The angular distance should be the angular distance that the pie plate has moved through in revolutions, radians, and degrees are 5.59 revolution and 2012.4° respectively.
In revolution, θ = 8.24 revolution.
In radian = θ = 57.78 rad.
In degree θ = 2966.4°.
Calculation of the angular distance:
Since
Pie diameter = 9 in
So, the circumference of the pie should be
P = πd = 9π in
And, rim of the pie rotates 158 in,
So,
1 Revolution of the pie is 9π in,
So, for 158 it should be
= 158 in / 9π in revolution
= 5.59 revolution
Now in the case when
1 revolution is 2πrad
So,
5.59 revolution = 5.59 × 2π = 87.79 rad.
And also, 1 revolution is 360°
5.59 revolution = 5.59 × 360 = 2012.4°
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a car traveling at 15 m/s slams on its brakes and the wheels lock. the car comes to rest after skidding 20 m. determine how far the car would skid if the car had been traveling, instead, at 45 m/s.
The distance travelled by the car if had been travelling at a speed of 45 m/s is 180 m.
What is the distance travelled by the car?
The distance travelled by the car is calculated by applying the following kinematic equation as shown below.
v² = u² + 2as
where;
v is the final velocity of the car when it stops = 0u is the initial velocity of the car = 15 m/ss is the distance travelled by the car = 20 ma is the acceleration of the car = ?0 = u² + 2as
-2as = u²
a = -(u²)/2s
a = - (15²) / (2 x 20)
a = -5.625 m/s²
The distance travelled by the car if had been travelling at a speed of 45 m/s is calculated as;
v² = u² + 2as
0 = u² + 2as
s = -(u²)/2a
s = -(45²) / (2 x - 5.625)
s = (45²) / (2 x 5.625)
s = 180 m
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If the sun mysteriously gets twice as massive as it is right now, what effect will it have on its pull on mars?.
If the sun mysteriously gets twice as massive as it is right now, it's pull on Mars will be twice as much.
What would happen if the sun were twice as massive?The Sun is 93 million miles away from Earth on average, but it is still vital to maintaining life as we know it. We would undoubtedly experience substantial changes in our lives if it were to decrease, grow, or change in any manner.Most people agree that the energy that powers planet Earth comes from the sun, which is at the heart of the solar system. Our climate and weather systems are built on the light and heat that our life-supporting star emits, which also helps to support the development of life on Earth. We are also subject to the gravitational pull of the sun, and how quickly we orbit it determines how long a year is.To learn more about sun, refer to
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(figure 1) shows the cost of locomotion as a function of body mass. using this plot, determine the amount of energy expended by usain bolt during the 100 m sprint.
Assuming Usain Bolt begins at rest (with zero initial velocity) and his motion is uniformly accelerated, his position at time t is given by
where a denotes the average acceleration and t denotes the time. Because the distance covered in our problem is S=100 m and the time taken is t=9.58 s, the average acceleration can be calculated by rearranging the previous formula:
1175.50 kg m/s
Usain Bolt's weight is 93.89 kg.
The average velocity in a 100-meter sprint is 12.52 metres per second.
The momentum can be calculated by taking the product of mass and velocity and multiplying it by
The following factors provide momentum:kg m/s
where denotes mass and denotes velocity
Thus, Usain Bolt's momentum can be calculated by plugging in the given values for
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an undamped 2.52 kg2.52 kg horizontal spring oscillator has a spring constant of 21.6 n/m.21.6 n/m. while oscillating, it is found to have a speed of 3.34 m/s3.34 m/s as it passes through its equilibrium position. what is its amplitude ????a of oscillation? ????
The undamped horizontal spring oscillator has an amplitude of 1.61 m when passing through its equilibrium position during oscillation.
It is given to us that -
Mass of the undamped spring oscillator, m = 2.52 kg
Spring constant during oscillation, k = 21.6 n/m
Speed of the spring oscillator, v = 3.34 m/s
We have to find out the amplitude of oscillation, say A.
