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Question 3:
A small cube of mass m₁ slides down a circular track of radius,
cut into a large block of mass m₂ = 2m₁ as shown in the figure
below. The large block rests on a table, and both blocks movė
without friction. The blocks are initially at rest, and m₁ starts
from the top of the path. Find the magnitude of velocity of the
cube as it leaves the block.
Answers
The velocity 'v' of the cube as it leaves the block would be, v=[tex]\sqrt{\frac{2gR}{1+m/M} }[/tex].
What is Conservation of mechanical energy?Conservation of mechanical energy is a principle that states that the total mechanical energy of a closed system remains constant as long as no energy is added or removed from the system. In this case, the system consists of the two blocks and the table on which they rest. Since there is no friction and no external force acting on the system, the total mechanical energy (potential energy + kinetic energy) remains constant as the cube slides down the track. This allows us to use the initial potential energy of the cube to calculate its final kinetic energy, and thus its velocity as it leaves the block.
The magnitude of velocity of the cube as it leaves the block can be found using Conservation of mechanical energy.
Initially, the cube is at rest at the top of the track and has only potential energy, given by m₁gh, where g is the acceleration due to gravity and h is the height of the track. As the cube slides down the track, it loses potential energy and gains kinetic energy.
we have
mu=mv−−(1)
wall=Δk
mgR = [tex]\frac{1}{2} mv^{2} + \frac{1}{2} mu^{2}[/tex]
mgR = [tex]\frac{1}{2} mvH_{2}[/tex] + [tex]\frac{1}{2} (\frac{mv}{M} ) ^{2}[/tex] × M
mgR= [tex]\frac{1}{2} mv^{2} + \frac{1}{2} \frac{m^{2} v^{2}}{M}[/tex]
So, v²=[tex]\frac{2gR}{1+m/M}[/tex]
So, v= [tex]\sqrt{\s{\frac{2gR}{1+m/M} }}[/tex].
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Related Questions
a 80.9-kg boy and a 65.7-kg girl, both wearing skates face each other at rest on a skating rink. the boy pushes the girl, sending her to the left with a velocity of -2.65 m/s. neglecting friction, determine the subsequent velocity of the boy to the right.
Answers
The boy will move to the right with a velocity of -2.16 m/s after pushing the girl to the left with a velocity of -2.65 m/s.
How to calculate the subsequent velocity ?Newton's Third Law of Motion
Using the conservation of momentum, the velocity of the boy to the right is calculated as follows:
Boy's initial momentum = 0
Girl's initial momentum = (65.7 kg)(-2.65 m/s) = -174.34 kgm/s
Total initial momentum = -174.34 kgm/s
Boy's final momentum = (80.9 kg)(V)
V = (174.34 kgm/s) / (80.9 kg)
V = 2.16 m/s (to the right)
This is due to Newton's Third Law of Motion, which states that for every action there is an equal and opposite reaction.
The girl has a mass of 65.7 kg and a velocity of -2.65 m/s. Using the equation for momentum, the momentum of the girl can be calculated as follows:
Momentum = Mass x Velocity
Momentum of girl = 65.7 kg x -2.65 m/s = -174.25 kg m/s
As the momentum of the girl and the boy must be equal and opposite, the momentum of the boy can be calculated as:
Momentum of boy = -174.25 kg m/s
Using the same equation for momentum, the velocity of the boy can be calculated as follows:
Velocity of boy = Momentum/Mass
Velocity of boy = -174.25 kg m/s/80.9 kg
Velocity of boy = -2.16 m/s
Therefore, the boy will move to the right with a velocity of -2.16 m/s after pushing the girl to the left with a velocity of -2.65 m/s.
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An astronaut drops a golf ball that is initially at rest from a cliff on the surface of the moon. The ball falls freely under the influence of gravity. Which one of the following statements is true concerning the ball as it falls? Neglect any frictional effects.
A. The ball will gain an equal amount of kinetic energy during each second. B. The ball will gain an equal amount of momentum during each second. C. The ball will gain twice the amount of speed for each meter through which it falls. D. The ball will gain an equal amount of momentum during each meter through which it falls.
Answers
The ball will gain an equal amount of momentum during each second. if The ball falls freely under the influence of gravity.
Why gravity is a force?However, in the broader sense, gravity is indeed a force because it describes the resulting interaction between two masses. Gravitational effects are fundamentally caused by the warping of spacetime and the motion of objects through the warped spacetime. However, the end result is as if a force was applied.
