The amount of the star's mass converted to energy in the explosion is 1.11 x 10^27 kg.
Calculating energy:
The mass-energy equivalence equation is used to calculate the mass that is converted to energy during a supernova explosion of a 3.2 x 10^31 kg star, producing 1.0 x 10^44 J of energy.
According to Einstein's mass-energy equivalence equation: E = mc² where, E = energy, m = mass, and c = speed of light This equation expresses the relationship between the mass of an object and the amount of energy that can be released from it.
So, to determine the mass that is converted to energy during the supernova explosion, we need to rearrange the equation as m = E/c². Now we have the following data: E = 1.0 x 10^44 Jc = 3.0 x 10^8 m/s² (speed of light). Substitute these values into the equation to get: m = E/c²m = (1.0 x 10^44 J)/(3.0 x 10^8 m/s)²m = 1.11 x 10^27 kg
Therefore, the supernova explosion of a 3.2 x 10^31 kg star converts 1.11 x 10^27 kg of its mass to energy.
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A bar magnet is falling through a loop of wire with constant velocity. The north pole enters first. As the south pole
leaves the loop of wire, the induced current (as viewed from above) will be in which direction?
a) is counterclockwise.
b) is along the length of the magnet
c) is zero
d) is clockwise
As the south pole leaves the loop of wire, the induced current (as viewed from above) will be in the clockwise direction.
Whenever a magnet is moved near a closed circuit or wire loop, an emf (electromotive force) is generated in the conductor. When the magnet moves in and out of the coil or loop, the magnitude and direction of this voltage changes, generating an induced current. This is referred to as Faraday's law of electromagnetic induction, which states that an emf is induced in a closed conductor when the magnetic flux through the surface enclosed by the conductor changes over time.
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A solid cylinder of mass M = 1.25 kg and radius R = 13.5 cm pivots on a thin fixed frictionless bearing a string wrapped around the cylinder pulls downward with a force of F = 7.259 N
What is the magnitude of the angular acceleration of the cylinder?
86.03259 rad/s^2
Consider that instead of force F, a block with mass 0.74 kg with force = 7.259 N is attached to the cylinder with a mass less string.
What is now the magnitude of the angular acceleration of the cylinder
39.3943 rad/s^2
How far does the mass M travel downward before T equals 0.49S and T equals 0.69 S.
0.62755 m
The cylinder is changed to one with the same mass and radius but a different moment of inertia starting from mass starting from rest. The mass is now moved. The distance of 0.448 mass in the time interval of 0.47 seconds.
Find the Inertia of the new cylinder
The inertia of the new cylinder is 0.0566 kgm². Other answers provided are correct.
How to find inertia?The moment of inertia of the new cylinder can be calculated using the formula:
I = (M × d²) / (4 × Δθ)
Where:
M = mass of the cylinder
d = distance moved by the mass
Δθ = change in angular displacement (in radians)
Substituting the given values:
I = (1.25 × 0.448²) / (4 × 0.47)
I = 0.0566 kgm²
Therefore, the moment of inertia of the new cylinder is 0.0566 kgm².
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two 4.0cm*4.0cm metal plates are separated by a 0.20-mm-thick piece of teflon. a. what is the capacitance? b. what is the maximum potential difference between the plates?
The capacitance of two metal plates separated by a 0.20-mm-thick is approximately 0.25 pF and the maximum potential difference between the plates is 8.4 kV.
a. The capacitance of two metal plates separated by a 0.20-mm-thick piece of Teflon is approximately 0.25 pF (picofarad).
b. The maximum potential difference between the two metal plates is determined by the permittivity of the dielectric material, which in this case is Teflon.
The permittivity of Teflon is about 2.1 and the capacitance of the plates is 0.25 pF, so the maximum potential difference between the plates can be calculated using the equation:
Vmax = (permittivity * Capacitance) / Area.
