an aerobatic airplane flying at a constant 60.0 m/s makes a horizontal turn of radius 255 m . the pilot has mass 80.0 kg . what is the bank angle of the airplane?

Green light of wavelength 540 nm is incident on two slits that are separated by 0.50 mm can be determined various steps.

(a) Physical quantities that can be determined using this information include:

Three physical quantities that can be determined using this information are:

(b)

Three changes that will each result in doubling the distance between the 0th and the first bright spot on the screen are:

Doubling the distance between the slits and the screen: The distance between the slits and the screen affects the spacing between bright fringes on the screen.

By doubling the distance between the slits and the screen, the spacing between bright fringes will be doubled.

Halving the distance between the slits: The distance between the slits affects the angle of diffraction of the light.

By halving the distance between the slits, the angle of diffraction will be doubled, resulting in the doubling of the distance between the 0th and the first bright spot on the screen.

Using light of half the wavelength: The wavelength of the light affects the spacing between bright fringes on the screen.

By using light of half the wavelength (i.e., 270 nm), the spacing between bright fringes will be halved, resulting in the doubling of the distance between the 0th and the first bright spot on the screen.

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The body position sense that orients us with respect to gravity and the immediate environment is a function of the vestibular system, which is located in the inner ear.

This system provides the brain with information about head position, acceleration, and movement, which in turn allows us to maintain balance and a sense of spatial orientation. Additionally, information from the eyes, muscles, and joints also contribute to body position sense, allowing us to integrate multiple sensory inputs and make accurate judgments about our position and movement in space. Overall, body position sense is a complex sensory and neural process that involves multiple inputs and processing centers in the brain.

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The maximum distance at which the eye can resolve two headlights at night, given a pupil diameter of 0.4 cm, is approximately 11,937.3 meters or 11.937 kilometers.

To calculate the maximum distance at which the eye can resolve two headlights at night, we can use the formula for the angular resolution of the human eye, which is based on the Rayleigh criterion:

θ = 1.22 * (λ / D)

Where:
θ = angular resolution in radians
λ = wavelength of light (average wavelength of visible light is approximately 550 nm, or 5.5 x 10^-7 meters)
D = diameter of the aperture (pupil diameter, given as 0.4 cm or 0.004 meters)

First, calculate the angular resolution:

θ = 1.22 * (5.5 x 10^-7 m / 0.004 m) = 1.678 x 10^-4 radians

Now, to find the maximum distance (d) at which the eye can resolve two headlights, we can use the formula

d = L / tan(θ)
Where:
L = distance between the headlights (assuming a standard separation of 2 meters)
Before calculating, we need to make sure that the angular resolution (θ) is in the same unit (radians) as the tangent function requires:
θ = 1.678 x 10^-4 radians
Now, calculate the maximum distance:
d = 2 m / tan(1.678 x 10^-4) ≈ 11937.3 meters
Therefore, the maximum distance at which the eye can resolve two headlights at night, given a pupil diameter of 0.4 cm, is approximately 11,937.3 meters or 11.937 kilometers.

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The horizontal force that her wrist must exert on her hand is 2,128 N.

Consider the rotational motion of the ice skater and the forces acting on her body.

The centripetal force required to keep the ice skater moving in a circle is provided by the tension force in her arms.

We can use the following equation to find the tension force:

F = mω²r

where F is the tension force, m is the mass of the ice skater, ω is the angular velocity (in radians per second), and r is the radius of the circle formed by the outstretched arms (i.e., half the distance between the hands).

First, let's calculate the radius:

r = 1.50 m / 2

  = 0.75 m

Next, let's calculate the angular velocity:

ω = 2.5 turns/s x 2π radians/turn = 15.7 radians/s

Now, let's calculate the mass of the ice skater's hands:

m_hands = 0.0125 x 50 kg = 0.625 kg

Finally, let's use the equation above to find the tension force:

F = mω²r = (50 kg + 2 x 0.625 kg) x (15.7 radians/s)² x 0.75 m

= 2,128 N

Therefore, the horizontal force that her wrist must exert on her hand is 2,128 N.

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The terminal velocity of a 90-kg (including any equipment) skydiver who jumps out of a plane can be found using the given data: air density of 1.0 kg/m3, a frontal surface area of 1.0 m2, and a drag coefficient of 0.8.What is terminal velocity.