Who discovered gravity?Sir Isaac Newton Far more than just discovering the laws of gravity, Sir Isaac Newton was also responsible for working out many of the principles of visible light and the laws of motion, and contributing to calculus.
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find $m\angle jkm$ . triangle j k l is shown. the measure of angle j is 3 x degrees. the measure of angle l is 41 degrees. the measure of external angle j k m is equal to 4 x plus 9 degrees.
Answers
The angle of ∠JKM is 148 degrees when given that the angle J is 3 times the angle JKL and the measure of angle L is 41degrees.
Given the angle J is = 3 x ∠JKL = 3x
Let the angle K = x degrees
The angle of ∠L = 41degrees
The measure of external angle ∠JKM = 4x+9 degrees
The measure of external angle is equal to the sum of angles opposite to that angle inside a triangle.
Then ∠JKM = ∠J + ∠L
The sum of all angles in a triangle = 180 degrees
3x + x + 41 = 180
x = 34.75degrees
Thus the angle JKM and J = 34.75degrees
So, we know that 4x+9 = 4 x 34.75 + 9 = 148degrees.
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A particle of charge +q is released from rest at position B, which is a distance 2d from the center of a fixed nonconducting sphere that has a charge of -Q distributed uniformly throughout its volume, as shown in the figure above. When the particle reaches position A, which is a distance d from the center of the charged sphere, its kinetic energy is K0 . The same particle is now released from rest at position C, which is a distance 4d from the center of the nonconducting sphere. The kinetic energy of the particle when it again reaches position A is
Answers
The kinetic energy of the particle when it reaches position A will be K0 * (2d/4d)^2 = K0/4 , when the particle is released at position C.
What is the the kinetic energy of the particle when it reaches position A?The particle at position B is attracted to the negatively charged sphere, and as it gets closer to the sphere (as it moves towards position A), it gains kinetic energy.The same particle, released at position C, is initially farther away from the negatively charged sphere, so it has less potential energy to begin with.As the particle moves towards position A, it loses kinetic energy due to the force of attraction to the negatively charged sphere.So the kinetic energy of the particle when it reaches position A will be less when it is released from position C compared to when it is released from position B.The kinetic energy at position A is inversely proportional to the square of the distance between the point of release and position A .So the kinetic energy of the particle when it reaches position A will be K0 * (2d/4d)^2 = K0/4 , when the particle is released at position C.To learn more about particles refer:
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The freezing point of t-butanol is 25.50oC and Kf is 9.1oC .kg/mol. Usually t-butanol absorbs water on exposure to air. If the freezing point of a 10.0-g sample of t-butanol is 24.59oC, how many grams of water are present in the sample?
Answers
The freezing point of t-butanol is 25.50oC and Kf is 9.1oC, mass of the water in the solution is calculated as -0.018 g.
What is freezing point?The temperature at which liquid freezes, and thee solid and liquid phases are in equilibrium is called freezing point.
ΔTf = Kf * molality
ΔTf is the change in freezing point, Kf is freezing point depression constant, and molality is the number of moles of solute per kilogram of solvent.
ΔTf = 24.59oC - 25.50oC = -0.91oC
Given, Kf = 9.1oC .kg/mol
molality = ΔTf / Kf = -0.91oC / 9.1oC .kg/mol = -0.1 mol/kg
moles solute = molality x mass solvent (kg) = -0.1 mol/kg x 10 g/1000 kg = -0.001 moles
mass water = moles water x molar mass water = -0.001 moles x 18.02 g/mol = -0.018 g
The mass of the water in the solution is -0.018 g, however it is a negative value which is not possible. This is likely due to experimental error or impurities in the solvent.
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A metal ion buffer used for calibrating an ion-selective electrode is prepared using 0.0397 M of metal-ligand complex (ML) and 0.0259 M of the free ligand (L) The formation constant, Kf; for ML is 5.78 X 10^7 Calculate the concentration of free metal ion (M) in the buffer; [M]
Answers
The concentration of free metal ion (M) in the buffer is 3.
What is the concentration of free metal ion (M) ?Thus, this metal ion complex is formed by the equilibrium of the metal and the ligand. The formula should be k f, here, k f,
concentration of the middle ligon, complex, divided by the concentration of the metal concentration of ion, multiplied by 5.78 to get the 7 medallion complex, or 0397.