Therefore, the maximum potential difference between the plates is 8.4 kV.
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a semi-circular gate on an inclined wall is in contact with water. calculate the resultant force of the water on the gate
The resultant force of the water on the semi-circular gate on an inclined wall can be calculated using the equations of hydrostatics.
R = √([tex]F1^2 + F2^2 - 2*F1*F2*cos[/tex])α, where 'R' is the resultant force and 'α' is the angle of the wall.
First, determine the pressure of the water at any given point along the gate. To do this, multiply the density of the water, 'ρ', by the acceleration of gravity, 'g', and then the vertical height of the water relative to the gate, 'h', to get the pressure 'p':
p = ρ*g*h
Second, determine the force acting on the gate. This is done by multiplying the pressure with the area of the gate, 'A':
F = p*A
Finally, find the resultant force, 'R', by adding the forces together and taking into account the angle of the wall:
R = √([tex]F1^2 + F2^2 - 2*F1*F2*cos[/tex])α
where α is the angle of the wall.
By following these steps, you can calculate the resultant force of the water on the semi-circular gate on an inclined wall.
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how to find the minimum thickness of a film such that reflected light undergo constructive interference
The minimum thickness of the film for constructive interference of reflected light would be t = 3*600/(2*1.4) = 850 nm.
The minimum thickness of a film required for constructive interference of reflected light can be calculated using the formula t = m*λ/(2*n),
where t is the minimum thickness of the film, m is the order of interference, λ is the wavelength of the light, and n is the index of refraction of the film.
For example, if the order of interference is 3, the wavelength of the light is 600 nm, and the index of refraction is 1.4,
the minimum thickness of the film for constructive interference of reflected light would be t = 3*600/(2*1.4) = 850 nm.
Constructive interference of reflected light occurs when the phase difference between the two waves is equal to an integral multiple of 2π.
This can be determined using the formula Δφ = (2π*m)/(λ*n), where Δφ is the phase difference, m is the order of interference, λ is the wavelength of the light, and n is the index of refraction of the film.
To achieve constructive interference, the minimum thickness of the film can be determined by ensuring that the phase difference is equal to an integral multiple of 2π.
The minimum thickness of a film required for constructive interference of reflected light can be calculated using the formula t = m*λ/(2*n),
where t is the minimum thickness of the film, m is the order of interference, λ is the wavelength of the light, and n is the index of refraction of the film.
Constructive interference can be achieved by ensuring that the phase difference between the two waves is equal to an integral multiple of 2π.
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two stationary point charges q1 and q2 are shown in the figure along with a sketch of some field linesrepresenting the electric field produced by them. what can you deduce from the sketch?
From the sketch, we can deduce that the two charges q1 and q2 are of opposite signs, as field lines start at the positive charge q1 and end at the negative charge q2. The field lines also indicate that the magnitude of the electric field produced by q1 is larger than that of q2.
Additionally, the field lines show that the electric field lines near the charges are denser, indicating a stronger electric field intensity near the charges. The direction of the electric field points from q1 to q2, which is consistent with the direction of the force that a positive test charge would experience if placed in the field. The field lines also show that the electric field is radial, i.e., the field lines point directly away from or towards each charge in a straight line, which is a characteristic of the electric field produced by a point charge. Finally, the density of the field lines decreases with distance from the charges, indicating that the electric field strength decreases with distance from the charges, following an inverse-square law.Learn more about electric field at: https://brainly.com/question/14372859
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what is the angular momentum of a 0.205 kg k g ball rotating on the end of a thin string in a circle of radius 1.45 m m at an angular speed of 11.6 rad/s r a d / s ?
The angular momentum of the ball rotating on the end of a thin string in a circle of radius 1.45 m m at an angular speed of 11.6 rad/s r a d / s is 6.07 × 10⁻⁶ kg m²/s.
Angular momentum is the quantity of motion that describes the rotation of a body about a fixed axis. It is a vector quantity that is the cross product of the position vector and the momentum vector.
