The direction of the impulse that the bat delivers to the ball is in the direction of motion of the ball.
The direction of the impulse that the bat delivers to the ball is in the direction of motion of the ball. This is due to the conservation of momentum. The impulse is the change in momentum of an object, and it is equal to the force applied multiplied by the time it is applied.
The conservation of momentum states that the total momentum of a system remains constant if there are no external forces acting on the system. In the case of a bat hitting a ball, the system includes both the bat and the ball.
When the bat hits the ball, the bat applies a force to the ball that changes the momentum of the ball. The impulse of the bat on the ball is in the direction of the motion of the ball, which is usually towards the fielders or outfielders.
This is due to the fact that the ball has to move in the direction of the force applied by the bat.
Therefore, the direction of the impulse that the bat delivers to the ball is in the direction of motion of the ball. The impulse can be expressed in units of Newton seconds (Ns), and it is equal to the force applied multiplied by the time it is applied.
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Calculate the potential energy of a rock with a mass of 55 kg as it sits on a cliff that is 27 m high
Answer:
The potential energy is zero since the rock isn't moving.
Calculate the Kinetic energy of an object with a mass of 15kg while sitting on a shelf that is 20m high.
Kinetic energy is energy of motion. If the object is sitting still, then it has no kinetic energy. It doesn't matter what its mass is, or how high the shelf is.
KE = 0
steam is compressed from 4 mpa and 300 c to 9 mpa isentropically. the final temperature of the steam is group of answer choices
The initial pressure of steam (P1) = 4 MPa, the Initial temperature of steam (T1) = 300°C = 573.15 K, Final pressure of steam (P2) = 9 MPaProcess: The given process is Isentropic Process Formula: For isentropic process, P1V1^γ = P2V2^γWhere γ = Cp / Cv = 1.3 (For Steam)And, V1 / T1^γ-1 = V2 / T2^γ-1,
Where V = Specific volume of steam solution: Specific volume of steam (V1) at initial state is given by, V1 = V2 = v (From the principle of the isentropic process).
Now, from the steam table, At 4 MPa (P1) and 573.15 K (T1), V1 = 0.1006 m³/kgAt 9 MPa (P2), V2 = V1 × (P1 / P2)^(1/γ)= 0.1006 × (4 / 9)^(1/1.3)= 0.080 m³/kg.
Let's use the formula for calculating the final temperature of the steamV1 / T1^γ-1 = V2 / T2^γ-1⇒ T2 = (V2 / V1)^(1/γ-1) × T1= (0.08 / 0.1006)^(1/1.3-1) × 573.15≈ 764.5 K≈ 491.5°C.
Therefore, the final temperature of the steam is 491.5°C (rounded off to one decimal place).
Hence, option D is correct.
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A thin film of oil with index of refraction n = 1.6 and thickness t = 75 nm floats on water. The oil is illuminated from above, perpendicular to the surface.
Part A): What is the longest wavelength of light, in nanometers, that will undergo destructive interference when it is shone on the oil?
Part B): What is the next longest wavelength of light, in nanometers, that will undergo destructive interference when it is shone on the oil?
Part C): What is the longest wavelength of light, in nanometers, that will undergo constructive interference when it is shone on the oil?
The longest wavelength of light that will undergo destructive interference is approximately 225 nm. The next longest wavelength of light that will undergo destructive interference is approximately 450 nm. The longest wavelength of light that will undergo constructive interference is approximately 150 nm.
To solve this problem, we can use the equation for interference in a thin film:
1) Destructive interference occurs when the path difference between the two reflected waves is equal to an odd multiple of half the wavelength.
2) Constructive interference occurs when the path difference is equal to an integer multiple of the wavelength.
Index of refraction of oil (n) = 1.6
Thickness of the oil film (t) = 75 nm
Part A) To find the longest wavelength of light that will undergo destructive interference, we consider the path difference between the top and bottom surfaces of the oil film. The path difference for destructive interference is given by:
2t = (2n - 1)(λ/2)
Simplifying and rearranging the equation, we can solve for λ:
λ = (4t)/(2n - 1)
Substituting the given values:
λ = (4 * 75 nm) / (2 * 1.6 - 1)
λ ≈ 225 nm
Part B) The next longest wavelength of light that will undergo destructive interference occurs when the path difference is equal to the next odd multiple of half the wavelength.
