The damping ratio of the system can be calculated as 0.13.
What is displacement?
Displacement at resonance, Xn = 0.6 inches
Displacement at very high RPM, Xv = 0.15 inches
Natural frequency of a system is:
f = (1/2π) * √(k/m)
where k is the stiffness of the system and m is its mass.
Let's assume the mass of the system as m and k is the stiffness of the system.
When the motor is at resonance, the frequency of the system is: n = f
where n is the frequency of the system.
When the motor is running at very high rpm, the frequency of the system is given as:v = f
where v is the frequency of the system.
Now, let's assume the damping coefficient of the system as c.
The displacement of the system:
X = [Xn * exp(-ζωnt)] * sin(ωdt)
where X is the displacement of the system, ζ is the damping ratio of the system, ωn is the natural frequency of the system and ωd is the frequency of the applied force.
The maximum value of the displacement is:
Xmax = Xn / (2ζ * √(1 - ζ²))
Here, Xmax = 0.6 inches when the motor is at resonance Xmax = 0.15 inches
when the motor is running at very high RPM, putting the given values of Xmax in the above equation, we can find the value of the damping ratio, ζ.
For resonance:0.6 = Xn / (2ζ * √(1 - ζ²))
=> 2ζ * √(1 - ζ²)
= Xn / 0.6=> 4ζ² * (1 - ζ²)
= Xn² / 0.36=> 4ζ⁴ - 4ζ² + 0.26244
= 0
Solving this quadratic equation gives us the value of ζ as 0.32.
For high RPM:
0.15 = Xn / (2ζ * √(1 - ζ²))
=> 2ζ * √(1 - ζ²)
= Xn / 0.15=> 4ζ² * (1 - ζ²)
= Xn² / 0.0225
=> 4ζ⁴ - 4ζ² + 1.728 = 0
Solving this quadratic equation gives us the value of ζ as 0.13.
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Which of Newton's laws explains why your hands get red when you press them hard against a wall?
O A.
Newton's law of gravity
O B.
Newton's first law of motion
O C.
Newton's second law of motion
O D.
Newton's third law of motion
a series circuit is a current divider and a parallel circuit is a voltage divider circuit. select one: a. true b. false
The given statement " A series circuit is a current divider and a parallel circuit is a voltage divider circuit " is True
In a series circuit, the electric current is the same through each component, and the total current is equal to the sum of the currents through each component. Therefore, the current is divided among the components.
In a parallel circuit, the potential voltage across each component is the same, and the total voltage is equal to the sum of the voltages across each component. Therefore, the voltage is divided among the components.
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4. what is the name of the region where the most common type of comets, long period comets, come from, and how many of these objects exist?
The region where most long period comets come from is called the Oort Cloud and it is estimated that it contains up to 2 trillion comets.
The region where most long period comets originate is known as the Oort Cloud. The Oort Cloud is a vast spherical region surrounding the Sun located roughly halfway between the orbits of Neptune and Proxima Centauri. It is estimated to contain up to two trillion icy objects, which are leftovers from the formation of the solar system. Long period comets, which take longer than 200 years to orbit the Sun, originate from the Oort Cloud and make their way towards the inner solar system. They are usually only visible when they come close enough to the Sun to be warmed and shed dust and gas, which form the visible tail of the comet. As they come closer to the Sun, the gravitational attraction of the planets often deflects their orbits and causes them to return to the Oort Cloud for millions of years before repeating the cycle.
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a net force of 89.0 n propels a 4.00-kg model rocket. after being launched from rest, how fast is the rocket traveling after 2.00 s? enter the numerical value in si units.
A net force of 89.0 n propels a 4.00-kg model rocket. after being launched from the rest, the rocket will be traveling at: a velocity of 44.5 m/s.
The net force of 89.0 N propels a 4.00-kg model rocket. After being launched from rest, the rocket will have an acceleration of 89.0 N/4.00-kg = 22.25 m/s².
After 2.00 seconds, the rocket's velocity will be 2.00s x 22.25m/s² = 44.5 m/s. Therefore, after 2.00 s, the rocket will be traveling at a velocity of 44.5 m/s.
