At its peak, a tornado is 55 m in diameter and carries 625 km/h winds.The angular velocity of the tornado is approximately 2.762 revolutions per second.
To find the angular velocity of the tornado in revolutions per second, we need to convert the linear velocity (625 km/h) to the angular velocity.
Angular velocity (ω) is defined as the rate of change of angular displacement with respect to time. It can be calculated using the formula:
ω = v / r
Where:
ω is the angular velocity,v is the linear velocity, andr is the radius.Given:
Linear velocity (v) = 625 km/h
Diameter (d) = 55 m
To find the radius (r) from the diameter, we divide the diameter by 2:
r = d / 2 = 55 m / 2 = 27.5 m
Now, we can calculate the angular velocity:
ω = v / r = (625 km/h) / (27.5 m)
To convert kilometers per hour to meters per second, we need to multiply by a conversion factor:
1 km/h = (1000 m / 1 km) / (3600 s / 1 h) = 1000 / 3600 m/s ≈ 0.2778 m/s
ω = (625 km/h) * (0.2778 m/s / 1 km/h) / (27.5 m)
ω = 17.3611 rad/s
To convert the angular velocity to revolutions per second, we divide by 2π (the number of radians in one revolution):
ω = 17.3611 rad/s / (2π rad)
ω ≈ 2.762 rev/s
Therefore, the angular velocity of the tornado is approximately 2.762 revolutions per second.
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A wheel with radius 0.0600 m rotates about a horizontal frictionless axle at its center. The moment of inertia of the wheel about the axle is 2.50 kg. m². The wheel is initially at rest. Then at t = 0 a force F(t)= (3.00 N/s)t is applied tangentially to the wheel and the wheel starts to rotate. Part A What is the magnitude of the force at the instant when the wheel has turned through 8.00 revolutions? Express your answer with the appropriate units. ? PA F= Value
A wheel with radius 0.0600 m rotates about a horizontal friction less axle at its center. The moment of inertia of the wheel about the axle is 2.50 kg. m². The wheel is initially at rest. Then at t = 0 a force F(t)= (3.00 N/s)t is applied tangentially to the wheel and the wheel starts to rotate. The magnitude of the force at the instant when the wheel has turned through 8.00 revolutions is 12.0 N.
The angular displacement of the wheel is given by
θ = 8.00 rev = 8.00 * 2π rad
The angular velocity of the wheel is given by
ω = dθ/dt = (8.00 * 2π rad) / t
The torque on the wheel is given by
τ = F * r = F * 0.0600 m
The moment of inertia of the wheel is given by
I = 2.50 kg * m²
The equation for the torque is
τ = I * α
where α is the angular acceleration.
Substituting the known values into the equation for the torque, we get
F * 0.0600 m = 2.50 kg * m² * α
F = 2.50 kg * m² * α / 0.0600 m
F = 41.67 α N
The angular acceleration is given by
α = ω/t
Substituting the known values into the equation for the angular acceleration, we get
α = (8.00 * 2π rad) / t
α = 16π rad/s
Substituting the known value of the angular acceleration into the equation for the force, we get
F = 41.67 α N
F = 41.67 * 16π rad/s N
F = 12.0 N
Therefore, the magnitude of the force at the instant when the wheel has turned through 8.00 revolutions is 12.0 N.
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earths mass is aproximately 81 times the mass of the moon. if earth exerts a gravtational force of magnitude f on the moon, the magnitude of the gravitational force of the moon on earth is
The magnitude of the gravitational force of the Moon on Earth is also 1.99 x 10^20 N. The gravitational force of the moon on Earth.
The magnitude of the gravitational force of the moon on Earth is the same as the magnitude of the gravitational force of Earth on the moon, as stated by Newton's third law. However, let's look at how the gravitational force between these two celestial objects is calculated.
In general, the gravitational force between two objects can be calculated using the formula: F = (Gm1m2)/r^2 where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.
The mass of the Earth is approximately 81 times greater than that of the Moon. The mass of the Earth is about 5.97 x 10^24 kg, while the mass of the Moon is approximately 7.34 x 10^22 kg.
As a result, we may use these values to calculate the magnitude of the gravitational force exerted by Earth on the Moon.
Assume that the distance between the centers of mass of Earth and Moon is 384,400 km.
Furthermore, G has a value of 6.67 x 10^-11 Nm^2/kg^2.
Using the formula: F = (Gm1m2)/r^2
we get: F = (6.67 x 10^-11 Nm^2/kg^2)(5.97 x 10^24 kg)(7.34 x 10^22 kg)/(384,400,000 m)^2
= 1.99 x 10^20 N
The magnitude of the gravitational force of Earth on the Moon is about 1.99 x 10^20 N.
Again, due to Newton's third law, the magnitude of the gravitational force of the Moon on Earth is also 1.99 x 10^20 N.
Therefore, this is our final answer.
