Consider a bicycle wheel with a radius of 30 cm and 16 spokes that is mounted with its axle fixed in a horizontal position. The number of spokes that pass close to an electronic eye are counted and registered on a computer. This meausre of the rate at which the wheel turns is used to observe the wheel's motion when a 50 g mass is hung from a string wrapped around the periphery of the tire. The wheel is held stationary with the weight hanging as shown and then released
Image for Consider a bicycle wheel with a radius of 30 cm and 16 spokes that is mounted with its axle fixed in a horizon
The wheel starts to spin, and spins faster and faster until the string slips off 5 second after release. The readings of the display device are summarized in the graph below.
Image for Consider a bicycle wheel with a radius of 30 cm and 16 spokes that is mounted with its axle fixed in a horizon
1. What is the angular velocity of the wheel (in rad/s) at t = 5.0 s?
2. What is the angular acceleration of the wheel (in rad/s2) before t = 5.0 s?
3. What is the acceleration of the hanging mass (in m/s2) during the time when the wheel's speed is increasing?
4. What is the tension in the string (in N) while the wheel's speed is increasing? (Tip: Draw the free-body diagram of the mass. You should have two forces.)
Answers
Angular velocity of the wheel at t = 5.0 s Angular velocity is the angle through which a point on a rotating object moves per unit time. It is usually measured in radians per second.
The formula to calculate angular velocity is: ω = θ/t where ω is angular velocity in radians per second θ is angular displacement in radians and t is the time taken in seconds Given that the wheel starts from rest and accelerates uniformly to a final angular velocity of 60 rad/s in 5 seconds and that the radius of the wheel is 30 cm, we can calculate the angular velocity of the wheel at t = 5.0 s.
Using the formula ω = θ/t
we haveθ = 1/2 * α * t²,
where θ = angular displacement
α = angular acceleration
t = time taken
Putting the given values into the formula, we get
θ = 1/2 * α * t² = 1/2 * 4π² * (30/100) * (5/16)² = 0.919 rad/s Therefore, the angular velocity of the wheel at t = 5.0 s is:ω = θ/t= 0.919/5.0 = 0.184 rad/s
Angular acceleration of the wheel before t = 5.0 s Angular acceleration is the rate of change of angular velocity of an object. It is usually measured in radians per second squared. The formula to calculate angular acceleration is: α = Δω/Δt where α is angular acceleration in radians per second squared Δω is change in angular velocity in radians per second Δt is the time taken for the change in angular velocity to occur Given that the wheel starts from rest and accelerates uniformly to a final angular velocity of 60 rad/s in 5 seconds, we can calculate the angular acceleration of the wheel before t = 5.0 s.
Using the formulaα = Δω/Δt
we have Δω = 60 - 0 = 60 rad/s
Δt = 5.0 - 0 = 5.0 s
Putting the given values into the formula, we get
α = Δω/Δt= 60/5.0= 12 rad/s²
Therefore, the angular acceleration of the wheel before t = 5.0 s is 12 rad/s².3. Acceleration of the hanging mass during the time when the wheel's speed is increasing
The acceleration of the hanging mass can be calculated using the formula: a = rα
where a is the tangential acceleration of the mass r is the radius of the wheelα is the angular acceleration of the wheel Before t = 5.0 s, the angular acceleration of the wheel is constant and equal to 12 rad/s². Therefore, the tangential acceleration of the hanging mass is: a = rα= (30/100) * 12= 3.6 m/s² Therefore, the acceleration of the hanging mass during the time when the wheel's speed is increasing is 3.6 m/s².4. Tension in the string while the wheel's speed is increasing
The free-body diagram of the mass when the wheel is rotating is shown below: Image for Consider a bicycle wheel with a radius of 30 cm and 16 spokes that is mounted with its axle fixed in a horizon From the free-body diagram, the forces acting on the mass are its weight (mg) and the tension in the string (T). Since the mass is moving in a circle, the net force acting on it is given by: F = ma = m ra = mrα where F is the net force acting on the mass m is the mass of the object r is the radius of the circleα is the angular acceleration of the objectSubstituting the given values into the formula, we get: F = ma = mra= (0.050 kg) * (30/100) * 12= 0.018 NSince the mass is not accelerating in the vertical direction, the net vertical force acting on it must be zero. Therefore, the tension in the string is: T = mg - F= (0.050 kg) * 9.81 m/s² - 0.018 N= 0.472 N Therefore, the tension in the string while the wheel's speed is increasing is 0.472 N.
