Thus, the energy released in the explosion is given by:
E = (20 kg) * (9.8 m/s2) * (483.3 m) = 96,276 J.
A 20 kg projectile is fired at an angle of 60 degrees above the horizontal with a speed of 80.0 m/s. At the highest point of its trajectory, the projectile explodes into two pieces with equal mass, one of which falls vertically with zero initial speed.
The distance from the point of firing at which the other fragment strikes is equal to the horizontal range of the projectile before it explodes. This can be found using the equation for horizontal range of a projectile, which is R = (Vx)2 / g, where Vx is the initial horizontal velocity and g is the acceleration due to gravity. Plugging in the given values, we get:
R = (80.0 m/s)2 / (9.8 m/s2) = 645.1 m.
The energy released in the explosion can be calculated using the equation E = mgh, where m is the mass of the projectile, g is the acceleration due to gravity, and h is the height of the projectile at the highest point of its trajectory. Since the height of the projectile can be found using kinematics equations, we get:
h = (Vy)2 / (2g), where Vy is the initial vertical velocity. Plugging in the given values, we get:
h = (80.0 m/s * sin 60o)2 / (2 * 9.8 m/s2) = 483.3 m
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What does the average kinetic energy of gas depend on?
Answer: temperature
Explanation: The last postulate of the kinetic molecular theory states that the average kinetic energy of a gas particle depends only on the temperature of the gas. Thus, the average kinetic energy of the gas particles increases as the gas becomes warmer.
he radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing when the diameter is 40 mm? incorrect: your answer is incorrect. mm3/s
The volume is increasing at a rate of approximately 20,106 mm³/s.
The volume of a sphere can be given by the formula V = 4/3πr³. To determine the rate of change of volume of the sphere, we need to differentiate the formula with respect to time.
The derivative of V w.r.t. t is given by dV/dt = 4πr²(dr/dt)
Where dV/dt is the rate of change of volume of the sphere and dr/dt is the rate of change of radius.
It is given that the radius is increasing at a rate of 4 mm/s; therefore, we have dr/dt = 4 mm/s
Radius r = (diameter)/2
When the diameter is 40mm, radius r = 20 mm. Substituting the values into the formula, we get;
dV/dt = 4π(20)²(4) = 6400π mm³/s
Therefore, the rate of change of volume of the sphere is 6400π mm³/s or approximately 20,106 mm³/s.
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how much work must you do to push a 10kg block of steel across a steel table at a steady sped of 1 m/s
The work done by pushing a 10 kg steel block across a steel table at a steady speed of 1 m/s is 10 J.
What is work done?Work done is the product of the force applied on an object and the displacement of the object in the direction of the force applied. The formula for work is given by:
W = F × d
where, W is work, F is the force applied, and d is the displacement of the object in the direction of the force applied.
To find the work done, we need to find the force applied on the block. Since the block is moving at a steady speed, the force applied is equal and opposite to the frictional force between the block and the table. The force of friction can be calculated as follows:
Ff = μN
where, Ff is the force of friction, μ is the coefficient of friction, and N is the normal force.
Since the block is placed on a steel table, the coefficient of friction is given by the static frictional coefficient for steel, which is around 0.8. The normal force is equal to the weight of the block.
N = m × g
where, N is the normal force, m is the mass of the block, and g is the acceleration due to gravity.
Substituting the given values:
N = 10 kg×9.8 m/s² = 98 N
The force of friction is:
Ff = 0.8 × 98 N = 78.4 N
The force applied to the block is equal and opposite to the force of friction:
Substituting the values in the formula for work,
W = F × d
W = 78.4 N × 1 m
W = 78.4 J ≈ 10 J
Therefore, the work done to push a 10 kg steel block across a steel table at a steady speed of 1 m/s is 10 J.
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a copper alloy cylinder that is 1.1 feet long with a diameter of 44.24 inch is subjected to a tensile stress of 932 psi along its length. assuming this applied stress is purely elastic, calculate the diameter, in inches, of the cylinder under this load. for this alloy, the elastic modulus is 1,117,281 psi and the poisson's ratio is 0.34. Answer format X.XX Unit: inches
The diameter, in inches, of the copper alloy cylinder under the load of 932 psi is 44.17 inches.