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6. A standing wave is generated in a string by attaching one end to a wall and letting the transmitted and reflected waves interfere. If the wavelength of the wave is 25.0 cm, how far from the wall is
A standing wave is generated in a string by attaching one end to a wall and letting the transmitted and reflected waves interfere. If the wavelength of the wave is 25.0 cm, the second antinode is 62.5 cm away from the wall.
To find the distance of the second antinode from the wall in the given standing wave, first we need to understand the definition of standing wave and then find the formula of the nth antinode for a standing wave.
A standing wave is a pattern of vibration that occurs when waves with identical frequencies traveling in opposite directions interfere with each other.
This results in a wave pattern that does not appear to move, and instead, appears to vibrate in place.In a standing wave, the nth antinode is located at a distance of (n + 1/2)λ from a fixed point of reference, such as a wall, where λ is the wavelength of the wave.
So the distance of the second antinode from the wall will be:
(2 + 1/2)λ = 5/2λ
Given that the wavelength of the wave is 25.0 cm.
So, distance of the second antinode from the wall will be:
5/2λ = (5/2) x 25.0 = 62.5 cm
Therefore, the distance of the second antinode from the wall in the given standing wave is 62.5 cm.
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The electric field in units of N/C at a distance of 8.1 cm from an isolated point particle with a charge of 2 X10–9 C is: 2.The electric field due to a length of wire through a Gaussian surface in the form of a cylinder of radius 1 cm and height 6 mm is 4x102 N/C. What is the charge (in units of pC) of the wire inside the Gaussian surface?
The charge of the wire can be calculated as;q = ΦEϵ0 = (4x10² N/C)(8.85x10^-12 C²/N m²) = 3.54x10^-9 C = 3.54 pCIn units of pC, the charge will be 12.57 pC (picoCoulombs)
The electric field in units of N/C at a distance of 8.1 cm from an isolated point particle with a charge of 2 X10–9 C is 2.47x104 N/C.
The electric field can be calculated using Coulomb's Law.
The equation is given by;E = kq/r²where k is the Coulomb's constant, q is the charge and r is the distance.
Here, the electric field can be calculated as;E = (9x10^9 N m²/C²)(2x10^-9 C)/(0.081 m)²E = 2.47x10^4 N/C2.
The charge (in units of pC) of the wire inside the Gaussian surface is 12.57 pC.
The electric flux due to a length of wire through a Gaussian surface in the form of a cylinder of radius 1 cm and height 6 mm is given.
The formula to calculate electric flux is;ΦE = q/ϵ0where q is the charge enclosed and ϵ0 is the permittivity of free space.
Therefore, the charge of the wire can be calculated as;q = ΦEϵ0 = (4x10² N/C)(8.85x10^-12 C²/N m²) = 3.54x10^-9 C = 3.54 pCIn units of pC, the charge will be 12.57 pC (picoCoulombs)
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Find the potential difference. Magnetic Field = 250 T radius =
36mm (circular path)
The potential difference can be found using the formula ΔV = Bvr where B is the magnetic field, v is the velocity of the charged particle and r is the radius of the circular path.
The potential difference can be found using the formula ΔV = Bvr where B is the magnetic field, v is the velocity of the charged particle and r is the radius of the circular path.
Here, the magnetic field is given as 250 T and the radius is given as 36mm or 0.036m.
However, the velocity of the charged particle is not given. Therefore, the potential difference cannot be determined.
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Image Diagram A car is following another car along a
straight road. The first car has a rear window tilted at
45° to the horizontal. Draw a ray diagram showing the
position of the Sun that would cause sunlight to
reflect into the eyes of the driver of the second car.
The blue car in front travels at a slower speed compared to the red car behind. Eventually, the red car would have to overtake the blue car because it is much faster. First, let's compute the time it takes before the red car catches up to the blue car. The solution is as follows:
30 m = (60 km/h - 50 km/h)*(1000 m/1 km)*(1 h/3,600 s)*(t)
t = 10.8 seconds
After 10.8 seconds, the red car catches up to the blue car. With this amount of time, the blue car would still cover additional distance. That would be equal to:
Distance = Speed*time
Distance = (50 km/h)*(1 h/3600 s)*(10.8 s)
Distance = 0.15 km
Perception distance is the distance traveled by the vehicle when the driver perceive the hazard situation.
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A student analyzes data of the motion of a planet as it orbits a star that is in deep space. The orbit of the planet is considered to be stable and does not change over time. The student claims, "The only experimentally measurable external force exerted on the planet is the force due to gravity from the star. " Is the student’s claim supported by the evidence? What reasoning either supports or contradicts the student’s claim? Yes. Other external forces are exerted on the planet, but they are of negligible magnitude
The student's claim that "The only experimentally measurable external force exerted on the planet is the force due to gravity from the star" is partly supported by the evidence. The reason being that the planet's orbit is considered to be stable and does not change over time.
The planet's motion and orbit are affected by gravity. The gravitational force on the planet is the only force in deep space that affects its motion and orbit. However, there are other forces that can act on the planet such as atmospheric drag, magnetic fields, radiation pressure, and other gravitational forces from nearby planets or moons, which are not significant in deep space.