Terminal velocity is the maximum velocity that a falling object can reach when air resistance is equal to the gravitational force acting on it. This is the point at which an object can no longer accelerate because the opposing forces are balanced. Terminal velocity can be computed using the formula: v = √(2mg/ρACd)where: v is the terminal velocity m is the mass of the objectρ is the air density A is the frontal surface area Cd is the drag coefficient of the object g is the acceleration due to gravity(9.81 m/s²)Substituting the provided values: v = √(2(90 kg)(9.81 m/s²)/(1.0 kg/m³)(1.0 m²)(0.8)) = 72.22 m/s Therefore, the skydiver's terminal velocity is 72.22 m/s.

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The angular acceleration of the merry-go-round is 4 rad/s².

To find the angular acceleration of the merry-go-round, follow these steps:

1. Convert the final angular speed from rev/s to rad/s:
Final angular speed = 0.50 rev/s * 2π rad/rev = π rad/s

2. Convert the number of revolutions to radians:
Number of revolutions = 2.0 rev * 2π rad/rev = 4π rad

3. Use the angular displacement equation to find the angular acceleration:
θ = ω₀ * t + 0.5 * α * t^2, where θ is angular displacement, ω₀ is initial angular speed (0 in this case), α is angular acceleration, and t is time.

4. Use the final angular speed equation to find time:
ω = ω₀ + α * t, where ω is final angular speed, ω₀ is initial angular speed (0 in this case), α is angular acceleration, and t is time.

5. Rearrange the final angular speed equation to find time in terms of angular acceleration:
t = (ω - ω₀) / α = π / α

6. Substitute the time expression into the angular displacement equation:
4π = 0.5 * α * (π / α)^2

7. Solve for angular acceleration:
α = 4 rad/s²

Hence, the angular acceleration of the merry-go-round is 4 rad/s².

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The distance the car skids before coming to a stop when driving down a hill with a slope of 5.0° at 18 m/s using conservation of energy is 19.84 meters.

Conservation of energy is the principle that the total energy of an isolated system cannot change. The energy can only be transformed from one form to another. The law of conservation of energy, also known as the first law of thermodynamics.

To determine how far you skid before stopping using conservation of energy, follow these steps:

Step 1: Calculate the initial kinetic energy of the car: [tex]KE_{initial} = (1/2) * 1700 kg * (18 m/s)^2 = 275400 J[/tex]

Step 2: Calculate the gravitational potential energy gained by the car [tex](PE_{gravity})[/tex]: firstly, to find h we need to express it in terms of the distance. h = distance * sin(angle)
So, [tex]PE_{gravity} = 1700 kg * 9.81 m/s^2 * distance * sin(5.0^\circ)[/tex]

Step 3: Calculate the work done by friction [tex](W_{friction})[/tex]: [tex]W_{friction} = 1.5 * 10^4 N * distance[/tex]

Step 4:  Apply conservation of energy: [tex]KE_{initial} + PE_{gravity} = W_{friction}[/tex], we get:
[tex]275400 J + (1700 kg * 9.81 m/s^2 * distance * sin(5.0^\circ)) = 1.5 * 10^4 N * distance[/tex]

Step 5: Solve for distance
[tex]distance * (1.5 * 10^4 N - 1700 kg * 9.81 m/s^2 * sin(5.0^\circ)) = 275400 J[/tex]
[tex]distance = 275400 J / (1.5 * 10^4 N - 1700 kg * 9.81 m/s^2 * sin(5.0^\circ))[/tex]

Using a calculator, the distance is approximately 19.84 meters. So, you skid about 19.84 meters before stopping.

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The maximum height to which the stone can rise, given that the work done is 40 J, is  40.82 m

First, we shall list out the given parameters from the question. This is given below:

We can obtain the maximum height to which the stone can rise as follow

Wd = mgh

40 = 0.10 × 9.8 × h

40 = 0.98 × h

Divide both sides by 0.98

h = 40 / 0.98

h = 40.82 m

Thus, the maximum height to which the stone can rise is 40.82 m

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The star located 10,000 light-years away from the galactic center would have a higher rotational velocity than the star located 26,000 light-years away.

The galaxy's rotational speed is not constant across its radius. The Milky Way, like most galaxies, has a dark matter halo that encloses the visible matter. The circular velocity profile of the Milky Way, which is almost flat beyond the Sun's location, offers a measure of the total mass distribution. The orbital velocities of material at various radii around the galactic center, such as gas and stars, can be measured to determine this profile.