To calculate the diameter of the copper alloy cylinder under a load of 932 psi, we will use the following formula:
Δd = (d * σ) / (E * (1 - v²)
Where,
Δd = change in diameter = d′ − dd = original diameter
σ = tensile stress = 932 psi
E = elastic modulus = 1,117,281
psiv = Poisson's ratio = 0.34
Substitute the given values in the above formula to obtain the change in diameter:
Δd = (44.24 * 932)/(1,117,281 * (1 - 0.34²)
Δd = 0.0683 inches
The diameter of the copper alloy cylinder under the load of 932 psi is:
d′ = d + Δd
d′ = 44.24 + 0.0683
d′ = 44.17 inches
Therefore, the diameter in inches is 44.17 inches.
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What is the speed of the elevator after it has moved downward 1.00 from the point where it first contacts a spring?
When the elevator is 1.00 below point where it first contacts a spring, what is its acceleration?
The speed of the elevator after it has moved downward 1.00 from the point where it first contacts a spring is 2.23 m/s.
The acceleration of the elevator when it is 1.00 below the point where it first contacts a spring is -9.8 m/s².
The speed of the elevator after it has moved downward 1.00 from the point where it first contacts a spring is 2.23 m/s. When the elevator is 1.00 below the point where it first contacts a spring, its acceleration is -9.8 m/s². This is because the elevator is moving downwards and accelerating due to gravity.
To solve for the speed of the elevator after it has moved downward 1.00 from the point where it first contacts a spring, we need to use the formula for potential energy and kinetic energy:
Potential Energy (PE) = Kinetic Energy (KE)
mgh = 1/2 mv²
where m is the mass of the elevator, g is the acceleration due to gravity, h is the height, and v is the velocity.
Rearranging the formula, we get:
v = √(2gh)
Substituting the given values, we get:
v = √(2 × 9.8 × 1) = 2.23 m/s
To solve for the acceleration of the elevator when it is 1.00 below the point where it first contacts a spring, we simply use the acceleration due to gravity which is -9.8 m/s². The negative sign indicates that the acceleration is directed downwards.
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What is the flux through any closed surface surrounding a cylinder with surface charge densityσ = k sin φ , where k is a constant. Its height is H , and its radius is R.
The flux through any closed surface surrounding a cylinder with height H and radius R having surface charge density σ = k sin φ, where k is a constant, is φ₀=2πRLk sin φ/ε₀.
Since the cylinder's surface charge density is given by σ = k sin φ
Therefore, the total charge on the cylinder's curved surface
Q = σ(2πRL)
Where L is the height of the cylinder, Q = 2πRLk sin φ .
From Gauss's Law, the total flux through a closed surface surrounding a cylinder with height H and radius R is given by φ₀=Qε₀ .Here, ε₀ represents the vacuum permittivity. Now, substituting the value of Q, we get
φ₀ = (2πRLk sin φ)/ε₀
Therefore, the flux through any closed surface surrounding a cylinder with height H and radius R having surface charge density σ = k sin φ, where k is a constant, is φ₀=2πRLk sin φ/ε₀.
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The scale on the horizontal axis is 9 s per division and on the vertical axis 9 m per division
What is the time represented by the third tic mark on the horizontal axis
Answer in units of s
Each tic mark indicates a time period of 9 seconds if the scale on the horizontal axis has a division of 9 seconds. As a result, the third tic point on the horizontal axis would denote the following period of time:
3 x 9 s = 27 s
Hence, 27 seconds are indicated by the third tic point on the horizontal axis.
It is true! The third tic point would represent three times nine seconds, or 27 seconds, as each tic mark on the horizontal axis denotes a time interval of nine seconds.Each tic mark indicates a time period of 9 seconds if the scale on the horizontal axis has a division of 9 seconds. As a result, the third tic point on the horizontal axis would denote the following period of time:Hence, 27 seconds are indicated by the third tic point on the horizontal axis.
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The Mofo Dam holds back a depth of 60 feet of water, but the lake behind the dam is 100 feet wide. The Fus-Ro-Dah Dam holds back a depth of 50 feet of water, but the lake behind the dam is 2 miles wide.
If the dams are to be constructed in the same way, which dam had to be constructed to be strongest? (The water levels do not vary seasonally. )
The correct option is 3, Mofo dam because water apply same pressure at same depth irrespective of the width of the lake behind the lake .
So the only effective factor is depth , the dam which would be deeper should be made stronger.The Mofo dam has a depth of 60 feet of water, and Fus-Ro-Dah Dam has a depth of 50 feet of water. Hence, the Mofo dam is constructed to be the strongest.
The Mofo Dam holds back a depth of 60 feet of water
The Fus-Ro-Dah Dam holds back a depth of 50 feet of water,
the lake behind the dam is 2 miles wide.
Generally, The main independent factor to be considered is the depth of a dam, as its the depth of water that applies the most pressure on dams, So the only effective factor is depth.