The angular momentum of a 0.205 kg k g ball rotating on the end of a thin string in a circle of radius 1.45 m m at an angular speed of 11.6 rad/s r a d / s can be calculated as follows:
L = IωL = Iω
Here, L is angular momentum,
I is the moment of inertia of the ball, and
ω is the angular velocity of the ball.
The moment of inertia of a uniform sphere can be calculated as follows:
I= (2/5)mr²I = (2/5)mr²
Here, m is the mass of the sphere, and r is the radius of the sphere.
Therefore, the moment of inertia of the ball is given by:
I = (2/5)mr²I = (2/5) × 0.205 × (0.00145)²I = 5.23 × 10⁻⁷ kg m²
Substituting this value into the expression for angular momentum:
L = IωL = 5.23 × 10⁻⁷ × 11.6L = 6.07 × 10⁻⁶ kg m²/s.
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a spherical capacitor has vacuum between its conducting shells and a capacitance of 125 pf . the outer shell has inner radius 9.00 cm . what is the outer radius of the inner shell? express your answer with the appropriate units.
For a spherical capacitor with a capacitance of 125 and a vacuum between its conducting shells, the outer radius of the inner shell is around 5.60 cm.
The capacitance of a spherical capacitor is given by:
C = 4πε₀[(r₁r₂)/(r₂-r₁)]
where C is the capacitance, ε₀ is the electric constant (8.85 x [tex]10^{-12}[/tex] F/m), r₁ is the radius of the inner shell, and r₂ is the radius of the outer shell.
In this case, we know that the capacitance C = 125 pF (picoFarads), r₂ = 9.00 cm, and we want to find r₁.
We can rearrange the equation to solve for r₁:
r₁ = (C × r₂)/(4πε₀ + C)
Substituting the values:
r₁ = (125 x [tex]10^{-12}[/tex] F × 0.09 m) / (4π × 8.85 x [tex]10^{-12}[/tex] F/m + 125 x [tex]10^{-12}[/tex] F)
r₁ ≈ 5.60 cm
Therefore, the outer radius of the inner shell is approximately 5.60 cm.
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when lighted, a 100-watt light bulb operating on a 110-volt household circuit has a resistance closest to
When lighted, a 100-watt light bulb operating on a 110-volt household circuit has a resistance closest to 0.99 ohms.
Resistance refers to the electrical property of a circuit component, such as a light bulb, that resists the flow of electrical current through it.
Ohm's law is a fundamental principle in electrical engineering that relates the resistance, voltage, and wattage in a circuit. It states that the resistance (R) is equal to the voltage (V) divided by the wattage (W).
W = 100 watts, V = 110 volts.
Use Ohm’s law to calculate the resistance (R):
R = V/W = 110/100 = 0.99 ohms.
Therefore, when a 100-watt light bulb is operating on a 110-volt household circuit, its resistance is approximately 0.99 ohms.
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if the sun is located at one focus of earth's elliptical orbit, the earth is at the other focus. question 20 options: true false
an n-type piece of silicon experiences an electric field equal to 0.1v/m. (a) calculate the velocity of electrons and holes in this material
In an n-type piece of silicon, the electric field causes the electrons to accelerate due to the attractive force between the negatively charged electrons and the positively charged electric field. This acceleration causes the electrons to reach a velocity of V = E/μ, where E is the electric field (0.1V/m) and μ is the mobility of electrons in silicon (1350 cm2/V⋅s). Therefore, the velocity of electrons in this material would be equal to 0.1V/m/1350cm2/V⋅s = 0.0741 cm/s.
The holes, on the other hand, experience a repulsive force due to the positive electric field. This causes the holes to decelerate, with a velocity of V = -E/μ. Therefore, the velocity of holes in this material would be equal to -0.1V/m/1350cm2/V⋅s = -0.0741 cm/s.