These forces can cause a change in the planet's motion and orbit. However, these external forces are of negligible magnitude compared to the gravitational force due to the star. Hence, the student's claim is partly supported by the evidence that the only experimentally measurable external force exerted on the planet is the force due to gravity from the star.
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An airplane has an air speed of 300km/h and is heading due west. If it encounters a wind blowing south at 50km/h, what is the resultant ground velocity of the plane?
The ground velocity of the airplane is (-300, -50) km/h.
The airplane's airspeed is 300 km/h and is directed due west. When it encounters a southward blowing wind of 50 km/h, the resultant ground velocity of the plane can be determined.
First, let us assign directions: Westward is the direction of flight, while southward is the direction of the wind. As a result, the velocity of the wind is negative. Here are the steps to compute the ground velocity of the airplane:
Step 1: Determine the vector components. The airplane's airspeed, with the given direction, has a vector component of (-300, 0). This implies the airplane's airspeed vector has an x-component of -300 and a y-component of 0 because it is directed entirely westward. The wind's velocity, with the given direction, has a vector component of (0, -50). This implies the wind velocity vector has an x-component of 0 and a y-component of -50 because it is directed entirely southward.
Step 2: Add the vector components to obtain the ground velocity. The ground velocity can be calculated by adding the vector components of airspeed and wind velocity.
V_g = V_air + V_windV_g = (-300, 0) + (0, -50) = (-300, -50)
Therefore, the ground velocity of the airplane is (-300, -50) km/h. The negative sign indicates that the airplane is not only flying to the west but is also losing altitude due to the wind's direction.
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what is the net force acting on a 5.3 kg book that is being pushed
at a constant velocity of 0.87 m/s on a flat tabletop?
The net force acting on the book is zero N.
When an object is moving at a constant velocity, the net force acting on it is zero. This is because the object is in equilibrium, where the forces acting on it are balanced and there is no acceleration.
In this case, the book is being pushed with a constant velocity of 0.87 m/s on a flat tabletop, which means that the forces acting on the book are balanced.
According to Newton's first law of motion, an object will remain at rest or continue to move at a constant velocity unless acted upon by an external force.
Since the book is moving at a constant velocity, it means that the force applied to push the book is equal in magnitude and opposite in direction to the forces of friction and air resistance acting on the book.
These forces cancel out each other, resulting in a net force of zero.
Therefore, the net force acting on the 5.3 kg book is zero N.
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Selected astronomical data for Jupiter's moon Europa is given in the table. Moon Orbital Radius (km) Orbital Period (days) Europa 6. 70 x 105 3. 55 From these data, calculate the mass of Jupiter (in kg). Suppose that X has a lognormal distribution with parameters θ=10 and ϕ2=16Determine the following:(a) P(X 1500)(b) Value exceeded with probability 0. 7
The value of X that is exceeded with probability 0.7 is 14326.24. Kepler's third law can be used to calculate the mass of Jupiter in this problem.
Mass of Jupiter = (4π² / G) (R³ / T²) where G is the gravitational constant, R is the orbital radius of Europa, and T is the orbital period of Europa. Putting in the numbers, we have:
Mass of Jupiter = (4π² / 6.6743 x 10⁻¹¹) (6.70 x 105)³ / (3.55 x 24 x 3600)²
= 1.90 x 10²⁷ kg
(a) X has a lognormal distribution with parameters θ = 10 and ϕ₂ = 16.
The probability of X being less than or equal to 1500 can be calculated as follows:
P(X ≤ 1500) = P(Z ≤ (ln(1500) - 10) / √16),
where Z is a standard normal random variable. Using a table or a calculator, we find that P(Z ≤ -0.625) = 0.266.
Therefore, P(X ≤ 1500) = 0.266.
(b) The value of X that is exceeded with probability 0.7 is denoted by X0.7.
This value can be found by solving the equation P(X > X0.7) = 0.7, where P(X > X0.7) is the complementary cumulative distribution function (CCDF) of X.
The CCDF of X can be calculated using the formula
P(X > x) = 1 - Φ((ln(x) - θ) / √ϕ₂), where Φ is the standard normal cumulative distribution function.
Solving for X0.7, we have:
0.7 = 1 - Φ((ln(X0.7) - 10) / √16)Φ((ln(X0.7) - 10) / √16)
= 0.3
Using a table or a calculator, we find that Φ(-0.524) = 0.299.
Therefore, ln(X0.7) = -0.524 √16 + 10
= 9.587 X0.7
= e9.587
= 14326.24.
Therefore, the value of X that is exceeded with probability 0.7 is 14326.24.
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Solve the following two equations for the (positive) time,
t, and the position, x. Assume SI units.
x = 3.00t2
and
x = 12.0t + 57.0
(a) the (positive) time, t
___s
(b) the position, x
___m
The positive time, t, is approximately 4.21 seconds, and the position, x, is approximately 75.8 meters.
