The focal length of this spherical mirror is f = 1.275 m, and the distance of the image is v = 1.532 m. The image is real, inverted, and smaller than the object, with a height of h' = -0.00337 m.
To determine the focal length of this spherical mirror, we need to use the mirror formula, which relates the distances of the object (u), image (v), and focal length (f). The formula is:
[tex]\frac{1}{f} = \frac{1}{u} + \frac{1}{v}[/tex]
where f is the focal length, u is the distance of the object from the mirror, and v is the distance of the image from the mirror.
In this case, the object is located at a distance of u = 1.86 m from the mirror, and its height is 4 cm or 0.04 m. Since the mirror is a sphere, the radius is half of the diameter or r = 2.55 m.
To find the distance of the image, we can use the mirror equation, which is:
[tex]\frac{1}{v} + \frac{1}{u} = \frac{1}{f}[/tex]
Rearranging this equation to solve for v, we get:
[tex]\frac{1}{v} = \frac{1}{f} - \frac{1}{u}[/tex]
Substituting the values of u and f, we get:
[tex]\frac{1}{v} = \frac{1}{f} - \frac{1}{1.86}[/tex]
Simplifying this expression, we get:
[tex]\frac{1}{v} = \left(\frac{1}{f} - 0.5376\right)[/tex]
To find the focal length, we need to find the distance of the image v, which is the distance from the mirror to the point where the reflected rays converge. Since the object is located beyond the center of curvature of the mirror, the image will be real, inverted, and smaller than the object.
Using the magnification formula, which relates the height of the object (h) and the height of the image (h'), we get:
[tex]\frac{h'}{h} = -\frac{v}{u}[/tex]
Substituting the values of h, u, and v, we get:
[tex]h' = \left(-\frac{v}{u}\right) h = \left(-\frac{v}{1.86}\right) \cdot 0.04[/tex]
Simplifying this expression, we get:
h' = -0.0022v
Since the image height is smaller than the object height, the negative sign indicates that the image is inverted.
Now, we can use the mirror equation to find the distance of the image:
[tex]\frac{1}{v} = \left(\frac{1}{f} - 0.5376\right)[/tex]
[tex]\frac{1}{v} = \frac{1}{f'}[/tex](where f' is the focal length in meters)
[tex]v = \frac{f'}{f' - 0.5376f'}[/tex]
Substituting the value of r = 2.55 m for the radius of the sphere, we can use the formula for the focal length of a spherical mirror:
[tex]f' = \frac{r}{2} = 1.275\text{ m}[/tex]
Substituting this value into the equation for v, we get:
[tex]v = \frac{f'}{f' - 0.5376f'} = 1.532\text{ m}[/tex]
Finally, we can use the magnification formula to find the height of the image:
h' = -0.0022v = -0.0022 * 1.532 = -0.00337 m
Since the image is inverted, the height is negative.
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at the sea level the plane can takeoff at the speed of 150 mi/hr. what is the required takeoff speed at albuquerque
The indicated airspeed (IAS) of the aircraft should be raised by roughly 2% for every 1,000 feet above sea level, according to a pilot's rule of thumb.
In order to generate enough lift during takeoff from a sea level airport, an aeroplane must attain a specific speed. Less dense air can be found at higher altitudes, such at Albuquerque, where the airport is situated at an altitude of 5,355 feet above sea level.
This necessitates a faster takeoff speed. Generally speaking, the plane's takeoff speed must rise by around 2% for every 1,000 feet of height. Under normal conditions and with conventional aeroplane characteristics, the estimated necessary takeoff speed at Albuquerque would be roughly 166 miles per hour.
The indicated airspeed (IAS) of the aircraft should be raised by roughly 2% for every 1,000 feet above sea level, according to a pilot's rule of thumb.
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higher takeoff speed to generate enough lift to take of
The required takeoff speed at Albuquerque would depend on several factors such as altitude, temperature, and runway length. If Albuquerque is at a higher altitude than sea level, the air is less dense and the plane would require a higher takeoff speed to generate enough lift to take off.
