When we see the brightest star in the constellation Orion just rising above your eastern horizon at 10 pm and One week later at 10 PM this same star will be at its highest point in the sky, directly overhead .
The position of Stars in the sky changes as the Earth rotates on its axis.
As the Earth rotates, different stars appear to rise in the east and set in the west.
If we see the brightest star in constellation Orion just rising above our eastern horizon at 10 PM, and 1 week later at 10 PM, this same star will be at its highest point in the sky, directly overhead.
This is because the Earth has rotated 1 full revolution in a week, which causes the star to move from the eastern horizon to the overhead position.
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the two lines on the p-v diagram are called isotherms, lines of constant temperature. which isotherm represents the higher temperature?
The two lines on the p-v diagram would be T2 because of their higher pressure if they were isotherms—lines of constant temperature.
What are the isotherms?An isotherm is a geographic line that connects locations with the same temperature at a particular time. The state of a gas will change on the PV diagram as it undergoes a thermodynamics process, drawing out a path as it progresses.
Isotherms are frequently used in meteorology to depict the temperature distribution at the Earth's surface, or to represent constant level or constant pressure on a chart.
A refrigerator operates isothermally. The refrigerator's mechanism goes through a lot of changes, but the temperature inside remains constant.
Therefore, the environment receives the heat energy that has been dissipated here. Another example of an isothermal process is the heat pump.
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discuss what will happen if the single cosinusoidal term on the rhs of of eq. 10.58 is replaced by two or more cosinusoidal terms, each with a different drive frequency.
Replacing the single co-sinusoidal term with two or more terms of different frequencies will lead to a more complex motion of the oscillator, with multiple oscillations superimposed on each other.
The resulting motion may exhibit resonance or chaotic behavior, depending on the frequencies of the driving forces and the natural frequency of the oscillator. This occurs when the frequency of the driving force matches the natural frequency of the oscillator, leading to a large amplitude oscillation. Frequencies of the driving forces are not in resonance with the natural frequency of the oscillator, the resulting motion may be chaotic, with the oscillator undergoing complex oscillations of varying frequencies and amplitudes.
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how long (in s) would it take to reach the ground if it is thrown straight down with the same speed?
If an object is thrown straight down with the same speed, the time it takes to reach the ground depends on the height from which it was thrown and can be calculated using the formula [tex]t = sqrt(2h/g)[/tex] where t is the time, h is the height, and g is the acceleration due to gravity, which is approximately equal to [tex]9.8 m/s^2[/tex] near the surface of the Earth.
If the object is thrown straight down with the same speed, it means that has zero initial velocity. In this case, the height h is simply the height from which the object was thrown.
Therefore:
[tex]t = sqrt(2h/g)[/tex]
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A sphere with radius 2. 0 mm carries a 3 μc charge. What is the potential difference, vb - va , between point b 3 m from the center of the sphere and point a 7 m from the center of the sphere? (the value of k is 9. 0 × 109 n∙m2/c2. )
The potential difference between point b and point a on the charged sphere with a 3 μC charge and a radius of 2.0 mm is [tex]1.57 * 10^5[/tex] volts.
The potential difference between two points on a charged sphere can be calculated using the formula for electric potential: V = k * Q / r, where k is Coulomb's constant ([tex]9.0 * 10^9 Nm^2/C^2[/tex]), Q is the charge on the sphere (3 μC), and r is the distance from the center of the sphere to the point in question. To find the potential difference, we subtract the potential at point a from the potential at point b.
Put values so find that the potential at point a is:
Va = k * Q / ra = ([tex]9.0 * 10^9 Nm^2/C^2[/tex]) * ([tex]3 * 10^-6 C[/tex]) / (7 m) = [tex]1.29 * 10^5[/tex] V.
And the potential at point b is:
Vb = k * Q / rb = ([tex]9.0 * 10^9 Nm^2/C^2[/tex]) * ([tex]3 * 10^-6 C[/tex]) / (3 m) = [tex]2.86 * 10^5[/tex] V.