Since we already found the first destructive interference wavelength in Part A, the next wavelength will be twice that value:
2λ = 2 * 225 nm = 450 nm
Part C) For constructive interference, the path difference is given by:
2t = mλ
Where m is an integer representing the order of constructive interference. To find the longest wavelength that will undergo constructive interference, we consider the first-order constructive interference:
2t = λ
Substituting the given values:
λ = 2 * 75 nm = 150 nm
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A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force? a) out of the page b) into the page c) downward d) to the right e) to the left
The direction of the magnetic force on the positive charge is to the right. Therefore, the correct answer is (d) to the right.
To determine the direction of the magnetic force on a positive charge entering a uniform magnetic field, we can use the right-hand rule for magnetic force.
If we point the thumb of our right hand in the direction of the velocity of the positive charge, and align our fingers with the magnetic field lines (in the direction of the field), then the palm of our hand will indicate the direction of the magnetic force.
In the given scenario, the positive charge is moving in the downward direction, and the magnetic field is directed into the page (represented by the x's in the figure).
Using the right-hand rule, if we point our thumb downward to represent the velocity and align our fingers into the page to represent the magnetic field, the palm of our hand will face to the right. Therefore, the direction of the magnetic force on the positive charge is to the right.
Therefore, the correct answer is d) to the right.
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Transform plate tectonic boundaries slide/move past each other, rubbing along the edges cause what types of damage?
Question 3 options:
tornadoes, flooding, destruction
hurricanes, flooding, wave surge
earthquakes, tsunami, landslides
blizzards, freezing conditions, snow drifts
Transform plate tectonic boundaries slide/move past each other, rubbing along the edges causing earthquakes, tsunami, landslides
What is earthquake?An earthquake is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves.
The answer is c is because when tectonic plates are rubbing against each other that’s how an earthquake is formed.
another reason the answer is C is because when the tectonic plates are moving together it can cause the land to slide.
the last reason the answer is C is because when the tectonic plates in the ocean move it can cause a tsunami.
Hence transform plate tectonic boundaries slide/move past each other, rubbing along the edges causing earthquakes, tsunami, landslides
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Through which of the following ways does the Sun primarily transfer its heat energy to the Earth?
A.
conduction
B.
radiation
C.
convection
D.
reflection
Answer:
B. Radiation
Explanation:
Transfer of heat energy through space by electromagnetic radiation
Which of the following orders represents the ordering found in an alphanumeric outline?
A. capital letters, Arabic numerals, Roman numerals, lowercase letters
B. Arabic numerals, capital letters, Roman numerals, lowercase letters
C. Roman numerals, lowercase letters, Arabic numerals, capital letters
D. Roman numerals, capital letters, Arabic numerals, lowercase letters
Answer: D
Explanation: It says that in the paragraph
Answer:
Roman numerals, capital letters, Arabic numerals, lowercase letters
Explanation:
A tetherball is attached to a pole with a 2.0-m rope. It iscircling at 0.20 rev/s. As the rope wraps around the pole itshortens. How long is the rope when the ball is moving at5.0m/s.
The length of the rope when the ball is moving at 5.0 m/s is approximately 0.925 meters. The calculation was based on the conservation of angular momentum .
To determine the length of the rope when the ball is moving at 5.0 m/s, we can use the conservation of angular momentum. The angular momentum of the system remains constant as the rope wraps around the pole.
The formula for angular momentum is given by:
L = Iω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
In this case, the moment of inertia remains constant as the mass of the ball and the pole do not change. Therefore, we have:
L1 = L2
The initial angular momentum, L1, is given by:
L1 = I1ω1
The final angular momentum, L2, is given by:
L2 = I2ω2
The moment of inertia is proportional to the square of the radius of the circular motion. Since the rope shortens, the radius decreases as well.
The initial radius, r1, is given by:
r1 = 2.0 m
The final radius, r2, is unknown.
The initial angular velocity, ω1, is given by:
ω1 = 0.20 rev/s * 2π rad/rev
= 1.26 rad/s
The final angular velocity, ω2, is given by:
ω2 = v/r2
where v is the linear velocity of the ball. In this case, v = 5.0 m/s.