To calculate this, we first need to know the net force of the rocket. This is equal to the thrust of the rocket (F = ma) multiplied by the mass of the rocket (m = 4.00 kg). We can then use this net force to calculate the acceleration of the rocket, which is equal to
F/m = 89.0 N/4.00 kg = 22.25 m/s².
Now that we know the acceleration of the rocket, we can use this to calculate the velocity of the rocket after 2.00 s. To do this, we multiply the acceleration by the time, which in this case is 2.00 s. This gives us an initial velocity of 2.00s x 22.25m/s² = 44.5m/s.
This means that after 2.00 s, the rocket will be traveling at a velocity of 44.5 m/s.
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an incompressible substance with a density of 1000 kg/m3 is isothermally compressed from 100 to 1000 kpa. determine the change in enthalpy. multiple choice question. 900 kj/kg 0 kj/kg 10 kj/kg 0.9 kj/kg
The change in enthalpy is 0 J/kg if the incompressible substance with a density of 1000 kg/m3 is isothermally compressed from 100 to 1000 kpa. Thus, option b is correct.
The given data is as follows:
The density of substance = 1000 kg/m3
In-compression pressure = 100 to 1000 kph
The given substance is incompressible. So its specific volume stays constant during the process. The work done is Zero.
Assuming that the process is Isothermal, the temperature remains steady.
The change in enthalpy is calculated by using the formula:
ΔH = m × C × ΔT
The density of mass is calculated by using the formula,
m = V × ρ = 1 m3 × 1000 kg/m3
m = 1000 kg
Change in enthalpy is calculated as:
ΔH = m × C × ΔT
ΔH = 1000 kg × 0 J/(kg·K) × 0 K
ΔH = 0 J/kg
Therefore we can conclude that the change in enthalpy is 0 J/kg.
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The complete question is-
an incompressible substance with a density of 1000 kg/m3 is isothermally compressed from 100 to 1000 kph. determine the change in enthalpy. multiple choice questions.
a.900 kj/kg
b. 0 kj/kg
c.10 kj/kg
d.0.9 kj/kg
what is the acceleration on a body that approached the arth and comes within 6 earth radii of the earth's surface
The acceleration on a body that approaches the Earth and comes within 6 Earth radii of the Earth's surface is known as the "gravitational acceleration."
This is caused by the gravitational pull of the Earth, which increases as the body approaches the Earth's surface. The acceleration is given by the equation a = GM/r², where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth. For a body that comes within 6 Earth radii of the Earth's surface, the acceleration would be equal to GM/36, where G is the gravitational constant and M is the mass of the Earth. This acceleration can be used to calculate the velocity of the body and its trajectory around the Earth.
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if the moon enters its waxing crescent phase tonight, then what lunar phase will you see in approximately two weeks? multiple choice question.
If the moon enters its waxing crescent phase tonight, then you will see the First Quarter lunar phase in approximately two weeks.
What is the lunar phase?
The Moon is in a specific position during a lunar phase. During the lunar phase cycle, it passes through four primary phases: the new moon, the first quarter, the full moon, and the last quarter. In the new moon phase, the Moon is between the Sun and Earth, and the side of the Moon visible to us is dark.
In contrast, in the full moon phase, the Moon is on the opposite side of the Earth from the Sun, and the side visible to us is entirely illuminated. The first quarter moon is half illuminated and half in shadow, with the illuminated portion appearing as a semi-circle.
The last quarter moon is also half illuminated and half in shadow, but the illuminated portion appears in the opposite direction from the first quarter moon. If the moon enters its waxing crescent phase tonight, you will see the first quarter lunar phase in approximately two weeks. This phase is also known as a half moon, and it occurs when the moon is one-quarter of the way through its orbit around the Earth.
During the first quarter, the illuminated portion of the moon increases each day, until it reaches the full moon phase.
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Why a liquid needs a container when a solid does not?
The correct option is B, a liquid needs a container when a solid does not Solids have definite shapes, and liquids fill their containers.
Solids are one of the three fundamental states of matter, along with liquids and gases. In a solid, the molecules are tightly packed together, and the substance maintains a fixed shape and volume. The particles in a solid are held together by strong intermolecular forces, which prevent them from moving freely.