According to the concept of Conservation of Energy, we can say that -
[tex]\frac{1}{2} mv^{2} = \frac{1}{2} kA^{2}[/tex] ------ (1)
where,
m = mass of the oscillator
v = speed of oscillation
k = Spring constant
A = Amplitude of oscillation
Now, substituting the given values in equation (1), we have
[tex]\frac{1}{2} mv^{2} = \frac{1}{2} kA^{2}\\= > \frac{1}{2} *2.52*(3.34)^{2} = \frac{1}{2} *21.6*A^{2}\\= > 28.11211 = 10.8A^{2}\\= > A^{2}=2.60\\= > A = 1.61m[/tex]
Therefore, the undamped horizontal spring oscillator has an amplitude of 1.61 m when passing through its equilibrium position during oscillation.
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what would a permanently magnetic substance be called? a. soft magnet c. hard magnet b. fast magnet d. quick magnet please select the best answer from the choices provided a b c d
The ideal response is C. Hard magnets are substances that are permanently magnetic.
What kind of magnet would you say is hard?An illustration of a naturally hard magnetic substance is iron. The strongest powerful permanent magnets were NdFeB, which are produced from powdered grains of various alloys in a pressure and at high temperatures.
How is a hard magnet created?Soft magnets possess low values for coercivity (Hc), whereas hard magnets have high values, allowing them to maintain their magnetization even in the absence of any applied field. The hysteresis loops of soft and hard magnets are contrasted in the picture on the right.
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A slinky is stretched by two forces. When the forces are removed, the slinky returns to its original length. The slinky has been __________ deformed.
A slinky is stretched by two forces. When the forces are removed, the slinky returns to its original length. The slinky has been permanently deformed.
What causes permanent deformed?
When a material is subjected to stresses that are greater than its yield strength and cause it to elongate, compress, buckle, bend, or twist, this permanent distortion is known as plastic deformation.
Plastic deformation occurs when a metal is sufficiently stressed to permanently alter its shape. A few atomic bonds are broken during plastic deformation, as was covered in the section on crystal defects, as a result of the movement of dislocations.
When a structural part of a rail vehicle experiences permanent deformation, its shape changes.
Therefore, A slinky is stretched by two forces. When the forces are removed, the slinky returns to its original length. The slinky has been permanently deformed.
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in situ quantification of the active sites turnover frequency and stability of ni-fe oxy hydrooxide for the oxygen evolution reaction
The intrinsic catalytic characteristics of nanoscale electro catalysts requires quantification of the active site count and site-specific turnover frequency (TOF).
How does turnover frequency and stability of ni-fe oxy hydroxide for the oxygen evolution reaction?Understanding the intrinsic catalytic characteristics of nanoscale electro catalysts requires quantification of the active site count and site-specific turnover frequency (TOF).
The understanding of Ni-Fe (oxy)hydroxides' electro catalytic activity and stability is hampered by the lack of efficient methods for measuring the Fe active site number and the intrinsic turnover frequency per active Fe site (TOFFe), despite the fact that Fe has been proposed as one of the most active noble-metal-free electro catalysts for the alkaline oxygen evolution reaction (OER).
The direct in situ quantification of the electrochemically active Fe site number and associated TOFFe values of Ni-Fe (oxy)hydroxides using previously unstudied Fe2+/3+ redox electrochemistry in alkaline solutions is described in this article.
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as like charges move closer together their lines of force bend farther away from the other charge and push together into a smaller space what does this indicate about the size of the forces between them
This indicates that the size of forces between the like charge are strong.
What is charge?
Electric charge is the property of subatomic particle. This property makes these particles to experience the electric force of attraction and repulsion. there are two type of charges, positive and negative charge. The force experienced by two like charges is of repulsion and that of unlike charges is attraction. These forces are proportional to the extend of charge.
What are like and unlike charges?
The charges that experience the electric force of attraction when brought closer are known as unlike charges. When +ve and -ve charges are brought closer they experience the electric force of attraction. The charges that experience the electric force of repultion when brought closer are known as like charges. When two +ve and +ve charges are brought closer they experience the electric force of repulsion.
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sixteen-year-old michael begins growing a marijuana plant in a corner of his family's garden. his father asks him to remove it because it is illegal. in kohlberg's terms, michael's father is demonstrating reasoning.
In Kohlberg's terms, Michael's father is demonstrating Conventional reasoning.
According to Kohlberg's Structural Theory of Moral Development, conventional moral reasoning is the second of three levels of moral reasoning. At this level, people have internalized the moral standards and expectations of those closest to them and typically base their moral decisions on these standards and expectations.
