The minimum height for the car to be safely released around a loop is determined by the minimum speed required for the car to remain in contact with the track, which is equal to the square root of the gravitational acceleration times the radius of the loop.
This is known as the "speed of a circular loop" formula, and it states that the minimum speed required for an object to go around a loop of radius "r" is equal to the square root of "g" (acceleration due to gravity) times "r".
In other words, the object must be traveling at a minimum velocity in order to remain in contact with the track and complete the loop without flying off. The height "h" at which the car is released is not a factor in this calculation, as it only affects the initial velocity of the car, which is not relevant to the minimum speed required to maintain contact with the track.
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The moon goes through a cycle of phases. This occurs because as the moon orbits Earth, different parts of the side of the moon illuminated by the sun face toward Earth. Select all of the correct statements from the following list.
a. Since a full moon occurs when the moon is on the opposite side of Earth as the sun, it is only visible at night.
b. Quarter phases occur between the new and full phases.
c. The moon orbits eastward around Earth once every 29.53 days.
d. The moon's phase changes because the moon rotates, causing differing parts of the side illuminated by the sun to face Earth.
e. Lunar eclipses happen infrequently—usually once every few years or so.
f. During the new phase, no sunlight reaches the side of the moon facing Earth.
g. The lunar phase changes as the moon passes in and out of Earth's shadow.
No sunlight hits the portion of the moon that faces Earth during the new phase. Between new and complete phases are quarter phases.
What is Earth called?Contrary to widespread opinion, Earth lacks a globally recognized name. A common misunderstanding of the earth's natural scientific name is "Terra."
What is planet Earth?Our own planet, Earth, is a world unto itself. Earth, the fourth from the sun, is the only planet in the known cosmos where the presence of life has been established. With a 3,959-mile radius, Earth is the fifth-largest planet within our solar system and the only one whose surface is known to have liquid water.
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5) choose the best answer. using the knowledge about the moon phases, how many spring and neap tides occur each month on average?
Instead, the phrase refers to the idea of the tide "springing forth." Regardless of the season, spring tides happen twice each lunar month.
What moon phases correspond to the neap and spring tides?When the Moon is full or new, when the Sun, Moon, and Earth are in alignment, spring tides always occur. Neap tides happen at the first and final quarter phases of the Moon, when the Moon is perpendicular to the Sun due to its orbit around Earth.
Most coastal areas have two high tides and two low tides each day, however other localities only experience one high tide and one low tide each day. Usually, the highs and lows aren't equal.
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what does this show about how living material is affected the shortest wavelengths in the electromagnetic spectrum
This demonstrates that the most harmful electromagnetic waves are those with the highest frequency and shortest wavelength.
Visible light, radio, television transmissions, microwaves, and X-rays are all examples of electromagnetic radiation, which is present in a broad variety of wavelengths and frequencies in the electromagnetic spectrum. The majority of the time, radiation with wavelengths far shorter than visible light has enough energy to remove electrons from atoms. It is referred to as Ionizing radiation.
The danger to living things increases generally with shorter wavelength. Very short wavelengths, including X-rays and gamma rays, can quickly harm living tissue, notwithstanding the dangers associated with longer wavelengths.
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The complete question is:
Sunburn is brought on by ultraviolet rays, and our bodies can be deeply penetrated by X rays. Gamma rays eliminate cancerous cells. What does this show about how living material is affected the shortest wavelengths in the electromagnetic spectrum?
which property of electromagnetic waves is least useful when identifying the objects emitting them?
A. Amplitude
B. Frequency
C. Speed
D. Wavelength
the constellation whose stars are used as pointers to the north celestial pole in the northern hemisphere at this time in history is
Polaris, which is the tip of the handle of the Little Dipper or the tail of the little bear in the constellation Ursa Minor, is indicated by the two stars at the end of the Dipper's "cup."
What is special about Ursa Minor?Polaris, the North or Pole Star, is by far the most important and well-known star in Ursa Minor. The star at the very end of the bear's lengthy tail is this. Polaris is significant because it is practically immediately over the North Pole. This means you can use it as a compass to locate your way north.