The angular velocity of the wheel at t = 5.0 s is 0.184 rad/s.2. Angular acceleration of the wheel before t = 5.0 s is 12 rad/s².3. Acceleration of the hanging mass during the time when the wheel's speed is increasing is 3.6 m/s².4. Tension in the string while the wheel's speed is increasing is 0.472 N.
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Related Questions
A 9.00 g bullet is fired horizontally into a 1.20 kg wooden block resting on a horizontal surface. The coefficient of kinetic friction between block and surface is 0.20. The bullet remains embedded in the block, which is observed to slide 0.390 m along the surface before stopping. Part A What was the initial speed of the bullet? Express your answer with the appropriate units. μΑ ? V = Value
Answers
The initial speed of the bullet before getting embedded into the wooden block is 0.39 m/s.
The mass of the bullet is 3 grams and it is embedded into the wooden block of mass 1.20 Kg.
The coefficient of friction between the block and the surface of block is 0.20. The bullet remains embedded into the block when it slides till 0.390m along the surface before stopping.
We know,
Work done by resistive force = Change in kinetic energy.
Resistive force = 0.009 x 0.20 x 0.390
Putting values,
0.009 x 0.20 x 0.390 = 0.5 x 0.009 x V²
V is the initial speed of the bullet.
V = 0.39 m/s.
The initial speed of the block is 0.39 m/s.
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. consider the replacement of the 400 mw san juan thermoelectric power plant in puerto rico, which uses heavy fuel oil to generate electricity, with a solar photovoltaic farm. the oil plant has a heat rate of 10,811 btu/kwh and a capacity factor of 53%. a. for installation of south-facing fixed tilt pv arrays, with tilt angle equal to the local latitude in san juan, how many acres of collector surface area would be required to replace the generation from the fuel oil plant? assume that the photovoltaic cells have an efficiency of 17%. b. by how many acres can the surface area in part (a) be reduced if single-axis tracking is added (with the collector tilt angle still equal to the local latitude)? c. what will be the annual fuel cost savings ($) if the oil power plant is retired, if heavy fuel oil costs $290 per metric ton and has a heating value of 39,500 btu/kg?
Answers
Annual saving energy produced *cost of oil/heating value is
$ 10020.46177.
Latitude and longitude: what are they?Latitudes are lines that are horizontal and show how far a location is from the equator. In relation to the meridian in Greenwich, England, longitudes are vertical lines that show the east and west directions. Latitude and longitude are used in conjunction to locate points or places on the globe by cartographers, geographers, and others.
Puerto Rico's capital city's latitude and longitude are 18° 27' 58.7988" North and 66° 6' 20.5956" West.
Local San Juan latitude divided by tilt angle equals 18.46 WBAN No. 11641 = for year = 5.5 provides information on solar radiation for flat plate collectors facing south with a fixed tilt.
KWh/m2/day = 5.5 KWh/m2/day (1 day =3600h)
Formula used-
Solar radiation at that place* Collector Area *Collector efficiency = Heat rate * Output
power*Capacity factor
1 KW= 3,412.14 BTU/h
Heat rate* output power* capacity factor = 10,811*400*10^3*0.53 BTU/h = 671699.2855
KW
Collector Area = 671699.2855*3600/5.5*0.17
= 25862218.48 m^2= 6390 acres
C.
Cost of oil = 290$ /10^3 kg
Energy produced= 400*10^3 KW = 1364856 *10^3 BTU/h
Heating value = 39,500 Btu/kg
Annual saving Energy produced *cost of oil/heating value
= $ 10020.46177
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We can roughly model a gymnastic tumbler as a uniform solid cylinder of mass 75 kg and diameter 1.0 m. If the tumbler rolls forward at .50 rev/s.A) how much total kinetic energy does he have? B) what percent of his total kinetic energy is rotational?
Answers
The gymnastic tumbler has a total kinetic energy of 0.9375 J, and 38.46% of that total kinetic energy is due to rotational motion.
What is kinetic energy?
Kinetic energy is the energy possessed by an object due to its motion. It is defined as the work required to accelerate an object of a certain mass from rest to its current velocity.