The potential difference between the two points is then:
Vb - Va = [tex]2.86 * 10^5 V - 1.29 * 10^5 V[/tex] = [tex]1.57 * 10^5[/tex] V.
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Describe something Joule believed that contradicted the beliefs of his peers.
Answer:
Joule, a 19th-century physicist, believed in the conservation of energy, which contradicted the beliefs of his peers at the time. His contemporaries believed that energy was a substance that could be created or destroyed. In contrast, Joule believed that energy could only be transformed from one form to another but could never be created or destroyed. He demonstrated this through a series of experiments where he showed that heat and mechanical work were equivalent forms of energy and that the total amount of energy in a closed system remained constant.
Joule's ideas challenged the established scientific beliefs of his time. They paved the way for the development of the first law of thermodynamics, which states that the total energy in a closed system is constant and cannot be created or destroyed. By proposing and demonstrating these ideas, Joule made significant contributions to the development of classical physics and helped lay the foundations of modern energy science.
Answer:
James Prescott Joule was a 19th-century British physicist who made significant contributions to the study of thermodynamics. One of his beliefs that contradicted the beliefs of his peers was the idea that heat was a form of energy.
At the time, the prevalent belief was that heat was a fluid-like substance called "caloric" that flowed from hot objects to cold objects. Joule challenged this idea and proposed that heat was actually a form of energy that could be transformed into other forms of energy, such as mechanical energy.
Joule's work showed that heat was a conserved quantity, much like energy, and that it could be quantified in terms of work done. This was a significant departure from the prevailing ideas of the time and helped lay the foundation for the study of thermodynamics.
what is the vertical component of the velocity just before the stone hits the ground, in meters per second?
The vertical component of velocity shortly before the stone reaches the ground equals the original vertical velocity ie, v m/s
The vertical component of an object's velocity right before impact can be computed using equations of motion. If we examine a gravity-affected item with a beginning velocity (v0) and no air resistance, its vertical velocity (v) may be given by the equation:
v = v0 - gt
where g is the gravitational acceleration (9.8 m/s2) and t is the time since the item was launched.
To calculate the vertical component of velocity immediately before the stone reaches the ground, we must first compute the time t required for the stone to reach the ground. The following equation may be used to compute this:
t = (v0 - v) / g
By reintroducing the value of t into the first equation, we obtain:
v = v0 - gt = v0 - g((v0 - v) / g) = v0 - (v0 - v) = v
It is crucial to note that this estimate assumes no air resistance and that the object is dropped from a height far lower than the radius of the Earth, allowing the curvature of the Earth to be ignored. In fact, air resistance may have a major impact on an object's velocity, particularly as it approaches the earth.
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There is a little island off the shore of Brazil where the weather is extremely consistent. From 1911 to 1990, the lowest temperature on the island was 18°C (64°F) and the highest temperature was 32°C (90°F). It is known that the liquid in a standard can of soft drink absorbs 20. 8 kJ of energy when its temperature increases from 18. 0°C to 32. 0°C. If the soft drink has a mass of 0. 355 kg, what is its specific heat capacity?
The specific heat capacity of the soft drink is 58.95 J/g°C.
What is the capacity ?The capacity of something is the maximum amount it can hold or contain. This can refer to physical items, like a bottle or a room, or it can refer to abstract concepts such as memory or knowledge. Capacity is usually measured in terms of volume, weight, or number of items. In terms of physical items, capacity is usually determined by the size, shape, and material used in the creation of the object. For abstract concepts, capacity is usually determined by the individual's ability or knowledge.
The specific heat capacity of the soft drink is 58.95 J/g°C.