The Indian name for the constellation Ursa Minor is Laghu Saptharishi where 'Laghu' means 'Small'. The name is sequential with the name Saptharishi for the constellation Ursa Major.The Ursa Minor Dwarf is a dwarf spheroidal galaxy discovered during the Palomar Sky Survey in 1955 by A.G. Wilson of the Lowell Observatory in the United States. It is a Milky Way satellite galaxy that may be found in the constellation Ursa Minor.
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what force besides gravity controls the orbit of a planet or moon?
Explanation:
Inertia. The physical law that states that objects in motion have a tendency to remain in motion also plays a role in keeping the planets in orbit.
an ant walks due east at a constant speed of on a sheet of paper that rests on a table. suddenly the sheet of paper starts moving southeast at . describe the motion of the insect relative to the table.
When the sheet of paper starts moving southeast at a constant speed, the motion of the ant relative to the table becomes a combination of two motions: the ant's original motion due east and the motion of the sheet of paper southeast.
What is relative motion of ant?To describe the motion of the insect relative to the table, we need to take into account both the ant's original motion and the motion of the sheet of paper. The ant's original motion due east at a constant speed can be represented as a vector, and the motion of the sheet of paper southeast can be represented as another vector. The sum of these two vectors represents the motion of the ant relative to the table.
Mathematically, if we represent the ant's original motion due east as a vector with magnitude and direction, and the motion of the sheet of paper southeast as a vector with magnitude and direction , then the motion of the ant relative to the table can be represented as the sum of these two vectors.
In this case, the ant's original motion due east and the motion of the sheet of paper southeast are both at right angles to each other, so the sum of the two vectors can be represented using the Pythagorean theorem. The magnitude of the resulting vector can be calculated as the square root of the sum of the squares of the magnitudes of the two vectors.
The direction of the resulting vector will be southeast, but the exact angle will depend on the magnitudes of the original vector and the vector representing the motion of the sheet of paper.
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it is raining, and there is practically no wind. while driving through the rain, you speed up. what happens to the angle of the rain relative to the horizontal that you observe from inside the car?
As you speed up while driving through the rain, the angle of the rain relative to the horizontal that you observe from inside the car will become more perpendicular. This is because the raindrops are being deflected by your car's movement, making them appear to be coming straight down.
Why is the angle of rain relative to Horizontal?When you're driving through the rain, the raindrops are initially hitting the windshield of your car at an angle. If you speed up, the velocity of your car increases, and this increases the deflection of the raindrops as they hit your windshield. The result is that the angle at which the raindrops hit the windshield appears to be more perpendicular, making it appear as though the rain is falling straight down. This is simply an optical illusion caused by the increased deflection of the raindrops due to your car's movement.
It's important to note that the actual angle of the rain relative to the horizontal hasn't changed. Rather, it's just the angle that you perceive from inside the car that has changed due to the increased deflection of the raindrops caused by your car's movement.
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a hockey player makes a slap shot exerting a constant force of 30.0 n on the hockey puck for 0.16 seconds. what is the magnitude of the impulse given to the puck?
The magnitude of the impulse given to the puck is 4.8 Ns.
I = F * t
where,
I = impulse = ?
F = force = 30.0 N
t = time = 0.16 s
I = (30.0 N) * (0.16s)
I = 4.8 Ns
In classical mechanics, the integral of a force, F, over the time period over which it acts, t, is referred to as the "impulse," denoted by the symbols J or Imp. Impulse also qualifies as a vector quantity since force does. When an object receives an impulse, its linear momentum also changes in direction and undergoes an analogous vector change. The newton second (Ns), a SI unit of impulse, and the kilograms meter per second (kgm/s), a SI unit of momentum, are identical in terms of dimensions.
