Please note that the "vet" in the second decay is not a recognized symbol or notation for beta decay. If you provide more specific information or correct any errors.
Neutrinos are subatomic particles that are electrically neutral and have very low mass. They interact weakly with matter, making them difficult to detect. In beta decay, neutrinos are often emitted along with the electron or positron to conserve certain properties, such as lepton number and angular momentum.During beta decay, the neutrino is denoted as νe (electron neutrino) or νμ (muon neutrino), depending on the type of decay involved. For example, in the beta decay of a neutron (n → p + e- + νe), an electron and an electron neutrino are emitted.The presence of neutrinos in beta decay was initially postulated by Wolfgang Pauli in 1930 to account for the conservation of energy, momentum, and angular momentum. Neutrinos were eventually detected experimentally in the 1950s, confirming their existence.
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a) Calculate the maximum kinetic energy of an ejected electron if a 420 m photon
strikes a piece of metal with a work function of 1.56eV [3]
b) What is the cutoff potential necessary to stop these electrons? [1]
a) The kinetic energy of ejected electron is 0.42 J .
b) The cutoff potential necessary to stop these electrons is approximately 1.56 volts.
a) To calculate the maximum kinetic energy of an ejected electron, we can use the equation:
Kinetic energy of ejected electron = Energy of incident photon - Work function
Energy of incident photon (E) = 420 mJ = 420 * 10^-3 J
Work function (W) = 1.56 eV
First, we need to convert the work function from electron volts (eV) to joules (J) since the energy of the incident photon is given in joules:
1 eV = 1.6 * 10^-19 J
Work function (W) = 1.56 eV * (1.6 * 10^-19 J/eV) ≈ 2.496 * 10^-19 J
Now we can calculate the maximum kinetic energy of the ejected electron:
Kinetic energy of ejected electron = Energy of incident photon - Work function
Kinetic energy of ejected electron = 420 * 10^-3 J - 2.496 * 10^-19 J
= 0.42 J
b) To calculate the cutoff potential necessary to stop these electrons, we can use the equation:
Cutoff potential (Vc) = Work function / electron charge
Work function (W) = 1.56 eV
First, we need to convert the work function from electron volts (eV) to joules (J):
Work function (W) = 1.56 eV * (1.6 * 10^-19 J/eV) ≈ 2.496 * 10^-19 J
Now we can calculate the cutoff potential:
Cutoff potential (Vc) = Work function / electron charge
Cutoff potential (Vc) = 2.496 * 10^-19 J / (1.6 * 10^-19 C)
Simplifying the expression, we find:
Cutoff potential (Vc) ≈ 1.56 V
Therefore, the kinetic energy of ejected electron is 0.42J and the cutoff potential necessary to stop these electrons is approximately 1.56 volts.
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When the Venera 14 probe landed on Venus's surface, its barometer measured an air pressure of 9.5 MPa. The surface acceleration due to gravity was measured to be 8.87 m/s2. If Earth's atmosphere with a pressure of 101 kPa raises mercury 0.760 m where gravitational acceleration is 9.81 m/s2. To what height in m to two significant digits would Venus's atmosphere raise liquid mercury?
The height to which Venus's atmosphere would raise liquid mercury is determined based on the given air pressure and surface acceleration due to gravity. The calculation involves comparing the pressure in Venus's atmosphere to Earth's atmosphere and using the difference to determine the height of the mercury column.
To calculate the height to which Venus's atmosphere would raise liquid mercury, we can use the principle of hydrostatic pressure. The pressure difference between two points in a fluid column is directly proportional to the difference in height.Given that Earth's atmosphere raises mercury to a height of 0.760 m when the pressure is 101 kPa and the acceleration due to gravity is 9.81 m/s^2, we can set up a proportion to find the height in Venus's atmosphere.
The ratio of pressure to height is constant, so we can write:
(9.5 MPa / 101 kPa) = (8.87 m/s^2 / 9.81 m/s^2) * (h / 0.760 m)
Solving for h, we can find the height to which Venus's atmosphere would raise liquid mercury.
By rearranging the equation and substituting the given values, we can calculate the height to two significant digits.
Therefore, the height to which Venus's atmosphere would raise liquid mercury can be determined using the given air pressure and surface acceleration due to gravity.
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If the mass of a planet is 3.10 1024 kg, and its radius is 2.00 106 m, what is the magnitude of the gravitational field, g, on the planet's surface?
The magnitude of the gravitational field on the planet's surface is approximately 45.88 N/kg.
The magnitude of the gravitational field, g, on the planet's surface can be calculated using the equation:
g = G * (m / r^2)
where G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2/kg^2), m is the mass of the planet, and r is the radius of the planet.
In this case, the mass of the planet is given as 3.10 x 10^24 kg, and the radius is given as 2.00 x 10^6 m.
Substituting these values into the equation, we get:
g = (6.67430 x 10^-11 N m^2/kg^2) * (3.10 x 10^24 kg) / (2.00 x 10^6 m)^2
Simplifying this calculation, we have:
g = 4.588 x 10^1 N/kg
Therefore, the magnitude of the gravitational field on the planet's surface is approximately 45.88 N/kg.
To understand the meaning of this value, we can say that for every kilogram of mass on the planet's surface, there is a gravitational force of 45.88 Newtons acting on it.
This force pulls objects towards the center of the planet. The larger the gravitational field, the stronger the force of gravity experienced.
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A 5.00 x 10² kg satellite is on a geosynchronous orbit where it completes the circular orbit in 23 hours 56 minutes. The mass of the Earth is 5.97 x 1024 kg. (Assumptions: Earth is spherically symmetric. Satellite goes in a circular orbit about the center of the Earth.) A. Estimate the distance of the satellite from the center of the Earth. B. What is the kinetic energy and gravitational potential of the satellite?
"The gravitational potential energy of the satellite is approximately -8.85 x 10¹⁰ Joules."
To estimate the distance of the satellite from the center of the Earth, we can use the formula for the period of a circular orbit:
T = 2π√(r³/GM)
where T is the period, r is the distance from the center of the Earth to the satellite, G is the gravitational constant (approximately 6.67430 x 10⁻¹¹ m³ kg⁻¹ s⁻²), and M is the mass of the Earth.
We are given the period T as 23 hours 56 minutes, which is equivalent to 23.933 hours.