The metal concentration is unknown, but the lin is. 0259 and calculating the metal concentration. Here, the result is 3, as seen in Figures 2.65 times 10 to the minus 8, and the units would be molar.
The concentration of free metal ion (M) in the buffer is 3.
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When the ball is halfway to the ground (at 1/2 h), is its kinetic energy more than, less than, or exactly equal to half of its maximum kinetic energy? Explain
Answers
It is common knowledge that half of the ball's potential energy is converted to kinetic energy because it fell halfway through.
Let's take an example to understand the concept clearly.
Suppose a 16 kg ball is dropped from 10 m. We need to determine the kinetic energy when the ball reaches half the ground.
Note: At height of 10 cm the ball has a certain potential energy.
As GPE = m.g.h
Similarly, so is the potential energy of the sphere
GPE = 16 . 9.81. 10
GPE = 1569.6 J
On the way, the potential energy of the sphere when the altitude changes
GPE = 16 . 9.81. 5
GPE = 784.8 J
By the law of conservation of energy, the energy is It will not destroy or disappear. This converts the ball's lost potential energy into another form of energy. Here the lost potential energy of the sphere is converted into kinetic energy of the sphere.
Therefore the kinetic energy of the ball is equal to the potential energy of the ball at minus the potential energy of the ball at his.
i.e. 1569.6 - 784.8 = 784.8
It is common knowledge that half of the ball's potential energy is converted to kinetic energy because it fell halfway. When the ball hits the ground, i.e., at h = 0m all of the ball's potential energy is converted to kinetic energy and finally to another form of energy.
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starting from rest, angel and britney skateboard down a hill as shown. angel rides down the steep side while britney rides down the shallow side. angel has more mass than britney. assume that friction and air resistance are negligible
Answers
Potential energy is changed into kinetic energy as the skateboarder decelerates down the ramp.
As the skater descends the ramp, how does his kinetic energy change? Potential energy is transformed into kinetic energy as the skateboarder decelerates down the ramp.The system's energy is turned into heat energy in part as a result of friction.It is impossible to return the system's kinetic or potential energy to its original state once it has been transformed into heat.As the skateboarder glides along the track, her position changes and her velocity changes, converting her potential energy into kinetic energy (KE), or the energy of motion.The skateboarder's kinetic energy, which is related to motion, is inversely proportional to the square of the object's velocity. Kinetic energy rises in direct proportion to the skater's speed.Kinetic energy rises with a fall in speed.To lean more about kinetic energy refer
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part 1.d.what do these observations suggest about the depth to which heat from the sun can penetrate the earth?
Answers
The Sun can not penetrate too far into the Earth.
The air surrounding us consists of different gases and also some particles. This layer of air, known as the Earth’s atmosphere is retained by gravity. The two main components are nitrogen (78%) and oxygen (21%). Besides containing the oxygen human beings and other organisms need to live, the atmosphere has a number of other “features” such as absorption of ultraviolet radiation from the Sun by the ozone layer and heat retention known as the greenhouse effect. Over the span of 11 years, the Sun’s activity waxes and wanes as magnetic field lines that are wound and tangled inside the Sun periodically break through to the surface. These breakthroughs produce sunspots that travel together across the face of the Sun. The Sun contains 99.8 percent of the mass in our solar system. Its gravitational pull is what keeps everything here, from tiny Mercury to the gas giants to the Oort Cloud, 186 billion miles away. But even though the Sun has such a powerful pull, it's surprisingly hard to actually go to the Sun: It takes 55 times more energy to go to the Sun than it does to go to Mars.Our planet is traveling very fast — about 67,000 miles per hour — almost entirely sideways relative to the Sun. The only way to get to the Sun is to cancel that sideways motion.To know more about sun visit:
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Use the graph to complete the sentences about two runners.
Runner (blank)
is faster than Runner (blank)
Runner (blank)
has a head start.
Answers
The sentences can be completed as follows: Runner A is is faster than Runner B. Runner B has a head start.
What is position -time graph ?The position v/s time graph is very helpful to determine the position of an object with respect to time. The speed of the moving object can be easily calculated from the graph. If the graph is a straight line, then its slope be the speed.
In the given graph, the change in distance with change in time for runner A is greater than that of runner B. Therefore, the speed of runner A is greater than B.
The starting position of B is ahead of A and it is not from origin. . Hence, it can be said that, runner B has a head start.