We can calculate the specific heat capacity of the soft drink using the following equation:
Specific heat capacity = (Energy absorbed) / (Mass * Change in Temperature)
In this case, the energy absorbed is 20. 8 kJ, the mass is 0. 355 kg, and the change in temperature is 14°C (32°C - 18°C). Plugging these values into the equation, we get:
Specific heat capacity = (20. 8 kJ) / (0. 355 kg * 14°C)
Specific heat capacity = 58.95 J/g°C
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if you wanted to sail around the globe but wanted to remain south of africa and south america, what single current could you use to speed up your trip?
Answer: electromagnetism
Explanation: hope this hel[ps
now describe the relationship between the force and the electric field. again, how are they related conceptually and mathematically?
The relationship between the force and the electric field is described by Coulomb's law is F = qE.
The relationship between the force and the electric field is described by Coulomb's law, which states that the force experienced by a point charge in an electric field is proportional to the magnitude of the charge and the electric field. Mathematically, Coulomb's law can be expressed as:
F = qE
where F is the force experienced by the point charge (q), E is the electric field, and q is the magnitude of the charge.
Conceptually, the electric field can be thought of as a field of force that is created by charged particles. A point charge placed in this field experiences a force proportional to both the magnitude of the charge and the strength of the field. This relationship between the electric field and the force experienced by a point charge forms the basis of Coulomb's law.
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A snow boarder weights 300 N. The area of snow border is 0.5 m2. What is pressure on the snow?
Answer:
600 Pa
Explanation:
see attachment
hope this helps
PLEASE HELP ASAP 30 POINTS AND BRAINLY IF RIGHT. The arrow in the photo represents a force.
Which force is equal but opposite to the one shown?
Answer:
the ancer is c I know it because I had the same test or it might have been different but it looks familiar to me
The direction of the electric field at point b is closest to which direction? A. Right B. Up C. Left D. Down
The electric field will be along the left direction.
What is electric field?An electric field is a region around the charge where its force of attraction or repulsion can be measured.
Given is the equipotential surface as shown in the image attached.
We know that electric field is the negative gradient of electric potential.
We can write -
E = - dV/dx
- dV = E dx
dV = - E dx
V = - ∫E dx
So, the electric field will be along the left direction.
Therefore, the electric field will be along the left direction.
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a stone is thrown vertically upward with a speed of 27.0 m/s m / s . part a how fast is it moving when it is at a height of 13.0 m m ?
The speed of the stone when it reaches a height of 13.0 m is
GIven:
Stone is thrown vertically upward with initial speed of (V0) 27.0 m/sTo calculate the speed one it reaches a certain height, we can use the formula as follows:
Vt² = V0² - 2*g*s
g = the acceleration due to gravity (9.8 m/s²)In the case above, V0 = 27 m/s and the s is 13 m. Plug these numbers to the formula above:
Vt² = V0² - 2*g*s
Vt² = 27² - 2 * 9.8 * 13
Vt² = 729 - 254.8
Vt² = 474.2
Therefore,
Vt = √474.2
Vt = 21.776 m/s
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a force pair is created when you push on a large crate that rests on the floor. the crate does not move when pushed. which free-body diagram correctly represents the forces acting on the crate? (note: vectors are not drawn to scale)
Each half of the force pair acts on a different object Free-body diagram correctly represents the forces acting on the crate.
In physics and engineering, a loose body diagram (FBD; additionally known as a pressure diagram) is a graphical example used to visualize the implemented forces, moments, and resulting reactions on a body in a given condition. It depicts a body or connected bodies with all the implemented forces and moments, and reactions, which act at the body(ies). The frame might also encompass multiple internal participants (along with a truss), or be a compact frame (together with a beam). a chain of loose bodies and other diagrams can be necessary to remedy complicated troubles.
Loose frame diagrams are used to visualize forces and moments implemented in a body and to calculate reactions in mechanics issues. those diagrams are frequently used to decide the loading of character structural components and to calculate inner forces inside a structure. they're used by maximum engineering disciplines from Biomechanics to Structural Engineering.
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How many centimeters is the moon moving away from the earth each year?
Moon is moving away by 3.8 centimeters every year from the earth.