Thus, we can rearrange the equation to solve for r2:
r2 = v/ω2
Substituting the known values, we get:
r2 = 5.0 m/s / ω2
Now, we can substitute the equation for the angular momentum to solve for r2:
I1ω1 = I2ω2
r1^2 * ω1 = r2^2 * ω2
Solving for r2, we have:
r2^2 = (r1^2 * ω1) / ω2
Plugging in the known values:
r2^2 = (2.0 m)^2 * 1.26 rad/s / (5.0 m/s / ω2)
r2^2 = 5.04 m^2 rad/s / (5.0 m/s / ω2)
r2^2 = 5.04 m^2 rad/s * (ω2 / 5.0 m/s)
r2^2 = 5.04 m^2 rad/s * (ω2 / 5.0 m/s)
r2^2 = 5.04 m^2 rad/s * ω2 / 5.0 m/s
Simplifying the units:
r2^2 = 5.04 m^3 rad / s^2
r2 = √(5.04) m
r2 ≈ 2.244 m
Therefore, the length of the rope when the ball is moving at 5.0 m/s is approximately 0.925 meters (2.244 m - 2.0 m).
The length of the rope when the ball is moving at 5.0 m/s is approximately 0.925 meters. The calculation was based on the conservation of angular momentum, where the initial angular momentum of the system equals the final angular momentum. By considering the initial radius, initial angular velocity, final radius, and linear velocity of the ball, we derived the equation and solved for the final radius. The result was approximately 2.244 meters, and by subtracting the initial rope length (2.0 meters), we found that the shortened length of the rope is approximately 0.925 meters.
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a positive charge moves with a velocity v in the direction shown. the magnetic field points in the z direction and v lies in the x-z plane. what is the direction of the force on the charge due to the magnetic field?
The force on the positive charge due to the magnetic field will be directed in the y-direction.
To determine the direction of the force on a moving charge in a magnetic field, we can use the right-hand rule.
According to the right-hand rule, if we extend the thumb, index finger, and middle finger of our right hand mutually perpendicular to each other, the thumb represents the velocity vector (v), the index finger represents the magnetic field vector (B), and the middle finger represents the direction of the force (F) acting on the charge.
In this case, we have the magnetic field pointing in the z-direction, which means the magnetic field vector (B) will point directly out of the page or screen toward you. The velocity vector (v) lies in the x-z plane, so it will be perpendicular to the magnetic field vector.
Using the right-hand rule, we can place our right hand with the thumb pointing in the positive x-direction (toward the right), the index finger pointing in the positive z-direction (out of the page), and the middle finger will naturally point in the positive y-direction (upward).
Therefore, the force acting on the positive charge due to the magnetic field will be directed in the y-direction, which is upward.
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a mass vibrates back and forth from the free end of an ideal spring of spring constant 20 N/m with an amplitude of .3 m. What is the kinetic energy of this vibrating mass when it is .3m from its equilibrium position?
a) .9 J
b) .45 J
c) zero
d) it is impossible to give an answer without knowing the object's mass
The kinetic energy of the vibrating mass when it is 0.3 m from its equilibrium position is 0.45 J (option b).
To calculate the kinetic energy of the vibrating mass, we need to know its mass. Since the question doesn't provide the mass, we cannot directly determine the kinetic energy without this information.
However, we can make an assumption and proceed with the calculation. Let's assume the mass of the vibrating object is "m" kg. In simple harmonic motion, the potential energy and kinetic energy are interchanged as the object oscillates. At the maximum displacement, when the mass is 0.3 m from its equilibrium position, all the potential energy is converted into kinetic energy.
The potential energy of the mass is given by: PE = (1/2)kx², where k is the spring constant and x is the displacement from the equilibrium position.
Since the amplitude of the oscillation is 0.3 m, the maximum displacement is also 0.3 m. Thus, the potential energy at this point is: PE = (1/2)(20 N/m)(0.3 m)² = 0.9 J.
As mentioned earlier, at the maximum displacement, all the potential energy is converted into kinetic energy. Therefore, the kinetic energy of the vibrating mass when it is 0.3 m from its equilibrium position is 0.9 J.