Solids have many properties that distinguish them from other states of matter. For example, they are usually denser and more rigid than liquids and gases. Solids can also be classified into different types based on their internal structure, such as crystalline solids, which have a regular and repeating pattern of atoms, and amorphous solids, which lack a definite long-range structure.
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Complete Question: -
Which best describes why a liquid needs a container when a solid does not?
A. Solids fill their containers, and liquids have definite shapes.
B. Solids have definite shapes, and liquids fill their containers.
C. Solids particles do not expand to fill their containers, and liquid particles do.
D. Solids particles expand to fill their containers, and liquid particles do not.
a planet of mass 4 x 10^14 kg is orbiting a parent star 548 km away. if the star is 83 times the mass of the planet, what speed must the planet have to keep a perfectly circular orbit around the star?
To find the speed of the planet in a perfectly circular orbit around the star, we can use the equation v = sqrt(Gm2 / r). Plugging in the given values, we get v = 1843.3 m/s. Therefore, the planet must have a speed of approximately 1843.3 m/s.
What Enlightenment idea is represented by the headline
The headline "Enlightenment ideas of freedom, equality, and justice for all" represents the idea of the Enlightenment that human beings are rational, capable of determining right from wrong, and deserving of rights and freedoms, such as freedom of speech, freedom of religion, and equality before the law.
These ideas were a major factor in the shift away from absolute monarchies, and towards governments of the people, by the people, and for the people. The Enlightenment period also saw the development of democracy and of the rule of law, where the government is subject to a set of laws, rather than relying on the whims of the ruler. Enlightenment thinkers sought to empower the individual, giving people the freedom to think and act as they pleased, rather than relying on the decisions of rulers.
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a new block of mass m is used. this block is made of a material that makes an elastic collision with the rod when the block and rod collide. will the hiehgt h increase, decrease, or stay the same?
The height h will stay the same when a new block of mass m is used and makes an elastic collision.
Thus, the correct answer is to stay the same.
What is an elastic collision?An elastic collision is a type of collision in which the total kinetic energy of two or more bodies involved in the collision is conserved. In this collision, the colliding bodies return to their initial state before the collision. That is, the total momentum and kinetic energy are conserved.
As a result, the initial and final energies of the system remain the same, implying that the height of the rod will stay the same as before. So, the height h will stay the same.
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if it takes 1 joule of work to move an object a distance of 1 meter with a force of 1 newton in 10 seconds, what should we expect about the amount of work required to move the same object the same distance but in 10 years
The amount of work required to move the same object the same distance but in 10 years will be the same as before is 1 Joule.
It is known that Work = Force x Distance. So, if it takes 1 Joule of work to move an object a distance of 1 meter with a force of 1 Newton in 10 seconds, we can find the force applied on the object.
The formula for force is:
F = m x a, where m is mass and a is acceleration
F = ma1 N = 1 kg x a
Thus, a = 1 m/s².
Now, we have:
F = 1 N, a = 1 m/s² and d = 1 m.
Putting all values in the formula for work done, we have:
W = F x d
W = 1 N x 1 m
W = 1 J
Thus, the work done to move the object is 1 Joule.
Now, if the object moves the same distance but in 10 years, it would make no difference to the work done. This is because work is calculated using force and distance only, and time does not matter here. Therefore, we can expect the same amount of work required to move the object the same distance.
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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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TRUE/FALSE. when air masses of different densities collide, the less dense air mass is forced to rise through frontal lifting.
TRUE. When air masses of different densities collide, the less dense air mass is forced to rise through frontal lifting.
In meteorology, a front is a transition area between two air masses of different densities. The atmosphere's temperature, moisture content, and wind direction are all influenced by these air masses. The types of fronts are warm, cold, stationary, and occluded fronts. The front types are determined by the characteristics of the air masses and the direction of their movement. The types of the front are Warm front: When a warm air mass replaces a cold air mass, it is called a warm front. Warm fronts typically move more slowly than cold fronts. Cold front: A cold front happens when a cold air mass replaces a warm air mass. They have steeper pressure gradients than warm fronts, and they travel faster. Rain, thunderstorms, and cold temperatures are all common with this type of front. Stationary front: This occurs when two air masses meet and neither advances. There is a lot of rain along the stationary front. Occluded front: This is a type of front that develops when a cold front overtakes a warm front. When the cool air catches up to the warm air, an occluded front forms. The fronts can cause precipitation to fall.