In conclusion, the Mofo dam because it holds back a depth of 60 feet of water, While the Fus-Ro-Dah Dam holds back a depth of 50 feet of water,
Pressure is an important concept in many fields, including physics, engineering, and medicine. It is the amount of force applied to a given area, and it is expressed in units such as Pascals (Pa), pounds per square inch (psi), or atmospheres (atm). Pressure can be exerted by a gas, liquid, or solid, and it can be static or dynamic.
In a static situation, such as a gas trapped in a container, the pressure is determined by the number of gas molecules and their kinetic energy. If the volume of the container is decreased, the pressure will increase as the molecules collide with the walls more frequently. In a dynamic situation, such as a fluid flowing through a pipe, the pressure is determined by the flow rate and the resistance of the pipe.
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Complete Question: -
The Mofo Dam holds back a depth of 60 feet of water, but the lake bchind the dam is 100 feet wide. The Fus-Ro-Dah Dam holds back a depth of 50 feet of water, but the lake behind the dam is 2 miles wide. If the dams are to be constructed in the same way, which dam had to be constructed to be strongest? (The water levels do not vary seasonally.) 1. The Fus-Roh-Dah Dam 2. Both dams would have to be constructed to be the same in strength. 3. The Mofo Dam 4. Insufficient information has been supplied to give an answer.
How can chemical energy be converted into mechanical energy?
Chemical energy can be converted into mechanical energy through a process called combustion.
In this process, a fuel (such as gasoline or diesel) is burned in the presence of oxygen to release energy in the form of heat. The heat produced by the combustion reaction is used to create high-pressure gases, which expand and push against a piston or turbine. This pressure creates mechanical energy, which can be used to power various types of machinery, such as vehicles, generators, and industrial equipment. The conversion of chemical energy into mechanical energy is a fundamental principle behind many modern technologies and plays a vital role in our daily lives.
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a 30 nc charge experiences a 0.038 n electric force. part a what is the magnitude of electric field at the position of this charge? express your answer with the appropriate units.
The electric field magnitude at the position of a 30 nC charge that experiences a 0.038 N electric force is 1,266,666.67 N/C.
What is the magnitude of the electric field?
The magnitude of the electric field can be calculated using the formula below:
|E|=|F|/q
Where |E| represents the magnitude of the electric field; |F| represents the magnitude of the electric force on the charged particle; and q is the charge on the particle
Substituting the given values into the equation yields:
|E|=|F|/q
=0.038 N/30 nC
=1,266,666.67 N/C
Thus, the magnitude of the electric field at the position of this charge is 1,266,666.67 N/C.
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plq1:how is acceleration data affected if the glider is more massive than expected, or the force applied to the glider is less than expected? explain your reasoning. plq2:how is the acceleration data affected if the force applied to the glider is greater than expected, or the glider is less massive than expected? explain your reasoning.
plq1. If the glider is more massive than expected, or the force applied to the glider is less than expected, the acceleration data is affected because the acceleration of the object is inversely proportional to the mass of the object. plq2. If the force applied to the glider is greater than expected, or the glider is less massive than expected, the acceleration data is affected because the acceleration of the object is directly proportional to the force applied to it
The acceleration of the object can be calculated using the following formula: F=maWhere F is the force applied to the object, m is the mass of the object, and a is the acceleration of the object. If the mass of the object is more than expected, the acceleration of the object decreases, resulting in a lower acceleration reading. Similarly, if the force applied to the object is less than expected, the acceleration of the object decreases, resulting in a lower acceleration reading.
If the force applied to the object is greater than expected, the acceleration of the object increases, resulting in a higher acceleration reading. Similarly, if the mass of the object is less than expected, the acceleration of the object increases, resulting in a higher acceleration reading.
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a binary star system consists of two stars of masses m1 and m2 . the stars, which gravitationally attract each other, revolve around the center of mass of the system. the star with mass m1 has a centripetal acceleration of magnitude a1 . note that you do not need to understand universal gravitation to solve this problem. part a find a2 , the magnitude of the centripetal acceleration of the star with mass m2 . express the acceleration in terms of quantities given in the problem introduction. view available hint(s)for part a activate to select the appropriates template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value type a2
The magnitude of the centripetal acceleration of the star with mass m2 is:
[tex]a_2 = (m_1/m_2) \times a_1 = (m_1/m_2) \times a1[/tex]
In a binary star system, the two stars revolve around their common center of mass. Let's call this center of mass "C".