The correct answer is not provided in the given options. Considering the assumption that the mass of the vibrating object is known, the kinetic energy is determined to be 0.45 J.
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An object executing simple harmonic motion has a maximum speed of 48 m/s and a maximum acceleration of 0.85 m/s²
Part A
Find the amplitude of this motion.
Express your answer using two significant figures.
The amplitude of this motion is approximately 2705.37 m, expressed with two significant figures.
To find the amplitude of an object executing simple harmonic motion, we can use the relationship between maximum speed, maximum acceleration, and amplitude.
In simple harmonic motion, the maximum speed (V(max)) occurs when the displacement (x) is zero, and the maximum acceleration (a(max)) occurs when the displacement is at its maximum. The relationship between these quantities is given by:
V(max) = ω * A
a(max) = ω² * A
Where ω represents the angular frequency and A represents the amplitude.
From the given information, V(max) = 48 m/s and a(max) = 0.85 m/s².
Dividing the equation for maximum acceleration by the equation for maximum speed, we get:
a(max) / V(max) = (ω² * A) / (ω * A)
Simplifying, we have:
a(max) / V(max) = ω
Substituting the given values, we have:
0.85 m/s² / 48 m/s = ω
Solving for ω, we find:
ω ≈ 0.0177 rad/s
Now, we can use the equation for maximum speed to find the amplitude:
V(max) = ω * A
Rearranging the equation, we have:
A = V(max) / ω
Substituting the values, we have:
A = 48 m/s / 0.0177 rad/s ≈ 2705.37 m
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A child pulls a sled up a snow-covered hill. The child does 504 J of work on the sled. If the child walks 15 m
up the hill, how large of a force must the child exert?
Answer: F = 33.6 N
Explanation: work = force · distance or W = F·s
Force F = W/s = 504 J/15 m
A small cork with an excess charge of +6.0 μC (1 μC = 10 -6 C) is placed 0.12 m from another cork, which carries a charge of -4.3 μC. a. What is the magnitude of the electric force between the corks? b. Is this force attractive or repulsive? c. How many excess electrons are on the negative cork? d. How many electrons has the positive cork lost?
Answer:
a.16.125 N b. The force is an attractive force. c. 2.68 × 10¹³ electrons d. 3.75 × 10¹³ electrons
Explanation:
a. What is the magnitude of the electric force between the corks?
The electrostatic force of attraction between the two corks is given by
F = kq₁q₂/r² where k = 9 × 10⁹ Nm²/C², q₁ = +6.0 μC = +6.0 × 10⁻⁶ C, q₂ = -4.3 μC = -4.3 × 10⁻⁶ C and r = distance between the corks = 0.12 m
Substituting the values of the variables into the equation, we have
F = kq₁q₂/r²
F = 9 × 10⁹ Nm²/C² × +6.0 × 10⁻⁶ C × -4.3 × 10⁻⁶ C/(0.12 m)²
= -232.2 × 10⁻³ Nm²/(0.0144 m)²
= -16125 × 10⁻³ N
= -16.125 N
So, the magnitude of the force is 16.125 N
b. Is this force attractive or repulsive?
Since the direction of the force is negative, it is directed towards the positively charged cork, so the force is an attractive force.
c. How many excess electrons are on the negative cork?
Since Q = ne where Q = charge on negative cork = -4.3 μC = -4.3 × 10⁻⁶ C and n = number of excess electrons and e = electron charge = -1.602 × 10⁻¹⁹ C
So n = Q/e = -4.3 × 10⁻⁶ C/-1.602 × 10⁻¹⁹ C = 2.68 × 10¹³ electrons
d. How many electrons has the positive cork lost?
We need to first find the number of excess positive charge n'
Q' = n'q where Q = charge on positive cork = + 6.0 μC = + 6.0 × 10⁻⁶ C and n = number of excess protons and q = proton charge = +1.602 × 10⁻¹⁹ C
So n' = Q'/q = +6.0 × 10⁻⁶ C/+1.602 × 10⁻¹⁹ C = 3.75 × 10¹³ protons
To maintain a positive charge, the number of excess protons equals the number of electrons lost = 3.75 × 10¹³ electrons
in the bohr model, how many electron wavelengths fit around this orbit?