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Explain why the transverse pulse traveling on a rope held by two people reflects in the opposite orientation each time it reaches a person.
Drag the terms on the left to the appropriate blanks on the right to complete the sentences. ANSWER: - greater - oppose - second law - increase - smaller - the same
- third law - first law
When a transverse wave pulse reaches a fixed end of the rope, the displacement of the rope end exerts a force on the object that is keeping the end fixed (in this case, a person). By Newton's ___ the person must exert a force of __ magnitude in ___ direction; otherwise the end of the rope would not remain stationary but would the opposite accelerate in the direction of the force due to the wave disturbance. Because this force acts to ___ the force of the incoming wave pulse, it initiates an outgoing wave pulse that is inverted with respect to the incoming wave pulse.
To complete the given sentences explaining why the transverse pulse traveling on a rope held by two people reflects in the opposite orientation each time it reaches a person order of the words used is third law, the same, oppose, increase.
When a transverse wave pulse reaches a fixed end of the rope, the displacement of the rope end exerts a force on the object that is keeping the end fixed (in this case, a person). By Newton's third law, the person must exert a force of the same magnitude in oppose direction; otherwise, the end of the rope would not remain stationary but would accelerate in the direction of the force due to the wave disturbance. Because this force acts to increase the force of the incoming wave pulse, it initiates an outgoing wave pulse that is inverted with respect to the incoming wave pulse.
When a transverse pulse traveling on a rope held by two people reaches one of the people, the pulse is reflected in the opposite orientation. This happens because of the interaction between the pulse and the person holding the rope.
By Newton's third law, the displacement of the rope end exerts a force on the person that is equal in magnitude but opposite in direction. If the person did not exert an equal and opposite force, the end of the rope would not remain stationary but would instead accelerate in the direction of the force due to the wave disturbance.
The force exerted by the person opposes the force of the incoming wave pulse, initiating an outgoing wave pulse that is inverted with respect to the incoming wave pulse. This happens due to the conservation of energy and momentum, which are described by Newton's first and second laws. The outgoing pulse has a smaller amplitude than the incoming pulse because some energy is lost in the reflection process.
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if you turn on your car headlights during the day, the road ahead of you doesn't appear to get brighter. why not?
If you turn on your car headlights during the day, the road ahead of you doesn't appear to get brighter.
This is because, during the day, the brightness from the sun overwhelms any additional light that would be provided by the headlights. When you turn on your headlights, they produce light that is visible, but during the day, the sun is brighter than the headlights, so the light from the headlights is not sufficient to make the road appear brighter. Besides, the headlights are designed to enhance vision in low-light conditions. As such, they aren't very useful during the day. Additionally, it's important to keep in mind that in some jurisdictions, driving with your headlights on during the day is illegal, so it's important to check your local laws before doing so.
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if you have an unmarked bar magnet and an identical unmagnetized bar of iron, how can you determine which is the magnet?
Iron that is not magnetic will be drawn to a bar magnet. An atom is like a current loop, if it is not observed than it is a magnet.
A piece of iron, which has magnetic qualities, aligns into two poles when placed in the magnetic field of a bar magnet.
If the north pole reports the side in front of it, it is the north pole, and if the south pole reports the south pole, it is the south pole. A piece of iron, which has magnetic qualities, aligns into two poles when placed in the magnetic field of a bar magnet.
Charges that are in motion within an atom produce electricity. The atoms can act as an equivalent current loop thanks to their rotational orbits. Iron is nevertheless drawn to magnetic fields despite their being no current.
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in uniform circular motion, which of the following quantities are constant? check all that apply. in uniform circular motion, which of the following quantities are constant?check all that apply. speed the magnitude of the net force centripetal acceleration instantaneous velocity
In a uniform circular motion, the speed, the magnitude of the net force, centripetal acceleration, and instantaneous velocity are all constant.