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when white light passes from the air into a different medium such as glass, it: a. is reflected backwards b. is refracted (bent) c. is dispersed into different colors d. more than one of the above e. is doppler shifted
When white light moves from air into a different material, such as glass, it is refracted (bent) due to a change in speed produced by the difference in refractive index.
The explanation for the above answer is
Refraction is the bending of light as it travels through different media. White light slows down and bends when it transitions from the medium of air to another one, such as glass. Because glass has a higher refractive index than air, light penetrates glass at a different speed than it would outside of it.
As a result, at the point where the air and the glass meet, the light is refracted or twisted. Snell's law describes how the angle of incidence and the difference in refractive indices affect how much bending occurs. The functioning of lenses and prisms is based on the phenomenon of refraction, which is essential for many optical systems.
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the photo shows an invention from the second industrial revolution. a man holds a device up near his mouth. there is a small aperture on one end of the device near the man's mouth. this aperture is attached to a cylinder on a small platform. two wire lead from the platform out of the picture. which invention does the photo show?
A new or original device, technique, composition, concept, or process is defined as an innovation. The photo show the invention of telephone.
What is invention?A new or original device, technique, composition, concept, or process is defined as an innovation. An innovation might be an enhancement to an equipment, product, or process that increases efficiency or reduces costs. It might even be a whole new notion. It is possible to patent a concept if it is distinct enough, either as a stand-alone innovation or as a society has developed over the work of others.
The photo shows an invention from the second industrial revolution. a man holds a device up near his mouth. there is a small aperture on one end of the device near the man's mouth. this aperture is attached to a cylinder on a small platform. two wire lead from the platform out of the picture. The photo show the invention of telephone.
Therefore, the photo show the invention of telephone.
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relative velocity. of airplanes a and b are moving southwest with speed , and north?west with speed , respectively, what is the relative velocity of b with respect to a?
The velocity of the an object in relation to another observer is referred to as its relative velocity. It is the pace at which the relative positions of two objects change over time.
What is relative velocity used for?When compared to another observer, an object's relative velocity is its speed. It is the pace at which the relative position with one thing in relation to another object changes over time.
Give an example of relative velocity.It combines an object's direction and speed. However, when we discuss relative velocity, it indicates that we're talking about velocity of one item in relation to another. And what exactly is relative velocity? An object's relative velocity is its speed in relation to another object, B.
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what is the magnitude of the weight, w , that can be supported by the right side of the jack for the given difference in elevation, 2.4 ft as shown?
The magnitude of the weight that can be supported by the right side of the jack can be calculated using the equation:
w = (force) * (distance)
where force is equal to the weight density of the material times its volume and distance is equal to the difference in elevation.
Since weight is equal to mass times acceleration due to gravity, we can write:
w = m * g
where m is the mass and g is the acceleration due to gravity, 9.8 m/s^2.
So the weight that can be supported by the jack can be calculated as follows:
w = m * g
w = (density * volume * g) * (distance)
w = (density * volume * 9.8 m/s^2) * (2.4 ft)
Here, we need to know the density of the material and its volume in order to calculate the weight that can be supported by the jack. Since this information is not provided, it is not possible to calculate the weight without additional information.
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if a person walks up the moving escalator with a speed of 0.49 m/s relative to the escalator, how long does it take to get to the top?
If a person walks up the moving escalator with a speed of 0.49 m/s relative to the escalator, it will take 26 seconds to get to the top.
What is velocity?Velocity and speed describe how quickly or slowly an object is moving. We frequently encounter circumstances when we must determine which of two or more moving objects is going faster. If the two are traveling on the same route in the same direction, it is simple to determine which is quicker. It is challenging to identify who is moving the fastest when their motion is in the other direction. The concept of velocity is useful in these circumstances. Learn what velocity means, how it is measured, an example of velocity, and how it differs from speed in this article.
The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.
The time it takes a person to walk up the escalator can be calculated using the equation:
t = d / (v_p + v_e)
where,
d = 13 m (length of the escalator)
v_p = 0.500 m/s (velocity of the person relative to the ground)
v_e = 0 (velocity of the escalator relative to the ground, since the person is walking against it)
Now, we get:
t = 13 / (0.500 + 0) = 26 s
So, it takes the person 26 seconds to walk up the escalator.