Galactic rotation is characterized by Kepler's third law, which states that for a galaxy with a spherically symmetric mass distribution, the rotation speed is proportional to the square root of the distance to the center. As a result, a star that is closer to the galactic center would have a higher rotational speed than one that is farther away.

Since we have two stars, one located 10,000 light-years from the galactic center and the other located 26,000 light-years from the galactic center, we can quickly determine which star has the higher rotational velocity using Kepler's third law. The star closer to the galactic center, which is located 10,000 light-years away, would have a higher rotational velocity than the star located 26,000 light-years away from the galactic center.

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The devices used by mechanical cooling thermostats to turn off early enough to prevent system overshoot or temperatures below the thermostat set point are called anticipators.

An anticipator is a small resistor that operates like a little heater inside your thermostat. The anticipator is the device that controls the duration of each heating cycle in old-style thermostats. This component essentially informs the heating and cooling system to cut off early. The mechanical thermostat anticipator is made up of two parts: the thermostat switch and the heat anticipator. When the thermostat switch turns off, the anticipator's heater stays on for a short period longer, avoiding overheating or undercooling of the controlled space.

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Option b. 4.86 million km2 of sea ice would remain in 2020 if the decline rate continued at 10% per decade.

Ocean ice is a significant piece of the World's environment framework, reflecting daylight and managing the planet's temperature. Be that as it may, environmental change has caused a decrease in how much ocean ice over ongoing many years, with a typical decay pace of around 10% each 10 years. This intends that for each decade that passes, how much ocean ice remaining is 90% of the earlier ten years' sum.

To work out how much ocean ice would stay in a specific year, we can utilize the recipe: remaining ice = (1-0.1)^n * beginning ice, where n is the quantity of many years that have passed and starting ice is how much ocean ice in the beginning year. For instance, in the event that there were 6 million km2 of ocean ice in the year 2000 and 20 years (twenty years) have passed, we can compute the excess ice in 2020 as follows: remaining ice = (1-0.1)^2 * 6 million km2, which approaches around 4.86 million km2.

This computation features the huge loss of ocean ice over a generally brief timeframe, with practically 20% of the ice vanishing more than twenty years. This deficiency of ocean ice has extensive ramifications for worldwide environment examples, natural life, and human networks living in the Cold.

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The complete question is:

every decade, the sea ice declines by 10 percent. if there were 6 million km2 of sea ice in the year 2000, how much would remain in 2020? group of answer choices are a. 7.85 b.4.86 c. 6.80 d. 3.67

When measuring angles of incidence and angles of refraction, always make sure to measure them from the normal line, which is perpendicular to the surface at the point of contact. This ensures accurate measurements and proper calculations in refraction scenarios.

When measuring angles of incidence and angles of refraction, it is essential to ensure that you always measure them using the correct tools or instruments.What is an angle?An angle is a measure of rotation, expressed in degrees, that two lines or sides create around a common point called the vertex. Two rays or lines originate from a single point and diverge in different directions to form an angle.Measuring anglesTo measure angles, you'll need a protractor, a device that's specifically built for this task. Place the protractor on the angle's vertex so that the base lines of the protractor are parallel to the lines or sides of the angle you're measuring.Angle of incidenceThe angle of incidence is the angle between the incident ray and the normal line to a surface, such as the surface of an optical lens, mirror, or prism. The angle of incidence is denoted by the Greek letter “θ” (theta).Angle of refractionThe angle of refraction is the angle between the refracted ray and the normal line to a surface, such as the surface of an optical lens, mirror, or prism. The angle of refraction is denoted by the Greek letter “θ” (theta).Therefore, when measuring angles of incidence and angles of refraction, it is essential to ensure that you always measure them using the correct tools or instruments. The angle measurement process is done using a protractor.

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People do weigh less near the equator because of the centrifugal force of the earth spinning. Yes, The centrifugal force counteracts gravity enough for even a marginal weight difference near the equator.

This is because the equator is further away from the center of the earth than the poles.

As a result, people at the equator are moving faster than those at the poles due to the earth's rotation. This movement generates centrifugal force, which reduces the gravitational force acting on a person at the equator by about 0.3%.

Therefore, a person weighs about 0.5% less at the equator than at the poles.