In the given question, Michael is unaware that marijuana is prohibited, but his grandfather has instructed him to take it out because it is forbidden. It is unlawful, according to his father. It demonstrates that his father is aware of the laws. He believes that they must follow it since it is their responsibility, or else his son would be punished for breaking the law.
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what will the frequency be if 0.160 kg are subtracted from the original mass? try to solve this problem without finding the force constant of the spring.
Frequencies in both cases are [tex]& f_2=1.225 \mathrm{H}_z[/tex] and [tex]}} \\& f_2=1.522 \mathrm{H}_z[/tex]
What is frequency ?The frequency of a repeated event is its number of instances per unit of time. It differs from angular frequency and is sometimes referred to as temporal frequency for clarification. One event occurs per second when measuring frequency in hertz.
The quantity of waves that pass a set location in a predetermined period of time is known as frequency. Therefore, if a wave passes through in half a second, the frequency is 2 per second. The frequency is 100 times per hour if it takes 1/100 of an hour.
According to the given information
We got to know
A) the frequency of two spring
[tex]f=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}[/tex]
for Same spring
[tex]f \propto \frac{1}{\sqrt{m}}[/tex]
So
[tex]& \frac{f_2}{f_1}=\sqrt{\frac{m_1}{m_2}} \Rightarrow f_2=f_1 \sqrt{\frac{m_1}{m_2}} \\[/tex]
[tex]& f_2=1.35 \times \sqrt{\frac{0.75}{(0.16+0.75)}} 2=222=1 \frac{1}{2} \\[/tex]
[tex]& f_2=1.225 \mathrm{H}_z[/tex]
B)
[tex]& f_2=f_1 \sqrt{\frac{m_1}{m_2}} \\& f_2=1.35 \times \sqrt{\frac{0.75}{(0.75-0.16)}} \\& f_2=1.522 \mathrm{H}_z[/tex]
Frequencies in both cases are [tex]& f_2=1.225 \mathrm{H}_z[/tex] and [tex]}} \\& f_2=1.522 \mathrm{H}_z[/tex]
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A stationary boat bobs up and down with a period of 2.1 s when it encounters the waves from a moving boat.
What is the frequency of the waves? If the crests of the waves are 8.8 m apart, what is their speed?
The frequency of the waves is 0.48Hz and their speed is 4.2m/s.
Define frequency.
The number of waves passing a fixed place in a unit of time is known as frequency.
Given ,
Time ,t is 2.1s
Frequency, F =1/t
F =1/2.1
F =0.48Hz
A periodic wave's wavelength, or the distance over which the wave's shape repeats, is its spatial period. It is the separation between neighboring wave points that correspond to the same phase, such as two adjacent crests, troughs, or zero crossings. It is a property of both traveling waves and standing waves as well as other spatial wave patterns. The spatial frequency is the wavelength's reciprocal. The Greek letter lambda ( λ) is frequently used to denote wavelength.
Speed ,v = λ / T.
v = 8.8/2.1
v =4.2m/s
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which of the following are postulates of the kinetic molecular theory of gases? multiple select question. the average kinetic energy of the gas particles is inversely proportional to the absolute temperature. the gas particles are in constant, random motion although they do move in straight lines. the gas particles do not exert attractive or repulsive forces on each other. collision of gas particles are assumed to be elastic. the volume of gas particles is negligible compared to the volume occupied by the gas.
The relationship between the absolute temperature and the average kinetic energy of the gas particles is inverse. Gas particle collisions are thought to be elastic.
When compared to the volume that the gas occupies, the volume of the gas particles is insignificant. There are no forces of attraction or repulsion between the gas particle. Although they travel in straight lines, the gas particles are constantly in a random motion.
What is particle collision?
There may be collisions between the particles and the wall during particle flows. The kinetic energy lost upon particle collision can cause frictional heat to be produced, walls to erode, particles to shatter or deform, be aggregated, or substances to become electrified.
What occurs when gases come together?
Gas molecules exclusively interact with one another through collisions; they do not apply any other forces. They don't adhere to one another. All gas molecule collisions are flawlessly elastic, and all kinetic energy is preserved.
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what is the capacitive reactance ????c of a 60.0 μf capacitor placed in an ac circuit driven at a frequency of ????