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in u.s. customary units, air pressure is measured in pounds per square inch. in the metric system, it is measured in pascals, and one pascal is equal to
In the metric system, air pressure is measured in pascals. One pascal is equal to a force of one newton per square meter.
Air pressure can be measured using different units. Pascal is a unit of pressure, defined as one newton per square meter. This unit is named after Blaise Pascal, a French mathematician, physicist, and philosopher who made important contributions to the fields of hydrodynamics and hydrostatics.
In the US customary system, air pressure is measured in pounds per square inch (psi), while in the International System of Units (SI), it is measured in pascals (Pa). The unit psi is used to measure pressure in liquids and gases, and it is defined as the amount of pressure exerted by a force of one pound-force per square inch.
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the intensity of the sound of a television commercial is 10 times greater than the intensity of the television program it follows. by how many decibels does the loudness increase?
The television commercial loudness increases by 10 decibels.
Increase in the Intensity of soundThe decibel (dB) scale is a logarithmic measure of sound intensity. The intensity of a sound is measured in watts per square meter and the decibel scale is a way to express the relative loudness of a sound, compared to a reference level.
A 10 dB increase in intensity is a 10-fold increase in sound power. This means that a sound with an intensity of 10 watts per square meter is 10 times louder than a sound with an intensity of 1 watt per square meter.
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Worked Calculate the number of electrons that a positively charged object gains if its charge decreases by 3,2 x 10-18 C.
The positively charged object gains 20 electrons when its charge decreases by 3.2 x 10^-18 C.
What is Positive Charge?
A positive charge is an electrical property of matter that describes the presence of more positively charged protons than negatively charged electrons in an atom or molecule. In other words, an object with a positive charge has lost one or more electrons, resulting in a net charge that is greater than zero.
We know that the charge on a single electron is 1.602 x 10^-19 C.
To calculate the number of electrons gained by a positively charged object when its charge decreases by 3.2 x 10^-18 C, we can use the formula:
number of electrons = (magnitude of charge lost) / (charge on a single electron)
number of electrons = (3.2 x 10^-18 C) / (1.602 x 10^-19 C)
number of electrons = 20
Therefore, the positively charged object gains 20 electrons when its charge decreases by 3.2 x 10^-18 C.
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2. according to our equations, what should be the relationship between the total current and the currents passing through each resistor? does your data show this relationship
According to Ohm's Law, the relationship between the total current and the currents passing through each resistor is that the total current is equal to the sum of the currents passing through each resistor.
What is Ohm's Law?This can be represented mathematically as I total = I₁ + I₂ + I₃ + ... where I total is the total current and I₁, I₂, I₃, etc. are the currents passing through each resistor.
This relationship is consistent with Kirchhoff's Current Law, which states that the sum of the currents entering and leaving a junction in a circuit must be equal to zero. Therefore, the current flowing through each resistor must add up to the total current in the circuit. Yes, this relationship is observed in data obtained from circuits.
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Please help. Due at Midnight!
The magnitude and direction of the net force on the center charge is 3.929 x 10⁻⁴ N.
What is unit of charge?The unit of charge is the Coulomb (C). It is named after French physicist Charles-Augustin de Coulomb and is defined as the amount of electric charge that flows through a circuit when a current of one ampere flows for one second. One Coulomb is also equivalent to the charge on approximately 6.24 x 10¹⁸ electrons. The Coulomb is one of the seven base SI units (International System of Units) and is used to measure electric charge in physics and engineering.
So, the magnitude of the net force on the center charge is 3.929 x 10⁻⁴ N. Since F12 is directed towards the left, and F23 is directed towards the right, the net force is also directed towards the left. Therefore, the direction of the net force on the center charge is to the left.
According to Coulomb's law to calculate the force exerted by each of the other charges on the center charge, and then add them vectorially.
Let's call the left charge Q1, the center charge Q2, and the right charge Q3.