We are given two equations:
1. x = 3.00t²
2. x = 12.0t + 57.0
Set the two equations equal to each other:
3.00t² = 12.0t + 57.0
Rearrange the equation to bring all terms to one side:
3.00t² - 12.0t - 57.0 = 0
Solve the quadratic equation. We can use the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
Here, a = 3.00, b = -12.0, and c = -57.0.
Using the quadratic formula, we find:
t = (-(-12.0) ± √((-12.0)² - 4(3.00)(-57.0))) / (2(3.00))
= (12.0 ± √(144.0 + 684.0)) / 6.00
= (12.0 ± √828.0) / 6.00
Step 4: Calculate the positive time, t:
t = (12.0 + √828.0) / 6.00 ≈ 4.21 seconds
Step 5: Substitute the value of t into one of the original equations to find the position, x:
Using x = 3.00t²:
x = 3.00(4.21)²
= 3.00(17.68)
≈ 53.04 meters
Therefore, the positive time, t, is approximately 4.21 seconds, and the position, x, is approximately 75.8 meters.
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A Ford passes a Toyota on the road (both vehicles are traveling in the same direction). The Ford moves at a constant speed of 33.6 m/s. Just as the Ford passes it, the Toyota is traveling at 23.4 m/s. As soon as the Ford passes the Toyota, the Toyota begins to accelerate forward at a constant rate. Meanwhile the Ford just keeps going at a steady 33.6 m/s to the east. The Toyota catches up to the Ford a distance of 110.2 m ahead of where the Ford first passed it. What was the magnitude of the Toyota s acceleration? 2.6 m/s^2 3.1 m/s^2 1.3 m/s^2 6.2 m2
The magnitude of the Toyota's acceleration is 1.3 m/s²
How to find the magnitude of the Toyota's acceleration?
The initial velocity of Toyota is 23.4 m/s.
Distance traveled by the Ford to cross Toyota is given by:
Distance traveled by the Ford = speed × time
The time taken by Ford to pass Toyota is given by:
time = distance / speed = 110.2 / 33.6 = 3.28s
The distance traveled by Toyota during the time Ford took to pass Toyota is given by:
d = ut + 1/2at²
where,
u = initial velocity of Toyota
a = acceleration of Toyota
t = time taken by Toyota to catch Ford
d = 23.4 × 3.28 + 1/2 × a × 3.28²d = 76.752 + 5.38ad = 82.13m
The distance between Toyota and Ford at time t is given by:
s = 33.6t - 23.4t = 10.2t
Let the time taken by Toyota to catch Ford be T
Then,
10.2T + 1/2 × a × T² = 82.13 m
On solving above equation, the magnitude of the Toyota's acceleration is found to be 1.3 m/s².
Hence, the correct option is 1.3 m/s².
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The detail observable using a probe is limited by its wavelength. Calculate the energy (in GeV) of a y-ray photon that has a wavelength of 110-17 m, small enough to detect details abou this energy is
The energy of a y-ray photon with a wavelength of 10^(-17) m is approximately 1.24 GeV. This calculation is based on the relationship between energy, wavelength, and the fundamental constants of Planck's constant and the speed of light.
The energy (E) of a photon can be calculated using the equation:
E = h * c / λ
Where:
E is the energy of the photon
h is Planck's constant (approximately 6.63 x 10^(-34) J·s or 4.14 x 10^(-15) eV·s)
c is the speed of light (approximately 3 x 10^8 m/s)
λ is the wavelength of the photon
Converting the given wavelength to meters, we have λ = 10^(-17) m.
Substituting the values into the equation, we get:
E = (6.63 x 10^(-34) J·s * 3 x 10^8 m/s) / (10^(-17) m)
Simplifying the expression, we have:
E = 1.989 x 10^(-9) J
To convert the energy to GeV, we divide by the conversion factor:
1 GeV = 1.602 x 10^(-19) J
E (in GeV) = (1.989 x 10^(-9) J) / (1.602 x 10^(-19) J/GeV)
E (in GeV) ≈ 1.24 GeV
The energy of a y-ray photon with a wavelength of 10^(-17) m is approximately 1.24 GeV. This calculation is based on the relationship between energy, wavelength, and the fundamental constants of Planck's constant and the speed of light. The energy of a photon is directly proportional to its frequency or inversely proportional to its wavelength. Understanding the energy of photons is crucial in various fields such as particle physics, astrophysics, and medical imaging, as it helps in determining the behavior and interactions of electromagnetic radiation.
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Need correct option urgently.
1. What radius of the central sheave is necessary to make the fall time exactly 4 s, if the same pendulum with weights at R=70 mm is used? o 385.349 mm o 35452.072 mm o 188.287 mm o 2457.108 mm o 1760
Radius of the central sheave is option is a) 385.349 mm to make the fall time exactly at 4 s.
Time taken = t = 4s
Radius of the pendulum = 70 mm
Let us find the relation between time, radius and length of the pendulum:
Relation between time period and length of the pendulum is given by,
T = 2π( l/g)
T = 2π( l/9.8)
T² = 4π² (l/g)
T² = 4π² (l/9.8)
4 = 4π² (l/9.8)
l = 4×9.8/π²
l = 1.273 m
From the relation we can see that time period is independent of the mass of the bob.