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a ball is thrown vertically upward from a height of feet with an initial velocity of feet per second. how high will the ball go?
The ball will go for a maximum height of roughly 62.25 feet.
Given that the acceleration due to gravity is 32 feet per squared second, we can integrate it with respect to t to calculate the velocity equation.
a(t) = -32 ft/s²
v(t) = ∫a(t) dt = ∫-32dt = -32t + C
The given initial velocity is 60 ft, so:
v(t) = -32t + C
v(0) = -32(0) + C
C = 60
Thus, the formula for v(t) in this case is -32t + 60.
Since velocity is always 0 (zero) at maximum height, you can calculate the time needed for the ball to reach maximum height:
v(t) = -32t + 60
0 = -32t + 60
t = 1.875 s
Put the time aside to calculate the formula for the distance equation.
s(t) = ∫v(t) dt = ∫(-32t + 60)dt = -16t² + 60t + C
Now, since we have the initial distance/height at 6 feet, we can calculate the C for the formula above. Remember that the initial time is 0.
s(t) = -16t² + 60t + C
s(0) = -16(0)² + 60(0) + C
6 = C
Thus, the calculation for distance is s(t) = -16t² + 60t + 6
Since we already found out the time needed to reach maximum height earlier, we can plug the number into the formula above:
s(t) = -16t² + 60t + 6
s (1.875) = -16(1.875)² + 60(1.875) + 6
≈ 62.25 feet.
Your question seems incomplete. The completed version is as follows:
A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 60 feet per second. How high will the ball go?HINT: The acceleration due to gravity is 32 feet per squared second
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a jetliner, traveling northward, is landing with a speed of 71.5 m/s. once the jet touches down, it has 796 m of runway in which to reduce its speed to 7.81 m/s. compute the average acceleration (magnitude and direction) of the plane during landing (take the direction of the plane's motion as positive).
The average acceleration is negative, indicating that the plane is slowing down. The required equation for average acceleration is a = [tex]\frac{(7.81 m/s - 71.5 m/s)}{ t}[/tex]
The average acceleration of the plane during landing can be calculated using the following equation:
a = [tex]\frac{V_f - V_i}{t}[/tex]
Where:
a = average acceleration
v f = final velocity = 7.81 m/s
vi = initial velocity = 71.5 m/s
t = time taken to reduce speed = [tex]\frac{(vf - vi) }{a}[/tex]
Substituting v f and vi in the equation, we get:
[tex]a = \frac{(7.81 m/s - 71.5 m/s)}{ t}[/tex]
Next, we can use the distance traveled during landing (796 m) and the average acceleration to find the time taken to reduce speed. We can use the equation:
[tex]d = vi \times t + (1/2) \times a \times t^2[/tex]
Where:
d = distance traveled = 796 m
Substituting the value of vi and a, we get:
[tex]796 m = 71.5 m/s \times t + (1/2) \times a \times t^2[/tex]
Solving for t:
[tex]t = \sqrt{(796 m / (1/2) \times a) + (71.5 m/s)^2 / a^2)}[/tex]
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what happens to area of the field of view when you increase the objective magnification from 4x to 40x?
The field of view decreases by 10 times, when you increase the objective magnification from 4x to 40x.
The field of view is inversely proportional to the magnification power, meaning that as the magnification increases, the field of view decreases. As such, when the magnification is increased from 4x to 40x, the field of view decreases. We will see less area of the object under microscope.
If magnification of objective lens is increased 10 times, the field of view will decrease 10 times.
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how much heat energy is absorbed by a 5 kg mass of heat capacity 2.1 kj/(kg-deg c) that is warmed from -3 to -1 deg c? 1 x10^5 j 21 kw 21,000 kg-m^2/sec^2 -2.1*10^4 j/sec 2.1 x 10^4 watts 105,000 watts
The 5 kilogramme mass therefore absorbs 21 kJ of heat energy. The other alternatives don't correspond to this outcome.