The motion of an object traveling along a circular path with a constant speed is known as uniform circular motion.
Speed: The speed of an object in uniform circular motion remains constant as the object moves in a circular path.
The magnitude of Net Force: In a uniform circular motion, an object is experiencing a net force towards the center of the circle. This net force is usually referred to as the centripetal force. The magnitude of the centripetal force is always constant in a uniform circular motion.
Centripetal Acceleration: Centripetal acceleration is the rate of change of velocity of an object in uniform circular motion. This acceleration is always constant, and can be calculated using the equation a = v²/r, where v is the speed of the object and r is the radius of the circle.
Instantaneous Velocity: Instantaneous velocity is the velocity of an object at a specific point in time. Since an object in uniform circular motion moves at a constant speed, the instantaneous velocity is also constant.
Therefore, in a uniform circular motion, all the given quantities are constant.
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if the gravitational force between two objects is 300 n and the mass of one object is 20.0 kg, while the other object is 30 kg, what is the distance between the objects?
The gravitational force between two objects is 300 N and the mass of one object is 20.0 kg, while the other object is 30 kg, we have to calculate the distance between the objects the distance is 3.67 m.
What is the distance between the objects?The formula for calculating gravitational force between two objects is given by F = G × m₁ × m₂ / r²
where, F = gravitational force between two objects, m₁ = mass of object 1, m₂ = mass of object 2, r = distance between the objects, G = gravitational constant G = 6.67 × 10⁻¹¹ N·m²/kg².
Now, we can use the above formula to calculate the distance between the objects. F = 300 N, m₁ = 20.0 kg, m₂ = 30 kg, G = 6.67 × 10⁻¹¹N·m²/kg². We have to find
r = ?, F = Gm₁m₂/ r²
r = 6.67 × 10⁻¹¹ × 20 × 30/ 300
r = 3.67m
Therefore, the distance between the objects is 3.67 meters.
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You're designing an external defibrillator that discharges a capacitor through the patient's body, providing a pulse that stops ventricular fibrillation. Specifications call for a capacitor storing 250 J of energy; when discharged through a body with R = 48 Ω transthoracic resistance, the capacitor voltage is to drop to half its initial value in 10 ms.
A) Determine the capacitance (to the nearest ) 10 μF).
B) Determine initial capacitor voltage (to the nearest 100 V) that meet these specs.
I need both correct answers to 2 significant figures.
a..... 1.04 x 10⁻⁴ Vi
b.... 9500 V
A) Determine the capacitance (to the nearest 10 μF).
First, we should identify the formula that we will use to solve the problem.
The formula that relates to capacitance is:
C = 2E / V². Where C is the capacitance in farads, E is the energy stored in joules, and V is the voltage across the capacitor in volts.
Converting the energy to joules, we have: E = 250J.
Now we know that the voltage needs to drop to half of its initial value in 10 ms. We can use the following formula to calculate the capacitance: C = R x t / ln(Vi / Vf) where R is the resistance in ohms, t is the time in seconds, Vi is the initial voltage, and Vf is the final voltage, which is half of the initial voltage.
B) Plugging in the given values, we get:
C = 48 x 0.01 / ln(Vi / (Vi / 2))Simplifying and solving for capacitance, we get:
C = 1.04 x 10⁻⁴ ViNow we can use the energy formula to solve for Vi:Vi = √(2E / C)
Plugging in the given values, we get:Vi = √(2 x 250 / 1.04 x 10⁻⁴)Simplifying and solving for Vi, we get:Vi = 9469 V
Therefore, the capacitance that meets these specifications is 100 μF and the initial capacitor voltage that meets these specifications is 9500 V, to the nearest 100 V.
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helppp pleaseeee enough points
The resistance of the copper wire of length 4 m and diameter 0.002 m is 2.25×10⁻² ohms.
What is resistance?Resistance is the opposition to the flow of current in a circuit.
To calculate the reistance of the copper wire, we use the formula below.