Capacitive reactance is measured in Ohms, just like resistance. 1,000,000 divided by 6.28 times 60 hertz times 106.1 microfarads, or 25 ohms, is the capacitive reactance.
The amount of charging a capacitor can accomplish depends on its capacitance. Capacitive reactance is a measurement of the capacitor's resistance to alternating current. The following formula can be used to determine a capacitor's capacitive reactance or impedance: The constant one million (or 106) divided by the product of 2p (or 6.28) times frequency times capacitance is known as capacitive reactance, abbreviated as x sub c (XC). where XC is the capacitance, expressed in ohms.
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Listed following are several objects in the solar system. Rank these objects from left to right based on their orbital period around the Sun from shortest to longest. A typical asteroid in the asteroid belt, a trojan asteroid, a typical kuiper belt object, a typical oort cloud object
All of the objects that have been listed in the question have been ranked on the basis of the orbital period around the Sun from shortest to longest in the solar system below.
The items included are all objects that are present in the solar system other than the planets, moons, and stars. These objects, just like every other body, have an orbit in which they revolve and their revolution takes place around the Sun as well.
The order on the basis of their orbital period around the Sun from shortest to longest is as thus -
A typical asteroid in the asteroid belt, a trojan asteroid, a typical Oort cloud object, a typical Kuiper belt object
The orbital period of the items is also as thus -
A typical asteroid - 3 to 6 years
A trojan asteroid - 150 to 200 years
A typical Oort cloud object - 200 years
A typical Kulper Belt object - About 10,500 years
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What is the acceleration of a racehorse that is running 19 m/s and the
track has a radius of 50 m?
The acceleration of a racehorse that is running 19 m/s and the track has a radius of 50 m is 7.22 m/s².
What is centripetal acceleration?Centripetal acceleration, the acceleration of a body in a circular orbit. Since velocity is a vector quantity (that is, it has both magnitude, velocity, and direction), as an object moves along a circular path, its direction and velocity constantly change, resulting in acceleration. The centripetal acceleration ac has a magnitude equal to the square of the body velocity v along the curve divided by the distance r from the center of the circle to the moving body. That is, α = v²/r. Centripetal acceleration has units of meters per second squared. The force that causes this acceleration is also directed toward the center of the circle and is called the centripetal force.
α = v²/r
Where, α = centripetal acceleration
r = radius (50 m)
v = velocity (19 m/s)
α = 19²/50
α = 7.22 m/s²
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A metal cools from an initial temperature of 225 oc to 25 oc and releases 160 j of heat energy. If the mass of the metal is 5. 0 g, what is its specific heat capacity?.
If a metal cools while releasing 160 j of heat energy, its specific heat capacity is 1.4222 J/kg. In the event that the metal weighs 5.0 g
Why is specific heat important? What does it mean?A amount of heat unit unit of mass needed to raise temperature temperature by one degree Celsius is known as the thermal inertia or specific heat. The ability to distinguish between various polymeric composites using specific heat can be useful in calculating the processing temperatures the volume of heat required
T₁ = 225°C
T₂ = 25°C
q = -160 J
m = 5.0 g
As we know,
q = mcΔT
Now,
-160 = 5*c*(T₂-T₁)
-160 = 5*c*(25-225)
c = -160/5(-200)
c = 0.16 J/g°c.
What distinguishes heat capacity from specific heat?Summary. The heat capacity of a thing is indeed the amount of energy needed to raise its temperature by one degree Celsius. The amount of energy required to raise the temperature od 1 gram of a substance by 1oC is known as its specific heat.
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what capacitor in series with a 100ω resistor and a 30.0 mh inductor will give a resonance frequency of 1040 hz ?
Capacitance is C = [tex]8.126[/tex] × [tex]10^{-4}[/tex]
What is Capacitance ?A material thing or device's capacitance is its ability to hold electric charge. The ratio of those two values is used to calculate the change in charge in response to an alteration in electric potential.
According to the given information
The RLC circuit's resonant frequency is determined by
f = [tex]\frac{1}{2\pi \sqrt{LC} }[/tex]
L is the circuit's inductance, and C is its capacitance.