In the Bohr model, the number of electron wavelengths that fit around a particular orbit is directly related to the principal quantum number of that orbit.
In the Bohr model of the atom, electrons are described as moving in discrete orbits around the nucleus. These orbits are quantized, meaning that only certain specific values of the electron's angular momentum are allowed.
The Bohr model also introduced the concept of electron wavelengths, which can be thought of as the "wave-like" behavior of electrons.
To determine how many electron wavelengths fit around a particular orbit in the Bohr model, we can consider the de Broglie wavelength of the electron.
According to the de Broglie hypothesis, the wavelength associated with a particle is given by the equation lambda = h/p, where h is the Planck constant and p is the momentum of the particle.
In the Bohr model, the allowed electron orbits have discrete angular momentum values, given by the equation L = n*[tex]\bar{h}[/tex], where n is the principal quantum number and [tex]\bar{h}[/tex] is the reduced Planck constant.
The momentum of an electron in an orbit is related to its angular momentum and the radius of the orbit by the equation p = L/r.
Substituting the expression for angular momentum into the de Broglie wavelength equation, we get
[tex]\lambda[/tex] = h/(n*[tex]\bar{h}[/tex]/r) = hr/(n*[tex]\bar{h}[/tex]).
The number of electron wavelengths that fit around the orbit is then given by the circumference of the orbit divided by the wavelength, i.e.,
(2*π*r)/[tex]\lambda[/tex] = (2*π*r)/(hr/(n*[tex]\bar{h}[/tex])) = (2*π*n*[tex]\bar{h}[/tex])/h.
Simplifying further, we find that the number of electron wavelengths that fit around the orbit is equal to 2*π*n, where n is the principal quantum number.
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Michelle is going to vacation in a location on the globe that is currently experiencing summer and daylight. According the model below, which location could Michelle be visiting? Location A - Axis Sun Location C Location B Equator Location D A) Location A B) Location B ) Location ( D) Location D
If the skateboarder started at the top of the ramp at 6 m and had a mass of 30 kg, and made it to the bottom going 8 m/s, how much energy was lost to friction?
Answer:
i dont know
Explanation:
sorry
if his eyes have a far point of 2.0 m , what is the greatest distance he can stand from the mirror and still see his image clearly? express your answer using two significant figures.
The greatest distance the person can stand from the mirror and still see their image clearly is 2.0 meters.
The far point of a person's eyes refers to the maximum distance at which they can see objects clearly without the aid of corrective lenses. If the far point is given as 2.0 m, it means that the person can see objects clearly up to a distance of 2.0 m.
To determine the greatest distance the person can stand from the mirror and still see their image clearly, we need to consider the concept of the virtual image formed by a mirror. When we look into a mirror, our eyes perceive a virtual image as if it were formed behind the mirror.
In this case, the person's eyes can focus clearly up to a distance of 2.0 m. To see their image clearly in the mirror, the person needs the virtual image formed by the mirror to be within this range.
Since the virtual image formed by a mirror is the same distance behind the mirror as the object is in front of it, the person needs to stand at a distance from the mirror equal to the maximum distance they can focus clearly.
Therefore, the greatest distance the person can stand from the mirror and still see their image clearly is 2.0 meters.
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If riding a lawnmower engine exerts 19 hp in one minute to move the lawnmower how much work is done
Answer:
the work done by the lawnmower is 236.14 J.
Explanation:
Given;
power exerted by the lawnmower engine, P = 19 hp
time in which the power was exerted, t = 1 minute = 60 s.
1 hp = 745.7 watts
The work done by the lawnmower is calculated as follows;
[tex]Work = Energy = \frac{Power}{time} \\\\Work = \frac{(19 \times 745.7)}{60} = 236.14 \ J[/tex]
Therefore, the work done by the lawnmower is 236.14 J.
a plane monochromatic electromagnetic wave with wavelength λ = 2.8 cm, propagates through a vacuum. its magnetic field is described by
uploaded image
where Bx = 3.1 X 10-6 T, By = 3.4 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. .
1) What is f, the frequency of this wave?
2) What is I, the intensity of this wave?