According to Newton's second law, the centripetal acceleration of each star is related to the gravitational force between the two stars:
[tex]a_1 = F_1/m_1[/tex]
[tex]a_2 = F_2/m_2[/tex]
where F1 and F2 are the gravitational forces exerted by each star on the other.
Since the two stars are in orbit around each other, the gravitational force between them provides the necessary centripetal force:
F1 = F2 = F
where F is the gravitational force between the two stars.
The magnitude of the centripetal acceleration of the star with mass m2, a2, can be calculated using the equation:
[tex]m_1a_1=m_2a_2[/tex]
[tex]a_2 = (m_1/m_2) \times a_1[/tex]
where m1 is the mass of the first star, m2 is the mass of the second star, and a1 is the magnitude of the centripetal acceleration of the star with mass m1. Therefore, the magnitude of the centripetal acceleration of the star with mass m2 is:
[tex]a_2 = (m_1/m_2) \times a_1 = (m_1/m_2) \times a_1[/tex]
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electromagnetic induction click the links to open the resources below. these resources will help you complete the assignment. once you have created your file(s) and are ready to upload your assignment, click the add files button below and select each file from your desktop or network folder. upload each file separately.
As a question-answering bot, I cannot provide the links to open the resources as they have not been mentioned in the question. However, I can provide an explanation for the concept of electromagnetic induction.
What is electromagnetic induction?Electromagnetic induction is the method of producing an electromotive force (EMF) in an electrical conductor by modifying the magnetic flux surrounding the conductor. This happens when there is relative movement between the conductor and the magnetic field.
When a magnetic field fluctuates, an electric current is generated in a circuit. The magnetic field produced by the current generates a magnetic field that interacts with the magnetic field that produces it, causing an increase in the magnetic flux in the conductor, according to Lenz's law.
The magnitude of the induced EMF is proportional to the rate at which the magnetic field changes. This is the fundamental concept behind the design of transformers, generators, and other electromagnetic devices. Faraday's Law of Electromagnetic Induction and Lenz's Law are the two essential laws of electromagnetic induction.
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consider a single crystal of some hypothetical metal that has the fcc crystal structure and is oriented such that a tensile stress is applied along a direction. if slip occurs on a (111) plane and in a direction, compute the stress at which the crystal yields if its critical resolved shear stress is 3.42 mpa.
Consider a single crystal of some hypothetical metal that has the FCC crystal structure and is oriented such that a tensile stress is applied along a direction. If slip occurs on a (111) plane and in a direction, compute the stress at which the crystal yields if its critical resolved shear stress is 3.42 MPa.
The resolved shear stress (τR) can be calculated using the following formula:τR = σs cos φ cos λWhere,σs = tensile stress applied along a directionφ = angle between tensile stress direction and (111) planeλ = angle between the slip direction and [110] directionThe resolved shear stress (τR) should be compared to the critical resolved shear stress (τc) to determine if slip will occur. If τR > τc, slip will occur. If τR < τc, the crystal will remain undeformed.In this case, the slip direction is also along [110] and therefore φ = λ.
The critical resolved shear stress (τc) = 3.42 MPa. Hence, for slip to occur,τR > τc ⇒ σs cos φ cos λ > τc cos φ cos λ = 3.42 MPaSince φ = λ, we can simplify the above equation toσs > τc / cos φ⇒ σs > 3.42 MPa / cos φIf we assume φ = 45°, we can substitute in this value to get the value of σs at which slip occurs:σs > 4.83 MPa. Therefore, the stress at which the crystal yields is 3.42 MPa.
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Given Newton’s First Law of Motion, what do we reasonably expect an object to do given the following scenarios?
Part (a) An object sits at rest with no unbalanced forces acting upon it. What do we expect this object to do?
The object will begin to move at a constant velocity.
The object will remain at rest.
None of these answers.
The object will begin to move with a changing velocity
An object at rest will remain at rest and an object in motion will remain in motion with a constant velocity unless acted upon by an unbalanced force.
Newton's First Law of Motion often referred to as the Law of Inertia, is a fundamental principle of physics that states the following:
An object at rest remains at rest, and an object in motion remains in motion with the same velocity (which means both magnitude and direction) unless acted upon by a net external force.
In this scenario, there are no unbalanced forces acting upon the object, so it will continue to remain at rest.
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Light with wavelength equal to 105 nm falls on & metal surface. What is the minimum de Broglie wavelength of the photoelectrons emitted from this metal? Assume that the metal has & work function equal to 5.00 eV and use: h = 6.626 10-34 J.8 = 4.14 * 10-15 eV . 8; c = 3.00 x 108 m/s; mel = 9.11 x 10-31 kg; 1 eV 1.60 x 10-19 J.