By rearranging the equation, we get
C = [tex]\frac{1}{(2\pi) ^{2}f^{2} L }[/tex]
and by substituting the inductance of the circuit L = 30mH = 0.030mH
The resonant frequency f = 1040 Hz
We need to find the value of the capacitance
By substituting the values in C
C = [tex]\frac{1}{(2\pi) ^{2}(1040)^{2}(0.03) }[/tex]
C = 0.0008126 [tex]u[/tex]C
C = [tex]8.126[/tex] × [tex]10^{-4}[/tex]
Capacitance is C = [tex]8.126[/tex] × [tex]10^{-4}[/tex]
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When a metal car is struck by lightning, the resulting electric field inside the car is?.
When a metal car is struck by lightning, the resulting electric field inside the car is zero.
What is Electric field ?The electric force per unit charge is referred to as the electric field. It is assumed that the field's direction corresponds to the force it would apply to a positive test charge.
The roof and walls of the car provide a path of less resistance than the interior of the car, which is why a person inside a car does not get struck by lightning.
When lightning is present, it is safer to sit under a car than to stand under a tree. Inside the car, there is no electric field.
The metal cage that encloses the occupants of cars protects them from lightning.
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The long straight wire in the figure carries a current i that is decreasing with time at a constant rate. The circular loops a, b, and c all lie in a plane containing the wire. The induced emf in each of the loops a, b, and c is such that.
The induced EMF in each of the loops a, b, and c is such that loop A has a counter-clockwise EMF, loop B has no induced EMF, and loop C has a clockwise EMF.
How is the direction of EMF decided?As given in the figure, the loops a, b, c are decreasing with time.The direction of current is left to right.Due to which , current is maximum at loop A and minimum at loop C .We know, if current is maximum then the magnetic field is also maximum.If magnetic field is maximum then induced magnetic field is minimum and hence induced EMF is also minimum.Because the EMF is minimum loop A will rotate counter-clockwise .Since, loop B is along the wire there is no magnetic field hence no EMF .And loop C is at minimum hence more EMF is generated and hence it rotates clockwise .What is EMF ?The highest potential difference between two electrodes of a galvanic or voltaic cell is what creates electromagnetic force. The characteristic has to do with how readily an element, molecule, or ion tends to gain (gain) or lose electrons.
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Without his glasses, Isaac can see objects clearly only if they
are less than 4.2 m from his eyes.
What focal length glasses worn 2.1 cm from his eyes
will allow Isaac to see distant objects clearly?
Express your answer using two significant figures.
Generally speaking, the object distance indicates that the light rays emanating from the object are parallel to one another, resulting in f=-4.221.
What kind of thing is a light ray like?A ray is defined as a small, usually straight-traveling beam of light. The laser or laser pointer's light beam is an illustration of a ray. According to the ray model of light, a ray moves in a straight line until it encounters an object, such as a mirror or the boundary between two materials.
image distance is v = 4.7 + (2.1 * 10-2) = -4.721 m the negative
means image is formed behind the lens
Generally the object distance is u = ∞ this mean the light ray coming from the object are parallel to each other.
So from lens equation
=-고=수
=> f = -4.721 m
What is a light ray, exactly?As an electromagnetic wave, light travels in straight lines along narrow beams of light, which are referred to as rays. Despite the fact that reflection or refraction can alter its direction, light always moves in a straight line.
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A diatomic element has six bonding electrons, six non-bonding electrons, and 2 anti-bonding electrons. What is the bond order?.
Bond order for the diatomic element is 2
A bond order is something that pairs two atoms with their atoms.
It is an atomic-level phenomenon in which elements share their electrons to fill their valence shell. It can also bind two or more substances together in a compound.According to molecular orbital theory, the bond order is half the difference between the bonding and antibonding electrons.
Mathematically, Bond Order = 0.5 (No of bonding electrons - No of anti-bonding electrons)Bonding electrons of the element = 6
Anti-bonding electrons of the element = 2
Difference = bonding electrons - anti-bonding electrons
= 6 - 2
= 4
Bond order = (0.5)*(difference)
Bond order = (0.5)*(4)
Bond order = 2
Bond order for the diatomic element has six bonding electrons, six non-bonding electrons, and 2 anti-bonding electrons is 2.
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current will travel along the path with the highest resistance. please select the best answer from the choices provided t f
False. Current will travel along the path with the lowest resistance. This is because electrons will take the path of least resistance in order to reach the point of lowest potential energy.