Substituting the known values into the equation, we can solve for r:
23.933 = 2π√(r³/(6.67430 x 10⁻¹¹ x 5.97 x 10²⁴))
Simplifying the equation:
√(r³/(6.67430 x 10⁻¹¹ x 5.97 x 10²⁴)) = 23.933 / (2π)
Squaring both sides of the equation:
r³/(6.67430 x 10⁻¹¹ x 5.97 x 10²⁴) = (23.933 / (2π))²
Simplifying further:
r³ = (6.67430 x 10⁻¹¹ x 5.97 x 10²⁴) x (23.933 / (2π))²
Taking the cube root of both sides of the equation:
r ≈ (6.67430 x 10⁻¹¹ x 5.97 x 10²⁴)°³³x (23.933 / (2π))°⁶⁶
Calculating the approximate value:
r ≈ 4.22 x 10⁷ meters
Therefore, the distance of the satellite from the center of the Earth is approximately 4.22 x 10⁷ meters.
To calculate the kinetic energy of the satellite, we can use the formula:
KE = (1/2)mv²
where KE is the kinetic energy, m is the mass of the satellite, and v is the velocity of the satellite.
Since the satellite is in a circular orbit, its velocity can be calculated using the formula for the circumference of a circle:
C = 2πr
where C is the circumference and r is the distance from the center of the Earth to the satellite.
Substituting the known values:
C = 2π(4.22 x 10⁷) ≈ 2.65 x 10⁸ meters
The time taken to complete one orbit is given as 23 hours 56 minutes, which is approximately 86,136 seconds.
Therefore, the velocity of the satellite can be calculated as:
v = C / time = (2.65 x 10⁸) / 86,136 ≈ 3077.6 m/s
Substituting the mass of the satellite (5.00 x 10² kg) and the velocity (3077.6 m/s) into the kinetic energy formula:
KE = (1/2)(5.00 x 10²)(3077.6)²
Calculating the value:
KE ≈ 2.37 x 10¹⁰ Joules
Thus, the kinetic energy of the satellite is approximately 2.37 x 10¹⁰ Joules.
To calculate the gravitational potential energy of the satellite, we can use the formula:
PE = -GMm / r
where PE is the gravitational potential energy, G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the distance from the center of the Earth to the satellite.
Substituting the known values:
PE = -(6.67430 x 10⁻¹¹ x 5.97 x 10²⁴ x 5.00 x 10²) / (4.22 x 10⁷)
Calculating the value:
PE ≈ -8.85 x 10¹⁰ Joules
The negative sign indicates that the gravitational potential energy is negative, representing the attractive nature of gravity.
Therefore, the gravitational potential energy of the satellite is approximately -8.85 x 10¹⁰ Joules.
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Two teams are having a tug of war. Each team exerts a force of 1500 N. What is the tension in the rope? Explain.
The tension in the rope is 3000 N.
The tension in the rope in a tug of war game can be found out by calculating the resultant force of the two teams pulling the rope. The tension in the rope is the same throughout the entire rope because it is the force being applied by both teams on the rope.
Tension is a force that is developed when a material is pulled or stretched in opposite directions. It is the pulling force applied by a rope or a cable. The tension force is always directed along the length of the rope or cable. Tension is also called tensile force. The tension formula is given as,
Tension (T) = Force (F) / Area (A)
Hence, The tension in the rope during a tug of war game is the sum of the forces applied by both teams. Each team applies a force of 1500 N. So, the resultant force is given as:
Resultant force = Force applied by team 1 + Force applied by team 2= 1500 N + 1500 N= 3000 N
Therefore, the tension in the rope is 3000 N.
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The hour-hand of a large clock is a 1m long uniform rod with a mass of 2kg. The edge of this hour-hand is attached to the center of the clock. At 9:00 gravity causes _____ Newton-meters of torque, and at 12:00 gravity causes _____ Newton-meters of torque.
At 9:00, gravity causes 9.81 N⋅m of torque and at 12:00, gravity causes zero torque.The hour hand of a large clock is a 1m long uniform rod with a mass of 2kg.
The edge of this hour hand is attached to the center of the clock. When the time of the clock is 9:00, the hand of the clock is vertical pointing down, and it makes an angle of 270° with respect to the horizontal. Gravity causes 9.81 newtons of force per kg, so the force on the rod is
F = mg
= 2 kg × 9.81 m/s2
= 19.62 N.
When the hand of the clock is at 9:00, the torque caused by gravity is 19.62 N × 0.5 m = 9.81 N⋅m. At 12:00, the hand of the clock is horizontal, pointing towards the right, and it makes an angle of 0° with respect to the horizontal. The force on the rod is still 19.62 N, but the torque caused by gravity is zero, because the force is acting perpendicular to the rod.Therefore, at 9:00, gravity causes 9.81 N⋅m of torque and at 12:00, gravity causes zero torque.
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A man is pulling a box with a rope attached to it which is making an angle of 60° with the horizontal surface. If the force applied by the man is 3.8 N and the box is displaced by 7.1 m along the horizontal surface while frictional force is 1.1 N, find the net work done on the box. Answer: Choose... Check
The net work done on the box is 21.225 Joules. Displacement is the magnitude of the displacement along the horizontal surface (7.1 m).
Work = Force * Displacement * cos(theta)
Force is the magnitude of the force applied (3.8 N).
Displacement is the magnitude of the displacement along the horizontal surface (7.1 m).
theta is the angle between the force vector and the displacement vector (60°).
Work_applied = 3.8 N * 7.1 m * cos(60°)
To calculate the work done against friction, we use the formula:
Work_friction = Force_friction * Displacement * cos(180°)
Since the frictional force acts opposite to the direction of motion, we take the cosine of 180°.
Work_friction = 1.1 N * 7.1 m * cos(180°)
Net work = Work_applied - Work_friction
Net work = (3.8 N * 7.1 m * cos(60°)) - (1.1 N * 7.1 m * cos(180°))
cos(60°) = 0.5
cos(180°) = -1
Net work = (3.8 N * 7.1 m * 0.5) - (1.1 N * 7.1 m * -1)
= 13.415 J + 7.81 J
= 21.225 J
Therefore, the net work done on the box is 21.225 Joules.