The force exerted on Q2 by Q1 is given by:
F₁₂ = k * |Q1| * |Q2| / r₁₂²
where k is Coulomb's constant, |Q1| and |Q2| are the magnitudes of the charges, and r₁₂ is the distance between them. Since Q1 is positive and Q2 is negative, the force F₁₂ is attractive and directed towards Q1. Because the distance between them is 2m, we can say:
F₁₂ = 9 x 10⁹ Nm²/C² * |52 x 10⁻⁶ C| * |3.10 x 10⁻⁶ C| / (2m)²
= 3.468 x 10⁻⁴ N (attractive)
The force exerted on Q2 by Q3 is given by:
F₂₃ = k * |Q2| * |Q3| / r₂₃²
where |Q3| is positive, and |Q2| is negative, so the force F23 is repulsive and directed away from Q3. The distance between them is also 2m, so:
F₂₃ = 9 x 10⁹ Nm²/C² * |3.10 x 10⁻⁶ C| * |68 x 10⁻⁶ C| / (2m)²
= 5.383 x 10⁻⁵ N (repulsive)
To find the net force on Q2, we need to add these two forces vectorially. Since they act along the same line, we can simply subtract their magnitudes:
Fnet = |F₁₂| - |F₂₃|
= 3.468 x 10⁻⁴ N - 5.383 x 10⁻⁵N
= 3.929 x 10⁻⁴ N.
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if you hold a 1.85 kg k g package by a light vertical string, what will be the tension in this string when the elevator accelerates as in the previous part?
The tension in the string of a 1.85 kg package held by a light vertical string will depend on the acceleration of the elevator. When the elevator accelerates, the force of acceleration on the package will be equal and opposite to the tension in the string, causing the tension to increase.
The equation for tension in a string is:
Tension = Mass x Acceleration
Therefore, in this case, the tension in the string is equal to 1.85 kg x Acceleration.
If we assume that the acceleration of the elevator is a constant rate, then the tension in the string can be calculated by multiplying the mass of the package by the acceleration of the elevator.
To sum up, the tension in the string of a 1.85 kg package held by a light vertical string will depend on the acceleration of the elevator. If the acceleration of the elevator is a constant rate, then the tension in the string can be calculated by multiplying the mass of the package by the acceleration of the elevator.
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a brick is falling from the roof of a three-story building. how many force vectors would be shown on a free-body diagram? name them
A brick is falling from the roof of three story building then free-body diagram would show only one force vector, which is the force of gravity acting on the brick.
A free-body diagram is used to graphically represent the forces acting on an object. It shows all of the forces acting on an object and can be used to analyze the motion of an object.
A free-body diagram for a falling brick would include two force vectors: Gravity or Weight.
If we consider only the brick and neglect air resistance, then there are two force vectors that would be shown on a free-body diagram of the brick:Force of gravity: The force of gravity, which pulls the brick downwards with a magnitude of its weight. This force is always present and directed downwards towards the center of the Earth. Normal Force: The normal force, which is the force exerted by the roof or any surface in contact with the brick that prevents it from falling through the surface. As the brick is falling, there is no contact force from the roof, so the normal force is zero.So, in this scenario, the free-body diagram would show only one force vector, which is the force of gravity acting on the brick.
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A dog can hear sounds in the range from 15
to 50,000 Hz.
What wavelength corresponds to the lower
cut-off point of the sounds at 20◦C where the
sound speed is 344 m/s?
Answer in units of m.
Explanation:
Speed of sound is 344
The frequency corresponding to the lower cut-off point is the lowest frequency which his 15Hz
F=15Hz
The relationship between the wavelength, speed and frequency is given as
v=fλ
Then,
λ=v/f
λ=v/f
λ=344/15
λ=22.93m
two students sit on a seesaw in a way that makes it balance and not move. when a third person pushes down on one side, that side moves down. what caused the seesaw to move?