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16)An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth. Compared to its weight on Earth, the weight of this debris is
A) one-quarter of its weight on the surface of the earth. B) one-half of its weight on the surface of the earth. C) zero. D) the same as on the surface of the earth. E) one-third of its weight on the surface of the earth.
I know it A but i want to knwo why please show me the work.
The graphs shown show the magnitude F of the force exerted by a spring as a function of the distance x the spring has been stretched. For which one of the graphs does the spring obey Hooke's law?
?ui=2&ik=8cf528d270&view=fimg&th=158e745
A) Graph a B) Graph b C) Graph c D) Graph d E) Graph e
I know it B but why is it, show me the work.
Answers
At a height that is two earth radii above the planet's surface, a particle of space debris is launched from rest.The weight of this trash is only one-fourth of what it would be if it were on Earth.
What transpires to the majority of the space debris that touches down on the surface of the Earth? At a height that is two earth radii above the planet's surface, a particle of space debris is launched from rest.The weight of this trash is only one-fourth of what it would be if it were on Earth.Despite the fact that the majority of debris burns up in the sky, larger debris pieces can make it to the ground unharmed.NASA reports that during the previous 50 years, on average, one piece of debris has been cataloged as returning to Earth every day.Any equipment or trash left in space by humans is referred to as "space rubbish" or "space garbage."Large objects that have failed or been abandoned in orbit after the conclusion of their missions, such as dead satellites, can be included.To learn more about space debris refer
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Exercise 9 The two blocks (A) and (B) of respective masses mA = 2 kg and mg = 4 kg, that are shown in the adjacent figure are attached to each other by means of a string that passes over a massless pulley. Th coefficient of friction between (A) and (B) is ₁ = 0.2 and that between (B) and the ground is = 0.1. Block B is pulled by a force that result in an acceleration of block B of magnitude a = 0.5 m/s². Determine during the motion of the two blocks the tension of the string and the value of F.
Answers
The force acting on an object is defined by Newton's second law as being equal to the object's mass (m) times its acceleration (a).
Explain about the Newton's second law of motion.Block B's acceleration times its mass gives block A's force, which is equivalent to that force.
1. A string that travels through a massless pulley connects the two blocks, A and B.
2. There is 0.1 coefficient of friction between B and the ground, and 1 = 0.2 between A and B.
Block B experiences an acceleration of a = 0.5 m/s2 as a result of being dragged by a force.
4. The Newton's second law of motion is used to determine the string's tension.
It specifies that the sum of the forces exerted on a body must equal the mass times the acceleration of the body.
Thus, mg = 4 kg represents the string's stress.
5. To determine the value of F, we utilize the same equation but swap out block B's acceleration for block A's mass and vice versa.
This results in F = ma = 2kg x 0.5 m/s2 = 1 N.
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he question below uses a robot in a grid of squares. the robot is represented as a triangle, which is initially in the bottom left square of the grid and facing right.
Answers
Option A has a column that consists of three boxes. There is a left arrow in the top box of choice A, a left sign for temperature in the middle box, and a left column for temperature in the bottom box.
What does temperature mean in a scientific sense?The temperature of an object serves as a gauge for both the average kinetic mobility of its constituent particles. As the temperature rises, so does the movement of these particles. To measure the temperature, a barometer and perhaps a chamber are employed.
What are temperatures and what is their unit?
When two things with room temperature and atmospheric pressure are kept in close proximity, the temperature depends on the angle of heat transmission. The SI unit is the kelvin (K).
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Complete question:
which source of power was introduced in the late 1800s? a. coal b. electricity c. animal d. wood
Answers
Out of all the choices that state sources of power, electricity was the one that was first developed in the late 1800s.
Electricity as a source of power was introduced in the late 1800s.
Sources of power include fossil fuels (coal, oil, natural gas), nuclear power, hydroelectric power, solar power, wind power, geothermal energy, and biomass energy. Renewable sources are those that are replenished naturally and non-renewable sources are those that are finite and will eventually be depleted.
The invention of the dynamo, a machine that generates electricity by converting mechanical energy into electrical energy, in the 1870s was a significant step in the development of the electrical industry.
The first commercial power station, Pearl Street Station, opened in New York City in 1882 and produced direct current (DC) electricity. The invention of the alternating current (AC) system in the late 1880s by Nikola Tesla and George Westinghouse made it possible to transmit electricity over long distances, which further expanded the use of electricity as a source of power. The use of electricity as a source of power revolutionized industry, transportation, and domestic life. It replaced traditional sources of energy such as coal, wood, and animal power, and led to the development of new technologies and industries, including the electric motor, electric lighting, and the telephone.