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The cyclic reversible process in the figure consists of: A. 2 isochoric \( (\mathrm{V}= \) constant) and 2 adiabatics \( (\mathrm{Q}=0) \) B. 2 isochoric \( (V= \) constant \( ) \) and 2 isothermals (
Based on the given options, the correct answer for the cyclic reversible process in the figure is option B 2 isochoric and 2 isothermal process.
The correct answer is B. 2 isochoric (V= constant) and 2 isothermals (T= constant) due to the following reasons:
An isochoric process is characterized by constant volume (V = constant), and an isothermal process is characterized by constant temperature (T = constant).
Therefore, in the cyclic reversible process shown in the figure, there are two parts where the volume remains constant (isochoric processes), and two parts where the temperature remains constant (isothermal processes).
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The complete question is attached in the image.
When an object with an electric charge of −0.080mC is 6.0 m from an object with an electric charge of 0.040mC, the force between them has a strength of 0.7989 N. Calculate the strength of the force between the two objects if they are 30.m apart. Round your answer to 2 significant digits.
The strength of the force between the two objects when they are 30.0 m apart is approximately 2.877 N (rounded to 2 significant digits).
The strength of the force between two charged objects can be calculated using Coulomb's Law:
F = k * (|q₁| * |q₂|) / r²
where F is the force, k is the electrostatic constant (k = 8.99 x 10^9 N·m²/C²), |q₁| and |q₂| are the magnitudes of the charges, and r is the distance between the charges.
Given:
Charge of object 1, q₁ = -0.080 mC = -0.080 x 10^(-3) C
Charge of object 2, q₂ = 0.040 mC = 0.040 x 10^(-3) C
Distance between the objects, r₁ = 6.0 m
Using the given values, we can calculate the strength of the force at 6.0 m:
F₁ = k * (|q₁| * |q₂|) / r₁²
F₁ = (8.99 x 10^9 N·m²/C²) * (| -0.080 x 10^(-3) C| * |0.040 x 10^(-3) C|) / (6.0 m)²
F₁ = (8.99 x 10^9 N·m²/C²) * (0.080 x 10^(-3) C * 0.040 x 10^(-3) C) / (6.0 m)²
F₁ = (8.99 x 10^9 N·m²/C²) * (0.032 x 10^(-6) C²) / (36.0 m²)
F₁ = (8.99 x 0.032 x 10^3) N
F₁ ≈ 287.68 N
Therefore, the strength of the force between the two objects when they are 6.0 m apart is approximately 287.68 N.
Now, let's calculate the strength of the force when the objects are 30.0 m apart:
Distance between the objects, r₂ = 30.0 m
Using Coulomb's Law, we can calculate the strength of the force at 30.0 m:
F₂ = k * (|q₁| * |q₂|) / r₂²
F₂ = (8.99 x 10^9 N·m²/C²) * (0.080 x 10^(-3) C * 0.040 x 10^(-3) C) / (30.0 m)²
F₂ = (8.99 x 10^9 N·m²/C²) * (0.032 x 10^(-6) C²) / (900.0 m²)
F₂ = (8.99 x 0.032 x 10^3) N
F₂ ≈ 2.877 N
Therefore, the strength of the force between the two objects when they are 30.0 m apart is approximately 2.877 N (rounded to 2 significant digits).
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EXERCISE 1. Two particles P and Q have masses 20 kg and 5 kg respectively. The particles are moving towards each other on a smooth horizontal plane and collide directly. The speeds of P and Q immediately before the collision are 2 ms" and 5 ms'Immediately after the collision, the speed of Pis 0.5 ms'' and its direction of motion is reversed. Find the speed and direction of motion of Q after the collision. 2. A particle P of mass 0.3 kg is moving with speed u ms" in a straight line on a smooth horizontal table. The particle P collides directly with a particle Q of mass 0.6 kg, which is at rest on table. Immediately after the particle collide, P has speed 2 ms' and Q has speed 5 ms. The direction of motion of P is reversed by the collision. Find the value of u. 3. A railway truck P, of mass 5000 kg is moving along a straight horizontal track with speed 15 ms' Truck P collides with a truck of mass 3000 kg which is at rest on the same track Immediately after the collision, they stuck together. After the collision, find a) the speed of the truck b) The lost kinetic energy in the collision.
The speed of particle Q after the collision is 5 m/s in the same direction as its initial velocity, the value of u is 8 m/s.
Exercise 1:
Mass of particle P (mP) = 20 kg
Mass of particle Q (mQ) = 5 kg
Initial velocity of P (vP1) = 2 m/s
Initial velocity of Q (vQ1) = -5 m/s (opposite direction)
Final velocity of P (vP2) = -0.5 m/s (reversed direction)
Final velocity of Q (vQ2) and its direction of motion.
Using the principle of conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision.
Total initial momentum = Total final momentum
(mP * vP1) + (mQ * vQ1) = (mP * vP2) + (mQ * vQ2)
(20 kg * 2 m/s) + (5 kg * -5 m/s) = (20 kg * -0.5 m/s) + (5 kg * vQ2)
40 kg m/s - 25 kg m/s = -10 kg m/s + 5 kg vQ2
15 kg m/s = -10 kg m/s + 5 kg vQ2
15 kg m/s + 10 kg m/s = 5 kg vQ2
25 kg m/s = 5 kg vQ2
vQ2 = 25 kg m/s / 5 kg
vQ2 = 5 m/s
Exercise 2:
Mass of particle P (mP) = 0.3 kg
Mass of particle Q (mQ) = 0.6 kg
Initial velocity of P (vP1) = u m/s (unknown)
Initial velocity of Q (vQ1) = 0 m/s (at rest)
Final velocity of P (vP2) = -2 m/s (reversed direction)
Final velocity of Q (vQ2) = 5 m/s
The value of u.
Using the principle of conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision.
Total initial momentum = Total final momentum
(mP * vP1) + (mQ * vQ1) = (mP * vP2) + (mQ * vQ2)
(0.3 kg * u m/s) + (0.6 kg * 0 m/s) = (0.3 kg * -2 m/s) + (0.6 kg * 5 m/s)
0.3u kg m/s = -0.6 kg m/s + 3 kg m/s
0.3u kg m/s = 2.4 kg m/s
u kg m/s = 2.4 kg m/s / 0.3
u kg m/s = 8 m/s
Exercise 3:
Mass of truck P (mP) = 5000 kg
Mass of truck Q (mQ) = 3000 kg
Initial velocity of truck P (vP1) = 15 m/s
Initial velocity of truck Q (vQ1) = 0 m/s (at rest)
a) The speed of the truck after the collision (vP2)
b) The lost kinetic energy in the collision
Using the principle of conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision.