Formula:
R = 4ρL/πd².................. Equation 1Where:
R = Resistance of the copper wireρ = Resistivity of the copper wire at 20°CL = Length of the copper wired = diameter of the copper wireπ = constant called PieFrom the question,
Given:
d = 0.002 mL = 4 mρ = 1.77×10⁻⁸ ohm-metreπ = 3.14Substitute these values into equation 1
R = (4×4×1.77×10⁻⁸)/(3.14×0.002²)R = 2.25×10⁻² ohmsHence, the resistance of the copper wire is 2.25×10⁻² ohms.
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which of the following are irreversible thermodynamic processes? check all that apply. which of the following are irreversible thermodynamic processes?check all that apply. the slow and adiabatic expansion of a gas the spontaneous flow of heat from a hot body to a cooler body the conversion of work to heat by friction the free expansion of a gas
Answer:
Explanation:
The irreversible thermodynamic processes are:
The conversion of work to heat by friction
The free expansion of a gas
The slow and adiabatic expansion of a gas is a reversible process, while the spontaneous flow of heat from a hot body to a cooler body is a natural, irreversible process, but it is not a thermodynamic process per se.
what is it called when you can see one image from one angle and a different image from a different angle?
The phenomenon in which an object appears to be different when viewed from different angles is known as a lenticular image. Lenticular printing is the process of producing these images.
What is Lenticular printing?Lenticular printing is a method of producing a lenticular image, which is a printed image that shifts as the viewing angle changes. Lenticular printing is a method of generating a composite image by interlacing two or more images using a lenticular lens.
A lenticular image is a picture that appears to alter when viewed from different angles. It is formed by placing a sheet of tiny cylindrical lenses or "lenticules" over a photo that has been divided into a number of frames. The frames are interlaced, resulting in a composite image that alters when viewed from different angles.
The lenticular function as lenses, refracting light at various angles and allowing each eye to see a distinct image. To generate the lenticular image effect, the interlaced images must be magnified and printed onto a lenticular lens. The result is a plastic sheet that appears to display a different image depending on the angle of the viewer's gaze.
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a rod undergoes a change in temperature. the change in length is: a rod undergoes a change in temperature. the change in length is:
It is a linear expansion, when a rod undergoes a change in temperature and there is a change in its length.
The length that a rod changes to as a result of a temperature change relies on the rod's initial length, the rate of temperature change, and the material's coefficient of linear expansion. The formula for linear expansion is:
ΔL = αL₀ΔT
Where ΔL is the change in length of the object, is the coefficient for linear expansion of the material in question, and L₀ is the initial length of the object.
Volumetric expansion refers to change in one dimension (volume), whereas linear expansion refers to change in one dimension (length) (volumetric expansion). The area thermal expansion coefficient connects a material's area changes to temperature changes.
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Complete question is:
A rod undergoes a change in temperature. the change in length is:
A. linear expansion
B. volumetric expansion
would a point closer to the center of the hard drive have a higher, lower, or the same linear acceleration?
A point closer to the center of the hard drive will have a lower linear acceleration than a point farther from the center. This is due to the fact that linear acceleration is inversely proportional to the radius of rotation. The acceleration is greatest at the outer edges and decreases toward the center.
Linear acceleration is the rate of change of the velocity of an object that moves in a straight line. It is also referred to as the object's increase in speed or decrease in speed. The same concept applies when it comes to hard drives.
It is pertinent to understand that linear acceleration decreases when the radius of the disk decreases, which means that the closer the point is to the center, the lower the linear acceleration would be. This is why the outermost tracks have higher transfer rates and are utilized more for storing data on hard drives.
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how far is the spring compressed question undergrad physics inclined plane where height is not given
The spring is compressed by 0.84 meters.
The potential energy of the block at the starting point is given by,
mgh = 2 x 9.8 x h, where h is the height of the starting point above the bottom of the incline.
Using the given inclination angle of 37 degrees, we can find h as,
h = 4.8 sin(37) = 2.88 m
We can equate the potential energy at the starting point to the energy stored in the compressed spring and the kinetic energy at the bottom of the incline,
mgh = 1/2 kx^2 + 1/2 mv^2
where x is the distance that the spring is compressed, v is the velocity of the block at the bottom of the incline, and k is the spring constant.