Because of its power of attraction, the moon pulls specific pieces of the Earth nearer to it more emphatically, making the flowing lump in the expanses of our planet. Since the Earth pivots a lot quicker than the moon, this lump happens somewhat in front of the last option, which, because of various actual peculiarities, drives the moon into a higher circle around Earth.
It's hazardously simple to underestimate the moon. Exactly the same thing is valid for the sun. In any case, if not for their everlasting presence in our skies, life on Earth would be extremely, not quite the same as what it is presently, and it wouldn't be an especially charming thing for us!
Notwithstanding, our main natural satellite - the moon - is really creating some distance from Earth. Its circle is getting bigger consistently!
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a 0.24 kg blob of clay is thrown at a wall with an initial horizontal velocity of if the clay comes to a stop in what is the average horizontal force on the clay due to the wall?
According to the solving the average force experienced by the clay = 42N.
How much average force as well as impulse is there?The term "impulse of force" refers to the sum of average force and time of application. according to Newton's second law. Providing the mass is constant, it is possible to calculate the impulse of force and discover that it equals the change in momentum of an object. Calculation.
According to the given information:Mass of the blob of clay is m=0.24kg
Initial velocity of the blob of clay is vi=16m/s
Final velocity of the blob of clay is vf=0m/s
The following formula can be used to calculate the change in the clay blob's linear momentum:
ΔP = M(vf - vi)
= (0.24 kg)(0m/s - ( - 16 m/s)
= 3.48 kg . m/s
So, the following formula can be used to calculate the average force that the clay encountered:
F[tex]_a_v_g[/tex] = ΔP/Δt
= (3.84 kg . m/s)/ 91ms
= (3.84 kg . m/s)/91 × 10⁻³ s
= 42N.
According to the solving the average force experienced by the clay = 42N.
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A 0.24 kg blob of clay is thrown at a wall with an initial velocity of 16 m/s. If the clay comes to a stop in 91 ms, what is the average force experienced by the clay?
A) 42 N
B) 26 N
C) 35 N
D) 51 N
describe the circuitry of three strings of patio lights plugged into the same extension cord. one whole string does not light, but all the bulbs in the other two strings do.
The connection of three strings of patio lights, One whole string does not light, but all bulbs in the other two strings do three strings are connected in series, while each string's bulbs are connected in parallel.
The voltage across each component in a parallel connection is equal to voltage throughout the network, despite each component being connected via a different path.
The three strings are connected in series, while each string's bulbs are connected in parallel. The remaining strings of bulbs will continue to glow even if one bulb in a string fails.
Therefore, three strings are connected in series while each string's bulbs are connected in parallel.
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a mass of 5 lb is acted upon by an upward force of 16 lb. the only additional force on the mass is the force of gravity. find the acceleration in ft/s2 . is this acceleration upward or downward?\
A mass of 5 lb is acted upon by an upward force of 16 lb. the only additional force on the mass is the force of gravity. The acceleration is -29 ft/[tex]s^{2}[/tex], which is downward.
The net force on the 5 lb mass is equal to the difference between the upward force and the force of gravity. The force of gravity can be calculated as follows:
fgravity = m . g
where,
m = 5 lb (mass)
g = 32.2 ft/[tex]s^{2}[/tex] (acceleration due to gravity)
So,
fgravity = 5 lb * 32.2 ft/[tex]s^{2}[/tex] = 161 lb
The net force on the mass can then be calculated as follows:
fnet = fupward - fgravity = 16 lb - 161 lb = -145 lb
Since the net force is negative, it acts in the downward direction. To calculate the acceleration, we use Newton's second law of motion:
f = ma
where,
m = 5 lb (mass)
a = acceleration
Solving for acceleration, we get:
a = fnet / m = -145 lb / 5 lb = -29 ft/[tex]s^{2}[/tex]
So, the acceleration is -29 ft/[tex]s^{2}[/tex], which is downward.
