The correct answer is Einstein proposed that light must be made up of packets to explain the photoelectric effect (particles). The frequency of a light packet affects how much energy it contains. Whether or not a single photon has enough energy to knock an electron loose determines whether or not a metal will emit electrons.
The kinetic energy of the electrons is precisely proportional to intensity because, according to wave theory, the energy of electromagnetic waves is uniformly distributed over the wavefront and solely depends on the intensity of the input light beam. However, it was discovered through experimentation that the kinetic energy is unrelated to the brightness of the incident light.
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a helicopter blade spins at exactly 80 revolutions per minute. its tip is 4.00 m from the center of rotation.
The average velocity will be 1.30 x 10⁻² m/ s.
What is velocity?Velocity is defined as the ratio of the distance moved by the object at a particular time. As a vector quantity, the velocity requires both the magnitude and the direction.
Given that a helicopter blade spins at exactly 80 revolutions per minute. Its tip is 4.00 meters from the rotational axis.
Use the formula to calculate the linear velocity.
V= d/t
V= velocity
d= distance
t= time
Here d will be the circumference of the blade
d= 2πr
We have:-
80 rev = 1min
1min/ 80= 60s/80
The average velocity will be calculated as below:-
Vavg= 2π( 10m ) / 80 x 60
Vavg= 0.01308 m / s
Vavg = 1.30 x 10⁻² m / s
Therefore, the average velocity will be 1.30 x 10⁻² m/ s.
The complete question is given below:-
A helicopter blade spins at exactly 80 revolutions per minute. its tip is 4.00 m from the center of rotation. What will be the average speed of the helicopter blade?
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Share an example of a phenotype you or someone you know has (ex: blue eyes). Which side of the family did that phenotype likely originate
In general, a phenotype is an inherited trait that we can observe.
Phenotypes include things like blood type, eye colour, and hair colour. If you have brown eyes, your eyes will be brown; if you have brown hair, your hair will be brown; or if you have an A blood type phenotypic, your blood type will be A.
Only the blue allele can be passed down from the homozygous blue-eyed parent. Either the blue allele or the brown allele can be inherited from the heterozygous brown-eyed parent. Children with a blue-brown genotype, or those with both the blue and brown alleles, will have brown eyes and a brown-eyed phenotype. Similar to this, children with a blue-blue genotype—two blue alleles—will have blue eyes and a blue-eye phenotype
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An ideal heat engine absorbs 94.5 kj of heat and exhausts 78.8 kj of heat in each cycle. what is the efficiency of the engine?
The efficiency of the engine is 17%
The answers to this exercise do not depend on the engine being of the Carnot design. Any heat engine that intakes energy as heat (from, say, consuming fuel) equal to
[tex]|Q_{H} |=[/tex]=94.5kJ and exhausts (or discards) energy as
heat equal to [tex]|Q_{L} |=[/tex]78.8KJ
will have these values of efficiency ε and network W
(a) Equation 20-12 gives ε=1- [tex]|\frac{Q_{L} }{Q_{H} }|[/tex] =1-0.8338624339 =0.17 =17%
What exactly does a Carnot engine do?Leonard Carnot proposed the Carnot engine, a theoretical thermodynamic cycle. It calculates the maximum possible efficiency of a heat engine during the process of converting heat into work and, conversely, working between two reservoirs.
Carnot cycle definition
An ideal reversible closed thermodynamic cycle in which the working substance undergoes four successive operations: isothermal expansion to a desired point, adiabatic expansion to a desired point, isothermal compression, and adiabatic compression back to its initial state.If we define the Carnot factor more broadly as the ratio of an active volume to total volume, the condition = 1/2 means that half of the volume is "active."To learn more about Carnot engine refer to
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What’s an example of potential energy? PLEASE HELP ILL CROWN YOU
A
Water behind a dam
B
A dart stuck in a dartboard
C
Plants using photosynthesis
D
A cow chewing grass
Answer: Its A its the best possible answer
Explanation:
its the best possible answer
Answer:
A. water behind a dam
Explanation:
today we were learning energy then our teacher told as so am sure am ryt
how many millicoulombs (mc) of charge is stored in a 152 µf capacitor when 150 v is applied to it? 1μf
About 22.8 millicoulombs of charge has been stored in a capacitor of capacitance 152 µf when a total voltage of 150 v is applied to this capacitor.
What does capacitance mean?The capacity of a component or circuit to gather and hold energy in the form of an electrical charge is known as capacitance. Devices that store energy include capacitors, which come in a variety of sizes and forms.
What sort of capacitance is that?When any capacitor is being linked to a battery with a specific voltage, its capacitance can be totally calculated by measuring the charge held on each plate.
What distinguishes a capacitor from a capacitance?The capacity of this capacitor that is calculated in order to store energy in the form of electric charge is known as the capacitance.
Here we know that we have,
C= 152 uf
V=150v
Q =?
Q= CV
= 152 x10^6 x 150
= 22800 x 10^6
= 22.8 x 10^6
= 22.8 millicoulomb
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How frequently should the product owner re-iterate the product vision to the scrum team?