Since the block is sliding without friction, we can use conservation of energy to find v as,
mgh = 1/2 mv^2
v^2 = 2gh
v = √(2gh)
Substituting this expression for v in the earlier equation,
mgh = 1/2 kx^2 + 1/2 m(2gh)
2gh = kx^2/m + 2gh
x^2 = 2ghm/k
x = √(2ghm/k)
Substituting the known values,
x = √(2 x 9.8 x 2 x 2.88 / 1000) = 0.84 m
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--The complete question is, A spring is fixed at the bottom end of an incline of inclination 37∘. A small block of mass 2 kg starts slipping down the incline from a point 4.8 m away (along the inclined plane) from the spring. The spring constant is 1000 N/m. How far is the spring compressed?--
how hard must she pull downward to raise herself slowly at constant speed? the mass of the person plus the bucket is 77 kg .
The person must pull downward with a force equal to her weight, which is approximately 760 N in order to raise herself slowly at a constant speed.
When the person pulls downward on the bucket, there are two forces acting on the system: the force of gravity pulling the person and the bucket down, and the force of the person pulling the bucket up. In order for the person to raise herself at a constant speed, the force she exerts on the bucket must be equal and opposite to the force of gravity pulling her down.
The force of gravity on the person and the bucket is equal to their combined weight, which can be calculated as mass times gravitational acceleration (77 kg x 9.81 m/s^2 = 755.37 N). Therefore, the person must exert a force equal to her weight (approximately 760 N) in order to counteract the force of gravity and raise herself at a constant speed.
Thus, to lift herself up slowly and steadily, the person needs to exert a downward force that is equivalent to her weight, which is around 760 Newtons.
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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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alston realizes that he wasn't paying attention when thana ran the simulation for which the charge was set to zero, and asks thana to describe the particle's motion. which response is correct?
Thana explains that when the charge is zero, the motion of the particle in the simulation is a straight line with a constant velocity.
The direction of the velocity depends on the initial conditions and the force acting on the particle. If there are no other forces acting on the particle, it will continue to move in a straight line with a constant velocity until it encounters another force or object. This is an example of Newton's First Law of Motion, which states that an object at rest will stay at rest and an object in motion will stay in motion with a constant velocity unless acted upon by an external force. If there is a force acting on the particle, it will change direction or speed up or slow down. This is an example of Newton's Second Law of Motion, which states that the force acting on an object is equal to its mass times its acceleration. The direction of the force is in the same direction as the acceleration. When the charge is zero, the particle does not experience any force, so it moves in a straight line with a constant velocity. This is a simple example of how particles can be modeled using physics simulations.
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one cycle of the power dissipated by a resistor ( ) is given by this periodic signal repeats in both directions of time. what is the amplitude of the pwm voltage signal applied across the 500- resistor
The maximum amplitude of the PWM voltage signal applied across the 500-ohm resistor is: Vmax=2*I*R=500*I
The power dissipated by a resistor during one cycle is given by the periodic signal. The PWM voltage signal applied across a 500 Ω resistor is analyzed in this question. The amplitude of the signal is determined below.
Pulse Width Modulation is the PWM. It's a process for varying the pulse width of a square wave, which changes the percentage of time the signal is high to low. The pulse width can be varied to create the desired output signal level. It is frequently utilized in applications where analog signals are required, including control systems, power supplies, and audio systems. The maximum voltage Vm of the PWM voltage signal can be found by calculating the RMS value of the pulse. The root-mean-square value is the square root of the mean of the square of the signal over a given period. If we use a pulse that has a duty cycle of 50%, this formula simplifies to: Vmax=Vm+0.5Vdc where Vdc is the average value of the pulse.
The maximum amplitude can be determined using this formula: Vmax=I*R where I is the current and R is the resistance. The current flowing through the resistor is proportional to the voltage applied to it, and the voltage is proportional to the duty cycle of the PWM signal, which varies from 0 to 1. Thus, the voltage applied to the resistor is proportional to the duty cycle and can be expressed as: V=Vmax*D where D is the duty cycle. Thus, the amplitude of the PWM voltage signal applied across a 500-ohm resistor is: Vmax=2*I*R=500*I. Using this equation, we can determine the maximum amplitude of the PWM voltage signal applied across the 500-ohm resistor.
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