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a control volume is a system that group of answer choices allows a transfer of matter across its boundary. always has a constant volume always contains the same matter. does not interact in any way with its surroundings.
A control volume is a system that always has a constant volume
What does "control volume" refer to?
A control volume is a volume of interest for a specific analysis in space. The control surface, which is a closed surface, is the surface of the control volume. A coordinate system that may be fixed, moving, or rotational is used to define the surface.
A control volume is a set area of space that is used to examine mass and energy balances for flowing systems using thermodynamics. An actual or hypothetical envelope may serve as the control volume's boundary. The control volume's perimeter is defined by the control surface.
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a charged particle a exerts a force of 2.38 n to the right on charged particle b when the particles are 12.9 mm apart. particle b moves straight away from a to make the distance between them 18.2 mm. what vector force does particle b then exert on a?
The magnitude of the force that particle b exerts on particle a is 0.86 N. To find the vector force, we need to determine the direction of the force. Since particle b is moving directly away from particle a, the force it exerts on particle a is in the opposite direction, i.e., to the left. Therefore, the vector force is -0.86 N in the x-direction.
What is the force?Force is an interaction between two objects that occurs when one object exerts a push or pull on the other. Forces can cause objects to accelerate, decelerate, or change direction. In classical mechanics, the force is described by Newton's second law of motion, which states that the rate of change of momentum of an object is proportional to the applied force.
We can use Coulomb's Law to calculate the magnitude of the force between the two charged particles:
[tex]\mathrm{F = k \times q_1 \times q_2 / r^2}[/tex]
where F is the force, k is the Coulomb constant, q1 and q2 are the charges of the particles, and r is the distance between them.
Let's assume that particle a has a positive charge and particle b has a negative charge. Then, we can write the following equation based on the information given:
[tex]\mathrm{2.38 N = k \times q_1 \times q_2 / (12.9 mm)^2}[/tex]
We also know that the distance between the particles increases to 18.2 mm. Since particle b moves away from particle a, the direction of the force it exerts on particle a is opposite to the direction of the force that particle a exerts on particle b.
To calculate the magnitude of the force that particle b exerts on particle a, we can use the same equation and substitute the new distance:
[tex]\mathrm{F' = k \times q_1 \times q_2 / (18.2 mm)^2}[/tex]
Since the charges q1 and q2 are the same, we can simplify the equation as follows:
F' = F × (12.9 mm / 18.2 mm)²
F' = 2.38 N × (0.709 mm / 1.0 mm)²
F' = 0.86 N
The magnitude of the force that particle b exerts on particle a is 0.86 N. To find the vector force, we need to determine the direction of the force. Since particle b is moving directly away from particle a, the force it exerts on particle a is in the opposite direction, i.e., to the left. Therefore, the vector force is -0.86 N in the x-direction.
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Calculate the work done by a 50 N force pushing a pencil 0.5 m
The workdone in pushing the pencil through a distance of 0.5 m is 25 J.
What is work?
Work is the product of force and distance.
To calculate the work done in pushing the pencil, we use the formula below.
Formula:
W = Fd................................. Equation 1Where:
W = Work done in pushing the pencilF = Force = 50 Nd = 0.5 mFrom the question,
Given:
W = 50×0.5W = 25 JHence, the work done is 25 J
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the automobile has a speed of 80 ft>s at point a and an acceleration having a magnitude of 10 ft>s2, acting in the direction shown. determine the radius of curvature of the path at point a and the tangential component of acceleration.
The tangential component of acceleration is calculated to be 8.66 ft/s² and the radius of curvature is 1280 ft.
The tangential acceleration is known to be a measure of the rate of change in the magnitude of a velocity vector.