Given:
Mass of the tumbler (m) = 75 kg
Diameter of the tumbler (d) = 1.0 m
Angular velocity (ω) = 0.50 rev/s
The radius (r) of the tumbler is half of its diameter, so r = d/2 = 0.5 m.
Linear velocity (v) = ω * r
v = (0.50 rev/s) * (0.5 m)
v = 0.25 m/s
a) Total kinetic energy (K_total) of the tumbler consists of both translational and rotational kinetic energy. The translational kinetic energy (K_trans) can be calculated using the formula:
K_trans = (1/2) * m * v^2
K_trans = (1/2) * (75 kg) * (0.25 m/s)^2
K_trans = 0.9375 J
b) The rotational kinetic energy (K_rot) can be calculated using the formula:
K_rot = (1/2) * I * ω^2
I = (1/2) * m * r^2
I = (1/2) * (75 kg) * (0.5 m)^2
I = 4.6875 kg·m²
K_rot = (1/2) * (4.6875 kg·m²) * (0.50 rev/s)^2
K_rot = 0.5859 J
Percentage of rotational kinetic energy = (K_rot / K_total) * 100
Percentage of rotational kinetic energy = (0.5859 J / (0.9375 J + 0.5859 J)) * 100
Percentage of rotational kinetic energy ≈ 38.46%
Therefore, the gymnastic tumbler has a total kinetic energy of approximately 0.9375 J, and approximately 38.46% of that total kinetic energy is due to rotational motion.
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An 18kg block moving at 6 m/s has kinetic energy of
Answers
½ × 18 × 6² = 324 J
hope that helps^^
A wire of a given material has an electric field of 0.100 mV/m when a potential is applied. The wire has 8.49 x 1028 conduction electrons per cubic meter and a mean free time between collisions of 2.50 x 10-14 s. What is the uniform current density in the wire
Answers
The uniform current density in the wire is 5.43 x 10²⁷ A/m².
Current density in the wireThe uniform current density in the wire is calculated as follows;
J = total current / total area
The given parameters:
Conduction of the wire = 8.49 x 10²⁸ e/m²time, t = 2.5 x 10⁻¹⁴ s\(J = \frac{I}{A} = \frac{Q}{At} \\\\J = \frac{8.49 \times 10^{28}e/m^3 \ \times \ 1.6 \times 10^{-19} \ C/e}{2.5 \times 10^{-14} \ s \ \times ( 0.1 \times 10^{-3} \ V/m)} \\\\J = 5.43 \times 10^{27} \ A/m^2\)
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How are the weight and the mass of an object related?
Answers
Answer:
The weight and the mass of an object are related because the weight of an object is a measure of the force exerted on the object by gravity, or the force needed to support it. w=mg
consider the horizontal beam depicted below. it is supported by two fulcrums. a weight is suspended from the right end of the beam by means of a massless rope segment. what is the direction of the force exerted on the beam by the fulcrum that is 0.80 meters from the left end of the beam?
Answers
The direction of the force exerted on the beam by the left fulcrum (F_left) will depend on the relative magnitudes of W and F_right. If F_right is larger than W, then F_left will be pointing upwards. If W is larger than F_right, then F_left will be pointing downwards.
Based on the information given, we can assume that the beam is in static equilibrium, meaning that the sum of all the forces acting on the beam must be zero. The weight suspended from the right end of the beam creates a downward force, and the two fulcrums create upward forces to balance it out.
To determine the direction of the force exerted on the beam by the fulcrum that is 0.80 meters from the left end, we need to consider the moments (torques) created by each force. The moment created by a force is equal to the force multiplied by the perpendicular distance from the force to the fulcrum.
Let's label the weight as W and the distance from the left end of the beam to the right fulcrum as L. The distance from the left end of the beam to the left fulcrum is then (2.4 - L) meters.
The moment created by the weight W is W * 2.4 meters (the distance from the weight to the left fulcrum).
The moment created by the fulcrum on the left is F_left * (2.4 - L) meters (the distance from the left fulcrum to the right fulcrum).
The moment created by the fulcrum on the right is F_right * 0.8 meters (the distance from the right fulcrum to the weight).