Additionally, if the temperature is higher, the air is less dense and the plane would also require a higher takeoff speed. The length of the runway at Albuquerque would also play a role in determining the required takeoff speed. Without more specific information, it is difficult to provide an exact answer to your question.
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15) monochromatic coherent light shines through a pair of slits. if the distance between these slits is decreased, which of the following statements are true of the resulting interference pattern? (there is more than one correct choice.) a) the distance between the maxima stays the same. b) the distance between the maxima decreases. c) the distance between the minima stays the same. d) the distance between the minima increases. e) the distance between the maxima increases.
Two of the correct statements regarding this are:
b) the distance between the maxima decreases
d) the distance between the minima increases
When monochromatic coherent light shines through a pair of slits, an interference pattern is created. This pattern is dependent on the distance between the slits. If the distance between the slits is decreased, the resulting interference pattern will be affected.
When the distance between the slits is decreased, the interference pattern becomes wider, and the distance between the maxima decreases. The distance between the minima, on the other hand, increases.
This is because the interference pattern is created by the interaction of waves, and when the distance between the slits is decreased, the waves interfere with each other differently.
This causes the pattern to shift and change. Therefore, the resulting interference pattern is affected by the distance between the slits.
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A 0. 300 kg
toy car moving with a speed of 0. 820 m/s
collides with a wall. The figure shows the force exerted on the car by the wall over the course of the collision
The negative sign indicates that the force is exerted in the opposite direction to the motion of the car. This force is applied over a short time interval and is relatively large, causing the car to experience a significant deceleration during the collision.
During the collision, the toy car experiences a change in momentum. Since momentum is conserved in the absence of external forces, the momentum of the car before the collision must be equal in magnitude and opposite in direction to the momentum after the collision.
The initial momentum of the car is given by:
p = mv = 0.3 kg * 0.82 m/s = 0.246 kgm/s
After the collision, the car comes to a stop, so its final momentum is zero. Therefore, the change in momentum is:
Δp = p_final - p_initial = -0.246 kg*m/s
The force exerted by the wall on the car during the collision can be calculated using the impulse-momentum theorem
J = Δp = FΔt
where J is the impulse, Δt is the time interval over which the force is applied, and F is the force
From the figure, we can see that the time interval for the collision is approximately 0.020 s. Therefore, the force exerted by the wall on the car is: F = Δp / Δt = -0.246 kg*m/s / 0.020 s = -12.3 N
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a drawing, provided by the manufacturer, that details permitted interconnections between the intrinsically safe and associated apparatus or between the nonincendive field wiring apparatus or associated nonincendive field wiring apparatus is called a
The drawing provided by the manufacturer, which details the permitted interconnections between intrinsically safe and associated apparatus or between nonincendive field wiring apparatus or associated nonincendive field wiring apparatus, is called a wiring diagram.
A wiring diagram typically includes detailed information about the wiring connections between components, as well as any necessary safety measures such as grounding or shielding. It may also include information about the voltage, current, and power requirements of the system, as well as any limitations or restrictions on the use of particular components or configurations.
This diagram is a critical part of the installation and maintenance process for intrinsically safe and nonincendive electrical systems, as it helps ensure that the correct connections are made and that the system operates safely and effectively.
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The complete question is:
A drawing, provided by the manufacturer, that details permitted interconnections between the intrinsically safe and associated apparatus or between the nonincendive field wiring apparatus or associated nonincendive field wiring apparatus is called a ______________
a star less luminous than our sun will have a habitable zone that is
A bow is drawn so that it has 40 J of potential energy. When fired, the arrow will have a kinetic energy of: Select one: O a. 80) o b. 20) O 0.60) O d. 40)
When a bow is drawn and has 40 J of potential energy, the arrow's kinetic energy when fired will be:
Your answer: d. 40 J
Explanation:
Potential energy is the energy that an object possesses due to its position, configuration, or state of being. It is stored energy that has the potential to do work in the future. The amount of potential energy that an object has depends on its position or configuration relative to other objects or systems. For example, a bow that is pulled back has potential energy that can be released as kinetic energy when it is released.