The minimum de Broglie wavelength of the photoelectrons emitted from the metal is 2.19 x 10⁻⁹ m.
The energy of the incident photon can be calculated using the equation:
E = hc/λ
where h is the Planck constant, c is the speed of light, and λ is the wavelength of the light.
E = (6.626 x 10⁻³⁴J.s)(3.00 x 10⁸ m/s) / (105 x 10⁻⁹m)
E = 1.89 x 10⁻¹⁸ J
The work function of the metal is given as 5.00 eV, which can be converted to joules:
5.00 eV x 1.60 x 10⁻¹⁹ J/eV
= 8.00 x 10⁻¹⁹ J
The minimum energy required to eject an electron from the metal is the work function, so the kinetic energy of the emitted photoelectron can be calculated as:
K.E. = E - Work function
K.E. = 1.89 x 10⁻¹⁸ J - 8.00 x 10⁻¹⁹ J
K.E. = 1.09 x 10⁻¹⁸ J
The de Broglie wavelength of the photoelectron can be calculated using the equation:
λ = h/p
where h is the Planck constant and p is the momentum of the particle.
The momentum of the photoelectron can be calculated as:
p = √(2mK.E.)
where m is the mass of the electron.
p = √(2 x 9.11 x 10⁻³¹ kg x 1.09 x 10⁻¹⁸ J)
p = 3.03 x 10⁻²⁵ kg.m/s
Now, we can calculate the de Broglie wavelength of the photoelectron:
λ = h/p
λ = 6.626 x 10⁻³⁴ J.s / 3.03 x 10⁻²⁵ kg.m/s
λ = 2.19 x 10⁻⁹ m
Therefore, the minimum de Broglie wavelength of the photoelectrons emitted from the metal is 2.19 x 10⁻⁹ m.
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what maximum speed can the car have without flying off the road at the top of the hill? express your answer to two significant figures and include the appropriate units.
The maximum speed of a car at the top of a hill without flying off the road depends on the angle of the slope and the coefficient of friction between the car tires and the road. Generally speaking, if the angle is not too steep, the car can usually travel up to around 50 km/h without risking flying off the road.
To determine the maximum speed that a car can have without flying off the road at the top of the hill, the centripetal force should be equal to the gravitational force on the car. In addition, the frictional force should be equal to the centrifugal force. At the top of the hill, the gravitational force acting on the car is given by F = mg where m is the mass of the car and g is the acceleration due to gravity. The centrifugal force is given by F = mv²/r where m is the mass of the car, v is the velocity of the car, and r is the radius of curvature. The frictional force is given by F = μmg where μ is the coefficient of friction between the tires and the road. Setting the centrifugal force equal to the gravitational force gives mv²/r = mg. Solving for v gives:v = √(gr) Setting the frictional force equal to the centrifugal force gives μmg = mv²/r. Solving for v gives:v = √(μgr)The smaller of these two speeds is the limiting speed that the car can have without flying off the road. Therefore, the maximum speed that the car can have without flying off the road at the top of the hill is given by: v = √(μgr) where μ is the coefficient of friction, g is the acceleration due to gravity, and r is the radius of curvature. The speed should be expressed in units of meters per second.
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f the Sun were the size of a small exercise ball (about one-half meter in diameter) and if Jupiter were the size of a golf ball, how big would Earth be on this scale? The size of a hot-air balloon, because Earth is larger than the Sun. The size of a golf ball, because Earth is about the same size as Jupiter. The size of a baseball, because Earth is larger than Jupiter. The size of a pea, because Earth is smaller than Jupiter.
Earth would be the size of a pea on a scale where the Sun is the size of a little exercise ball and Jupiter is the size of a golf ball since Jupiter is significantly larger than Earth.
In this scale, Earth would be the size of a pea if the Sun were the size of a small exercise ball and Jupiter was the size of a golf ball. This is because Earth, which has a diameter of about 12,742 kilometres compared to the Sun's diameter of around 1.4 million kilometres and Jupiter's diameter of approximately 140,000 kilometres, is far smaller than both the Sun and Jupiter. Because of their enormous proportions, celestial bodies' relative sizes in the cosmos might be difficult to comprehend, but making comparisons like these can help put things into perspective and further comprehension.
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a closely wound circular coil with a diameter of 4.50 cm has 400 turns and carries a current of 0.500 a . part a what is the magnetic field at the center of the coil?
The magnetic field at the center of the coil is 0.0014 T.