Since the beam is in equilibrium, the sum of these moments must be zero:
W * 2.4 + F_left * (2.4 - L) - F_right * 0.8 = 0
We want to solve for F_left, so we can rearrange the equation:
F_left = (F_right * 0.8 - W * 2.4) / (2.4 - L)
We know that the weight is pulling the beam down, so F_right (the force exerted on the beam by the right fulcrum) must be pointing upwards to balance it out.
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describe what form of electromagnetic radiation does a radio use?
Answers
You see a plane directly overhead at 1622 m.3.51 seconds later, you hear the sonic boom. The speed of sound is 344
s
m
How fast is the plane traveling? Round your answer to 2 decimal places.
s
m
What is the Mach Number for the plane? Round your answer to 2 decimal places.
Answers
The Mach number for the plane is approximately 3.51.
To find the speed of the plane, we can use the equation:
Speed of sound = Speed of the plane / Time taken
Given: Speed of sound (v) = 344 m/s
Time taken (t) = 3.51 seconds
Let's calculate the speed of the plane:
Speed of plane = Speed of sound × Time taken
Speed of plane =\(344 m/s * 3.51 s\)
Speed of plane ≈ 1206.44 m/s
Rounded to 2 decimal places, the speed of the plane is approximately 1206.44 m/s.
To find the Mach number of the plane, we need to divide the speed of the plane by the speed of sound:
Mach number = Speed of plane / Speed of sound
Mach number ≈ \(1206.44 m/s / 344 m/s\)
Mach number ≈ 3.51
Rounded to 2 decimal places, the Mach number for the plane is approximately 3.51.
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Why don't normal everyday collisions result in fusion?
Answers
A squirrel standing on a branch shoots an acorn toward a hole in the tree. To determine how the potential energy of the acorn changes in relation to the earth, the position of what two objects must be considered?
a
The position of the acorn and the earth
b
The height of the branch and the position of the acorn
c
The position of the acorn and the width of the hole in the tree
d
The position of the squirrel on the branch and the earth
Answers
The positions to be considered are the position of the acorn and the earth.
What is potential energy?The potential energy is the energy that is possessed by a body by virtue of its position. Hence, the potential energy of a body changes as its position changes.
Hence, to determine how the potential energy of the acorn changes in relation to the earth, the positions to be considered are the position of the acorn and the earth.
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define the unit of time and unit of length
Answers
The base unit for time is the second (the other SI units are: metre for length, kilogram for mass, ampere for electric current, kelvin for temperature, candela for luminous intensity, and mole for the amount of substance). The second can be abbreviated as s or sec.
Answer:
hope you like
Explanation:
A unit of time is any particular time interval, used as a standard way of measuring or expressing duration.Its SI unit is second
A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. Its SI unit is meter
What type of corrective lenses would an eye doctor most likely prescribe for a patient with astigmatism?.
Answers
They are often the best choice for contact lens wearers with an astigmatism, because they're specifically designed to address the problem. The special shape of a toric lens creates different refractive, or focusing, powers that can help correct either a corneal or a lenticular astigmatism.
true or false? Sound travels faster trough water than air
Answers
Answer:
true
Explanation:
Sound travels faster in water compared with air because water particles are packed in more densely.
A bottle of water has approximately 800 times the amount of particles as a bottle of air.
it is proposed to use a small waterfall to turn an electricity generator. 10 meter cube of water fall 50m per minute. only one-fifth of its energy can be obtained usefully
Answers
This question is related to density where 16.7 kW power is used.
What is Density?Density is defined as mas per unit volume. It is denoted by ρ
We know the density of water is 1000kg/m³.
The given volume is 10m³. we have to find the mass. i.e. 10000 kg.
We know that \(Density =\frac{mass}{Volume}\)
Mass = Density x Volume
Mass = 1000kg/ m³ x 10m³ = 10000kg.
Here, We know that work against gravity is mgh.
So, 10000 kg x 10 m/s² x 50m = 5000000J.
But only one fifth of its energy is used.
5000000 / 5 = 1000000
Now we have the work done and time, so lets solve power.
Power=work done /time
1000000/60sec.
Power =16666.67 or 16.7kW
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If a Ferrari, with an initial velocity of 10 m/s, accelerates at a rate of 50 m/s2 for 3
seconds, what will its final velocity be?
Answers
Answer:
we know that
a (acceleration)= {v (final velocity)-u (initial velocity) } / t (time)
so if we have to find v, so it will be:
at/u=v
so 50 * 10= 500
divided by 3s
so the answer is 166.67 m/s.