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If we know the mass of the ball, the spring constant, and the maximum displacement (or amplitude) of the ball from its equilibrium position, we can calculate the speed at which the ball passes through its equilibrium position each time.

The speed at which the ball passes its equilibrium position each time depends on the amplitude and period of its motion.

Assuming the ball is executing simple harmonic motion, the time period (T) of the motion can be calculated using the formula:

T = 2π√(m/k)

where m is the mass of the ball and k is the spring constant.

Once we know the time period of the motion, we can calculate the speed at which the ball passes through its equilibrium position using the formula:

v = A/T

where A is the amplitude of the motion.

If the amplitude of the motion is not given, we can assume that it is equal to the maximum displacement of the ball from its equilibrium position. For a mass-spring system, this maximum displacement is equal to the amplitude of the oscillation.

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Answer:

36,125KiloJoules.

Explanation:

K.E= 1/2MV².

that's 0.5 X 10,000 X 85.

which equals 36, 125, 000 Joules or 36,125 Kilo Joules.

Answer:

36,125,000 Joule is the answer according to the formula KE=1/2×m×(v)2

When unpolarized light passes through a polarizer at 60 degrees from the vertical, the intensity of the light is halved.

Unpolarized light, which consists of light waves vibrating in all planes perpendicular to the direction of propagation, does not have a specific direction of oscillation. This means that its electric field is randomly polarized in all directions perpendicular to the direction of motion. Polarization refers to the direction in which the electric field is oscillating.

Polarized light waves have an electric field that is oscillating in only one direction, whereas unpolarized light has an electric field that is oscillating in all directions perpendicular to the direction of motion. A polarizer is a filter that polarizes light waves by allowing only those waves that are oscillating in a particular direction to pass through. If unpolarized light passes through a polarizer at a 60-degree angle to the vertical, only half of its intensity will be able to pass through.

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Based on the data collected from the three trials, we can find the average acceleration of the fan cart on a horizontal track. To do this, we will calculate the mean of the six acceleration values provided:

(0.642 + 0.622 + 0.651 + 0.618 + 0.664 + 0.604) / 6 = 3.801 / 6 = 0.634 m/s^2

Now, the mass of the fan cart is 480 g, which we will convert to kg:

480 g * (1 kg / 1000 g) = 0.48 kg

After adding 120 g to the cart, the new mass becomes:

0.48 kg + (120 g * 1 kg / 1000 g) = 0.48 kg + 0.12 kg = 0.60 kg

Next, we need to determine the gravitational force acting on the cart along the incline. This can be calculated using the formula:

F_gravity = m * g * sin(theta)

where m is the mass of the cart, g is the gravitational constant (approximately 9.81 m/s^2), and theta is the angle of inclination.

F_gravity = 0.60 kg * 9.81 m/s^2 * sin(4.5°) ≈ 0.60 kg * 9.81 m/s^2 * 0.078 ≈ 4.72 N

Now, we'll calculate the force exerted by the fan using the formula:

F_fan = m * a

where m is the mass of the cart, and a is the average acceleration calculated earlier.

F_fan = 0.60 kg * 0.634 m/s^2 ≈ 0.38 N

Since the gravitational force (4.72 N) is greater than the force exerted by the fan (0.38 N), the cart will not be able to overcome gravity and will accelerate down the incline.

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Sounds can be changed in a variety of ways depending on the source of the sound and the type of change you want to make. Here are a few examples:

The cause of the change depends on the type of change being made. For example, changing the pitch of a sound is caused by altering the frequency of the sound wave, while changing the volume is caused by altering the amplitude of the sound wave.

In general, changes to sound waves can be caused by physical manipulation of the sound source, such as adjusting the properties of a musical instrument, or by electronic processing of the sound signal using digital signal processing techniques.

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If the flywheel's rotational velocity is constant and the force applied by the ant is strong enough, the ant will adhere to the wheel's rim without slipping.

In this case, the ant's tangential velocity will be the same as the wheel's tangential velocity, and the centripetal force acting on the ant will be supplied by the frictional force.Using F = ma, we know that a = v^2/r. We can then substitute the value for the angular velocity and wheel radius to get the centripetal acceleration.

The centripetal force on the ant is m*ac. This centripetal force is supplied by the ant's grip on the wheel. Since the ant can hold on to the wheel with a force much greater than its own weight, it is safe to assume that the force of the grip is greater than the centripetal force.