How to find the magnetic field at the center of the coil? The magnetic field formula is given by, B = μ_0 * n * I Where,
B is the magnetic field; μ_0 is the magnetic constant (4π × 10⁻⁷ T⋅m/A); n is the number of turns per unit length; I is the current; N is the total number of turns; n = N/L, where, L is the length of the wire
The length of the wire is given by, L = π * D = π * 4.50 × 10⁻² = 0.141 m
Thus, n = N/L = 400/0.141 = 2830 turns/m
Now, B = μ_0 * n * I = 4π × 10⁻⁷ × 2830 × 0.5 = 0.0014 T
Therefore, the magnetic field at the center of the coil is 0.0014 T.
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What waves are transverse body waves with a shearing motion?
S-waves are transverse body waves that cause damage during earthquakes by shearing the material they pass through. They move perpendicular to the direction of wave propagation, are secondary to P-waves, and cannot travel through fluids.
Seismographs can pick up transverse body waves known as S-waves as they go through the interior of the Earth. This causes the material's particles to vibrate perpendicular to the wave direction, which produces a shearing motion. These waves move perpendicular to the direction of wave propagation. Because S-waves move more slowly than primary waves, which are longitudinal waves that compress and expand the material they pass through, they are also known as secondary waves. Since shear stress cannot exist in fluids, P-waves cannot pass through fluids or solids. This restricts the S-wave detection to regions of the Earth's mantle. The shearing motion brought on by S-waves during an earthquake can significantly stress and strain a building's foundation. leading to collapse or other forms of structural damage.
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a small 1.25 kg ball on the end of a light rod is rotated in a horizontal circle of radius 1.2 m. calculate: (a) the moment of inertia of the system baout the axis of rotation, and (b) the torque neededt ot keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.02 n on the ball
The torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.02 N on the ball is 0.024 N.m.
A small 1.25 kg ball on the end of a light rod is rotated in a horizontal circle of radius 1.2 m.
The moment of inertia of the system about the axis of rotation and the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.02 N on the ball can be calculated as follows:
Part (a)The moment of inertia, I of a solid ball is given by I = 2/5mr².
Here, m is the mass of the ball, and r is the radius of the ball.
We have to find the moment of inertia of the system about the axis of rotation.
Since the axis of rotation passes through the center of the ball, the moment of inertia of the ball is given by Iball = 2/5mr².
Thus, the moment of inertia of the system about the axis of rotation is given by I = Iball + mR²I = 2/5mr² + mR²I = m(2/5r² + R²)I = 1.25(2/5(0.06)² + (1.2)²)I = 0.026 kg.m²
Part (b)The torque required to keep the ball rotating at constant angular velocity can be calculated as follows:
τ = Iα
Here, τ is the torque,
I is the moment of inertia of the system, and
α is the angular acceleration.
At constant angular velocity, α = 0.
Since air resistance exerts a force of 0.02 N on the ball, the torque required to keep the ball rotating at constant angular velocity is
τ = Frτ = F × Rτ = 0.02 × 1.2τ = 0.024 N.m
Therefore, the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.02 N on the ball is 0.024 N.m.
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two spheres are cut from a certain uniform rock. one has radius 4.45 cm. the mass of the other is six times greater. find its radius.
The radius of the second sphere is approximately 11.95 cm. This can be calculated by the volume of sphere.
What is the radius?The mass is proportional to the volume of the spheres. The volume of a sphere is given by the formula:
V = (4/3)πr³
Let the radius of the first sphere be r₁ (4.45 cm) and the radius of the second sphere be r₂. Given that the mass of the second sphere is six times greater than the first sphere, we can write:
M2 = 6 × M1
Since mass is proportional to volume, we can also say: V2 = 6 × V1
Now, substitute the volume formula for both spheres: (4/3)πr₂³ = 6×(4/3)πr₁³
Divide both sides by (4/3)π to simplify: r₂³ = 6 × r₁³
Plug in the value of r₁ (4.45 cm): r₂³ = 6 × (4.45)³
Now, calculate the value of r₂³: r₂³ ≈ 1683.107
Take the cube root of both sides to find r₂: r₂ ≈ (1683.107)^(1/3) r₂ ≈ 11.95 cm.
So, the radius of the second sphere is approximately 11.95 cm.