Total initial momentum = Total final momentum
(mP * vP1) + (mQ * vQ1) = (mP * vP2) + (mQ * vQ2)
(5000 kg * 15 m/s) + (3000 kg * 0 m/s) = (5000 kg * vP2) + (3000 kg * vQ2)
75000 kg m/s = 5000 kg vP2 + 3000 kg * vQ2
Since the trucks stuck together after the collision, their final velocity (vP2) will be the same.
vP2 = vQ2 = v (let's assume)
75000 kg m/s = 5000 kg * v + 3000 kg * v
75000 kg m/s = 8000 kg * v
v = 75000 kg m/s / 8000 kg
v = 9.375 m/s
a) The speed of the truck after the collision is 9.375 m/s.
b) To find the lost kinetic energy, we need the initial kinetic energy before the collision and the final kinetic energy after the collision.
Initial kinetic energy = (1/2) * mP * [tex]vP1^2[/tex]= (1/2) * 5000 kg * [tex](15 m/s)^2[/tex]
Final kinetic energy = (1/2) * (mP + mQ) *[tex]v^2[/tex] = (1/2) * (5000 kg + 3000 kg) * [tex](9.375 m/s)^2[/tex]
Lost kinetic energy = Initial kinetic energy - Final kinetic energy
Substituting the values and calculating will give the lost kinetic energy in the collision.
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Part A How long does it take light to reach us from the Sun, 1.50 x X10 8km away? t =
The speed of light is 299,792,458 meters per second or approximately 3.00 x 10^8 meters per second.
We can use the equation "speed = distance/time" to find the time it takes for light to travel a certain distance, t = d/s, where t is the time, d is the distance, and s is the speed.
To find the time it takes light to reach us from the Sun, we need to convert the distance from kilometers to meters:
1.50 x 10^8 km = 1.50 x 10^11 m
Now we can use the equation:
t = d/s = (1.50 x 10^11 m) / (3.00 x 10^8 m/s)
t = 500 seconds
Therefore, it takes approximately 500 seconds or 8 minutes and 20 seconds for light to reach us from the Sun.
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The cars of a long coated by pulling them wider a happerom which also the of 10000 kg that the engine store op meg under the hopperendom Express your answering the significant figures
The given problem statement mentions a car with a long coat that is expanded by pulling them wider with a hopper weighing 10000 kg. Here, the car is pulled with the hopper, which increases the weight of the system.
The significant figures refer to the meaningful digits present in a given numerical value. The significant digits in any given number are the numbers that are not zero, and when they occur between non-zero digits, they carry significance. For example, 2.3 has two significant figures, and 120.03 has five significant figures.
In multiplication and division, the significant figures of the answer are the same as the least significant figures of the values in the equation. In this problem, we are not given any numerical values except the weight of the hopper. Thus, there is no significance of figures in this problem statement. Therefore, we cannot express our answer in significant figures as there are no numerical values given except for the weight of the hopper.
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Consider two objects of masses m₁= 8.775 kg and m₂ = 4.944 kg. The first mass (m₂) is traveling along the negative y-axis at 48.38 km/hr and strikes the second stationary mass m₂, locking the two masses together. What is the velocity of the first mass before the collision? What is the velocity of the second mass before the collision? What is the final velocity of the two masses? What is the total initial kinetic energy of the two masses? What is the total final kinetic energy of the two masses? How much of the mechanical energy is lost due to this collision?
The initial velocity of the second mass (m₂) is 0 as it is stationary. To find the initial velocity of the first mass (m₁), we will use the equation for kinetic energy.Kinetic energy = 1/2 mv²where m is the mass of the object and v is its velocity.
The kinetic energy of the first mass can be found by converting its velocity from km/hr to m/s.Kinetic energy = 1/2 (8.775 kg) (48.38 km/hr)² = 1/2 (8.775 kg) (13.44 m/s)² = 797.54 JSo the total initial kinetic energy of the two masses is the sum of the kinetic energies of the individual masses: 797.54 J + 0 J = 797.54 JThe final velocity of the two masses can be found using the law of conservation of momentum.
According to the law of conservation of momentum, the momentum before the collision is equal to the momentum after the collision.m₁v₁ + m₂v₂ = (m₁ + m₂)vfwhere m₁ is the mass of the first object, v₁ is its velocity before the collision, m₂ is the mass of the second object, v₂ is its velocity before the collision, vf is the final velocity of both objects after the collision.
Since the second mass is stationary before the collision, its velocity is 0.m₁v₁ = (m₁ + m₂)vf - m₂v₂Substituting the given values in the above equation and solving for v₁, we get:v₁ = [(m₁ + m₂)vf - m₂v₂]/m₁= [(8.775 kg + 4.944 kg)(0 m/s) - 4.944 kg (0 m/s)]/8.775 kg = 0 m/sSo the initial velocity of the first mass is 0 m/s.
The momentum of the system after the collision is:momentum = (m₁ + m₂)vfThe total final kinetic energy of the system can be found using the equation:final kinetic energy = 1/2 (m₁ + m₂) vf²Substituting the given values in the above equation, we get:final kinetic energy = 1/2 (8.775 kg + 4.944 kg) (0.9707 m/s)² = 25.28 JThe mechanical energy lost due to this collision is the difference between the initial kinetic energy and the final kinetic energy:energy lost = 797.54 J - 25.28 J = 772.26 JThus, the mechanical energy lost due to this collision is 772.26 J.
Initial velocity of the first mass = 0 m/sInitial velocity of the second mass = 0 m/sFinal velocity of the two masses = 0.9707 m/sTotal initial kinetic energy of the two masses = 797.54 JTotal final kinetic energy of the two masses = 25.28 JEnergy lost due to this collision = 772.26 J.
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The average surface temperature of a planet is 292 K. Part A What is the frequency of the most intense radiation emitted by the planet into outer space?
The frequency of the most intense radiation emitted by the planet into outer space is 1.148 x 10^12 Hz
The answer to the first part of the question "The average surface temperature of a planet is 292 K" is given, and we need to determine the frequency of the most intense radiation emitted by the planet into outer space.
Frequency can be calculated using Wien's displacement law.