In conclusion, the force with which the ant must hold on to stay on the wheel at point III is equal to the centripetal force exerted on it, which is equal to its mass multiplied by its centripetal acceleration, which is equal to m*v^2/r.

The mass of the ant is given as 1 gram (0.001 kg), and the radius of the wheel is given as 0.4 m. The linear velocity v can be calculated using the formula v = ωr. Therefore, the force required to keep the ant on the wheel at point III is:F = m*v^2/rF = 0.001*[(2*2*3.14*0.4)^2]/0.4F = 9.92 N (approximately)

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The direction of the induced electric field is given by Lenz's law, which states that the direction of the induced field is such that it opposes the change in magnetic flux that is inducing it.

The movement of the bar upward in the field is what in this instance is responsible for the shift in magnetic flux. The induced electric field will induce a current in the bar that flows in a direction that produces a magnetic field that opposes the upward field in order to counteract this shift in flux.

We can calculate the direction of the current flow in the bar using the right-hand rule for current. Our fingertips will curl in the direction of the magnetic field created by the current if we point our thumb in the direction of the induced current.

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An ammeter always connected in series and a voltmeter always in parallel in a circuit.

An ammeter is always connected in series because it is used to measure the current flowing through a particular part of a circuit. When an ammeter is connected in series, all of the current flowing through the circuit also flows through the ammeter. By measuring this current, the ammeter can provide an accurate reading of the current in that part of the circuit. If an ammeter were connected in parallel, it would change the resistance of the circuit and interfere with the current flow, giving an inaccurate reading.

A voltmeter is always connected in parallel because it is used to measure the voltage difference between two points in a circuit. When a voltmeter is connected in parallel, it is connected across the two points where the voltage difference is to be measured. This means that the voltmeter has a very high resistance, which ensures that it draws very little current from the circuit and does not affect the voltage being measured. If a voltmeter were connected in series, it would change the resistance of the circuit and interfere with the voltage being measured, giving an inaccurate reading.

Hence, an ammeter always connected in series and a voltmeter always in parallel in a circuit.

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The power for the voltage source is -6.5744 W and the power for the current source is 0.02424 W (both to three significant digits).

To find the voltage Vab, we can use the voltage divider rule, which states that the voltage across a resistor in a series circuit is proportional to its resistance. In this case, Vab is the voltage across R2 and R3 in series, so:

Vab = Vo * (R2 + R3) / (R1 + R2 + R3)

= 9.84 * (9 + 6) / (10 + 9 + 6)

= 4.608 V

To find the current Ij, we can use Kirchhoff's current law, which states that the total current flowing into a junction is equal to the total current flowing out of the junction. In this case, the current flowing into node b is equal to the current flowing out of node b, so:

Ij = (Vc - Vab) / R3

= (4.296 - 4.608) / 6

= -0.052 A

Note that the negative sign indicates that the current is flowing in the opposite direction of the assumed direction.

To find the power for the voltage and current source, we can use the formulas P = V * I and P = I^2 * R, respectively. For the voltage source, the power is:

Pvg = Va * (Vc - Va) / R1

= 16 * (4.296 - 16) / 10

= -6.5744 W

Note that the negative sign indicates that the power is being dissipated, rather than generated.

For the current source, the power is:

Pig = Ij^2 * R2 = (-0.052)^2 * 9 = 0.02424 W

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Complete question:

m mo Vs( R1 = 10 kN2 R2 =9 k12 R3 = 6 kN2 The measured nodal voltages are: Va = 16 V Vo = 9.84 V Vc = 4.296 V Find voltage Vab and the current 11. Vab = mA Ij = (within three significant digits) What is the power for the voltage and current source in watts? Pvg = Pig = (within three significant digits)

1) current

2) in series

3) voltage

4) In parallel

Ammeters are connected in series with the component or part of the circuit being measured, so that the entire current flows through the ammeter. This means that the ammeter must have a very low resistance, so that it does not significantly alter the current being measured. Typically, ammeters have a built-in shunt resistor to achieve this low resistance.

On the other hand, voltmeters are connected in parallel with the component or part of the circuit being measured, so that they measure the voltage across the component or part. This means that the voltmeter must have a very high resistance, so that it does not draw significant current from the circuit and alter the voltage being measured. Typically, voltmeters have a built-in series resistor to achieve this high resistance.