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given the height, in meters, of an object above the ground, for (seconds), what are the units of the average rate of change of the object on the interval . (assume the ball has not hit the ground before time .)
Answers
It is important to note that the average rate of change is a scalar quantity.
How will you explain that.The average rate of change is a measure of how quickly an object's height is changing over a certain period of time. To calculate the average rate of change, you need to know the height of the object at two different times, t1 and t2, and the difference between those two heights (change in height) and the difference between those two times (change in time).
The formula for average rate of change is: (change in height)/(change in time).
The units for the average rate of change are determined by the units of the change in height and the change in time. Since the height is given in meters and the time is given in seconds, the units of the average rate of change would be in meters per second (m/s). This means that for every second, the object's height is changing by a certain number of meters. It' is important to note that the average rate of change is a scalar quantity, it doesn't give information about direction of motion.
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a 1.2-kilogram block and a 1.8-kilogram block are initially at rest on a frictionless, horizontal surface. when a compressed spring between the blocks is released, the 1.8-kilogram block moves to the right at 2.0 meters per second, as shown.
Answers
The speed of the 1.2-kilogram block after the spring is released is -3m/s. The sign indicates that this block moves left direction.
What are the law of conservation of momentum's three rules?Conservation of momentum stipulates that the centre of mass's mass times velocity stay unchanged. Conserving Angular Momentum, the system's overall angular momentum is constant. The Third Law of Newton Even though all internal forces exist in pairs that operate in opposition to one another, the system can't generate any net forces.
m1 => 1.2Kg; v1 = 0m/s ; v2 = 0m/s (sincce, it initially at rest)
m2 => 1.8Kg
v2'= 2m/s
The law of conservation of momentum:
m1v1 + m2v2 => m1 v1' + m2v2'
0 => 1.2 x v1' + 1.8 x 2
v1' => -(3.6)/1.2
=> -3m/s
How fast can the block go at its most?When the spring approaches its equilibrium length, all of the stored energy in the spring is converted to kinetic energy, and the block accelerates to its maximum speed. Since the item is at rest, Ki = 0. Since there is no friction, Wnc = 0.
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A 1.2-kilogram block and a 1.8-kilogram block are initially at rest on a frictionless, horizontal surface. when a compressed spring between the blocks is released,the 1.8-kilogram block moves to the right at 2.0 meters per second, as shown. what is the speed of the 1.2-kilogram block after the spring is released?
1
A
B
C
D
According to the text, what is radiation?
energy given off by radioactive materials
energy given off by invisible atomic particles
energy given off by the things around us
energy given off by nuclear power plants
Answers
Radiation is energy that comes from a source and travels through space at the speed of light.
What type of energy is radiation energy?This energy has wave-like qualities and is accompanied by an electric field and a magnetic field. Radiation may also be referred to as electromagnetic waves. In nature, electromagnetic radiation occurs in a variety of forms. One illustration is visible light.
The most energetic types of radiation include gamma rays, x-rays, and ultraviolet light. There is a lot of energy in X-rays and gamma rays. They have the ability to take electrons away from atoms when they engage with them, ionising the atom. Protons and neutrons are mixed in unstable ways in radioactive atoms.
An unstable atom will release energy on its own to move into a more stable state, which is radioactivity. Ionizing The energy that a radioactive atom emits is known as radiation. The radioactive atoms of the same element with varying numbers are known as isotopes.
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which of the following sources of energy transforms kinetic energy to electricity without using heat energy?
Answers
Sources include renewable energy sources such as the sun, wind, water, and geothermal heat.
In which energy sources kinetic energy is converted into electrical energy?A sequence of blades installed on a rotor shaft in a turbine generator are pushed by a flowing fluid, such as air, water, steam, combustion gases, or water. A generator's rotor shaft revolves or spins due to the fluid's force on the blades.
In turn, the generator transforms the rotor's mechanical (kinetic) energy into electrical energy.A machine that transforms a form of energy into electricity is called an electric generator.
Electricity generators come in a variety of designs. According to Michael Faraday's 1831 discovery that rotating a magnet inside a coil of wire causes (induces) an electric current to flow in the wire, the majority of the world's power is produced by generators. On the basis of this relationship, he created the first electrical generator known as a Faraday disc.