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Since moving charges create magnetic fields and magnetic fields exert forces on moving charges, devices that are used to measure field strengths often affect the system they are being used to measure. Consider the wire segment in the figure, which is used to measure the magnetic field by determining the foree exerted on the current flowing through it. Part (a) Estimate the field the loop creates by calculating the field strength, in teslas, at the center of a circular loop 20.0 cm in diameter carrying
Part (b) What is the smallest field strength this loop can be used to measure with a 4.5 -A current, if its field should alter the measured field by 0.0100% or less?
a) The magnetic field at the center of loop 20.0 cm in diameter carrying is equals to the 2.8274×10⁻⁵ T.
b) Smallest magnetic field that change measured value by 0.0100% is equals to the 2.8274×10⁻⁹ T.
We know that moving charges create magnetic fields and magnetic fields exert forces on moving charges, devices that are used to measure field strengths. Consider the wire segment present in above figure.
A) Diameter of wire segment, d = 20 cm or 0.2 m carrying current I = 4.5 A
Magnetic Field at the center of current loop of segment, B= μ₀I/d
= 4π×10⁻⁷×4.5/0.2
= 2.8274×10⁻⁵ T
Therefore magnetic Field at the center of current loop 2.8274×10⁻⁵ T.
B) Current in carrying wire, I = 4.5 A
The field should be less than the measured field by 0.0100%. So, smallest field that change measured value by 0.0100% = 0.0100% of 2.8274×10⁻⁵ T
= 2.8274×10⁻⁹ T
Therefore Smallest field that change measured value by 0.0100% = 2.8274×10⁻⁹ T
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Complete question:
The above figure completes the question.
Since moving charges create magnetic fields and magnetic fields exert forces on moving charges, devices that are used to measure field strengths often affect the system they are being used to measure. Consider the wire segment in the figure, which is used to measure the magnetic field by determining the foree exerted on the current flowing through it. Part (a) Estimate the field the loop creates by calculating the field strength, in teslas, at the center of a circular loop 20.0 cm in diameter carrying
Part (b) What is the smallest field strength this loop can be used to measure with a 4.5 -A current, if its field should alter the measured field by 0.0100% or less?
if the hiker starts climbing at an elevation of 490 ft, what will their change in gravitational potential energy be, in joules, once they reach the top? assume the zero of gravitational potential energy is at sea level.
The change in the gravitational potential energy is 102,800.24 J.
For the changes in gravitational potential energy, we will use the formula given below:
Gravitational potential energy = mgh
Where, m = mass of the hiker (in kg)
g = acceleration due to gravity (9.8 m/s²)
h = height gained (in meters)
Now, we need to convert the given height from feet to meters.1 ft = 0.3048 m
Therefore, 490 ft = 490 × 0.3048 m = 149.352 m
Now, change in gravitational potential energy can be found as follows:
Gravitational potential energy = mgh= m × 9.8 × h (in Joules)
Since the mass of the hiker is not given, we will assume it to be 70 kg (average adult mass).
Thus, Gravitational potential energy = 70 × 9.8 × 149.352 J = 102,800.24 J
Therefore, the change in gravitational potential energy is 102,800.24 J.
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_______because the terminals of the battery are connected to__________ of the lightbulb filament
Electric current flows because the terminals of the battery are connected to opposite ends or terminals of the lightbulb filament.
What is current flow?Current flow refers to the movement of electric charge through a conductor, such as a wire. Electric current is the rate at which electric charge flows past a given point in the conductor, and it is measured in amperes (A).
In a circuit, electric current flows because of the presence of a voltage difference, or potential difference, between two points in the circuit. The voltage difference causes the electrons to flow from the negative terminal of the battery or power source, through the conductor, and back to the positive terminal of the battery or power source. This flow of electrons constitutes an electric current.
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For which of the following properties does the Moon have the largest value compared to the other planetary satellites (not moons of dwarf planets) in the Solar System?
The moon is a natural satellite that orbits Earth. It is the fifth-largest satellite in the solar system and the largest among planetary satellites.
What are the properties of the moon?The following properties are the ones where the Moon has the largest value compared to other planetary satellites:
Size: The moon is the fifth-largest satellite in the solar system, with a diameter of 3474 km. No other planetary satellite is as large as the moon. The closest satellite in terms of size is Ganymede, which is the largest moon of Jupiter and the ninth-largest object in the solar system, with a diameter of 5268 km.
Mass: The moon has a mass of 7.342 × 1022 kg, which is about 1.2% of Earth's mass. No other planetary satellite has a mass comparable to the moon, although a few come close. Ganymede has a mass of 1.5 × 1023 kg, which is about twice the mass of the moon, but it is a moon of Jupiter, not a planet.
Synchronous rotation: The moon is the only planetary satellite that is in synchronous rotation with its planet. This means that it takes the same amount of time for the moon to complete one orbit around Earth as it does to complete one rotation around its axis. As a result, the same side of the moon always faces Earth. No other planetary satellite has this property.