The Principle of Lowest Resistance: Exploring Electron Flow
The concept of electrons traveling along paths of least resistance is a fundamental principle of electrical engineering. This principle, known as the principle of lowest resistance, states that electrons will take the path of least resistance in order to reach the point of lowest potential energy. This phenomenon has implications in various areas of electrical engineering, from circuit design to power distribution.
The basic principle of lowest resistance can be demonstrated with a simple circuit. Imagine a circuit with two parallel paths, one with a higher resistance and one with a lower resistance. When a voltage is applied to the circuit, electrons will flow along the path of least resistance, which in this case is the one with the lower resistance.
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A tugboat pulls with a constant net horizontal force of 5000 N and causes the ship to move through a harbor. How much work is done on the ship if it moves a distance of 3000m?
15000000 Joule work is done on the ship if it moves a distance of 3000m.
What is work done?The amount of force multiplied by the distance moved in the force's direction is known as the work done by a force acting on an item. Work has no direction and only magnitude. Work is a scalar quantity as a result. SI unit of work is joule.
Given parameters:
horizontal force applied on the tugboat is: F = 5000N.
The tugboat moves a distance: d =3000m.
Hence, The work done on the ship is = Fd = 5000N × 3000m = 15000000 Joule.
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Argon gas has several industrial uses, including arc welding and steel making. Argon is nonflammable and nontoxic, and so can be kept at room temperature (T = 19° C). Companies can buy Argon gas in cylinders which are kept at pressure of P = 246 psi. In this problem you may assume that ideal gas law still holds.
A) How much average kinetic energy (in J) does each atom of the argon gas in the cylinder have?
B) If the volume is 197L, how many moles of Argon are inside?
A. The average kinetic energy for each atom of argon gas in the cylinder is 6.04 × 10⁻²¹ Joule.
B. The number of moles of argon inside the cylinder is 1.38 × 10² mol.
The formula to calculate the average kinetic energy for monoatomic gas is
KE = 3/2 kT
T = the temperature (K)KE = 1.5 kT
KE = 1.5 × 1.38 × 10⁻²³ × 292
KE = 6.04 × 10⁻²¹ J
For every ideal gas applies the ideal gas equation
PV = nRT
P = the pressure (Pascal)PV = nRT
1.7 × 10⁶ × 1.97 × 10⁻¹ = n × 8.314 × 292
3.35 × 10⁵ = n × 2.43 × 10³
n = 1.38 × 10² mol
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Air in an ideal Diesel cycle is compressed from 4 L to 0.25 L, and then it expands during the constant pressure heat addition process to 0.50 L. Under cold air standard conditions, determine the thermal efficiency of this cycle.
Under cold air standard conditions, Then the thermal efficiency of this cycle is 61.38%.
n= 1- ((a^x)-1)/(x*e^(x-1) *(a-1)
n=thermal efficiency
e=compression ratio= v1/v2
a=cut off ratio=V3/V2
x=Cp/Cv=1.4 for air
v1=4L
v2=0.25L
v3=0.5 L
e= 4/0.25=16
a= 0.5/0.25 =2
n= 1- ((2^1.4)-1)/(1.4*16^(1.4-1) *(2-1) = .6138 = 61.38%
A system's thermal efficiency is determined by how much work is produced for every unit of heat input. Work is produced by heat engines. The percentage of heat that is converted into usable work is expressed as thermal efficiency.
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suppose that 20 j of work is needed to stretch a spring from a0 cm to 2a0 cm. 80 j of work is needed to stretch it from a1 cm to 2a1 cm. what is the natural length of the spring. note that a0 and a1 are some constants and the unit is cm instead of m
Let L be the natural length,
Since 20J of work is needed to stretch the spring from a₀ cm to 2a₀ cm,
We have,
20 = k/2 [ (2a₀-L)² - (a₀-L)²] --------- eq 1
Again,
80 J of work is needed to stretch the spring from a₁ cm to 2a₁ cm,
80 = k/2 [ (2a₁-L)² - (a₁-L)²] ---------- eq 2
Now,
eq 2 / eq 1
k/2 [ (2a₀-L)² - (a₀-L)²] / k/2 [ (2a₁-L)² - (a₁-L)²] = (80/20)
a₁(3a₁ - 2L) / a₀(3a₀ - 2L) = 4
3a₁² - 2La₁ / 3a₀² - 2La₀ = 4
3a₁² - 2La₁ = 12a₀² - 8La₀
L(8a₀ - 2a₁) = 12a₀² - 3a₁²
L = (12a₀² - 3a₁²) / (8a₀ - 2a₁)
Therefore the required length of spring or the natural length is (12a₀² - 3a₁²) / (8a₀ - 2a₁).