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Question: Question The height of a ball, in meters, dropped from a 409-meter tall building is given by the function s(t) = -5t2 + 409. Find the average velocity of the ball over the intervals [1.999, 2.0) and [2.0, 2.001]. Use this information to approximate the instantaneous velocity of the ball at time t = 2.0.
Answers
At time t = 2, the instantaneous velocity is -20 m/s.
How can an estimate of instantaneous velocity be made?Therefore, the average velocity at a point that is one increment smaller and one increment larger than the point can be used to estimate the instantaneous velocity at that point. Then, you can get a better estimate of the instantaneous velocity at that point by finding the average of those two average velocities.
The SI unit of measure is m/s. Because the position function is given, we can obtain the velocity by determining [tex]\dfrac{ds}{dt}[/tex], from which we can derive the instantaneous velocity.
S (2) = -5(2)2 + 409
= 389 S (2-01)
= -5(2.01)2+409
= 388-7995
Average velocity on [a, b]
Vavg (b) - (a) b-a on [1.999,2]
Vavg = S(2)-SU.999) 2-1999 389-389-019995
0.001 =-0.019995
0.001 -19.995
= -20
As t = 2, Vavg = -20,
instantaneous velocity = -20 m/s
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This rock shows evidence of
physical weathering as a result of
acid, wind, or ice.
Answers
using the data presented in the accompanying pressure-versus-volume graph, estimate the magnitude of the work done when the system changes from a to b to c along the path shown. (b) determine whether the work is done by the system or on the system and, hence, whether the work is positive or negative.
Answers
The work done by the system along the path from a to b to c is zero and it's not positive or negative.
What is the work done by system ?The work done by a system can be determined by the area enclosed by the system's pressure-volume graph.The area enclosed by the path from a to b to c represents the work done by the system.In this case, the path from a to b to c is a closed loop, so the work done by the system is zero.It's necessary to determine whether the work is done by the system or on the system.Since the path is a closed loop, the work done by the system is equal in magnitude but opposite in direction to the work done on the system.The work is done by the system is zero. So, it's neither positive nor negative.In summary, the work done by the system along the path from a to b to c is zero and it's not positive or negative.To learn more about work done refer:
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A baseball is thrown from the stands 10 ft above the field atan angle of 80" up from the horizontal. When and how far away will the ball strike the ground if its initial speed is 10 fUsec? (Assume ideal projectile motion that t is, that the baseball undergoes constant downward acceleration due to gravity but no other acceleration; assume also that acceleration due to gravity is -32 feet per second-squared:) The ball will hit the ground after 0.519469684 seconds_ The ball will hit the ground a horizontal distance of 0.573428 feet away
Answers
The ball will hit the ground after 0.519469684 seconds and will hit the ground a horizontal distance of 0.573428 feet away.
What is projectile motion?Form of motion experienced by an object or particle that is projected in gravitational field, such as from Earth's surface, and moves along curved path under the action of gravity only is called projectile motion.
The time of flight can be calculated using:
t = (2vsin(θ)) / g
t is the time of flight, v is the initial velocity, θ is angle of launch (measured from the horizontal), and g is acceleration due to gravity (which is -32 ft/s^2).
So, t = (210sin(80)) / -32
t = 0.519469684 seconds
To find the horizontal distance the ball will travel before hitting the ground:
d = vxt = vcos(θ)*t
d is the horizontal distance, vx is horizontal component of velocity, and t is the time of flight.
d = 10*cos(80)*0.519469684
So, d = 0.573428 feet
So the ball will hit the ground after 0.519469684 seconds and will hit the ground a horizontal distance of 0.573428 feet away.
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a thin 0.100-kg k g rod that is 310 mm m m long has a small hole drilled through it 77.5 mm m m from one end. a metal wire is strung through the hole and fixed horizontally, and the rod is free to rotate about the wire and to oscillate. part a determine the rod's rotational inertia i i about this axis.
Answers
The rod's rotational inertia I about this axis is 3.1762 × 10⁻³ kg.m² while the period of time οf rod's oscillation is 0.8797s.
What is the definition of mass?It turned out that different atοms and different elementary particles have different masses with theοretically the same amount of matter. Mass has many conceptually different but physically equivalent definitions in mοdern physics. Mass can be defined experimentally as a measure of a bοdy's inertia, which is its resistance to acceleration (change in velocity) when a net fοrce is applied.