LED lights will only work if the current is flowing in one direction. Which type of current would be best for powering an LED light bulb?
A.
Alternating current (AC) because with AC, the current flows steadily in one direction.
B.
Direct current (DC) because with DC, the current flows steadily in one direction.
C.
Direct current (DC) because DC provides more power but over shorter distances.
D.
Alternating current (AC) because with AC, the current periodically reverses.
Answers
Answer:
c
Explanation: i took the same text and got a 90
Direct current (DC) would be best because with DC, the current flows steadily in one direction. correct answer be Option (B).
What are direct current and alternating current?There are two main methods for creating electric current. Direct current (DC) and alternating current (AC) are these (AC).
Direct current is a technique in which electricity consistently flows in the same direction, like the flow of a river. It discusses how electricity generated by solar panels, batteries, and other sources flows.
On the other hand, alternating current (AC) is a method in which the positive and negative sides are alternately switched at regular intervals, thereby altering the direction of the energy flow. This is the electricity that is provided by a plug-in or a generator. Both the electricity generated at power plants and the electricity delivered to homes are transmitted using alternating current.
So, Direct current (DC) would be best for LED lights will only work if the current is flowing in one direction.
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A discordant igneous intrusion
Select one:
a.
cuts across bedding planes.
b.
will consist dominantly of pyroclasts.
c.
parallels sedimentary rock layering.
d.
produces deadly explosions.
Answers
A discordant igneous intrusion cuts across bedding planes. Here is the detailed explanation of the given question:Explanation:The Discordant igneous intrusion is the formation of an igneous rock mass when magma is injected into a host rock and cools there.
This form of igneous intrusion does not conform to the stratification or layering of the existing rock mass because it cuts across it.Therefore, a discordant igneous intrusion cuts across bedding planes.Option (a) is correct. It is the only option that describes the features of discordant igneous intrusion. Hence, the correct answer is option (a).
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A testable prediction is a(n) ______. Group of answer choices a. hypothesis b. experiment c. exercise d. variable
Answers
Answer :A testable prediction is also known as a hypothesis.
Explanation: I think
A testable prediction is a hypothesis. (a)
1. Compare the speed that light waves travel in air to the speed that sound waves travel in the air. How many times faster do light waves travel in air in comparison to sound waves in air?
Water-1500 meters per second
steel-5000 meters per second
Air-335 meters per second
Answers
Answer:
895522 times faster.
Explanation:
From the question given above, the following data were obtained:
Speed of sound in air (v) = 335 m/s
Speed of light in air (c) = 3×10⁸ m/s
How many times faster =.?
To obtain how many times faster light travels in air than sound, do the following
c : v => 3×10⁸ : 335
c/v = 3×10⁸ / 335
c/v = 895522
Cross multiply
c = 895522 × v
From the illustrations made above, we can see that the speed of the light in air (c) is 895522 times the speed of sound in air.
Thus, light travels 895522 times faster than sound in air.
Two 7th grade students made models of a population of bacteria before and after they were treated with an antibiotic for several generations. Use the models to answer the question.
Which statement below is the best explanation regarding the accuracy of the student’s models?
Answers
Answer:
A
Explanation:
After treating with an antibiotic for several generations, bacteria will develop antibiotic resistance.
How do bacteria develop resistance against antibiotics?Antibiotic resistance occurs when bacteria, fungi, and other microorganisms learn to resist the medications meant to kill them. That implies that the germs survive and develop. Treatment for resistant infections can be challenging and perhaps impossible.
Bacteria can evolve antibiotic resistance through mutation and selection. For instance, although some bacteria have evolved to create enzymes to inactivate the antibiotic, others have built biochemical "pumps" that can remove an antibiotic before it reaches its target.
Antibiotic usage is the primary contributor to antibiotic resistance. While some bacteria die when humans take antibiotics, resistant bacteria can live and even proliferate. Antibiotic usage increases the prevalence of microorganisms with resistance. The more we use antibiotics, the more antibiotic resistance will develop in bacterias.
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Which of the following is not true about elements.
Answers
Answer:
C
Explanation:
elements are classified as covalent, ionic, metallic
to identify all the approximately 20,000 to 25,000 genes in human DNA.