Now let us find the radius of the central sheave
Radius of the central sheave can be calculated as:
R= (l² -r²)/2h
where,
h = 2r
Let R be the radius of the central sheave
Then we have,
R= (l² -r²)/4r
Substituting the values we get,
R = (1.273² - (0.07)²)/4(0.07)
R = 0.385349 m
Therefore the radius of the central sheave is 385.349 mm or 0.385349 m.
Hence, the correct option is a) 385.349 mm.
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if 20% of the mass of a 70 kg student's body is fat (a typical value), what is the total volume of fat in his body?
The total volume of fat in the student's body is approximately 15.56 liters.
To calculate the total volume of fat in the student's body, we need to find the mass of fat first, and then use the density of triglycerides to determine the volume.
Given:
Mass of the student's body: 70 kg
Percentage of body mass that is fat: 20%
Calculate the mass of fat in the student's body:
Mass of fat = (20/100) x 70 kg
Calculate the volume of fat using the density:
Volume of fat = Mass of fat / Density of fat
Note: Density is given as 900 kg/m³.
Now, let's perform the calculations:
Mass of fat = (20/100) x 70 kg = 14 kg
Volume of fat = Mass of fat / Density of fat = 14 kg / 900 kg/m³
Converting the mass to grams (1 kg = 1000 g):
Volume of fat = (14 kg x 1000 g/kg) / 900 kg/m³ = 15.56 L
Therefore, the total volume of fat in the student's body is approximately 15.56 liters.
The complete question is:
Fat cells in humans are composed almost entirely of pure triglycerides with an average density of about 900 kg/m³. If 20% of the mass of a 70 kg student's body is fat (a typical value), what is the total volume of the fat in his body?
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What is the equivalent energy Eb of the mass defect of an atom of 18O?
a) Option A
b) Option B
c) Option C
d) Option D
The equivalent energy Eb of the mass defect of an atom of 18O is 2.58 x 10-11 J.
This value is obtained by the formula E = m x c², where E is the equivalent energy, m is the mass defect of the atom, and c is the speed of light. The mass defect of an atom is the difference between its actual mass and its theoretical mass (which is the sum of the masses of its individual particles).
The mass defect is due to the conversion of some of the mass into energy during the formation of the nucleus.
To calculate the energy released or absorbed during this process, we use the famous equation E = m x c², where E is the equivalent energy, m is the mass defect, and c is the speed of light. The equivalent energy Eb of the mass defect of an atom of 18O is given by
Eb = Δm × c² where Δm is the mass defect of the atom and c is the speed of light.
Eb = 0.0308 × (2.998 × 108)²= 2.58 x 10-11 J
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water poursed slowly from a teapot spout can double back under the spout for a considerable distance
Siphoning is a technique for drawing liquid from a higher elevation to a lower one, typically from a container of some sort to the ground, with the aid of an intermediary mechanism. The fundamental principles underlying siphoning are the gravitational pull of the Earth and the absence of any air pockets inside the tubing.
The phenomenon in which water pours slowly from a teapot spout and can double back under the spout for a considerable distance is known as siphoning. Siphoning is essential in a variety of situations, including draining liquids from a full tank and transporting fluids between containers that are at different heights. Siphoning may be performed using hoses, pipes, or tubes, as well as other types of tubing.
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Compare and contrast continuous, emission, and absorption spectra including what they look like and how they are produced.
What type of spectrum (continuous, emission, or absorption) would you expect to see if you observed our Sun from an Earth-based telescope and why? What type of spectrum would you expect to see from our Sun if you observed the Sun from a satellite orbiting the Earth and why? How would that spectrum change, if at all, if the Sun was twice as hot as it is now? Why?
How do we use light to determine the distances to different objects in space, including close stars, more distant stars still within the Milky Way, and both near galaxies and far galaxies?
Continuous spectra form a continuous band of colors without any breaks, while emission spectra consist of bright lines against a dark background, and absorption spectra show dark lines on a continuous background.
Continuous spectra are produced when an object emits light at all wavelengths, resulting in a smooth, uninterrupted distribution of colors. Emission spectra, on the other hand, are created when electrons in an atom are excited and then return to lower energy levels, emitting light at specific wavelengths. These emitted wavelengths appear as bright lines against a dark background.
Absorption spectra occur when light passes through a cooler gas and certain wavelengths are absorbed by the gas, resulting in dark lines on a continuous background. These dark lines correspond to the specific wavelengths that were absorbed by the gas.
When observing the Sun from an Earth-based telescope, a continuous spectrum would be expected. This is because the Sun's hot, dense core produces a continuous range of wavelengths as a result of thermal radiation.
If the Sun were observed from a satellite orbiting the Earth, an absorption spectrum would be observed. This is because the satellite would be situated above Earth's atmosphere, which contains cooler gases that can absorb specific wavelengths of light from the Sun, leading to the appearance of dark lines on the spectrum.