The seesaw moved when a third person pushed down on one side. This is because the seesaw is a simple machine that consists of a long plank balanced in the middle with a pivot point that allows it to move up and down.
When the two students sit on the seesaw in a way that makes it balance and not move, they are evenly distributed on each end. However, when the third person pushes down on one side, this distribution of weight becomes unequal, and the seesaw moves in the direction of the heavier side.
The heavier end of the seesaw moves down while the lighter end moves up. This is because the heavier side creates more force, or torque, on the pivot point, causing the seesaw to tilt towards that side.
As a result, the seesaw moves and is no longer in balance.
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a wire with a current of 4 amps is in a magnetic field of 2 tesla. the magnetic field is oriented perpendicular to the wire. what is the magnitude of the force per unit length on the wire?
The magnitude of the force per unit length on the wire carrying a current of 4 amps in a magnetic field of 2 Tesla, oriented perpendicular to the wire will be 8 N/m.
It can be determined using the formula F = BIL,
where F is the force per unit length,
B is the magnetic field,
I is the current and
L is the length of the wire.
For the given data, B = 2 T, I = 4 A, L = 1 meter.
Therefore, F = BIL= 2 T x 4 A x 1 m= 8 N/m. Thus, the magnitude of the force per unit length on the wire is 8 N/m.
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why does it take more energy to convert liquid water to steam than it does to convert ice to liquid water
The water molecules require more energy to be further separated and converted into steam than it does to convert ice to liquid water, because liquid water has a higher specific heat capacity than ice, which means that it requires more energy to raise its temperature.
In order to convert liquid water into steam, the water molecules must absorb a large amount of energy. This energy is used to overcome the strong intermolecular forces of attraction between the water molecules that hold them in their liquid state. This energy is known as the latent heat of vaporization.
In contrast, when ice is converted into liquid water, the energy required is only enough to overcome the weaker intermolecular forces of attraction that hold the ice in its solid state. This energy is known as the latent heat of fusion.
Once the ice has been converted to liquid water, the water molecules require more energy to be further separated and converted into steam than they did to overcome the weaker forces that held them together as a solid ice block. This is because liquid water has a higher specific heat capacity than ice, which means that it requires more energy to raise its temperature.
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calculate the average force on the person if he is stopped by a padded dashboard that compresses an average of 1.00 cm. calculate the average force on the person if he is stopped by an air bag that compresses an average of 15.0 cm.
The average force on the person if they are stopped by an airbag that compresses an average of 15.0 cm is approximately 70,000 N.
To calculate the average force on a person,
Average force = (change in momentum) / (time interval)
Assuming that the person's initial velocity is constant, we can simplify the formula to,
Average force = (mass of the person) x (change in velocity) / (time interval)
Now, let's consider the two scenarios,
Stopped by a padded dashboard that compresses an average of 1.00 cm:
Assuming the person's initial velocity is known and constant, we need to know the time interval it takes for the person to stop after hitting the dashboard. Without this information, we cannot calculate the average force.
Stopped by an airbag that compresses an average of 15.0 cm:
The time interval for an airbag to deploy and cushion the person's impact is typically very short (about 0.03 seconds), so we can assume that the time interval is negligible in this case. Therefore, we can use the simplified formula above.
Let's assume the mass of the person is 70 kg and their initial velocity is 30 m/s. The change in velocity is the final velocity (0 m/s) minus the initial velocity (30 m/s), which is -30 m/s. The negative sign indicates that the person's velocity is decreasing.
Using the formula,
Average force = (mass of the person) x (change in velocity) / (time interval)
= (70 kg) x (-30 m/s) / (0.03 s)
= -70,000 N
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An object in free fall is accelerating downwards, so its velocity is continually increasing. Because of this, its momentum is continually increasing as well, apparently contradicting the principle of conservation of momentum. Which of Newton's laws can we use to show that momentum is actually being conserved for an appropriately defined system?