Kinetic energy, on the other hand, is the energy that an object possesses due to its motion. It is the energy that an object possesses because it is in motion and is able to do work by causing a change in another object's motion or position. The amount of kinetic energy that an object has depends on its mass and its velocity. For example, a moving car has kinetic energy that can be transferred to another object if it collides with it.
When the bow is drawn, it stores potential energy. When fired, this potential energy is converted into kinetic energy for the arrow. In an ideal situation with no energy loss, the arrow's kinetic energy will be equal to the bow's potential energy. Therefore, the arrow will have a kinetic energy of 40 J.
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help me please oml 2 one
Color: Both the bromine gas and steak have a brownish color.
What is bromine gas?Bromine gas is a reddish-brown, nonflammable, and highly toxic gas with a very strong, unpleasant odor. It is composed of two heavy, diatomic, halogen molecules, Br2, and is the only nonmetal element that exists as a liquid at room temperature. Bromine gas is denser than air and is soluble in water and organic solvents.
Texture: The bromine gas is a gas and therefore has no texture, while the steak is solid and has a firm texture.
Temperature: The bromine gas is a gas and therefore has a lower temperature than the steak, which is at room temperature.
Bromine Gas and Juice:
Color: The bromine gas is brownish and the juice is a yellowish or orange color.
Texture: The bromine gas is a gas and therefore has no texture, while the juice is a liquid and has a smooth texture.
Temperature: The bromine gas is a gas and therefore has a lower temperature than the juice, which is at room temperature.
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.A cannonball is launched upward with a velocity of 73.5 m/s at an angle of 20 degrees above the
horizontal.
(a) How long is the cannonball in the air?
(b) How far away does it land?
() How high does it travel? Cut your time in half!
Answer:
time of flight=( 2U sinx ) ÷ g
Explanation:
a)
u=73.5m/s , x= 20° , g =10m/s^2 then t= {2×73.5 × sin 20°} ÷ 10 = 134.2 ÷ 10 = 13.42 sec b) range is the distance, range= (u^2 sin 2 x ) ÷g = ({73.5 }^2 × sin 2 × 20 )÷ 10 =4025.3÷10 = 402.53meters. I couldn't finish the question so sorry
after a sci a patient may experience all of the following except: a. spasticity b. resting tremor c. autonomic dysreflexia d. orthostatic hypotension
The right response is resting tremor (option b). A patient may have spasticity, autonomic dysreflexia, and orthostatic hypotension following a spinal cord injury (SCI). SCI is not often linked to resting tremor.
SCI can interfere with the body's ability to communicate with the brain, leading to a variety of physical symptoms. Spasticity, which manifests as stiffness, muscle spasms, and increased muscle tone, is a frequent consequence. Patients with SCI at or above the T6 level may develop autonomic dysreflexia, a potentially fatal illness that is characterised by an abrupt rise in blood pressure. When someone stands up, their blood pressure drops, causing lightheadedness and dizziness. This condition is known as orthostatic hypotension.
While essential tremor, Parkinson's disease, and other neurological illnesses are frequently linked to resting tremor, SCI is not typically one of them.
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The right response is resting tremor (option b). A patient may have spasticity, autonomic dysreflexia, and orthostatic hypotension following a spinal cord injury (SCI). SCI is not often linked to resting tremor.
SCI can interfere with the body's ability to communicate with the brain, leading to a variety of physical symptoms. Spasticity, which manifests as stiffness, muscle spasms, and increased muscle tone, is a frequent consequence. Patients with SCI at or above the T6 level may develop autonomic dysreflexia, a potentially fatal illness that is characterised by an abrupt rise in blood pressure. When someone stands up, their blood pressure drops, causing lightheadedness and dizziness. This condition is known as orthostatic hypotension.
While essential tremor, Parkinson's disease, and other neurological illnesses are frequently linked to resting tremor, SCI is not typically one of them.
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at 2.1 km from the transmitter, the peak electric field of a radio wave is 350 mv/m . what is the peak electric field 10 km from the transmitter?
The peak electric field 10 km from the transmitter is approximately 15.435 mV/m.