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The change in the internal energy of the system can be calculated using the first law of thermodynamics, which states that the change in the internal energy of a system is equal to th added to the system minus the work done by the system on the surroundings.

The formula for this is:ΔU = Q - W where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system on the surroundings. In this case, 5 kJ of heat is added to the system, and the system does 2 kJ of work on the surroundings. Therefore, the change in internal energy is:ΔU = Q - WΔU = 5 kJ - 2 kJΔU = 3 kJSo, the change in the internal energy of the system is 3 kJ.
The change in internal energy of the system can be calculated using the first law of thermodynamics: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. In this case, Q = 5 kJ and W = 2 kJ.

So, ΔU = 5 kJ - 2 kJ = 3 kJ.

The change in the internal energy of the system is 3 kJ, considering we neglect the change in the bulk energy.

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To generate a magnetic field of strength 24e-6 T at the center of the loop, a current of approximately 4.4 A is required in a loop of wire with a radius of 0.035 m.

The magnetic field generated by a current-carrying loop of wire depends on the current and the geometry of the loop. The magnetic field strength at the center of the loop is given by the formula B = μ₀I/(2r), where B is the magnetic field strength, μ₀ is the magnetic constant (equal to 4π x 10^-7 T m/A), I is current, and r is the radius of the loop. In this case, we are given the magnetic field strength B and the radius of the loop r, and we want to find the current I that will produce that field strength. Rearranging the formula, we get I = 2Br/μ₀. Plugging in the given values, we get I = 2 x 24e-6 T x 0.035 m / (4π x 10^-7 T m/A), which simplifies to 1.2 A. Therefore, a current of 1.2 A is required in the loop of wire to generate a magnetic field of strength 24e-6 T at the center of the loop.

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Audible things: birds singing, wind howling. Clouds forming and lightning are not audible because they don't produce sound waves.

Of the choices given, two things are discernible: birds singing in the trees and wind yelling.

Mists framing and lightning streaking across the sky are not perceptible on the grounds that they don't deliver sound waves. Mists framing are a visual peculiarity brought about by changes in temperature and dampness in the air, and lightning produces electromagnetic waves however not sound waves.

Birds singing in the trees and wind crying are both perceptible in light of the fact that they produce sound waves. Birds produce sound by vibrating their vocal ropes, and the subsequent sound waves can head out through the air to be heard by people. Wind can make objects vibrate, delivering sound waves that can likewise be heard by people.

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The force, in N, applied to the cannonball can be calculated using Newton's Second Law of Motion, which states that the force applied to an object is equal to its mass times its acceleration:

Force = mass x acceleration

Plugging in the given values, we get:

Force = 5 kg x 8 m/s^2 = 40 N

Therefore, the force applied to the cannonball was 40 N.

Answer:

The resistance of the original aluminum wire is 1/100 ohm.

Explanation:

A wire's resistance is proportional to its length and inversely proportional to its cross-sectional area. When a wire is cut into ten equal segments and stacked, its length is decreased by one-tenth yet its cross-sectional area stays constant.

Let R denote the original aluminium wire's resistance.

When the wire is cut into ten equal sections and stacked, the resistance of each component is ten times that of the original wire (since the length is one-tenth and the cross-sectional area stays constant). As a result, the resistance of one portion is 10R.

The resistance of the whole cone is 1 ohm when all 10 pieces are stacked. As a result, one portion has a resistance of 1/10 ohm.

Equating the resistance of one part to 10R, we get:

10R = 1/10 ohm

Solving for R, we get:

R = 1/100 ohm

Therefore, the resistance of the original aluminum wire is 1/100 ohm.

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The image distance is negative, this means the image is formed behind the mirror, at a distance of 13.33 cm behind the sunglasses.

Since the sunglasses have a convex surface, we can use the mirror equation:

1/f = 1/do + 1/di

where f is the focal length of the mirror, do is the object distance (the distance between the object and the mirror), and di is the image distance (the distance between the mirror and the image).

In this case, f = -20.0 cm (since the mirror is convex), do = 40.0 cm (since your face is 40.0 cm from the sunglasses), and we want to find di.

Substituting these values into the mirror equation, we get:

1/(-20.0 cm) = 1/(40.0 cm) + 1/di

Simplifying this equation, we get:

-0.05 = 0.025 + 1/di

Subtracting 0.025 from both sides, we get:

-0.075 = 1/di

Dividing both sides by -0.075, we get:

di = -13.33 cm.

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