Momentum may be demonstrated to be conserved for a properly described system using Newton's third law.
Newton's third law may be used to show that momentum is preserved for a system that is adequately defined. The Earth is being drawn towards the item in an equal and opposing force to that of gravity acting on the object while it is in free fall. As a result, the object's momentum is transferred to the Earth, which has a considerably higher mass and is hence more difficult to detect. The system's overall momentum—that of the Earth and the object—remains preserved. An open system like this one allows momentum to be shared with the environment while yet adhering to conservation standards.
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A skydiver of mass 95kg ,before opening his parachute, falls at t1 with V1= 11m/s and at t2 with t2 v2=27m/s; supposing friction is zero, find the distance covered between t1 and t2
The skydiver covered a distance of approximately 94.9 meters before opening his parachute between t1 and t2, assuming no air resistance or friction.
v = final velocity = v2 = 27 m/s
u = initial velocity = v1 = 11 m/s
a = acceleration = g = 9.8 m/[tex]s^2[/tex]
s = (v² - u²) / 2a
s = (27² - 11²) / (2 x 9.8) = 94.9 meters
Resistance measures an item's potential to impede the drift of electrical present-day through it. it's far measured in ohms (Ω). Resistance is decided by way of the bodily residences of an item, along with its dimensions, material, and temperature. while electric-powered present-day flows thru a conductor, it encounters resistance that slows down its float. This resistance is as a result of the collisions among electrons and the atoms inside the conductor.
Resistance can be laid low with changes inside the bodily properties of the conductor, such as duration, cross-sectional region, or temperature. an extended or narrower conductor may have higher resistance, even as a much broader conductor could have decreased resistance. understanding resistance is critical for designing and working electrical circuits. with the aid of controlling the resistance of a circuit, engineers can make sure that the appropriate amount of current flows to electricity the devices linked to it.
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7) you drop a stone down a well that is 9.5 m deep. how long is it before you hear the splash? the speed of sound in air is 343 m/s and air resistance is negligible
If you drop a stone down a well that is 9.5 m deep, it will take approximately 0.028 seconds for you to hear the splash. This is because the speed of sound in air is 343 m/s, and air resistance is negligible.
The question is about finding the time it will take for the sound of the splash to reach the surface of the well. Given data:
Depth of the well = 9.5 m
Speed of sound in air = 343 m/s
We have to find the time it will take for the sound of the splash to reach the surface of the well.
Let's assume that "t" is the time that the sound of the splash takes to reach the surface of the well.
Using the formula:
t = Distance/Speed
Using the above formula, let's find the time it will take for the sound of the splash to reach the surface of the well.
Distance = Depth of the well = 9.5 m
Speed = Speed of sound in air = 343 m/s
So, the time is:
t = Distance/Speed
t = 9.5/343
t = 0.0277 s ≈ 0.028 s
Therefore, the time it will take for the sound of the splash to reach the surface of the well is 0.028 s
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2. how many times a minute does a boat bob up and down on ocean waves that have a wavelength of 36.0 m and a propagation speed of 4.80 m/s?
The boat will bob up and down on ocean waves that have a wavelength of 36.0 m and a propagation speed of 4.80 m/s once every 7.50 seconds.
To solve the given question, we must use the formula:
n= v/f
Where: v is the velocity of the wave (in m/s)f is the frequency of the wave (in Hz)n is the number of cycles per second
Therefore, the frequency of the wave (in Hz) can be calculated by using the formula:
f= v/λ
where: v is the velocity of the wave (in m/s)λ is the wavelength of the wave (in m)
The frequency of the wave is 0.1333 Hz (approx).
Now, the number of cycles per second (n) is: n = v/λ
We can solve for n by dividing the velocity of the wave by the wavelength of the wave.