To find the peak electric field 10 km from the transmitter, we can use the inverse square law.
This law states that the intensity of a wave (such as the electric field in this case) is inversely proportional to the square of the distance from the source.
Here's a step-by-step explanation:
1. Note the initial distance (d1) and electric field (E1):
d1 = 2.1 km, E1 = 350 mV/m.
2. Convert d1 to meters:
d1 = 2100 m.
3. Note the final distance (d2):
d2 = 10 km.
4. Convert d2 to meters:
d2 = 10,000 m.
5. Use the inverse square law formula:
E2 = E1 * (d1²) / (d2²).
6. Plug in the values:
E2 = 350 * (2100²) / (10,000²).
7. Calculate E2:
E2 ≈ 15.435 mV/m.
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a pendulum is swinging upward and is halfway toward its highest position, as shown, when the string breaks. which of the paths shown best represents the one that the ball would take after the string breaks?
The option A is best representation of the path that the ball would take after the string breaks.
When the string of a pendulum breaks, the ball's path will follow the laws of motion, specifically the law of conservation of energy. As the ball was halfway to its highest position, it had a certain amount of potential energy.
When the string broke, this potential energy would convert to kinetic energy, causing the ball to move in a straight line tangent to the point where the string broke.
Therefore, the path that the ball would take after the string breaks would be a straight line away from the pivot point of the pendulum, as shown in option A. The other paths shown do not follow the laws of motion and do not account for the conservation of energy. Option (A) is the correct answer.
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Note the full question is
A pendulum is swinging upward and is halfway toward its highest position, as shown, when the string breaks. which of the paths shown best represents the one that the ball would take after the string breaks?
A) A
B) B
C) C
D) D
E) E
. for schrodinger's equation of the h2 molecule, the kinetic energy has contributions from a. electrons only b. nuclei only c. both electrons and nuclei d. only one electron and one nucleus
The kinetic energy in Schrödinger's equation for the H2 molecule includes contributions from both electrons and nuclei. Thus the correct option is C.
The kinetic energy term in Schrödinger's equation for the H2 molecule refers to the energy involved in the motion of the particles. The H2 molecule comprises two hydrogen nuclei and two electrons, therefore the electrons and the nuclei both contribute to the kinetic energy.
The nuclei contribute to the kinetic energy by their mobility, whereas the electrons do so through their wave-like behaviour. The H2 molecule's kinetic energy term in Schrödinger's equation includes contributions from both electrons and nuclei, making option C the right response.
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The kinetic energy in Schrödinger's equation for the H2 molecule includes contributions from both electrons and nuclei. Thus the correct option is C
explanation - For Schrödinger's equation of the H2 molecule, the kinetic energy has contributions from both electrons and nuclei. This is because the kinetic energy term in the equation accounts for the motion of all particles in the system, which in this case includes both the electrons and nuclei of the H2 molecule. Therefore, options a, b, and d are incorrect.
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a circuit breaker is rated for a current of 15 a rms at a voltage of 240 v rms. (a) what is the largest value of imax that the breaker can carry?
The largest value of I_max that the breaker can carry is approximately 21.21 A.
Given a circuit breaker rated for 15 A RMS at 240 V RMS, we want to find the largest value of Imax (maximum current) that the breaker can carry. To do this, we'll use the following formula:
I_max = √2 * I_RMS
Where I_RMS is the rated current in RMS, which is 15 A in this case.
Substitute the value of I_RMS into the formula:
Imax = √2 * 15 A
Calculate the value of Imax:
Imax ≈ 21.21 A
Therefore approximately 21.21 A is the largest value of Imax that the breaker can carry.
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is a mirror magnetic or nonmagnetic
if the display is located 12.8 cm from the 12.0- cm focal length lens of the projector, what is the distance between the screen and the lens?
The distance between the screen and the lens of the projector is approximately 6.19 cm.