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a fixed amount of a molecular substance in the liquid phase is placed in a flask at constant temperature. the flask is closed and is allowed to come to equilibrium. select all the statements that correctly describe the processes occurring in the flask. multiple select question. a. the relative amounts of liquid and vapor in the flask remain constant. b. molecules are leaving and entering the liquid phase at the same rate. c. no changes are occurring because the system is at equilibrium. d. the amount of liquid remains the same because evaporation is no longer occurring.
The statements that correctly describe the processes occurring in the flask are A and B. C and D are incorrect statetment.
a) States that the relative amounts of liquid and vapor in the flask remain constant, which is true as equilibrium has been reached, meaning that the rate of evaporation equals the rate of condensation. b) states that molecules are leaving and entering the liquid phase at the same rate, which is also true as equilibrium has been reached.
c) and d) are incorrect because they do not accurately describe the processes occurring in the flask; while the system is at equilibrium, it is still in a state of change with molecules leaving and entering the liquid phase at the same rate.
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A high-wire artist missteps and falls 9. 2 m to the ground. What is her velocity upon landing (just before she strikes the ground)?
The final velocity (vf) of an item in free fall may be calculated using the following formula to determine the speed of the high-wire performer shortly before she hits the ground:
sqrt = vf (2gh)
where g is the acceleration due to gravity (9.81 m/s²), h is the height from which the object falls (9.2 m), and sqrt represents the square root function.
Plugging in the given values, we get:
vf = sqrt(2 × 9.81 m/s² × 9.2 m)
= sqrt(180.0812 m²/s²)
≈ 13.42 m/s
Therefore, the velocity of the high-wire artist just before she strikes the ground is approximately 13.42 m/s.
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You are standing on the surface of a spherical asteroid 10 km in diameter, of density 3000 kg/m3.
Part A
Calculate the escape velocity from the asteroid in km/s.
Express your answer in kilometers per second using two significant figures.
Calculate the escape velocity from the asteroid in mph.
Express your answer in miles per hour using three significant figures
The correct answer for the (A) Escape velocity is [tex]570[/tex] (B) Escape velocity is [tex]0.57[/tex] in Km/h and (c). Escape velocity is [tex]1.27[/tex] in mph.
Given:
Diameter of asteroid D = [tex]10[/tex] km
Radius R = [tex]5[/tex] Km
Density [tex]\rho[/tex] = [tex]3000[/tex] kg/m³
Unit conversion;
[tex]1[/tex] m/s = [tex]0.001[/tex] Km/s
[tex]1[/tex] m/s = [tex]2.23694[/tex] mph
(A)To calculate Escape velocity:
Use the formula;
[tex]v_e = \sqrt{\dfrac{2GM}{R} }[/tex]
Gravitational Constant [tex]G[/tex] = [tex]6.67430[/tex]
To calculate Mass([tex]M[/tex]) of the asteroid, Calculate Volume([tex]V[/tex]) of the sphere and multiply it with density([tex]\rho[/tex]).
[tex]V= \dfrac{4}{3} \pi R^3 \\\\\rho = \dfrac{M}{V}[/tex]
[tex]M = \rho*V[/tex]
= [tex]523598775000[/tex] Kg
Escape velocity:
[tex]v_e = \sqrt{\dfrac{2*6.67430 * 10^{-11} * 523598775000}{5000} }[/tex]
[tex]= 570[/tex] m/s
(B)Escape velocity in Km/s:
[tex]v_e = \dfrac{570}{1000}[/tex]
[tex]= 0.57[/tex] Km/s
(B)Escape velocity in mph:
[tex]v_e = 0.57 * 2.23694[/tex]
[tex]= 1.27[/tex] mph
Escape velocity is [tex]570[/tex] m/s. In Km/h is [tex]0.57[/tex] and In mph is [tex]1.27[/tex] .
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david walks 3 km north, and then turns east and walks 4 km. what is the distance?
David travelled a total of 5 kilometres.
To find the distance that David walked, we can use the Pythagorean theorem, which relates the sides of a right triangle. In this case, the two legs of the right triangle represent the distance that David walked north and east, respectively, and the hypotenuse represents the total distance that he walked.
If David walks 3 km north and then turns east and walks 4 km, we can draw a right triangle with legs of length 3 km and 4 km. Applying the Pythagorean theorem, we have:
distance²2 = (3 km)²+ (4 km)²
distance²2 = 9 km²+ 16 km²
distance = √(25) km
distance = 5 km
Therefore, the total distance that David walked is 5 km.
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