Answers
To identify all the approximately 20,000 to 25,000 genes in human DNA, scientists use a combination of technique such as DNA sequencing, genome annotation, gene expression analysis, and comparative genomics.
The identification of genes in human DNA involves a multi-step process. It typically begins with DNA sequencing, which generates the raw sequence data. This data is then analyzed and compared to known gene sequences using computational methods. Genome annotation tools are used to identify coding regions and regulatory elements within the DNA sequence. Gene expression analysis technique, such as RNA sequencing, help determine which genes are actively transcribed in specific tissues or under certain conditions. Comparative genomics, comparing DNA sequences across different species, aids in identifying conserved genes and their functions. These techniques collectively contribute to the identification of the thousands of genes in the human DNA.
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which of the following statements correctly describe the principal quantum number, n? select all that apply
-n can have any positive whole number number
-the value of n determines the shape of an orbital
-the value of n are restricted by the value of l
-the higher the value of n, the lower the energy value
-the lower the value of n, the greater the probability that the electron is closer to the nucleus
Answers
n can have any positive whole number, the lower the value of n, the greater the probability that the electron is closer to the nucleus.
Atomic nuclei include electrically superb protons and electrically neutral neutrons. those are held together with the aid of the strongest regarded fundamental pressure, called the robust force. The nucleus makes up lots much less than. 01% of the volume of the atom, but commonly contains more than 99.9% of the mass of the atom.
A nucleus is a group of debris referred to as protons, which are undoubtedly charged, and neutrons, which can be electrically neutral. Protons and neutrons are in flip made from particles referred to as quarks.
The nucleus controls and regulates the sports of the cellular (e.g., growth and metabolism) and consists of the genes, and systems that comprise the hereditary facts. Nucleoli are small in our bodies and are regularly seen inside the nucleus. The gel-like matrix wherein the nuclear components are suspended is the nucleoplasm.
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Q1: What causes light from a star to be red-shifted?
a. The distance between us and the star.
b. The chemical composition of the star.
c. The speed of the star away from us.
d. Temperature differences
Answers
The speed of the star away from us causes light from a star to be red-shifted. So the correct option is C.
Redshift refers to the phenomenon in which the wavelength of light from a star is stretched, causing it to shift towards the red end of the electromagnetic spectrum. This occurs due to the Doppler effect, which is the change in frequency or wavelength of a wave as the source and observer move relative to each other. When a star is moving away from us, the wavelengths of light it emits are stretched, leading to a redshift.
The distance between us and the star (a) does not directly cause redshift, although the distance can affect the overall brightness and apparent magnitude of the star. The chemical composition of the star (b) and temperature differences (d) can influence the specific spectral features and colors of the star's light but are not the primary causes of redshift.
It is the speed of the star away from us (c) that primarily determines the extent of the redshift. The greater the speed at which the star is moving away, the higher the redshift observed. This relationship is a fundamental principle of cosmology and has been instrumental in discovering the expansion of the universe.
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when was the last time that all four of the gas giant planets were aligned on the same side of the sun?
Answers
The last time all four gas giant planets – Jupiter, Saturn, Uranus, and Neptune – were aligned on the same side of the Sun was in 1981.
Planetary alignment refers to the scenario when planets in our solar system form a straight line in relation to the Sun. This phenomenon is relatively rare due to the varying orbital periods of these planets.
Jupiter takes about 11.9 Earth years to complete one orbit around the Sun, while Saturn's orbit takes approximately 29.5 Earth years. Uranus and Neptune have even longer orbital periods, taking around 84 and 165 Earth years, respectively. These differences in orbital periods mean that true alignment of all four gas giants is not a frequent occurrence.
It is important to note that such alignments do not have any significant effects on our daily lives or Earth's environment. Although some people may associate planetary alignments with disasters or astrological predictions, these claims lack scientific basis.
In summary, the last time all four gas giant planets were aligned on the same side of the Sun was in 1981. This event is relatively rare due to the planets' differing orbital periods, and it does not have any notable impact on Earth or its inhabitants.
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A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1600 kPa. The working fluid is air, which enters the compressor at 40∘C at a rate of 850m3/min and leaves the turbine at 650∘C. Assuming a compressor isentropic efficiency of 85 percent and a turbine isentropic efficiency of 88 percent, determine
(a) the net power output,
(b) the back work ratio, and
(c) the thermal efficiency.