To determine the distance between the screen and the lens of the projector, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens (12.0 cm)
v = distance of the image (screen) from the lens (unknown)
u = distance of the object (display) from the lens (12.8 cm)
Plugging in the values into the lens formula:
1/12.0 = 1/v - 1/12.8
Now, let's solve for v:
1/v = 1/12.0 + 1/12.8
1/v = (12.8 + 12.0) / (12.0 * 12.8)
1/v = 24.8 / 153.6
v = 153.6 / 24.8
v ≈ 6.19 cm
Therefore, the distance between the screen and the lens of the projector is approximately 6.19 cm.
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water is drawn from a well in a bucket tied to the end of a rope whose other end wraps around a cylinder of mass 50 kg and diameter 25 cm. as you turn this cylinder with a crank, the rope raises the bucket. if the mass of a bucket of water is 20 kg, what torque must you apply to the crank to raise the bucket of water at a constant speed?
m_c (mass of cylinder)=50 kg
d=25 cm so r=12.5 cm = 0.125 m m_b
(mass of bucket)=20 kg
So using the equations: RT = � = I � RT= I � (m_b)g-T= (m_b)aR And from what I understand, this is the same as the tangential acceleration? (m_b)g-T=(m_b) � r = F T= ( i � ) / r (m_b)g -(( i � ) / r ) = m � r � ( ((m_b)r) + (I /R ) ) = (m_b)g Leaving us with the final : � = ((m_b)g)/(((m_b)r) + (I /r)) Using this equation, I found I = 0.390625 and the final answer would be 35 rad/s^2 Sorry for such a long post--this is my first time on the website and I read the rules so hopefully I've done everything correctly! Thank you all!
/
a satellite circles a spherical planet of unknown mass in a circular orbit of radius 2.5×107 m . the magnitude of the gravitational force exerted on the satellite by the planet is 110 n .
Since we don't know the mass of the satellite or its velocity, we can't solve for the mass of the planet with the given information alone. We would need at least one more piece of information to do so.
Answer - Based on the given information, we can use the equation for gravitational force:
F = (G * m1 * m2) / r^2
where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
Since we don't know the mass of the planet, we can't directly solve for it. However, we can use the fact that the satellite is in a circular orbit, which means that the gravitational force is equal to the centripetal force:
F = (m * v^2) / r
where m is the mass of the satellite and v is its velocity.
We can solve for m by rearranging the equation:
m = (F * r) / v^2
Now we can use this mass value and plug it into the original equation for gravitational force, along with the given values for r and F, to solve for the mass of the planet:
110 N = (G * m * m_planet) / (2.5x10^7 m)^2
m_planet = (110 N * (2.5x10^7 m)^2) / (G * m)
where G is a constant equal to 6.67x10^-11 N*m^2/kg^2.
Unfortunately, since we don't know the mass of the satellite or its velocity, we can't solve for the mass of the planet with the given information alone. We would need at least one more piece of information to do so.
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the command module of the apollo spacecraft can be modelled as a truncated cone with a base diameter of 3.9 meters, a diameter at the upper (apex) end of 1.3 meters and a length of 3.5 meters. suppose the base of the spacecraft is encircled by a metal ring which is an excellent conductor. the magnitude and direction of the earth's magnetic field do not vary significantly over a distance the size of the spacecraft. if the spacecraft is oriented while in orbit so that its long axis is parallel to the earth's magnetic field, which has a magnitude of 1.0 x 10-4 t, and it then rotates about a perpendicular axis, which one of maxwell's equations allows us to calculate how much current will flow in the metal ring?
The Maxwell's equation that allows us to calculate the current flowing in the metal ring is Faraday's Law of Electromagnetic Induction, which states that the magnitude of the induced EMF (electromotive force) is equal to the rate of change of magnetic flux through a conducting loop.
In this case, the rotating Apollo spacecraft generates a changing magnetic flux through the metal ring due to its motion through the Earth's magnetic field. Therefore, an EMF is induced in the metal ring, which causes a current to flow.
To calculate the magnitude of this current, we need to know the rate of change of the magnetic flux through the metal ring. This can be found by taking the time derivative of the magnetic flux. Since the spacecraft is rotating about a perpendicular axis, the magnetic flux through the metal ring will vary sinusoidally with time. Therefore, we can express the time-varying magnetic flux through the metal ring as:
Φ(t) = Φmax sin(2πft)
where Φmax is the maximum magnetic flux through the metal ring, f is the frequency of the spacecraft's rotation, and t is time.
