the angle between the static friction force and the displacement of the box is 90 degrees. In this case, the work done by the static friction force is given by the dot product of the force and the displacement, which is equal to Fdcos(theta), where theta is the angle between the force and the displacement. Since cos(90) = 0, the work done by the static friction force is zero.
Note that although the static friction force does no work on the box, it does provide the necessary force to keep the box in place and prevent it from sliding around as the truck accelerates.
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A 0. 50-m long solenoid consists of 800 turns of copper wire wound with a 5. 0 cm radius. When the current in the solenoid is 12 a, the magnetic field at a point 1. 0 cm from the central axis of the solenoid is.
The magnetic field at a point 1.0 cm from the central axis of the solenoid is 1.6 x 10^-3 T.
The magnetic field (B) inside a solenoid can be calculated using the formula:
B = μ_0 * n * I / L
where μ_0 is the vacuum permeability (4π x 10^-7 T m/A), n is the number of turns per unit length, I is the current in the solenoid, and L is the length of the solenoid.
For the given solenoid, the number of turns per unit length can be calculated as follows:
n = 800 turns / 0.5 m
n = 1600 turns/m
At a point 1.0 cm from the central axis of the solenoid, the magnetic field can be calculated as follows:
B = μ_0 * 1600 turns/m * 12 A / (0.05 m)
B = 1.6 x 10^-3 T.
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A star that begins with a mass 8 to 20 times that of the Sun’s mass will
A star that begins with a mass between about 8 and 20 times the Sun's mass will end up with a core that is too massive to be supported by electron pressure. Such a star comes to a violent end. Neutron star form when fusion ends.
What is a neutron star?
A type of celestial object known as a neutron star is created from the remains of a massive star that has experienced a supernova explosion. With a mass comparable to that of the sun but squeezed into a sphere about 20 kilometres in diameter, neutron stars are extraordinarily dense. Because of this tremendous density, the gravitational field is approximately one billion times greater than on Earth.Neutrons are non-charged subatomic particles that make up nearly the whole mass of neutron stars. The neutron star is effectively a huge atomic nucleus since these neutrons are crammed so closely together.To know more about neutron star, click the link given below:
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Which type of forces are subjected in truss?
Tension and compression forces act on diagonal and vertical members respectively in a truss structure.
A truss is a construction that comprises of a progression of interconnected triangles, intended to disperse stacks and give security. The powers that follow up on a bracket can be characterized into two kinds: pressure and pressure powers.
Tension powers are powers that draw on a part, like a rope or link. In a support, strain powers follow up on the corner to corner individuals that structure the triangles. These individuals are under pressure since they are being pulled separated.
Compression forces are forces that push on a part, like a segment or shaft. In a support, pressure powers follow up on the upward individuals that associate the top and base harmonies of the bracket. These individuals are under pressure since they are being crushed together.
Notwithstanding pressure and pressure powers, brackets can likewise be exposed to twisting minutes and shear powers, which are brought about by outer burdens following up on the support.
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A mass of 0. 40 kg, hanging from a spring with a spring constant of 160 n/m, is set into an up-and-down simple harmonic motion. What is the speed of the mass when moving through the equilibrium point? the starting displacement from equilibrium is 0. 10 m.
Given:
[tex]m=0.40kg[/tex]
[tex]k=160\frac{N}{m}[/tex]
[tex]A=0.10m[/tex]
We know that the velocity of a mass attached to a spring is greatest when passing through equilibrium. Using the following formulas we can compute velocity.
[tex]v_{max} =\pm Aw[/tex] and [tex]w=\sqrt{\frac{k}{m} }[/tex] [tex]\Longrightarrow v_{max} =\pm A\sqrt{\frac{k}{m} }[/tex]
[tex]\Longrightarrow v_{max} =\pm A\sqrt{\frac{k}{m} }[/tex]
[tex]\Longrightarrow v_{max} =\pm (0.10)\sqrt{\frac{160}{0.40} }[/tex]
[tex]\Longrightarrow v_{max} =\pm (0.10)(20) }[/tex]
[tex]\Longrightarrow v_{max} =\pm 2.0\frac{m}{s}[/tex]
A car starts from rest on a curve with a radius of 130m and tangential acceleration of 1.3m/s2 .Through what angle will the car have traveled when the magnitude of its total acceleration is 2.2m/s2 ?
the car's angle of travel be when its entire acceleration is 2.2m/s2 = 23.58°
What causes acceleration?Acceleration is the change in speed that occurs quickly. Generally speaking, but not always, acceleration denotes a shift in speed. Even while it travels in a circular motion, an object's velocity direction is changing, thus it keeps gaining speed.
What is velocity, and what is the SI unit of acceleration?In physics, acceleration is the rate at which an object's velocity varies in relation to time. The result of all forces acting on an item is its acceleration, according to Newton's Second Law. The SI unit for acceleration is the metre squared (m s2).
According to the given information:Tangential acceleration, at = 1.2 m/s²
Total acceleration, a = 3 m/s²
Let the angle is Ф.
According to the formula
a² = a[tex]_t[/tex]² + ar²
9 = (1.2)² + ar²
ar =3 m/s²m
tanФ = 0.4364
Ф = 23.58°
the car's angle of travel be when its entire acceleration is 2.2m/s2 = 23.58°
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In the diagram, R1= 40.0 ohms,
Answer:
58.7Ω
Explanation:
You want the equivalent resistance of 40Ω in series with the parallel combination of 25.4Ω and 70.8Ω.
Parallel resistorsThe equivalent resistance of two parallel resistors, r1 and r2 is ...
req = 1/(1/r1 +1/r2)
For the two given parallel resistors, that is ...
1/(1/25.4 +1/70.8) ≈ 18.69 . . . . ohms
Equivalent resistanceThe circuit has a 40Ω resistor in series with this, so the equivalen resistance is ...
40 +18.69 = 58.69Ω ≈ 58.7Ω
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Additional comment
Since the given resistor values are expressed to 0.1 ohms, we have rounded the answer to the same precision. The exact value is 141158/2405 as shown in the calculator display—assuming the given values are exact.