Speed of the automobile = 80 ft/s
Acceleration of the automobile a = 10 ft/s²
Construct a triangle with 30°, 60°, 90° with vector a as the hypotenuse, t and n as the legs.
an is the centripetal acceleration along n direction.
at is the tangential acceleration along t direction.
sinθ = an/a
an = a sinθ = 10 sin30° = 10(1/2) = 5 ft/s²
cosθ = at/a
at = a cosθ = 10 cos30° = 10(1/√2) = 10(0.866) = 8.66 ft/s²
From centripetal acceleration, we know,
an = v²/r
r = v²/an = 80²/ 5 = 1280 ft
Thus, the tangential component of acceleration is 8.66 ft/s² and the radius of curvature is 1280 ft.
The given question is incomplete without the figure. It is given in the attachment below.
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What galaxy type is full of gas and dust?
Answer: I hope this helps it between Irregular galaxies or Sprial galaxies I think it’s Sprial
Explanation:
Irregular galaxies tend to contain lots of gas and dust. As a consequence, irregular galaxies contain copious star formation
Spiral galaxies have a lot of gas, dust and newly forming stars. Since they have a lot of hot, young stars, they are often among the brightest galaxies in the universe. About 20% of all galaxies are spirals. We live in a spiral galaxy called the Milky Way.
Spiral galaxies are made up of young stars, gas, and dust. You can see the dust in the dark spots of the spiral arms. The gas and dust are used to make new stars, and these baby stars glow very brightly. Astronomers use these facts to determine that spirals are typically young galaxies.
You have been hired by a moving company, and your first assignment is to move heavy bedroom furniture including dressers. The company handbook states that all drawers should be removed from the dresser prior to moving it down a flight of stairs and that all dressers should be lifted instead of being dragged across floors to avoid friction. Explain how the handbook is using Newton's first and second laws of motion. Your answer should be three to four sentences in length and use proper grammar and punctuation. PLEASE HELP!!
The company handbook is using Newton's first law and second laws of motion to ensure the safe and efficient movement of heavy bedroom furniture.
By removing the drawers from the dressers before moving them down the stairs, the company is reducing the mass of the object being moved, making it easier to handle in accordance with Newton's first law of motion, which states that an object at rest will remain at rest and an object in motion will remain in motion with a constant velocity, unless acted upon by an external force. By lifting the dressers instead of dragging them, the company is reducing friction, which can cause the dressers to slow down or stop, and making it easier to move the dressers in accordance with Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
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a sheet of glass having an index of refraction of 1.40 is to be coated with a film of material having a refractive index of 1.55 such that yellow light with a wavelength of 580 nm (in vacuum) incident normally is preferentially transmitted. what is the minimum thickness of the film in nm that will achieve this result?
The minimum thickness of the film is 169.35 nm.
Wave interference is when two waves collide while traveling through the same medium. A wave is a point-by-point combination of two waves. Constructive interference occurs when the resulting wave is larger than either source wave. Destructive interference occurs when the resulting wave is smaller than the two source waves. Initial wavelength = π due to dense medium.
Δφ1 = π (4dnb/λ)
The minimum thickness of the film is reached after the result is calculated as
Δφ12 = Δφ1 − Δφ2
d= [tex]\frac{525}{3.1}[/tex]
d= 169.35 nm
Minimum thickness of the film will be 169.35 nm.
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at absolute zero temperature, state the pressure that a fluid exerts on its system container.
At absolute zero temperature, all molecules of a fluid would have zero kinetic energy and would be at rest. Therefore, the fluid would exert zero pressure on its system container.
This is because pressure arises due to the collision of molecules with the walls of the container, and at absolute zero temperature, there is no molecular motion or collision. At absolute zero temperature, there is no molecular motion or collision, and therefore, there can be no pressure. The molecules are frozen in place, and they cannot exert any force on the walls of the container. This means that the pressure of the fluid is zero at absolute zero temperature.
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Can someone help with this
OE is the required direction. Option B
What is the resultant force?Generally, The resultant force is the overall force acting on an object, taking into account the magnitude and direction of all individual forces acting on it. It can be calculated by adding or subtracting the individual forces vectorially, taking into account their direction and magnitude.