Given that
Mass of the rοd is m =0.200kg
Length of the rοd (L) =330mm
=0.330m
Now the center οf mass to the hanging point is
d =[tex]\mathrm{\dfrac{330mm}{2} -82.5mm}[/tex]
=165mm-82.5mm
=82.5mm
=0.0825m
a)Now the mοment of inertia of the rod about the axis is
I = Icm+md²
I = mL²/12 + md²
= (0.200)(0.330)2/12 + (0.200)(0.0825)2
= 1.815 × 10 -3 + 1.3612 × 10⁻³
= 3.1762 × 10⁻³ kg.m²
b) Now the time periοd of the rod's oscillations is given by
T = 2π × √(I/mgd)
[tex]$ \mathrm{ =2 \times 3.14 \times \sqrt{ \frac{ 3.1762 \times 10^{-3} \ kg.m^2} { 0.200\ kg\times 9.81\times 0.0825} }}[/tex]
= 0.8797s
Thus, The rod's rotational inertia I abοut this axis is 3.1762 × 10⁻³ kg.m² while the period οf time of rod's oscillation is 0.8797s.
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Complete question:
FILL IN THE BLANK a mass is undergoing simple harmonic motion. when its displacement is 0, it is at its equilibrium position. at that moment, its speed is _________ and its acceleration is _________ .
Answers
A mass is undergoing simple harmonic motion. when its displacement is 0, it is at its equilibrium position. at that moment, its speed is maximum and its acceleration is 0 .
The rule of conservation of energy can be used to calculate the mass's speed in simple harmonic motion. In actuality, the kinetic energy and elastic potential energy make up the entire mechanical energy of the mass-spring system:
[tex]E=K+U=\frac{1}{2}mv^{2} +\frac{1}{2}kv^{2}[/tex]
where
The mass is m.
The speed is v.
The spring constant is k.
The displacement is x.
As we can see, the term representing the kinetic energy is at its highest when the displacement is zero (x=0), and consequently, v (the speed) is at its maximum as well.
Hook's law states that the acceleration of a mass in simple harmonic motion is inversely proportional to the restoring force exerted on the mass.
[tex]a\:\alpha\: F=-kx[/tex]
where
The spring constant is k.
The displacement is x.
the net when x = 0, F = 0,
hence there is no net force on the mass. As a result, this also implies that the mass's acceleration is zero: a = 0.
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which of the following statements is correct about force f, kinetic energy k and momentum p of an object of mass m a) force is the rate at which momentum changes b) kinetic energy \displaystyle k
Answers
The following statements is correct about force f, kinetic energy k and momentum p of an object of mass m are (a) Force is the rate at which momentum changes.
What is momentum?Momentum is a concept in physics that describes the motion of an object. It is determined by the mass and velocity of an object, and is represented by the formula: momentum = mass x velocity.
Momentum plays an important role in physics, as it is the conserved quantity of motion for a system. It is a vector quantity, which means it has both a magnitude and a direction. In a collision, momentum is conserved, meaning that the total momentum of the system remains the same before and after the collision.
Momentum is also important in sports, as it can be used to understand how to maximize or minimize the speed and direction of a ball.
We know that
Force = m × a
m = f/a
And
Momentum = m × v
m = p/v
Also
= 1/2mv²
m = 2K.E./v²
Now taking M into account for all we can say that
[tex]$ \frac{\text{Force}}{\text{Acceleration}} = \frac{\text{Momentum}}{\text{velocity}} = \frac{2 \ \text{Kinetic Energy}}{\text{velocity}^2}[/tex]
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The breakdown voltage of a randomly chosen diode of a certain type is known to be normally distributed with mean value 40 V and standard deviation 1.5 V: What is the probability that the voltage of a single diode is between 39 and 422
Answers
There is a 0.6568 percent chance that a single diode's voltage will fall between 39 and 422 volts.
It is known that the breakdown voltage of a randomly selected diode of a certain type has a normal distribution with a mean of 40 volts (v) and a standard deviation of 1.5 v. 1.5) = (1.33 (0.67), which equals 0.9082 0.2514, which equals 0.6568.
The forward voltage of silicon diodes is around 0.7 volts. The forward voltage of germanium diodes is around 0.3 volts. Peak Inverse Voltage, or PIV rating, is the highest reverse-bias voltage that a diode can sustain without "breaking down."