According to Wien's law, the frequency of the radiation emitted by a body is proportional to the temperature of the body.
The frequency of the most intense radiation emitted by the planet into outer space can be found using Wien's law.
The formula for Wien's law is:
λ_maxT = 2.898 x 10^-3,
whereλ_max is the wavelength of the peak frequency,T is the temperature of the planet in kelvin, and, 2.898 x 10^-3 is a constant.
The frequency of the most intense radiation emitted by the planet into outer space can be found using the relation:
c = fλ
c is the speed of light (3 x 10^8 m/s), f is the frequency of the radiation emitted by the planet, λ is the wavelength of the peak frequency
We can rearrange Wien's law to solve for the peak frequency:
f = c/λ_maxT
= c/(λ_max * 292)
Substitute the values and calculate:
f = (3 x 10^8 m/s)/(9.93 x 10^-7 m * 292)
= 1.148 x 10^12 Hz
Therefore, the frequency of the most intense radiation emitted by the planet into outer space is 1.148 x 10^12 Hz.
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6. The electric potential function in a volume of space is given by V(x,y,z) = x2 + xy2 + 2yz?. Determine the electric field in this region at the coordinate (3,4,5).
The electric potential function in a volume of space is given by V(x,y,z) = x2 + xy2 + 2yz.The electric field in the region at the coordinate (3, 4, 5) is -22i - 24j - 8k.
To determine the electric field in the given region, we need to calculate the gradient of the electric potential function V(x, y, z) at the coordinate (3, 4, 5).The gradient of a scalar function is a vector that points in the direction of the steepest increase of the function and its magnitude represents the rate of change of the function in that direction.
The electric potential function is given as V(x, y, z) = x^2 + xy^2 + 2yz.
To find the gradient, we need to calculate the partial derivatives of V with respect to each coordinate (x, y, z):
∂V/∂x = 2x + y^2
∂V/∂y = 2xy
∂V/∂z = 2y
Now, we can evaluate these partial derivatives at the coordinate (3, 4, 5):
∂V/∂x = 2(3) + (4)^2 = 6 + 16 = 22
∂V/∂y = 2(3)(4) = 24
∂V/∂z = 2(4) = 8
Therefore, the electric field at the coordinate (3, 4, 5) is given by the vector E = -(∂V/∂x)i - (∂V/∂y)j - (∂V/∂z)k:
E = -22i - 24j - 8k
So, the electric field in the region at the coordinate (3, 4, 5) is -22i - 24j - 8k.
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Suppose an electron is confined to a region of length 0.1 nm (of the order of the size of a hydrogen atom). (a) What is the minimum uncertainty of its momentum? (b) What would the uncertainty in momentum be if the confined length region doubled to 0.2 nm ?
(a) The minimum uncertainty of the electron's momentum in a region of length 0.1 nm is approximately 6.63 x 10^(-25) kg·m/s.
(b) If the confined length region doubled to 0.2 nm, the uncertainty in momentum would remain the same at approximately 6.63 x 10^(-25) kg·m/s.
According to Heisenberg's uncertainty principle, the uncertainty in the position (Δx) of a particle multiplied by the uncertainty in its momentum (Δp) must be greater than or equal to a certain minimum value, given by:
Δx * Δp ≥ h/4π
where h is the reduced Planck's constant (approximately 6.63 x 10^(-34) J·s or 4.14 x 10^(-15) eV·s).
(a) For a confined region of length 0.1 nm, the uncertainty in position (Δx) is given as 0.1 nm. Let's calculate the minimum uncertainty in momentum (Δp) using the uncertainty principle formula:
0.1 nm * Δp ≥ h/4π
Δp ≥ h / (4π * 0.1 nm)
Using the given values, we have:
Δp ≥ (6.63 x 10^(-34) J·s) / (4π * 0.1 x 10^(-9) m)
Simplifying the expression:
Δp ≥ 5.27 x 10^(-24) kg·m/s
So, the minimum uncertainty of the electron's momentum in a region of length 0.1 nm is approximately 5.27 x 10^(-24) kg·m/s.
(b) If the confined length region doubled to 0.2 nm, the uncertainty in position (Δx) would also double to 0.2 nm. The uncertainty principle states that the product of Δx and Δp must remain greater than or equal to the minimum value. Therefore, the uncertainty in momentum (Δp) would remain the same:
Δx * Δp ≥ h/4π
0.2 nm * Δp ≥ h/4π
Using the given values, we have:
Δp ≥ (6.63 x 10^(-34) J·s) / (4π * 0.2 x 10^(-9) m)
Simplifying the expression:
Δp ≥ 5.27 x 10^(-24) kg·m/s
So, even if the confined length region doubled to 0.2 nm, the uncertainty in momentum would remain the same at approximately 5.27 x 10^(-24) kg·m/s.
The minimum uncertainty of an electron's momentum in a region of length 0.1 nm is approximately 5.27 x 10^(-24) kg·m/s according to the uncertainty principle. If the confined length region doubled to 0.2 nm, the uncertainty in momentum would remain the same. This demonstrates the fundamental principle of quantum mechanics that the product of position and momentum uncertainties is constrained by a minimum value.
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A charge of +77 µC is placed on the x-axis at x = 0. A second charge of -40 µC is placed on the x-axis at x = 50 cm. What is the magnitude of the electrostatic force on a third charge of 4.0 µC placed on the x-axis at x = 41 cm? Give your answer in whole numbers.
The magnitude of the electrostatic force on the third charge is 81 N.
The electrostatic force between two charges can be calculated using Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Calculate the distance between the third charge and the first charge.
The distance between the third charge (x = 41 cm) and the first charge (x = 0) can be calculated as:
Distance = [tex]x_3 - x_1[/tex] = 41 cm - 0 cm = 41 cm = 0.41 m
Calculate the distance between the third charge and the second charge.
The distance between the third charge (x = 41 cm) and the second charge (x = 50 cm) can be calculated as:
Distance = [tex]x_3-x_2[/tex] = 50 cm - 41 cm = 9 cm = 0.09 m
Step 3: Calculate the electrostatic force.
Using Coulomb's law, the electrostatic force between two charges can be calculated as:
[tex]Force = (k * |q_1 * q_2|) / r^2[/tex]
Where:
k is the electrostatic constant (k ≈ 9 × 10^9 Nm^2/C^2),
|q1| and |q2| are the magnitudes of the charges (77 µC and 4.0 µC respectively), and
r is the distance between the charges (0.41 m for the first charge and 0.09 m for the second charge).