The direction of the resultant force is the same as the direction of the net force acting on the object, and its magnitude is equal to the vector sum of all the individual forces acting on the object.
Like charges repel each other( law of electrostatics ) since the central charge is negatively charged, other charges will be
attracted to it,.
Hence the direction of the resultant electric field will be towards
-Q (OE)
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in a certain region of space the electric potential increases uniformly from east to west and does not vary in any other direction. the electric field:
In this case, the electric field in that area will cause a charged particle to experience a force in the direction of the increasing electric potential if it is discharged at a position with a lower electric potential.
When the electric potential is known to stay constant in a particular area of space, what is the electric field in that area?Zero There is no direction of greatest increase if the electric potential is constant. Therefore, anywhere inside the region of continuous electric field, the electric field is zero and the gradient of the electric potential is also zero.
What factors determine the electric field potential in a particular area of space?Only the x coordinate, where a and b are constants, determines the field potential in a specific area of space. Discover the space charge's Q(x) distribution. As V=ax3+b, the electric field potential at a given location in space only depends on the x coordinates.
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determine the stretch in spring ac (in cm.) for for equilibrium of the 1.9-kg block. the springs are shown in the equilibrium position. determine the stretch in spring ac in cm.
The stretch in spring ac (in cm.) for the equilibrium of the 1.9-kg block. the springs are shown in the equilibrium position is 0.9 cm.The two springs are in equilibrium when the block is suspended between them.
The two springs have the same spring constants (k), and the same force is exerted on the block by each spring. Therefore, the distance between the block and the wall is equal to the stretch in spring AC. In order to determine the stretch in spring AC, we can use the equation F = k * x, where F is the force exerted by the spring, k is the spring constant, and x is the stretch in the spring.
Since the mass of the block is 1.9 kg, the force exerted by the spring is 1.9 kg * 9.8 m/s2, which is equal to 18.82 N. We also know that the spring constant is equal to 18 N/m. Substituting these values into the equation yields 18.82 N = 18 N/m * x. Solving for x gives us a stretch of 0.9 cm.
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suppose an artificial satellite has been put into circular orbit about the earth, at a distance from the center of the earth equal to 1/4 the distance from the earth's center to the moon's center. in terms of the moon's period tm, what will be the period of the satellite?
The formula [tex]Ts = (tm^2 / rm^3)^(1/2) * (rm / 4)^(3/2)[/tex] if an artificial satellite has been put into circular orbit about the earth, at a distance from the center of the earth equal to 1/4 the distance from the earth's center.
To find the period of the satellite, we can use Kepler's Third Law of Planetary Motion, which states that the square of the period of a planet or satellite is proportional to the cube of its average distance from the center of the planet or central body. Mathematically, this can be expressed as:
[tex]T^2 = k * r^3[/tex]
where T is the period, r is the average distance from the center of the planet or central body, and k is a constant of proportionality.
Since we know the period of the moon (tm), we can find the constant of proportionality for the moon's orbit. Assuming the moon's orbit is circular, we have:
[tex]tm^2 = k * rm^3[/tex]
where rm is the average distance from the center of the earth to the moon's center.
Using this relationship, we can find k:
[tex]k = tm^2 / rm^3[/tex]
Next, we can use k to find the period of the satellite, given that the average distance from the center of the earth to the satellite is 1/4 the distance from the center of the earth to the moon's center
[tex]rs = rm / 4[/tex]
So the period of the satellite, Ts, is:
[tex]Ts^2 = k * rs^3[/tex]
[tex]Ts^2 = (tm^2 / rm^3) * (rm / 4)^3[/tex]
[tex]Ts = (tm^2 / rm^3)^(1/2) * (rm / 4)^(3/2)[/tex]
So the period of the satellite in terms of the moon's period (tm) is given by the formula:
[tex]Ts = (tm^2 / rm^3)^(1/2) * (rm / 4)^(3/2)[/tex]
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