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learning goal: to understand the role of friction in a state of equilibrium. a chair weighing 70.0 n rests on a level floor that is not frictionless. a man pushes on the chair with a force f
Given details :
Weight of chair W = 70 NForce P = 39 NAngle = 38°1.Force equilibrium in x direction
∑ [tex]F{x}[/tex] = 0
F - 39 cos Ф = 0
As Ф = 38°
F = 39 cos38°
F = 30.73 N
Force equilibrium in y direction
∑ [tex]F{y}[/tex] = 0
N = W + P sin38°
= 70 + 39 sin38°
N = 93.79 N
Thus the normal force on chair = 93.79 N
From the free body diagram
F = μN
30.73 = μ x 93.79
μ = 30.73 / 93.79 = 0.32
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A lemming running 2.87 m/s runs off a horizontal cliff. It lands in the water 5.32 m from the base of the cliff. What is the lemming's change in height when it reaches the water?
(Unit = m)
16.77m is the lemming's change in height when it reaches the water.
An example of a projectileA thing is said to be in projectile motion when it has been fired into the air. After the initial force that launches the object, it only experiences the force of gravity. It is what it is—a projectile—and the path it took to get there is what it was.
You can tell from the situation that this projectile is a Type 1 projectile, or a horizontal projectile. Before you can resolve this issue, you will need a few things.
You must first examine the information you were given:
Vix = 2.87 m/s
dx = 5.32m
Your height or vertical distance are what you need. The following is the usual formula for projectile displacement:
d = Vit +1/2gt²
Specifically, you only need to enter the y-components to obtain the vertical distance. Now keep in mind that a horizontal projectile initially moves only forward and not vertically. Your vi = om/s, leaving you with the following equation:
dy = Viyt + 1/2 gt²
dy = (0m/s)t + 1/2 gt²
dy = 1/2 gt²
However, if you examine your issue, you will discover that no time has been allotted. You can resolve it using the information provided by deriving it from the x component formula:
dx = Vixt
Plug in your knowledge and find a solution for your ignorance.
dx = Vixt
5.32m = (2.87m/s)t
5.32/2.87= t
t = 1.85s
You can solve for your vertical distance/displacement now that you know the time:
dy = 1/2 gt²
dy = 1/2 (9.8 × 1.85²)
dy = 16.77m.
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Answer:
the answer is -16.8
Explanation:
it’s negative because your going down and you have to round off to match the significant digits.
two objects a and b move toward each other with speeds of 10 m/s and 2 m/s, respectively. the mass of a is 2 kg and that of b is 10 kg. after a head-on, perfectly inelastic collision, the speed of a and b is? g
Answer:
The speed of a and b will be same about 3.333 m/s after collision.
Explanation:
In a perfectly inelastic collision the bodies gets attached to each other after collision .
In this type of collision the final kinetic energy gets lowered than the initial one. Whereas the momentum before and after the collision still remains constant.
Thus we apply the theory of conservation of momentum.
M1V1+ M2V2 = (M1+M2)V
Thus V= 40/12 =3.33 m/s
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a student pulls a 60 newton sled with a force having a magnitue of 20 newtons what is the magnitude of the force that the sled exerts n the students
The magnitude of the force exerted by the sled on the student is 20N
Concept:
Every action on one body causes an equal and opposite response on the other, according to Newton's third rule of motion. It implies that if a body is pulled toward itself by a human, the body will also draw the person toward itself with the same force.
The direction of the body's response to the person will be in opposition to the direction of the person's response to the body.
The sled will similarly exert the same amount of effort on the student to drag him backward in the opposite direction as the student exerts on the sled to pull it forward.
The sled's weight moves in a vertically downward direction, therefore it has no bearing on the reaction force the sled exerts on the learner.
Consequently, the sled's force on the student was of the following magnitude: 20N
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