The amount of heat energy absorbed by an object can be calculated using the equation:
Q = m * c * ΔT
where Q is the heat energy absorbed, m is the mass of the object, c is the heat capacity, and ΔT is the change in temperature.
In this case, the mass of the object is 5 kg, the heat capacity is 2.1 kJ/(kg-°C), and the change in temperature is -3°C to -1°C, so:
Q = 5 kg * 2.1 kJ/(kg-°C) * ( -1°C - (-3°C) )
= -5 * 2.1 * 2 = -21 kJ
So, 21 kJ of heat energy is absorbed by the 5 kg mass. None of the other options match this result.
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What can occur when air rises in a low pressure system?
When air rises in a low-pressure system, it can lead to the formation of clouds and precipitation, such as rain or snow. The rising air also cools and condenses, releasing latent heat, which can further contribute to the development of the storm.
What happens in a low-pressure system?A low-pressure system is a weather pattern characterized by a region of lower atmospheric pressure compared to the surrounding areas. It is often associated with unsettled and stormy weather.
How are clouds formed?Clouds are formed when moist air rises and cools, causing water vapour to condense into tiny water droplets or ice crystals. This process occurs when the temperature of the air decreases, either because it is rising, or because it is mixing with cooler air.
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does this mean that positive charges create positive fields and negative charges create negative fields?
Yes, that is correct because, Positive charges create positive electric fields, and negative charges create negative electric fields.
The force of the field is determined by the magnitude of the charge and the distance from the charge. Electric fields generated by a positive charge will repel other positive charges, and attract negative charges, while electric fields generated by a negative charge will repel other negative charges, and attract positive charges.
Electric fields are a physical field that surrounds electrically charged particles and exerts force on all other charged particles in the vicinity. The electric field is defined as the electric force per unit charge. It is measured in volts per meter (V/m) and is calculated by dividing the electric force by the charge of the particle.
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7. is gravity force an attractive or repulsive force? is gravity force a weaker force or stronger force (in terms of its strength)?
Gravity is an attractive force, meaning that it pulls objects towards each other. It is considered a relatively weak force compared to other forces in the universe, but its strength is proportional to the mass of the objects involved and the distance between them. Over large distances and for massive objects, gravity can be a very strong force.
What causes the attractive force of gravity?The attractive force of gravity is caused by the masses of objects and the distance between them. According to Newton's law of universal gravitation, the strength of the gravity force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. The greater the masses of the objects and the closer they are to each other, the stronger the attractive force of gravity will be between them. This fundamental principle helps to explain why objects are pulled towards each other, creating the attractive force of gravity.
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Use the conversion table above. Some aliens are traveling in a group decide to take a vacation before they return to their home planet. There is a great store that they want to visit, and it's 3.6 x 10 15 km from their current location. How many light-years is that?
A. 3.79 light-years
B. 267 light-years
C. 379 light-years
D. 2.6 light-years
A distance of 3.6 x 10¹⁵ km in light - years is 379 light - years.
option C.
What is light year?
A light year is a unit of measurement of length or distance that is equal to the distance traveled by light in one year in a vacuum. It is approximately equal to 9.46 trillion kilometers (5.88 trillion miles).
3.6 x 10¹⁵ km can be converted into light year as follows;
1 ight year = 9.5 x 10¹² km
= ( 3.6 x 10¹⁵ km ) / ( 9.5 x 10¹² km / 1 Ly )
= 378.95 Ly
= 379 light - years.
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a cube with sides of length 7.6 m is centered on the origin. calculate the electric flux through the cube due to a charge of -2 nc at z
One can easily verify that the flux through the front face is zero, while that through the right face is the opposite of that through the left one or –48N⋅m 2 /C.
2 /C. Thus the net flux through the cube is :
ϕ=(–72+24–16+0+0+16)N⋅m2/C=–48N⋅m 2 /C.