For a project to be successful, the product owner should invest somewhere between 60 and 100 percent of their time and effort in it.
In many aspects of product development, the scrum product owner assumes leadership. They will eventually need to use their extensive market knowledge to plan and communicate their vision to stakeholders. They will have to put on their developer hats one more time in order to assist the team in achieving its sprint objectives. Depending on the technical and commercial factors of the situation, different levels of frequency are ideal, but generally speaking, one release every four to six iterations would be regarded as the maximum.
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procedure C, describe how you thought the time to drop the pen from 1.0 meters high would
compare to dropping from 50.0 meters? Do you think it would take 50 times longer to drop from
50 meters? Explain.
1.428 s is the calculated time.
distances relative to the earthly acceleration do not take any initial distance or initial speed if you set the origin of your referential on the origin of your movement and assume that your ball has no initial speed as it is. The most amazing and unexpected truth about falling things is that, in a given location, all items fall toward the center of the Earth with the same constant acceleration, regardless of their mass, if air resistance and friction are low.
So here is the most straightforward formula for this:
+(1/2) *(9.81 m/s^ (2)) *t^ (2) = +10 m.
The result is that t = √ (20 m/ (9.81 m/s (2)))
=√ (2.039 s2)
distances relative to the earthly acceleration do not take any initial distance or initial speed if you set the origin of your referential on the origin of your movement and assume that your ball has no initial speed as it is. The most amazing and unexpected truth about falling things is that, in a given location, all items fall toward the center of the Earth with the same constant acceleration, regardless of their mass, if air resistance and friction are low.
vertical (and only) axis of a drawing must be pointed downward.
So here is the most straightforward formula for this:
+(1/2)*(9.81 m/s^(2))*t^(2) = +10 m.
The result is that t = √ (20 m/(9.81 m/s(2)))
= √(2.039 s2)
=1.428 s.
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She varies the level of noise in the environment and records the blood pressure of each participant. In this experiment, the level of noise is the
It appears that subjective qualitative measurements are insufficient indicators to determine how noise affects cognitive function.
It is highly advised to use novel indicators, such as brain signal analysis and power spectral density analysis, while evaluating cognitive function while exposed to noise. It is recommended that more research be done on the impacts of additional psychoacoustic factors, such as tone and noise pitch (treble or bass) at high exposure levels. "Attention" refers to the active cognitive selecting process. Daily tasks include physical motions, emotional reactions, and perceptual and cognitive processes all heavily depend on attention. When processing of quantitative information is constrained, the attention system regulates behavior of people based on spatial and temporal aspects.
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A constriction in a pipe reduces its diameter from 4.0 cm to 2.0 cm. where the pipe is narrow the water speed is 8.0 m/s. where it is wide the water speed is:_______
a. 2.0 m/s
b. 4.0 m/s
c. 8.0 m/s
d. 16 m/s
e. 32 m/s
Option a) 2.0m/s
So, where it is wide, speed is 2 m/s
CalculationAccording to equation of continuity
A1V1 =A2V2
A1= [tex]\pi[/tex][tex](2*10^{-2}) ^{2}[/tex]
A2 = [tex]\pi (1*10^{-2}) ^{2}[/tex]
V2 = 8m/s
solving by the equation, we have
v1 = 2 m/s
Equation of continuityAn equation that describes the movement of a certain amount is known as a continuity equation or transport equation. It can be generalized to apply to any substantial quantity, but it is especially straightforward and effective when applied to conserved quantities.
Since mass, energy, momentum, electric charge, and other natural quantities all remain constant under the proper circumstances, continuity equations can be used to explain a wide range of physical events.
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A soccer ball was kicked toward the goal. The horizontal component of velocity was 22 m/s and the vertical component was 12 m/s. What is the magnitude of the resultant velocity of the soccer ball?.
The magnitude of the resultant velocity of the soccer ball is: 25.059 m/s
The formula for projectile motion that we will use to solve this exercise is:
vf= √[v(x)² + v(y)²]
Where:
vf= final velocityv(x)= horizontal component of velocityv(y)= vertical component of velocityInformation about the problem:
v(x)= 22 m/sv(y)= 12 m/svf=?Applying the final velocity formula we have:
vf= √[v(x)² + v(y)²]
vf= √[(22 m/s)² + (12 m/s)²]
vf= √[484 m²/s² + 144 m²/s²]
vf= √[628 m²/s²]
vf= 25.059 m/s
What is projectile motion?The projectile motion is the motion whose trajectory describes a parabola having a horizontal and a vertical component of motion.
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a golf ball of mass 0.05 kg travels down the fairway with a velocity of 60m/s what is teh kinetic energy
The kinetic energy will decrease by 4J.
The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.
first-order kinetic energy KE i\s =0.5×m×v
Final Kinetic Energy = 0.5 mV (K.E. 1/2 0.5(3355) =
2/2 KE difference = KE f-KE i
KE difference
Difference in KE = 1/4(925)
Difference in KE = -16/4 = 4J.
Consequently, kinetic energy will decrease by 4J.