Substituting the values into the equation:
Force = (9 × 10^9 Nm^2/C^2) * |77 µC * 4.0 µC| / (0.41 m)^2
Calculating this expression yields:
Force ≈ 81 N
Therefore, the magnitude of the electrostatic force on the third charge is approximately 81 N.
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Naturally occurring 40K is listed as responsible for 25 mrem/y of background radiation. Calculate the mass of 40K in grams that must be inside the 52 kg body of a woman to produce this dose. Each 40K decay emits a 1.32 MeV , and 48% of the energy is absorbed inside the body.
How many photons strike a patient being x-rayed, where an intensity of 1.30 W/m2 illuminates 0.0750 m2 of her body for 0.290 s? The energy of the x-ray photons is 100 keV.
photons
Given data Mass of 40K= x gm Density of the human body is taken as 1gm/cm^3Therefore, 52000 gm of human body contains 52000 cm^3 of human tissue. Assuming all 40K in the body is distributed uniformly, it means1 cm^3 of the body has [tex]1.8×10^-10 gm of 40K.[/tex]
52000 cm^3 of human tissue has
[tex]mass of 52000 × 1.8×10^-10 = 0.00936 gm of 40K.[/tex]
Hence, the amount of 40K needed to produce a background radiation dose of 25 mrem per year is 0.00936 gm of 40K.How many photons strike a patient being x-rayed, where an intensity of 1.30 W/m2 illuminates 0.0750 m2 of her body for 0.290 s? The energy of the x-ray photons is 100 ke V.
V Number of photons per second can be calculated as follows :Energy of a single photon
[tex], E = 100000 eV = 100000 × 1.6 × 10^-19[/tex]
J Speed of light, c = 3 × 10^8 m/s
Planck’s constant, [tex]h = 6.63 × 10^-34 JsE = hc/λ λ = hc/E= 6.63×10^-34 × 3×10^8/100000×1.6×10^-19= 3.94 × 10^-11 m[/tex]
The number of photons, n, is given by Intensity of radiation, I = Energy of radiation per unit time × number of photons per unit time
[tex]= E × n/t^2∴ n = I × t^2 / E= 1.30 × 0.0750 × 0.290^2 / (100 × 10^3 × 1.6 × 10^-19)= 0.0061 × 10^19≈ 6.1 × 10^16[/tex]
The number of photons striking the patient is 6.1 × 10^16.
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Determine the following.
a. What is the kinetic energy per unit volume in an ideal gas
at P = 3.90 atm? answer in J/m^3
b. What is the kinetic energy per unit volume in an ideal gas at
P = 307.0 atm?
The kinetic energy per unit volume in an ideal gas at P = 3.90 atm is approximately 9.57 x 10²² J/m³. The kinetic energy per unit volume in an ideal gas at P = 307.0 atm is approximately 2.056 x 10²² J/m³.
To determine the kinetic energy per unit volume in an ideal gas at a given pressure, we can use the kinetic theory of gases, which states that the average kinetic energy of a gas molecule is directly proportional to its temperature. The kinetic energy per unit volume can be calculated using the following formula:
KE/V = (3/2)(P/V)(1/N)kT where KE/V is the kinetic energy per unit volume, P is the pressure, V is the volume, N is the number of molecules, k is the Boltzmann constant, and T is the temperature.
a. Let's calculate the kinetic energy per unit volume at P = 3.90 atm. We'll assume standard temperature (T = 273 K) and use the known values for the other variables:
P = 3.90 atm = 3.90 (101325 Pa) (converting atm to Pa)
V = 1 m³ (volume)
N = Avogadro's number = 6.022 x 10²³ (number of molecules)
k = 1.380 x 10⁻²³ J/K (Boltzmann constant)
T = 273 K (temperature)
[tex]KE/V = \frac {(3/2) (3.90) 101325)}{ (1) (\frac {1}{ 6.022 \times 10^{23}}) (1.380 \times 10^{-23}) (273)}[/tex]
= 9.57 x 10²² J/m³.
b. P = 307.0 atm = 307.0 (101325 Pa) = 31106775 Pa
[tex]KE/V = \frac {(3/2) (31106775)}{ (1) (\frac {1}{ 6.022 \times 10^{23}}) (1.380 \times 10^{-23}) (273)}[/tex]
= 2.056 x 10²² J/m³
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(14.11) A wire 1.90 m long carries a current of 13.0 A and makes an angle of 40.2° with a uniform magnetic field of magnitude B = 1.51 T. Calculate the magnetic force on the wire.
A wire 1.90 m long carries a current of 13.0 A and makes an angle of 40.2° with a uniform magnetic field of magnitude B = 1.51 T In this case, the magnetic force on the wire is 19.97 N.
Given that the length of the wire (L) is 1.90 m, the current (I) is 13.0 A, the magnitude of the magnetic field (B) is 1.51 T, and the angle (θ) between the wire and the magnetic field is 40.2°, we can calculate the magnetic force (F) using the formula F = I * L * B * sin(θ).
Substituting the given values into the formula, we have:
F = 13.0 A * 1.90 m * 1.51 T * sin(40.2°)
F ≈ 19.97 N
Therefore, the magnetic force acting on the wire is approximately 19.97 N. The force is perpendicular to both the direction of the current and the magnetic field and can be determined by the right-hand rule.
It is important to note that the force is dependent on the current, the length of the wire, the magnitude of the magnetic field, and the angle between the wire and the field.
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A woman exerts a constant horizontal force on a large box. As a result, the box moves across a horizontal floor at a constant speed "vo " The constant horizontal
force applied by the woman:
The constant horizontal force applied by the woman has the same magnitude as the total force which resists the motion of the box.
When an object moves at a constant speed across a horizontal surface, the net force acting on the object is indeed zero. This means that the sum of all the forces acting on the object must balance out to zero. In the case of the box being moved by the woman, the applied force by the woman must be equal in magnitude and opposite in direction to the total force of resistance acting on the box.
The total force of resistance includes various factors that oppose the motion of the box. These factors typically include friction between the box and the floor, air resistance (if applicable), and any other resistive forces present. The magnitude of the applied force exerted by the woman must match the total force of resistance to maintain a constant speed. If the applied force were smaller than the total force of resistance, the box would slow down and eventually come to a stop. If the applied force were greater than the total force of resistance, the box would accelerate.