Taking the time derivative of this expression, we get:
dΦ/dt = Φmax (2πf) cos(2πft)
This expression gives us the rate of change of magnetic flux through the metal ring, which is proportional to the induced EMF. Finally, by applying Ohm's Law (V = IR) to the metal ring, we can calculate the current flowing in the ring. The current is given by:
I = V/R
where V is the induced EMF and R is the resistance of the metal ring. The resistance of the ring depends on its material properties and dimensions.
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Potable water is ____.
A. also known as industrial wastewater
B. also known as irrigation water
C. also known as sewage
D. also known as groundwater
E. fit for drinking
Potable water is fit for drinking. Option E
What is portable water?Potable water is water that is safe for human consumption and considered fit for drinking. It is free from harmful bacteria, viruses, chemicals, and other contaminants that can cause health problems.
Potable water can come from different sources such as groundwater, surface water, or treated wastewater, and it is typically treated and disinfected to ensure its safety before being distributed to consumers.
Portable water isn't known as industrial wastewater, irrigation water, groundwater and sewage.
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what is the typical voltage drop (in volts) across the collector and emitter (vce) of a bjt when in saturation?
The VCE voltage drop in saturation for a typical BJT can be assumed to be between 0.1V and 0.3V.
How VCE voltage drop in saturation for a typical BJT?The voltage drop across the collector and emitter (VCE) of a bipolar junction transistor (BJT) when it is in saturation depends on several factors such as the type of BJT, the collector current, and the biasing conditions.
However, as a general rule of thumb, the VCE voltage drop in saturation for a typical BJT can be assumed to be between 0.1V and 0.3V, depending on the specific characteristics of the transistor. This value may vary based on the operating conditions and the specific transistor used.
It's worth noting that the VCE voltage drop in saturation is typically lower than the voltage drop in the active region, where the BJT behaves as a current amplifier. In the active region, the VCE voltage drop can range from a few tenths of a volt up to several volts, depending on the transistor's characteristics and operating conditions.
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the threshold frequency (minimum frequency) of aluminum for the photoelectric effect is in the ultraviolet range. what will happen if infrared light shines on the aluminum surface?
Any electromagnetic radiation with a frequency lower than 9.84 x 10¹⁴ Hz (infrared, microwave, radio waves) will not cause the photoelectric effect in aluminum.
If infrared light shines on the aluminum surface, no electrons will be emitted via the photoelectric effect because the frequency of infrared light is lower than the threshold frequency of aluminum. The photoelectric effect occurs when a photon with enough energy (frequency) is absorbed by an electron in a metal, causing the electron to be emitted from the metal.
The minimum frequency or threshold frequency ([tex]f_{t}[/tex]) of a metal can be calculated using the equation:
[tex]f_{t}[/tex] = Φ ÷ h
where Φ is the work function of the metal (the minimum energy required to remove an electron from the metal) and h is Planck's constant. For aluminum, Φ = 4.08 eV.
Converting Φ to joules and using h = 6.626 x 10⁻³⁴ J s, we get:
Φ = 4.08 eV x 1.6 x 10⁻¹⁹ J/eV
Φ = 6.528 x 10⁻¹⁹ J
[tex]f_{t}[/tex] = 6.528 x 10⁻¹⁹ J ÷ 6.626 x 10⁻³⁴ J s
≈ 9.84 x 10¹⁴ Hz
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what does the technique of interferometry allow?what does the technique of interferometry allow?it allows two or more telescopes to obtain a total light-collecting area much larger than the total light-collecting area of the individual telescopes.it allows us to determine the chemical composition of stars.it allows two or more telescopes to obtain the angular resolution of a single telescope much larger than any of the individual telescopes.it allows the same telescope to make images with both radio waves and visible light.it allows astronomers to make astronomical observations without interference from light pollution.
The technique of interferometry allows two or more telescopes to obtain the angular resolution of a single telescope much larger than any of the individual telescopes.