3) What is Sz, the z-component of the Poynting vector at (x = 0, y = 0, z = 0) at t = 0?
4) What is Ex, the x-component of the electric field at (x = 0, y = 0, z = 0) at t = 0?
Sz, the z-component of the Poynting vector at (x = 0, y = 0, z = 0) at t = 0 is 0.
A monochromatic electromagnetic wave with wavelength λ = 2.8 cm, is propagating through a vacuum and its magnetic field is described by B = 8.4 sin(2π(1.0 × 10^9)t - 2π(1.0 × 10^4)x) µT.
The Poynting vector can be used to explain this in more detail. The Poynting vector can be calculated using the formula [rmS = rmE times B over rm2mu], where is the permeability of the medium through which the wave is propagating and E is the electric field.
The equation for the electric field is E = cB, where c is the vacuum speed of light.
The above formula can be used to determine S = 0 for the Poynting vector for the given wave.
The Poynting vector has a z-component of 0 at (x = 0, y = 0, z = 0) and t = 0.
The energy motion thickness of an electromagnetic field can be shown utilizing the Poynting vector, named after John Henry Poynting.
According to the definition, the Poynting vector is the result of the vector product of the electric and magnetic fields: 2.22) S → = E → × H →
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results: is the sum of the square of the maximum voltages across r and l, vr2 vl2, equal to the square of voltage across both elements, vrl2 in accordance with eq.2?
In general, the sum of the squares of the voltages across individual components may not necessarily be equal to the square of the voltage across both elements combined. It would depend on the nature of the circuit and the relationship between the voltage across the components.
It would depend on the nature of the circuit and the relationship between the voltage across the components. To determine if the sum of the square of the maximum voltages across resistor (R) and inductor (L), Vr^2 and Vl^2 respectively, is equal to the square of the voltage across both elements, Vrl^2, in accordance with equation (2), we need to have more context and information about the specific equation and circuit being referred to. The relationship between Vr^2, Vl^2, and Vrl^2 would depend on the specific circuit configuration and the equations governing its behavior.
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hi:):):):):):):):):):):):):):):):):):):):):):):):)
Answer:
hi. :)))))))))))))))))))))
A wire is carrying current vertically downward. What is the direction of the force on this wire due to Earth's magnetic field?
Please answer in relation to the Right-hand rule.
The requried force on the wire due to Earth's magnetic field will be perpendicular to both the current direction and the magnetic field direction.
According to the right-hand rule, if a current-carrying wire is held in the right hand with the thumb pointing in the direction of the current, the direction in which the fingers curl represents the direction of the magnetic field around the wire.
In this case, the wire is carrying the current vertically downward. If we apply the right-hand rule, we can curl our fingers around the wire in the direction of the magnetic field. The direction of the magnetic field is horizontally perpendicular to the wire, pointing toward the north.
Therefore, the force on the wire due to Earth's magnetic field will be perpendicular to both the current direction and the magnetic field direction. Using the right-hand rule again, if we extend our right-hand thumb in the direction of the current (downward) and curl our fingers in the direction of the magnetic field (northward), our palm will face east. This indicates that the force on the wire will be directed eastward.
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of the following, where would the weight of an object be the least? 2000 miles above earth's surface at the equator at the south pole at the north pole at the center of earth
The weight of an object would be the least at the center of the Earth. 2000 miles above earth's surface at the equator at the south pole at the north pole at the center of earth.
The weight of an object depends on the gravitational force acting on it. The gravitational force is inversely proportional to the square of the distance between the object and the center of the Earth. As the object moves farther away from the center of the Earth, the gravitational force decreases.
At the center of the Earth, the distance between the object and the center is at its minimum. Therefore, the gravitational force and consequently the weight of the object would be the least at the center of the Earth.
In contrast, as the object moves further away from the center of the Earth, such as 2000 miles above the Earth's surface, the distance between the object and the center increases, resulting in a stronger gravitational force and a greater weight.
Thus, of the options provided, the weight of an object would be the least at the center of the Earth.
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An airplane traveling 919 m above the ocean at 505 m/s is to drop a case of twinkies to the victims below. How much time before being directly overhead should the box be dropped? What is the horizontal distance between the plane and the victims when the box is dropped?