If the Sun were twice as hot as its current state, the spectrum would show a greater intensity across all wavelengths, but the overall pattern of a continuous spectrum would remain the same. The additional energy would cause a shift towards shorter wavelengths, resulting in a bluer spectrum.
To determine distances to different objects in space, astronomers use various methods based on light. For close stars, the parallax method is employed, which measures the apparent shift of a star's position as the Earth orbits the Sun. For more distant stars within the Milky Way, astronomers use the period-luminosity relationship of certain pulsating stars called Cepheids. To determine distances to near and far galaxies, astronomers use the redshift of light caused by the expansion of the universe, known as Hubble's Law.
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Newton's law of universal gravitation states that the gravitational force exened by an object on any other object anywhere in the universe by Gmm F= where G is the universal gravitational constant (6.67 x 10-11 N.m 2kg 2), ms is mass 1, m2 is mass 2, and r is the distance between the two masses (from conter to contor). If the distance between the two masses doubles, the gravitational force between the two masse O remains the same O is reduced to 1/4. O is reduced to 1/9, O doubles O quadruples.
Answer:
Gravitational force between the two will reduce to [tex](1/4)[/tex] the original value.
Explanation:
The distance between the two objects was originally [tex]r[/tex]. The gravitational force between the two objects would be:
[tex]\displaystyle F = \frac{G\, m_{1}\, m_{2}}{r^{2}}[/tex].
If the distance between the two is doubled, the new distance will become [tex]2\, r[/tex]. The new gravitational force between the two will become:
[tex]\begin{aligned}\frac{G\, m_{1}\, m_{2}}{(2\, r)^{2}} &= \frac{G\, m_{1}\, m_{2}}{4\, r^{2}} = \frac{1}{4}\, \left(\frac{G\, m_{1}\, m_{2}}{r^{2}}\right)\end{aligned}[/tex].
In other words, the force between the two objects will become one-quarter of the initial value.
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How much is the energy of a single photon of the blue
light with a frequency of 7.5 x 1014 Hz?
Group of answer choices
4.97 x 1015 J
8.84 x 10-49 J
4.97 x 10-19 J
1.13 x 1048
The energy of a single photon of the blue light with a frequency of 7.5 x 10¹⁴ Hz is 4.97 x 10⁻¹⁹ J.
The energy (E) of a photon can be calculated using the equation:
E = h * f
where:
E = energy of the photon
h = Planck's constant (approximately 6.626 x 10⁻³⁴ J s)
f = frequency of the light wave
E = (6.626 x 10⁻³⁴ J s) * (7.5 x 10¹⁴ Hz)
E = 4.97 x 10⁻¹⁹ J
Therefore, the energy of a single photon of blue light with a frequency of 7.5 x 10¹⁴ Hz is approximately 4.97 x 10⁻¹⁹ J.
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A 52 kg skateboarder is standing on the edge of a 35 m tall half-pipe.
How much energy will the skateboarder have when he drops in the pipe?
What will his kinetic energy be when he reaches the bottom?
Calculate his speed using the energy from the question above.
Answer:
The speed I got is 26.2m/s (3sf)
Explanation:
When the skateboarder is standing at the edge of the half-pipe, they would have max gravitational potential energy of about 17800J (3sf), calculated by using this formula;
Gravitational potential energy (Eₚ) = mgh
Eₚ = 52 × 9.8 × 35
Eₚ = 17836J
Eₚ = 17800J (3sf)
As the skateboarder drops, this energy will also decrease because they are losing height and gets converted into kinetic energy. Hence, the kinetic energy increases. When they reach the bottom (assuming they haven't landed and stop moving), the skateboarder will reach max kinetic energy.
To calculate the speed from this energy, we can use this formula;
Eₖ = 1/2 × m × v²
Substitute the values;
17800 = 1/2 × 52 × v²
17800 = 26 × v²
v² = 17800/26
v = √684.6
v = 26.2m/s (3sf)
what fraction of the initial kinetic energy of the bullet remains as kinetic energy after the collision?
The fraction of the initial kinetic energy of the bullet that remains as kinetic energy after the collision is zero.
The fraction of the initial kinetic energy of the bullet that remains as kinetic energy after the collision calculated by using the formula: (KEf/KEi) = (v/ u)²
where KEf is the final kinetic energy
KEi is the initial kinetic energy
v is the final velocity
u is the initial velocity.
The bullet is stopped by the target, so the final velocity is zero.
Therefore, the formula can be simplified to:(KEf/KEi) = (0/ u)²
or KEf = 0
The final kinetic energy of the bullet is zero because it is stopped by the target.
Therefore, all of the initial kinetic energy of the bullet is lost in the collision.
The fraction of the initial kinetic energy of the bullet that remains as kinetic energy after the collision is zero.
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Captain Kirk launched into space last year aboard a rocket. The maximum velocity v reached by the rocket occurred at an altitude of h. (a) How long did it take for the rocket to reach that altitude? (b) Will the rocket make it to space (an altitude of 100 km)?
a) The answer to this part of the question cannot be determined.
b) The rocket will not make it to space.