What does the cube's center's electric flux look like?There will be six faces made from the number of field lines that emerge from charging. The number of field lines traveling across a given area is known as the electric flux. The flux moving through any one of the cube's faces is equal to the cube's overall flux divided by six.
Since they are parallel to the field lines and don't intersect any of them, the flux going through the top, bottom, front, and rear sides of the cube is zero. For these sides, the normal vector n is parallel to the field, and cos is equal to zero.
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a coin of 3 cm diameter is placed 3 m in front of a parallel wall on which is hung a circular flat mirror. a person stands 9 m from the wall. what is the smallest- diameter mirror in which the observer can just see the reflected edge of the coin (i.e., the image of the coin just fills the mirror)?
Using mirror's equation, The smallest diameter mirror in which the observer can just see the reflected edge of the coin is 6 cm.
We must compute the size of the mirror's produced image in order to identify the lowest diameter mirror that would allow the spectator to just view the coin's reflected edge.
We must first determine how far the picture is from the mirror. In order to compute this, use the mirror equation:
[tex]\frac{1}{f} = \frac{1}{d} + \frac{1}{d'}[/tex]
where f is the mirror's focal length, d and d' are the object's and image's distances from the mirror, respectively.
Since the mirror is flat, the focal length is determined by dividing the radius in half. Therefore, we may apply the formula:
[tex]f = \frac{R}{2}[/tex]
This results from substituting it into the mirror equation:
[tex]\frac{2}{R} = \frac{1}{3} + \frac{1}{d'}[/tex]
Calculating d':
[tex]d' = \frac{3R}{ (R-6) (R-6)}[/tex]
The mirror's diameter, D, is equal to 2R. As a result, the minimal diameter of the mirror, at which the spectator can only see the coin's edge reflected, can be calculated as follows:
[tex]D = 2R = \frac{2d' (R - 6)}{ 3}[/tex]
d' = 9, thus we can condense it to:
D = 18 / 3 = 6 cm
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A 5 kg mass has 100 J of potential energy with respect tothe ground. Approximately how high above the ground is
the mass?
The height of the 5kg mass object with respect to the ground is 2.04m.
How to calculate height?Potential energy refers to the energy possessed by an object because of its position (in a gravitational or electric field), or its condition (as a stretched or compressed spring, as a chemical reactant, or by having rest mass).
Potential energy = mass × height × acceleration due to gravity
According to this question, a 5kg mass has 100 J of potential energy with respect to the ground. The height can be calculated as follows:
100J = 5kg × 9.81 × h
100 = 49.05h
h = 2.04m
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where does the energy come from to power atp synthase?
In order to produce ATP, the ATP synthase utilizes free free energy of an electrical potential of proton produced by the respiratory chain.
What is the best explanation of energy?Energy's "ability to accomplish labor" refers to its ability to exert a force that moves an item. Despite the vagueness of the phrase, energy actually refers to the force which moves objects. The two types of energy are energy and potential energy.
How energy is made?Nearly majority of the world's energy is produced by steam turbines using carbon fuels, nuclear energy, biofuels, thermal, etc solar thermal energy. Solar photovoltaics, wind turbines, water turbines, gas turbines, and other important electricity generation technologies.
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which formula (assuming the signs are correct) would be used to find current i if power p and voltage v are given?
Formula that would be used to find current i if power p and voltage v are P = V * I
I = P/V
Energy flow or conversion rate is measured in units of time as ower. One joule per second, or one watt, is the definition of power in the International System of Units.
Voltage is the variation in electric potential between two places. It is sometimes referred to as electric pressure, electric tension, or potential difference. The work required to transport a test charge between two places in a static electric field correlates to this.
The rate at which electrons move across a conductor is called electric current. The ampere is the SI unit for electrical current. A substance's molecular structure contains tiny particles called electrons. These electrons can be held firmly at times or loosely at other times.