Answer:
a. 13.7 s b. 6913.5 m
Explanation:
a. How much time before being directly overhead should the box be dropped?
Since the box falls under gravity we use the equation
y = ut - 1/2gt² where y = height of plane above ocean = 919 m, u = initial vertical velocity of airplane = 0 m/s, g = acceleration due to gravity = -9.8 m/s² and t = time it takes the airplane to be directly overhead.
So,
y = ut - 1/2gt²
y = 0 × t - 1/2gt²
y = 0 - 1/2gt²
y = - 1/2gt²
t² = -2y/g
t = √(-2y/g)
So, t = √(-2 × 919 m/-9.8 m/s²)
t = √(-1838 m/-9.8 m/s²)
t = √(187.551 m²/s²)
t = 13.69 s
t ≅ 13.7 s
So, the box should be dropped 13.69 s before being directly overhead.
b. What is the horizontal distance between the plane and the victims when the box is dropped?
The horizontal distance x between plane and victims, x = speed of plane × time it takes for box to drop = 505 m/s × 13.69 s = 6913.45 m ≅ 6913.5 m
select three parts of a circular saw
spindle
trigger
base
handle
key
chuck
Answer:
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A 60kg bowling ball collides with a 0.005kg bee with a force of 0.02N. The force the bee exerts is
Answer:
0.02N
Explanation:
According to Newton's 3rd Law of motion, the bee exerts the same force on the bowling ball as the bowling ball exerts the force on the bee.
We have that for the Question "A 60kg bowling ball collides with a 0.005kg bee with a force of 0.02N. The force the bee exerts is" it can be said that The force the bee exerts is
F=0.02N
From the question we are told
A 60kg bowling ball collides with a 0.005kg bee with a force of 0.02N. The force the bee exerts is
Generally the Newtons equation for Motion is mathematically given as
This law perceives two bodies who collide as having forces which are equal as the magnitudes in opposite directions
Therefore
V^2= 2as
Hence
The force the bee exerts is
F=0.02N
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If a 120-W lightbulb emits 3.5 % of the input energy as visible light (average wavelength 550 nm) uniformly in all directions.
PART A: How many photons per second of visible light will strike the pupil (4.0 mm diameter) of the eye of an observer 2.2 m away?
PART B: How many photons per second of visible light will strike the pupil (4.0 mm diameter) of the eye of an observer 1.5 km away?
part a: N= 4.39 x 10^10 photons/second. part b: N = 8.25 photons/second are the answers.
The energy of a photon of wavelength 550 nm can be calculated as follows:
h*c/λ = 6.626 x 10^-34 x 3 x 10^8 / (550 x 10^-9)
wavelength = 3.6 x 10^-19 J.
In one second, a 120-W lightbulb emits energy as visible light in the following amount:
120 x 0.035 = 4.2 W.
As a result, the number of photons emitted per second can be computed as follows:
N = Power/Energy of a photon
N = 4.2/3.6 x 10^-19
N = 1.17 x 10^16 photons/second
PART A: The area of a 4.0-mm diameter pupil is given by the following formula:
A = πr^2
A = π(2.0 mm)^2
A= 3.14 x 4.0 x 10^-6 m^2
The distance from the bulb to the pupil is 2.2 m.
The bulb radiates in all directions, therefore the power per unit area is given by:
P = Power/4πr^2
P = 4.2/(4π(2.2)^2)
P = 0.04 W/m^2
The number of photons striking the pupil per second is determined by the following formula:
N = P*A/E
N = (0.04)(3.14 x 4.0 x 10^-6)/3.6 x 10^-19
N = 4.39 x 10^10 photons/second
PART B: The bulb is now 1.5 km distant from the pupil.
The power per unit area at this distance is:
P = Power/(4πr^2)
P = 4.2/(4π(1500)^2)
P = 2.98 x 10^-10 W/m^2.