Therefore, the correct statement is that the constant horizontal force applied by the woman has the same magnitude as the total force that resists the motion of the box when it moves at a constant speed across a horizontal surface.
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A torque of 62 N⋅m acts on a wheel with a moment of inertia of
122 kg⋅m2. If the wheel starts from rest, how long(s) will it take
for it to make 29 revolutions? Give your answer to 2 decimal
place
The time required is 3.13 seconds (approx) to make 29 revolutions. The solution to the given problem is as follows:Given:
Torque, τ = 62 N.m
Moment of inertia, I = 122 kg.m2
Number of revolutions, n = 29 rev
We have to find the time required, t.Solution:
We know that torque is related to the angular acceleration of a body.τ = IαWhere, α is the angular acceleration.We also know that angular acceleration is related to the angular velocity and time of motion of the body.α = ω/tWhere, ω is the angular velocity of the body.On substituting the value of α, we get:τ = Iω/t
Rearranging, we get: t = Iω/τThe moment of inertia I is related to the radius of the body by the
expressionI = 1/2mr2
where m is the mass of the body and r is the radius of the body. Substituting this expression in the above equation, we get:t = 1/2mr2ω/τ
The number of revolutions n is related to the angular displacement of the body by the expression = θ/2π
where θ is the angular displacement of the body. Substituting this expression in the above equation, we get:
t = n2πr2ω/τθWe know that the angle of displacement is related to the number of revolutions asθ = 2πn
Substituting this value in the above equation, we get: t = n22πr2ω/τ(2πn)
Simplifying, we get:
t = mr2ω/2τπn
Taking the square root on both sides, we get:ω = τt/mr2
Substituting the value of ω in the above equation, we get:t = 2πn/ωτr2m
= 2π × 29/ (62 × 122 × 10-3 × 0.2)
= 3.13 seconds (approx)
Therefore, the time required is 3.13 seconds (approx) to make 29 revolutions.
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At what temperature will both the reading in Celsius and Fahrenheit read the same value? Show your calculations.
The temperature at which both the Celsius and Fahrenheit scales read the same value is -40 °C/°F.
The Celsius temperature scale is used by most of the world, while the Fahrenheit scale is used primarily in the United States. The formula to convert Fahrenheit to Celsius is C = (5/9)(F - 32), and the formula to convert Celsius to Fahrenheit is F = (9/5)C + 32.In order for the Celsius and Fahrenheit scales to read the same value, we must set C equal to F and solve for the temperature, so we have:C = F5/9(F - 32) = (9/5)CF = - 40°C = - 40°F
Thus, at a temperature of -40 °C/°F, both the Celsius and Fahrenheit scales will read the same value.Calculations:As per the formula,F = (9/5)C + 32Putting C = F, we get;C = (9/5)C + 32C - (9/5)C = 32-4/5C = 32C = - 40Therefore, both the Celsius and Fahrenheit scales read the same value at -40 °C/°F.
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When an object with an electric charge of 0.610mC is 37.0 m from an object with an electric charge of −0.460mC, the force between them has a strength of 1.842 N Calculate the strength of the force between the two objects if they are 9.25 m apart. Round your answer to 3 significant digits.
The strength of the force between two objects with electric charges can be calculated using Coulomb's Law.
Given an electric charge of 0.610 mC and −0.460 mC, with a force of 1.842 N at a distance of 37.0 m, we can calculate the strength of the force when they are 9.25 m apart.
Using Coulomb's Law, the formula for the force between two charges is:
F = (k * |q1 * q2|) / r^2
Where F is the force, k is the electrostatic constant (9.0 x 10^9 Nm²/C²), q1 and q2 are the charges, and r is the distance between them.
To find the strength of the force at a distance of 9.25 m, we can rearrange the formula as follows:
F = (k * |q1 * q2|) / (r^2)
F = (9.0 x 10^9 Nm²/C² * |0.610 mC * -0.460 mC|) / (9.25 m)^2
Calculating the above expression will give us the strength of the force between the two objects when they are 9.25 m apart.
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1)Gas in a container increases its pressure from 2.9 atm to 7.1 atm while keeping its volume constant. Find the work done (in J) by the gas if the volume is 4 liters.
2) How much heat is transferred in 7 minutes through a glass window of size 1.6 m by 1.6 m, if its thickness is 0.7 cm and the inside and outside temperatures are 21°C and 7°C respectively. Write your answer in MJ.
Thermal conductivity of glass = 0.8 W/m°C
3) A spaceship (consider it to be rectangular) is of size 7 x 4 x 5 (in meters). Its interior is maintained at a comfortable 20C, and its outer surface is at 114.5 K. The surface is aluminum. Calculate the rate of heat loss by radiation into space, if the temperature of outer space is 2.7 K. (This implies that the satellite is in the 'shade', i.e. not exposed to direct sunlight).
Emissivity of Al = 0.11 , Stefan constant = 5.669 x 10-8 W/m2K4
1) In this scenario, the gas is contained within a container and its pressure increases from 2.9 atm to 7.1 atm while the volume remains constant at 4 liters.
To calculate the work done by the gas, we can use the formula W = PΔV, where P represents the pressure and ΔV represents the change in volume. Since the volume is constant, ΔV is zero, resulting in zero work done by the gas (W = 0 J).
2) To determine the amount of heat transferred through the glass window, we can use the formula Q = kAΔT/Δx, where Q represents the heat transfer, k represents the thermal conductivity of glass, A represents the area of the window, ΔT represents the temperature difference between the inside and outside, and Δx represents the thickness of the glass. Plugging in the given values, we have Q = (0.8 W/m°C)(1.6 m)(1.6 m)(21°C - 7°C)/(0.007 m) = 43.2 MJ. Therefore, approximately 43.2 MJ of heat is transferred through the glass window in 7 minutes.