This is achieved by combining the signals received by the telescopes to create a single image with a higher resolution. Interferometry is especially useful for studying objects with small angular sizes, such as stars and planets.
Additionally, interferometry allows astronomers to make astronomical observations without interference from light pollution, as it can separate the signals from the object being observed from the background light.
However, interferometry does not directly determine the chemical composition of stars, although it can provide information about their temperature and other physical properties.
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The majority of Venus's surface is:
A. volcanic plains with flowing lava.
B large, flat mesas with tiny valleys.
C. thick, soupy clouds of hydrogen.
D. frozen dunes of dust and sand.
Answer:
C.
Explanation:
When Venus surface get bit cold when weather hits the planet gets soupy clouds and etc.
calculate the period of a horizontal mass-on-a-spring system where the stiffness of the spring is 500 n/m and the mass of the system is 25.7 kg.
The period of the horizontal mass-on-a-spring system with a stiffness of 500 N/m and a mass of 25.7 kg is approximately 1.424 seconds.
We'll use the following terms in our calculation: stiffness of the spring (k), mass of the system (m), and period (T).
The formula to calculate the period of a mass-on-a-spring system is:
T = 2π √(m/k)
where:
T = period (in seconds)
m = mass of the system (25.7 kg)
k = stiffness of the spring (500 N/m)
Now, we'll plug in the values:
T = 2π √(25.7 kg / 500 N/m)
To calculate the square root:
T = 2π √(0.0514)
T = 2π × 0.2266
Finally, multiply by 2π:
T ≈ 1.424 seconds
So, the period of the horizontal mass-on-a-spring system is approximately 1.424 seconds.
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019 (part 1 of 2) 10.0 points
A Carnot engine has a power output of
197 kW. The engine operates between two
reservoirs at 20◦C and 425◦C.
How much thermal energy is absorbed each
hour?
Answer in units of J.
020 (part 2 of 2) 10.0 points
How much thermal energy is lost per hour?
Answer in units of J.
Thermal energy is absorbed each hour is 13.53 x 10¹² J and thermal energy lost per hour is 7.092 x 10¹² J.
What is the Carnot engine's operating principle?a technique of isothermal gas expansion that is reversible. In this process, the ideal gas in the system receives amount heat from a heat source at a high temperature Thigh, expands and does work on surroundings. a technique of adiabatic gas expansion that is reversible. The system is thermally insulated throughout this process.
Temp_cold = 20°C + 273.15 = 293.15 K
Temp_hot = 425°C + 273.15 = 698.15 K
efficiency = 1 - (Temp_cold / Temp_hot)
= (698.15 K * 293.15 K) / (698.15 K)² - (293.15 K)²
efficiency = 0.524 or 52.4%
thermal energy absorbed/ hour = power output / efficiency
= 197 kW / 0.524
= 375.95 MJ/h x 3.6 x 10⁶ J/kWh = 13.53 x 10¹² J
thermal energy is lost per hour
W = power output x time = 197 kW x 1 h = 197 kWh
W = 197 kWh x 3.6 x 10⁶ J/kWh = 7.092 x 10¹²1J
Since the engine is running in a cycle, the system's internal energy is equal to zero, hence U = 0.
Q = ΔU + W
hence, thermal energy lost per hour = Q = W = 7.092 x 10^11 J
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catching a wave, a 73.2-kg surfer starts with a speed of 1.44 m/s, drops through a height of 1.84 m, and ends with a speed of 8.89 m/s. how much nonconservative work was done on the surfer?
The nonconservative work done on the surfer is 2845.5 J.
We can use the work-energy theorem to solve this problem. The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. In this case, we can calculate the initial and final kinetic energies of the surfer and find the difference, which will give us the net work done.