Using the equation for the number of photons striking the pupil per second,
N = P*A/E
N = (2.98 x 10^-10)(3.14 x 4.0 x 10^-6)/3.6 x 10^-19
N = 8.25 photons/second
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An Otto cycle with compression ratio of 10. The air is at 100 kPa, 27 °C, and 500 cm³ prior to the compression stroke. Temperature at the end of isentropic expansion is 1000 K. Determine the followings:
a) Highest temperature and pressure in the cycle b) amount of heat transferred, c) thermal efficiency, and d) mean effective pressure. Use constant specific heat approach - k-1.4, cp= 1.005 kJ/kg.K cv=0.718 kJ/kg.K, R = 0.287 kJ/kg.K
An Otto cycle is used in gasoline engines to convert the thermal energy of burning gasoline into mechanical work. It consists of four stages: compression, heat addition, expansion, and exhaust. The compression ratio is defined as the ratio of the volume of the combustion chamber at the beginning of the compression stroke to the volume of the combustion chamber at the end of the expansion stroke.
Compression ratio, r = V1/V2 Here, V1 = Initial volume of air before compression stroke = 500 cm³V2 = Volume of air after the compression stroke. As the compression ratio is given as 10, the volume of air after the compression stroke, V2 = V1/10 = 500/10 = 50 cm³.
Temperature and pressure can be calculated using the following equations.
PV¹⁴ = Constant (P₁V₁¹⁴) T₁/V₁ = T₂/V₂ (isentropic process)
a) The highest temperature can be found at the end of the combustion stroke.
Here, V3 = V2T3/T2 = V4T4/T3T1V1¹⁴ = V2V3¹⁴ Pmax = T3V3/V2 = T4V4/V3 = P4
b) Amount of heat transferred, Qn = Cn (T4 - T1) Where Cn is the specific heat at constant volume.
Qn = Cn (T4 - T1) = cv (T4 - T1)
c) Thermal efficiency,
η = (Wnet)/Qn = (Qn - Qout)/Qn = 1 - (Qout/Qn) = 1 - (cv (T3 - T2))/(cv (T4 - T1))
d) Mean effective pressure, MEP = (Pmax - Pmin)/2 = (P4V3/V4 - P2V1/V2)/2
The formula for the constant specific heat approach - k-1.4, cp= 1.005 kJ/kg.K cv=0.718 kJ/kg.K, R = 0.287 kJ/kg.K is given below.
Cn = cp/(k-1) = 1.005/(1.4 - 1) = 1.005/0.4 = 2.5125 kJ/kg.Kcv = R/(k-1) = 0.287/(1.4 - 1) = 0.287/0.4 = 0.7175 kJ/kg.K
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Calculate the attenuation in decibels per meter for a TM1 wave between copper planes 1.5 cm apart with air dielectric. Frequency is 12GHz. For the same frequency and spacing, a glass dielectric with εr=4 and ε′′/ε′=2×10−3 is introduced. Calculate the attenuation from both dielectric and conductor losses. [HINT: Do not ignore the effect of the glass filling to the cutoff frequency!]
The attenuation from the dielectric (air) is 0 dB/m. The attenuation from both dielectric and conductor losses for the glass dielectric is approximately 0.063 dB/m.
To calculate the attenuation in decibels per meter (dB/m) for a TM1 wave between copper planes 1.5 cm apart with an air dielectric, we can use the following formula:
Attenuation (dB/m) = α * (1/λ)
where α is the attenuation constant and λ is the wavelength.
The attenuation constant can be calculated as:
α = (2π * frequency * ε′′) / (c * ε′)
where frequency is the given frequency (12 GHz), ε′′ is the imaginary part of the relative permittivity (dielectric loss factor), ε′ is the real part of the relative permittivity, and c is the speed of light.
For air dielectric, εr (relative permittivity) is approximately 1, so ε′ = εr = 1.
Substituting the given values into the formula:
α = (2π * 12 × 10⁹ Hz * 0) / (3 × 10⁸ m/s * 1) = 0.
Now, let's calculate the attenuation for the glass dielectric with εr = 4 and ε′′/ε′ = 2 × 10⁻³.
Since the glass dielectric is introduced, the relative permittivity becomes εr = 4 and ε′ = εr - ε′′ = 4 - (2 × 10⁻³ * 4) = 3.992.
Using the same formula as before:
α = (2π * 12 × 10⁹ Hz * 2 × 10⁻³) / (3 × 10⁸ m/s * 3.992) = 0.063 dB/m
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