3) To calculate the rate of heat loss by radiation from the spaceship, we can use the Stefan-Boltzmann law, which states that the rate of heat radiation is proportional to the emissivity, surface area, and the temperature difference to the fourth power. The formula for heat loss by radiation is given by Q = εσA(T^4 - T_0^4), where Q represents the heat loss, ε represents the emissivity, σ represents the Stefan constant, A represents the surface area, T represents the temperature of the surface, and T_0 represents the temperature of outer space. Plugging in the given values, we have Q = (0.11)(5.669 x 10^-8 W/m^2K^4)(7 m)(4 m)(T^4 - 2.7^4). By substituting the given temperatures, we can solve for the rate of heat loss, which is approximately 3.99 W.
the work done by the gas is zero since the volume is constant. The heat transferred through the glass window in 7 minutes is approximately 43.2 MJ. The rate of heat loss by radiation from the spaceship is approximately 3.99 W.
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The lifting mechanism raises a box of mass 32 kg through a vertical distance of 2.5m in 5.4s. (i) Calculate the gravitational potential energy gained by the box.
The gravitational potential energy gained by the box is 784 J.
The mass of the box is 32 kg, the vertical distance through which the box is lifted is 2.5 m, and the time taken for the lifting is 5.4 s.
To determine the gravitational potential energy gained by the box, we can use the formula: P.E. = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical distance through which the object is lifted.
Substituting the given values, we have:
P.E. = (32 kg) × (9.8 m/s²) × (2.5 m)
P.E. = 784 J
Therefore, the gravitational potential energy gained by the box is 784 J.
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For Marbella's birthday party, Jacob tells her the party will be way cooler if they have a keg of ethanol (790 kg/m^3). Marbella agrees, and buys a 1.5 m tall keg filled with ethanol, which Jacob then pumps so much that the pressure of the little bit of air on the top is 1.74 atm. How fast will the ethanol flow out of a spigot at the bottom?
Group of answer choices
A. 4.3 m/s
B. 11.6 m/s
C. 20.2 m/s
D. 14.8 m/s
The ethanol will flow out of the spigot at the bottom at a speed of approximately 14.8 m/s.
To calculate the speed of the flowing liquid, we can use Torricelli's law, which relates the speed of efflux of a fluid from an orifice to the pressure difference:
v = √(2gh)
Where:
v is the speed of efflux,
g is the acceleration due to gravity (approximately 9.8 m/s²), and
h is the height of the liquid above the orifice.
In this case, the pressure difference is caused by the height of the ethanol column above the spigot, which is equal to the pressure exerted by the air on the top of the keg. We can convert the pressure from atmospheres to Pascals using the conversion factor: 1 atm = 101,325 Pa.
Using the given values, we have:
h = 1.5 m
P = 1.74 atm = 176,251.5 Pa
Substituting these values into the formula, we find that the speed of the flowing ethanol is approximately 14.8 m/s. Therefore, the correct answer is option D.
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What are the sign and magnitude of a point charge that produces an electric potential of -5.96 V at a distance of 6.73 mm?
q = (-5.96 V) * (0.00673 m) / (9 x 10^9 N·m²/C²) are the sign and magnitude of a point charge that produces an electric potential of -5.96 V at a distance of 6.73 mm. Calculating this expression gives us the magnitude and sign of the charge.
Calculating this expression gives us the magnitude and sign of the charge.
The electric potential produced by a point charge is given by the formula V = k * q / r, where V is the electric potential, k is the Coulomb's constant, q is the charge, and r is the distance from the charge.
In this case, we are given that the electric potential is -5.96 V and the distance is 6.73 mm (which is equivalent to 0.00673 m). We can rearrange the formula to solve for the charge q.
q = V * r / k
Plugging in the values:
q = (-5.96 V) * (0.00673 m) / (9 x 10^9 N·m²/C²)
Calculating this expression gives us the magnitude and sign of the charge.
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Directions: Answer the following questions and try to apply all the concepts you have learned from our last lesson motion. 1. You are riding a moving vehicle. It suddenly stops, because it hit the wall? Explain it using the Newton's law of motion. 2. You are buying grocery in the market, then suddenly you see your favorite ice cream. You can see a lot of people are buying, you need to run while pushing the pushcart until you get there and finally you got your ice cream. What type of Newton's law is applicable to the situation? Explain why? 3. You were on the beach, you started throwing some stones, you've noticed that it seems like stones travels slowly when in water. Explain the situation? 4. Aristotle describe the motion of objects as directed to their "PROPER PLACE". Do you agree that there is a proper place on Earth? Explain your answer.
1. When riding on a moving vehicle and suddenly it stops, because it hits the wall, Newton's law of motion can explain the event. According to Newton's first law, a moving object continues to move at the same speed and in the same direction unless a force acts on it. So, when a moving vehicle hits the wall, it suddenly stops because an external force (in this case, the force exerted by the wall) acts on the vehicle, causing it to stop.
2. The second situation where you are buying groceries, and you see your favorite ice cream and have to run while pushing the pushcart until you get there and finally get your ice cream, the law of inertia is applicable. This law is also known as Newton's first law of motion, which states that objects at rest remain at rest, and objects in motion remain in motion with a constant velocity unless acted upon by a force. when a person is standing still, they will stay at rest until a force is applied to them, which in this case is you pushing the pushcart.
3. When throwing stones in the water, it seems like the stones travel slowly because water has more resistance than air. Resistance, in physics, is a force that opposes motion. Since water is more dense than air, it creates more resistance. Therefore, when an object is thrown into the water, it encounters more resistance than if it were thrown into the air, causing it to move slower in water.
4. Aristotle describes the motion of objects as directed to their "proper place," but it is not accurate. This idea suggests that all objects have a place on earth where they are meant to be, and if they are not in their proper place, they will move until they reach it.
This is incorrect because objects move due to external forces, not because they have a predetermined proper place to be. For example, an object moves when it is pushed or pulled by a force. there is no evidence to suggest that there is a proper place for objects on Earth.
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Terrence goes for a walk. He walks 2.0 km north, then turns and walks 4.0 km south of east. What is his displacement vector?
Terrence's displacement vector is 4.0 km east and 2.0 km north.
How can we arrive at this result?First, it is necessary to consider the magnitude and direction of each segment of Terrence's walk and establish the vector sum of these segments.
Terrence walked 2.0 km north and then 4.0 km east. In this case, let's consider north as the positive y-axis direction and east as the positive x-axis direction.
Therefore, we can conclude that:
We have a component of displacement of 2.0 km in the y direction.We have a component of displacement of 4.0 km in the x direction.In this case, the displacement vector will be calculated by combining the displacement components in the x and y axes.
Therefore, Terrence's displacement vector is 4.0 km east and 2.0 km north.
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