The initial kinetic energy of the surfer is:
[tex]K_i = (1/2) * m * v_i^2[/tex]
[tex]K_i = (1/2) * 73.2 kg * (1.44 m/s)^2[/tex]
K_i = 75.7 J
The final kinetic energy of the surfer is:
[tex]K_f = (1/2) * m * v_f^2[/tex]
[tex]K_f = (1/2) * 73.2 kg * (8.89 m/s)^2[/tex]
K_f = 2921.2 J
The change in kinetic energy is:
ΔK = K_f - K_i
ΔK = 2921.2 J - 75.7 J
ΔK = 2845.5 J
According to the work-energy theorem, this change in kinetic energy must be equal to the net work done on the surfer. Therefore, the nonconservative work done on the surfer is:
W_nc = ΔK
W_nc = 2845.5 J
So, the nonconservative work done on the surfer is 2845.5 J.
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what are reasons that a promontory will be more vulnerable to wave erosion than a bay? multiple select question. waves bend around a promontory and strike it from both sides. larger waves enter into a bay than strike a promontory. a promontory will receive more wave action than a bay. powerful waves focus most of their energy at a promontory.
The reasons that a promontory will be more vulnerable to wave erosion than a bay;- Waves bend around a promontory and strike it from both sides,- Powerful waves focus most of their energy at a promontory and - A promontory will receive more wave action than a bay.
A promontory is more vulnerable to wave erosion than a bay due to the following reasons:
1. Waves bend around a promontory and strike it from both sides: This phenomenon, called wave refraction, concentrates the wave energy on the promontory, making it more prone to erosion.
2. A promontory will receive more wave action than a bay: Bays are generally more sheltered and have a lower exposure to waves, whereas promontories are exposed to the full force of waves, leading to more erosion.
3. Powerful waves focus most of their energy at a promontory: Due to the shape of the coastline, waves tend to focus their energy on the headlands, like promontories, which makes them more vulnerable to erosion compared to bays.
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a common way to describe acceleration is to express it in multiples of g, earth's gravitational acceleration. if a dragster accelerates at a rate of 39.2 m/s2, how many g's does the driver experience?
The acceleration of the dragster in multiple of g, when he accelerates at a rate of 39.2 m/s², is 4g.
To express the acceleration of the dragster in multiples of g, we need to divide the acceleration by the acceleration due to gravity on Earth.
Number of g's = (Acceleration of the dragster) / (Earth's gravitational acceleration)
First, we need the value of Earth's gravitational acceleration, which is approximately 9.81 m/s².
Now, we can use the given acceleration of the dragster (39.2 m/s²) and the formula:
Number of g's = (39.2 m/s²) / (9.81 m/s²) = 4
Therefore, the driver of the dragster experiences an acceleration equivalent to about 4 times the acceleration due to gravity on Earth.
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how far from the nut of the guitar must a fret (and your finger) be placed on this string to play g (392 hz )?
To play G note (392 Hz) on a guitar string, place the fret and your finger at a distance of approximately 40.4 cm (or 16 inches) from the nut of the guitar.
The distance that the fret and your finger must be placed from the nut of the guitar is determined by the length of the string that is allowed to vibrate when the string is plucked. The length of the vibrating string determines the frequency of the sound produced by the guitar string.
The distance from the nut of the guitar to the fret that must be placed to play a G note with a frequency of 392 Hz can be calculated using the formula:
[tex]L = (v / 2f) * (n^2 - 1)[/tex]
where L is the length of the string from the nut to the fret, v is the velocity of the wave (which is dependent on the tension and mass per unit length of the string), f is the frequency of the note, and n is the fret number (with n=1 corresponding to the distance from the nut to the first fret).
For a standard guitar tuning and using typical values for the velocity of the wave and string tension, the distance from the nut to the third fret would be approximately 40.4 cm to play a G note with a frequency of 392 Hz.
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Please help I need to answer fast the fate of my graduation depends on it.
First, we need to find the total mass of the system by adding the masses of the two objects: m_total = m1 m2 = 50.0 kg 75.0 kg = 125.0 kg Next, we can plug in the given force and mass values into the equation: F = ma 40.0 N = 125.0 kg * a Solving for a: a = 40.0 N
125.0 kg * a
Solving for a:
a = 40.0 N / 125.0 kg
a = 0.32 m/s^2
Therefore, the acceleration of the system is 0.32 m/s^2.