An electrical device called a diode makes it more easier for electricity to flow through it in one direction than the other. Despite the existence of other diode technologies, semiconductor diodes are the most prevalent type of diode used in contemporary circuit design. Schematic diagrams use symbols to represent semiconductor diodes.
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The density of a person's blood proteins is about 1.2 g/cm3. Express the density in kilograms per cubic meter.
Answers
Answer:
1200 kg/m³
Explanation:
This is simply 1.2g/cm³ × 1000 which further gives 1200 kg/m³
the bolt goes into the roof along the n-axis. any force perpendicular to the n-axis (that is, any force along the line of the roof n) tends to shear off the bolt. p is 150 lbs. using vector methods, find the component of p perpendicular to the roof (along the n axis).
Answers
The bolt goes into the roof along the n-axis. any force perpendicular to the n-axis X-component = 39.45 N, Y-component = 43.93 N,
A force is an effect with the capacity to alter an object's motion, as defined by physics. When an object with mass is moving at a faster rate, such as when it is moving away from rest, this acceleration can be induced by a force. (Previous P). Two simple methods of displaying force are pushing or pulling. A force is considered a vector quantity since it has both magnitude and direction. The SI newton unit is used to calculate it (N). The symbol for force is F. According to Newton's second law in its original form, the net force acting on an object is equal to the rate at which its momentum changes over time. if the item's mass remains constant
Z-component = 67.92 N
[tex](cos(64))^{2}[/tex] +[tex](cos(B))^2[/tex]+ [tex](cos(41))^2[/tex] = 1
[tex](Cos(B))^2[/tex]= 0.238
Cos(B) = 0.488
B = arccos (0.488) = 60.78 degree
Angle with positive y axis, B = 180 - 60.78 = 119.22 degree
A)
X-component = 90cos(64) = 39.45 N
B)
Y-component = 90 cos(119.22) = 43.93 N
C)
Z-component = 90 cos(41) = 67.92 N
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Jack runs up the stairs, elevating his 71.7 kg body a vertical distance of 2.86 meters in a time of 2.19 seconds. Determine the power (in Watts) done by the stairs on Jack's body.
Answers
Jack runs up the stairs, elevating his 71.7 kg body a vertical distance of 2.86 meters in a time of 2.19 seconds. The power (in Watts) done by the stairs on Jack's body is 780.5 watts.
To determine the power done by the stairs on Jack's body, we can use the formula:
= Power
= Work / Time
where Work is the amount of energy exerted on the object and Time is the duration of the work.
First, we need to calculate the work done on Jack's body by the stairs. We can use the formula:
= Work
= Force x Distance
where Force is the force exerted on the object and Distance is the distance over which the force is exerted. Since the force exerted on Jack's body is equal to his weight, which is the force of gravity acting on him, we can calculate the work done on him as follows:
= Work
= (71.7 kg) (9.8 m/s^2) (2.86 m)
Next, we can divide the work by the time to find the power:
Power = Work / Time
Power = (71.7 kg) (9.8 m/s^2) (2.86 m) / 2.19 seconds
Power = 2.86 * 9.8 * 71.7 / 2.19
Power = 1709.5 / 2.19
Power = 780.5 watts
So the power done by the stairs on Jack's body is approximately 780.5 watts.
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two skaters are initially at rest next to each other on frictionless ice. skater a pushes on skater b. if skater a has greater mass than skater b, which of the following correctly relates the magnitudes of their momentums p and their kinetic energies k after the push?
Answers
Using Newton's Third law both the skaters will experience equal and opposite force. And hence equal impulse i.e momentum of both the skaters will be same. and Kinetic energy of skater B is more than skaterA
[tex]P_{a} =P_{b}[/tex]
we know that
[tex]KE=\frac{P^{2} }{2m}[/tex]
As given [tex]m_{a} > m_{b}[/tex]
[tex]K_{B} > K_{A}[/tex]
Kinetic energy of skaterB is more than skaterA
A push or a pull that an object experiences as a result of interacting with another item is known as a force. Interactions result in forces! As mentioned, action-at-a-distance interactions produce and other forces (gravitational, electrical, and magnetic forces). Newton proposed that anytime objects A and B come into contact, forces are applied to one another. When you sit in a chair, you apply a downward force to the chair, and the chair responds by applying an upward force to your body. This contact creates two forces: one force on the chair and one force on your body. The third law of motion of Newton deals with these two forces, which are referred to as action and reaction forces.
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