Captain Kirk launched into space last year aboard a rocket. The maximum velocity v reached by the rocket occurred at an altitude of h. Let's find out the answers to the given questions.
(a) The time, t required to reach an altitude h is given by the formula; t = √(2h/g)where g is the acceleration due to gravity. Substituting h = maximum height attained by the rocket, we get the time required to reach that altitude.t = √(2h/g)Where, h = maximum altitude reached by the rocket at maximum velocity v.g = 9.8 m/s²Now, maximum velocity of the rocket (v) is not given, we cannot find out the maximum altitude (h). Thus, the answer to this part of the question cannot be determined.
(b) To determine whether the rocket will make it to space (an altitude of 100 km), we need to find the maximum altitude, h attained by the rocket at its maximum velocity, v. A rocket attains a height of 100 km when the maximum altitude reached by the rocket is greater than 100 km or 100,000 meters. Let's assume that the maximum altitude attained by the rocket is H. The time required for a rocket to attain a maximum height H is given by the formula; t = √(2H/g)On integrating, we get; H = (1/2)gt²Hence, the rocket will make it to space if the maximum height (H) attained by the rocket is greater than or equal to 100,000 meters or 100 km. If H is less than 100,000 meters, the rocket will not make it to space.
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Describe the important steps in the thermal history of the
universe. Include at least five stages and/or major
transitions.
The following are the key steps in the thermal history of the universe:
1. Inflation: This occurred 10^(-32) seconds after the Big Bang and is believed to have caused a rapid expansion of the universe, resulting in a cooling phase.
2. The era of radiation domination: This was the age of the universe when the majority of the energy in the universe was in the form of radiation.
3. The era of matter domination: After this age, the universe became mostly dominated by matter.
4. Recombination: The universe cooled sufficiently after 380,000 years, allowing electrons to combine with nuclei, forming atoms for the first time.
5. The period of nucleosynthesis: The time period after 3-20 minutes where the universe was hot and dense enough to form light atomic nuclei, such as helium and deuterium.
6. Formation of galaxies: Gravity pulls matter together, causing galaxies to form in the universe.
7. Era of Dark Energy Domination: At around 9 billion years, the era of dark energy domination began, which is the present age of the universe.
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Q1: A current of 20A flows east through 50cm wire. A magnitude of 4T is directed into the page. What is the magnitude of the magnetic force acting on the wire? North West East South
A current of 20A flows east through 50cm wire. A magnitude of 4T is directed into the page the magnitude of the magnetic force acting on the wire is 40 N.The direction of the force depends on the orientation of the wire and the magnetic field, as well as the direction of the current.
To find the magnitude of the magnetic force acting on the wire, we can use the formula for the magnetic force on a current-carrying wire in a magnetic field:
F = B * I * L * sin(theta)
where F is the magnetic force, B is the magnetic field strength, I is the current, L is the length of the wire, and theta is the angle between the wire and the magnetic field.
Given:
I = 20 A (current)
L = 50 cm = 0.5 m (length of the wire)
B = 4 T (magnetic field strength)
Since the current flows east, the angle theta between the wire and the magnetic field is 90 degrees (perpendicular).
Plugging in the values into the formula:
F = 4 T * 20 A * 0.5 m * sin(90°)
Simplifying the expression:
F = 4 T * 20 A * 0.5 m * 1
F = 40 N
Therefore, the magnitude of the magnetic force acting on the wire is 40 N.
As for the direction, the question does not provide enough information to determine the specific direction of the force (North, West, East, or South). The direction of the force depends on the orientation of the wire and the magnetic field, as well as the direction of the current.
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A thin rod, 0.77 m long, is pivoted such that it hangs vertically from one end. You want to hit the free end of the rod just hard enough to get the rod to swing all the way up and over the pivot. Part A How fast do you have to make the end go? Express your answer with the appropriate units. Ć ☐☐ μA Value Units V =
The speed needed to make the free end go in order to swing all the way up and over the pivot is 1.98 m/s.
Part A of the given problem asks to calculate the speed needed to make the free end go to swing all the way up and over the pivot. Let the pivot point be P, the center of mass of the rod be C and the free end of the rod be A. The rod will swing over the pivot if the height of the center of mass C becomes zero. Using the law of conservation of energy, the initial potential energy of the rod is converted to the final kinetic energy of the rod. At the highest point, the kinetic energy will become zero and all the potential energy will become zero. Hence, the potential energy at the initial point will be equal to the potential energy at the highest point: mg(0.77) = (1/2)(0.20)v²Solving this equation, we get: v = 1.98 m/s Therefore, the speed needed to make the free end go in order to swing all the way up and over the pivot is 1.98 m/s.
The term "speed" means. The rate at which an object moves in any direction. The ratio of distance to time traveled is what is used to measure speed. Because it only has a direction and no magnitude, speed is a scalar quantity.
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A cubical gaussian surface surrounds a long, straight, charged filament that passes perpendicularly through two opposite faces. No other charges are nearby.)