Use constant specific heats with
cv=0.821kJ/kg?
K,cp=1.108kJ/kg?
K, and k=1.35.
Answers
Answer:
a) 6498.84 kW
b) 0.51
c) 0.379
Explanation:
See the attached picture below for the solution
Given-
Temperature at state 1 \(T_{1}\) is 40 degree cel. This is equal to the 313 K.
Temperature at state 1 \(T_{2}\) is 650 degree cel. This is equal to the 923 K.
To know the mass flow rate use the idol gas equation. Idol gas equation for a substance can be given as,
\(PV=nRT\)
Rewrite this equation for \(n\),
\(n=\dfrac{PV}{RT}\)
Put the value of known variable from the question,
\(n=\dfrac{100\times\dfrac{850}{60} }{0.287\times 313}\)
\(n=15.77\)
Thus the value of n is 15.77 kg/sec.
Temperature at state 2 is,
In Bryon cycle we know that the processes 1-2 and 3-4 are isotropic. Hence,
\(T_{2} =T_{1}\left (1+ \dfrac{r_{p}^{\dfrac{\gamma-1}{\gamma}-1} }{c_{v} } \right )\)
\(T_{2} =313\left (1+ \dfrac{16^{\dfrac{1.35-1}{1.35}-1} }{0.821 } \right )\)
\(T_{2} =700\)
Temperature at state 3 is,
\(T_{3} =\dfrac{T_4}{1+c_p(r_p^{\dfrac{\gamma-1}{\gamma}-1}-1)}\)
Put the value in above equation we get,
\(T_3=1682\)
Net power output is,\(W=mc_p(T_i{n}-T_{out})\)
\(W=mc_p(T_3-T_2-T_4+T_{1})\)
\(W=15.77\times1.109(1682-700-923+313)\)
\(W=65\)
Thus the net power output is 70 watt.
The back work ratio,
\(r_b=\dfrac{T_2-T_1}{T_3-T_4}\)
\(r_b=\dfrac{700-313}{1682-923}\)
\(r_b=0.51\)
Hence the back work ratio is 0.51.
The thermal efficiency-\(\eta=\dfrac{W}{Q_{in}}\)
\(\eta=\dfrac{65}{mc_p(T_3-T_2)}\)
\(\eta=0.379\)
Hence, for the given problem the net power output is 70 watt,the back work ration is 0.51, and the thermal efficiency is 0.379.
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A patient has an ongoing history of cancer. She has a tumor in the abdominal region, and has been undergoing treatment for it. There may be other tumors and a potential blockage in the surrounding area that need to be investigated. The imaging technique that might provide the most information in this case is . Joe has ongoing issues with his throat and feels some sort of blockage or abnormality as he swallows. The doctor decides to use X-ray imaging to visualize Joe’s internal anatomy as he swallows to help determine the nature of the problem. will be used for this procedure.
answer: 1. a CT scan
2. Fluoroscopy
Answers
Answer:
the answer is at the BOTTOM OF THEIR QUESTION
Explanation:
IT IS CORRECT BTW
A 2kg mass moving at 1 m/s has a kinetic energy equal to...?
Answers
Answer:
kinetic energy = 1/2mv2
= 1/2 x 2 x 3^2
= 9J
Explanation:
A sample of lead is heated up to a temperature of 100°C and then placed in a sample of water with an initial temperature of 5°C. If the mixture is thermally isolated from its surroundings, then it:
exchanges no thermal energy with the environment outside the system as it comes to a final temperature.
gains thermal energy from the environment outside the system as it comes to a final temperature.
both gains and loses thermal energy to the environment outside as it comes to a final temperature.
loses thermal energy to the environment outside as it comes to a final temperature.
None of these choices are correct.
Answers
If the mixture is thermally isolated from its surroundings, then it, loses thermal energy to the environment outside as it comes to a final temperature. The correct answer is d.
When the sample of lead is placed in the water, heat will flow from the lead to the water until they reach a common final temperature. Since the final temperature will be less than the initial temperature of the lead, heat must have flowed out of the lead into the surroundings, causing the lead to lose thermal energy to the environment outside the system.
Since the mixture is thermally isolated from its surroundings, no thermal energy is exchanged between the system (lead and water) and the environment during the process. However, heat can still flow within the system itself until thermal equilibrium is reached. Option d is correct.
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