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6. an aluminum cube has sides of length 1.80 m. what is the resistance between two opposite faces of the cube?
the resistance between two opposite faces of the cube is 1.53×10−8Ω.
What do you mean by resistance between two opposiye faces of cube?Along the 'face' diagonal, between two vertices. = 3 R 4 is the equivalent resistance between two vertices along the face diagonal.
Resistance R is provided by:
R = ρl/A
Where r denotes resistivity, l the length parallel to which current flows, and A the area through which current flows
In this instance,
[tex]R = pl/(l^2) = p/l ([/tex] (taking side of cube as l) (taking side of cube as l)
We know that by dividing the cube into 27 smaller cubes, the volume of the cubes eventually equals the initial volume of the cube.
(essentially, mass conservation, but density cancellation on both sides)
[tex]l^3 = 27a^3l^3 = 27a^3[/tex] (a is the side of one tiny cube) (a is the side of one small cube)
a = l/3
As a result, resistance across two opposed faces of a tiny cube is as follows:
r = (a)/a2 =/a = 3/l = 3R
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what magnitude charge creates a 1.0 n/c n / c electric field at a point 1.0 m m away? express your answer in nanocoulombs.
By using Coulomb's law, we can find the electric field at a point-
E = kQ / r²
where E is the electric field, k is the Coulomb constant (9 x 10^9 Nm²/C²), Q is the magnitude of the charge creating the field, and r is the distance from the charge.
Given- the electric field is 1 N/C and the distance is 1 m, we can solve for Q:
Q = Er² / k
Q = (1 N/C) * (1 m)² / (9 x 10^9 Nm²/C²)
Q = 1.11 x 10^-9 C
Converting to nanocoulombs:
Q = 1.11 x 10^-9 C * (10^9 nC/C) = 1.11 nC
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If a ball is thrown straight up into the air with an initial velocity of 50 ft/s, it height in feet after t second is given by y=50t-16t^2. Find the average velocity for the time period begining when t=1 and lasting (i) 0.1 seconds (ii) 0.01 seconds (iii) 0.001 seconds. Finally based on the above results, guess what the instantaneous velocity of the ball is when t=1.
The instantaneous velocity of the ball when t=1 is approximately 18 ft/s. The change in location divided by the change in time gives the average velocity during a time period.
What is velocity, exactly?A particle or object's movement with respect to time is expressed vectorially as velocity. The meter per second (m/s) is the accepted unit of velocity magnitude (also known as speed). Alternately, the magnitude of velocity can be expressed in centimeters per second (cm/s).
(i) For t=1 to t=1.1 seconds:
y = 50t - 16[tex]t^{2}[/tex]
Change in position: y(1.1) - y(1)
= 50(1.1) - 16[tex](1)^{2}[/tex] - (50(1) - 16[tex](1)^{2}[/tex])
= 35.64 - 34
=1.64
Change in time: 1.1 - 1 = 0.1
Average velocity = Change in position / Change in time
= 1.64 / 0.1
= 16.4 ft/s
(ii) For t=1 to t=1.01 seconds:
y = 50t - 16[tex]t^{2}[/tex]
Change in position: y(1.01) - y(1)
= 50(1.01) - 16[tex](1.01)^{2}[/tex] - (50(1) - 16[tex](1)^{2}[/tex])
= 50.5 - 16.32- 50 - 16
= 34.18 - 34
= 0.18
Change in time: 1.01 - 1 = 0.01
Average velocity = Change in position / Change in time
= 0.18 / 0.01
= 18 ft/s
(iii) For t=1 to t=1.001 seconds:
y = 50t - 16[tex]t^{2}[/tex]
Change in position: y(1.001) - y(1)
= 50(1.001) - 16[tex](1.01)^{2}[/tex] - (50(1) - 16[tex](1)^{2}[/tex]
= 50.05 - 16.032 -50 - 16
= 34.018 -34
=0.018
Change in time: 1.001 - 1 = 0.001
Average velocity = Change in position / Change in time
= 0.018/ 0.001
= 18 ft/s
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