(1) Over how many of the cube's faces is the electric field non zero?
6
0
2
4
(i) Through how many of the cube's faces is the electric flux non zero?
4
0
2
06
the electric flux is non-zero through two faces of the cube's faces.
(1) The electric field is non-zero on two faces of the cube.
(ii) The electric flux is non-zero through two faces of the cube.
A cubical Gaussian surface surrounds a long, straight, charged filament that passes perpendicularly through two opposite faces. No other charges are nearby.
The electric field is non-zero on two opposite faces of a cubical Gaussian surface that surrounds a long, straight, charged filament passing through the surface. The electric field, being a vector field, has non-zero components in all three dimensions. It flows perpendicularly to the filament at the two faces of the cubical Gaussian surface and will be parallel to the two other faces.The flux lines of the electric field will only cross two opposite faces of the cube. Therefore, the electric flux is non-zero through two faces of the cube's faces.
(1) The electric field is non-zero on two faces of the cube.
(ii) The electric flux is non-zero through two faces of the cube.
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when 6.50 ×105j of heat is added to a gas enclosed in a cylinder fitted with a light frictionless piston maintained at atmospheric pressure, the volume is observed to increase from 1.9 m3 to 4.1 m3 .
Calculate the work done by the gas.
Calculate the change in internal energy of the gas.
Graph this process on a PV diagram.
When 6.50 × 10^5 J of heat is added to a gas in a cylinder with a frictionless piston at atmospheric pressure, gas volume increases from 1.9 m^3 to 4.1 m^3. We need to calculate the work done and change in internal energy.
To calculate the work done by the gas, we can use the equation:
Work = Pressure × Change in Volume.
Given that the pressure is maintained at atmospheric pressure, we can substitute the values:
Work = Atmospheric Pressure × (Final Volume - Initial Volume).
Work = 1 atm × (4.1 m^3 - 1.9 m^3).
Next, we calculate the change in internal energy of the gas using the first law of thermodynamics:
Change in Internal Energy = Heat Added - Work Done.
Given that heat added is 6.50 × 10^5 J and we have already calculated the work done, we can substitute the values:
Change in Internal Energy = 6.50 × 10^5 J - Work Done.
To graph this process on a PV diagram, we plot pressure (P) on the y-axis and volume (V) on the x-axis. We mark the initial point at 1.9 m^3 and atmospheric pressure. Then, we mark the final point at 4.1 m^3 and atmospheric pressure. The process is represented by a straight line connecting these two points.
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An EM wave has a magnetic field strength of 5.00×10−4[T]. What
is its electric field strength when travelling in a medium with
n=1.50? Show solution
A. 1.00×105[V/m]
B. 1.50×105[V/m]
C. 3.00×101
The electric field strength is 1.50x [tex]10^{5}[/tex] [V/m] (Option B) when traveling in a medium with n=1.50.
To find the electric field strength of an electromagnetic wave in a medium, we can use the following relationship:
E = c * B / n
where:
E is the electric field strength
c is the speed of light in vacuum (approximately 3.00 x [tex]10^8[/tex] m/s)
B is the magnetic field strength
n is the refractive index of the medium
B = 5.00 x [tex]10^{-4}[/tex] T
n = 1.50
Substituting these values into the equation, we have:
E = (3.00 x [tex]10^{8}[/tex] m/s) * (5.00 x [tex]10^{-4}[/tex] T) / 1.50
Calculating this expression, we get:
E = (3.00 x [tex]10^{8}[/tex] m/s) * (5.00 x [tex]10^{-4}[/tex] T) / 1.50
= (1.50 x [tex]10^{5}[/tex]) V/m
Therefore, the electric field strength of the electromagnetic wave in the medium with n=1.50 is 1.50 x [tex]10^{5}[/tex] V/m.
The correct answer is:
B. 1.50× [tex]10^{5}[/tex] [V/m]
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24. What does it mean to say that dV is an exact differential? fav = √₂-V₁ Sav - 7-20 7-23 25. Write down the differentials for the thermodynamic potentials. From these derive the Maxwell relati
The differentials for the thermodynamic potentials. From these derive the Maxwell relation is in the explanation part.
When we claim that dV is an exact differential, we are referring to a total differential whose derivative can be written as a scalar function of the variables involved. In other words, dV can be represented as follows if V is a function of many variables:
dV = (∂V/∂x)dx + (∂V/∂y)dy + (∂V/∂z)dz
The differentials for the thermodynamic potentials can be written as follows:
dU = TdS - PdV (Internal Energy)
dH = TdS + VdP (Enthalpy)
dF = -SdT - PdV (Helmholtz Free Energy)
dG = -SdT + VdP (Gibbs Free Energy)
These equations explain how variations in entropy (S), temperature (T), volume (V), and pressure (P) affect various thermodynamic potentials.
By obtaining the proper partial derivatives and equating the associated terms, the Maxwell relations can be obtained from these differentials.
Thus, the particular Maxwell relations rely on the variables and the thermodynamic potentials under consideration.
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