Therefore,
n= v/λ= (4.80 m/s) / (36.0 m)= 0.1333 Hz
So, the boat bob up and down 0.1333 times a minute on ocean waves that have a wavelength of 36.0 m and a propagation speed of 4.80 m/s.
1 Hz = 60 seconds,
0.1333 Hz = 7.50 seconds.
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magnus has reached the finals of a strength competition. in the first round, he has to pull a city bus as far as he can. one end of a rope is attached to the bus and the other is tied around magnus's waist. if a force gauge placed halfway down the rope reads out a constant 1400 newtons while magnus pulls the bus a distance of 1.55 meters, how much work does the tension force do on magnus? the rope is perfectly horizontal during the pull.
The work done by the tension force on Magnus is 2170 J.
What is work?
Work is the product of the force acting on an object and the distance through which the object moves. In other words, work is accomplished when a force is used to transfer energy to an object, causing the object to move some distance as a result.
The force of 1400 N, Distance of 1.55 meters, and a rope tied around Magnus's waist.
The work done by the tension force on Magnus is the product of the force exerted by the tension force and the distance through which Magnus is moved.
W = Fd
where W = Work done by the tension force on Magnus
F = Force of tension force
= 1400 Nd
= Distance moved by Magnus
= 1.55 m
Substituting these values:
W = 1400 N x 1.55 mW
= 2170 J
Hence, the work done by the tension force on Magnus is 2170 J.
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the cantilevered beam is made of a36 steel and is subjected to the loading shown. determine the displacement at b using the method of superposition. for a36 steel beam, the moment of inertia i
Thus using method of superposition, the total displacement is 0.0276.
A36 steel beam is used Cantilever beam is loaded. The moment of inertia is I. For A36 steel beam, I = 6667 in4 (approx.)As per the method of superposition, the total displacement of the beam at point B is given as follows:δtotal = δP + δWWhere,δP is the displacement of point B due to the point loadδW is the displacement of point B due to the uniformly distributed load.
Considering point load,P = 1500 lb. Distance of the point load from point B = 5 ft. Thus, the moment at point B due to point load can be calculated as follows: MBP = PL = 1500 × 5 = 7500 lb-ft. Similarly, considering uniformly distributed load,W = 200 lb/ft. Thus, the moment at point B due to uniformly distributed load can be calculated as follows:Mbw = (wL2)/12Where,L is the length of the beam= 10 ft
Therefore, Mbw = (200 × 102)/12 = 1667 lb-ft (approx.)Thus, total moment at point B,M = MBP + MBW= 7500 + 1667= 9167 lb-ft. Thus, using the formula for deflection of cantilever beam,δP = (PbL2)/(2EI) = (1500 × 52)/(2 × 29 × 106 × 6667) = 0.0026 inδW = (WbL3)/(3EI) = (200 × 5103)/(3 × 29 × 106 × 6667) = 0.024 in
Therefore, the displacement at point B is 0.0276 in.
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why do the phases of venus show that the solar system is in a heliocentric model instead of a geocentric model?
The phases of Venus show that the solar system is in a heliocentric model instead of a geocentric model because the heliocentric model states that the Sun is at the center of the solar system, while the geocentric model states that Earth is at the center of the universe.
The phases of Venus can only be explained in the heliocentric model because the planet is orbiting the Sun.The phases of Venus are an important piece of evidence supporting the heliocentric model proposed by Nicolaus Copernicus. The geocentric model was the widely accepted model of the universe until the 16th century when Copernicus proposed the heliocentric model, which suggested that the Sun is at the center of the solar system and the Earth and other planets orbit around it.
The phases of Venus show that it orbits the Sun and not the Earth because, as it orbits the Sun, different portions of the planet's sunlit side are visible from Earth. This can only occur in a heliocentric model because Venus is between the Earth and the Sun in its orbit, which causes it to pass through phases. Therefore, the phases of Venus are not consistent with a geocentric model, which suggests that Venus orbits the Earth.
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