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Frank wright is a stereo buff who will go to great lengths when making stereo equipment purchases. He believes having the right equipment is important because he wants to impress the people who will see the stereo when they visit his home. If you were the marketing vp for quality electronics, inc. And your market was primarily made up of people just like wright, which influence source would you most likely build into your promotional messages?.
reference group influences source would most likely build into your promotional message
Promoting something is all that promotional messages are. However, the secret to a successful promotional message is to avoid being overly pushy. What does "salesy" mean? messages that are unclear in terms of their value to a customer Messages that seem to be excessively promotional messages that lack a distinct call to action excessively capitalizing phrases or using buzzwords like "free" As we hinted at previously, several cell carriers discourage the usage of the word "free" and the capitalization of whole words when it comes to text marketing (TODAY, SALE, SIGN UP). The various phone providers may consider such approaches to be spam and limit their use. Your number might consequently be blocked, which would seriously hinder your capacity to converse.
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Two objects undergo simple harmonic motion on a
smooth table. Object B has twice the frequency and
twice the amplitude of object A. How does the
angular speed, maximum speed, and maximum
acceleration of object B compare to that of object
A? Object B has:
a. one-half the angular speed, one-fourth the
maximum speed, and one-sixth the maximum
acceleration of object A.
b. twice the angular speed, quadruple the
maximum speed, and six times the maximum
acceleration of object A.
c. twice the angular speed, twice the maximum
speed, and eight times the maximum
acceleration of object A.
d. twice the angular speed, quadruple the
maximum speed, and eight times the maximum
acceleration of object A.
The acceleration is maximum when the displacement of the object is maximum.
We understand that speed is most when y=zero, displacement is zero, and acceleration is zero, this means that the machine is in equilibrium. therefore, at a factor in simple harmonic motion, the maximum pace can be calculated by the usage of the formulation v=Aω. the rate may be most in easy harmonic movement, while the acceleration is zero.
The pendulum oscillating backward and forward from the suggested role is an example of easy harmonic movement. Bungee leaping is an example of simple harmonic motion. The jumper oscillates up and down in the present process SHM because of the pliancy of the bungee wire.
The maximum displacement of the bob from its implied role. OA or OB is called its amplitude. because the bob is at its lowest position on point O. Its potential power is minimal whilst its kinetic power is maximum.
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4. The diagram shows two forces of 5 N and 8 N acting at 120° to each other. Calculate the resultant of these two forces and state its direction relative to the 5 N force. Illustrate your answer with an appropriate vector diagram.
The magnitude of the resultant force is 11.4 N.
What is the resultant force?The resultant force is the force that has the same effect both in magnitude and in direction as the two or more forces acting at the same time. We know that force is a vector quantity, this implies that both the magnitude and the direction of the force are all important. This is why we have to factor in the direction of the force at all times.
Now, we can see that, it is possible to obtain the resultant force from the parallelogram law of vectors. We can see that;
R = √ P^2 + Q^2 - 2PQ Cos θ
P = 5 N
Q = 8 N
θ = 120°
R = √(5^2 + 8^2 - (2 * 5 * 8) cos 120
R = 11.4 N
The direction of the 5N force is obtained as;
Tan^-1 (8/5)
= 58 degrees
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What is the quantum number n of a particle of mass m confined to a one-dimensional box of length l when its energy is 2 h2/ml2?
The quantum number of a particle of mass m confined to a one-dimensional box of length l when its energy is 2 h2/ml2 is 4.
What is quantum number?
The collection of numbers known as quantum numbers is used to describe an electron's position and energy in an atom. The four categories of quantum numbers are primary, azimuthal, magnetic, and spin quantum numbers.
Given that,
Eₙ = 2h²/mL²,
The equation for the energy of a particle of mass m confined to a one-dimensional box of length L is given by:
[tex]E_n = \frac{n^{2} h^{2}}{8mL^{2}}[/tex],
Equating this equation with the energy given in the question.
i.e. Eₙ = 2h²/mL².
We get,
[tex]\frac{n^{2} h^{2}}{8mL^{2}} = \frac{2h^{2}}{mL^{2}}[/tex]
[tex]\frac{n^{2}}{8} = 2[/tex]
[tex]n = \sqrt{16}[/tex]
n = 4
Therefore,
The quantum number of a particle of mass m confined to a one-dimensional box of length l when its energy is 2 h2/ml2 is 4.
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What is the relationship between a boats volume and the amount of mass it can hold
The relationship between a boats volume and the amount of mass is known as Archimedes' principle
Archimedes' principle states that an object displaces its personal weight in a liquid.
So calculate the weight of the boat from the mass. Calculate the quantity of liquid that has this equal weight. that is the quantity of boat underneath the waterline.
Divide that variety with the aid of the vicinity of the boat (duration instances width). this is the depth the boat sinks to.
what is Archimedes principle in easy words?
Archimedes' principle states that a body immersed in a fluid is subjected to an upwards force identical to the burden of the displaced fluid. that is a primary condition of equilibrium. We take into account that the above force, referred to as pressure of buoyancy, is placed in the centre of the submerged hull that we name centre of buoyancy.
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I need help with this word puzzle too, it’s kinda confusing to me
The answer for this word puzzle is given below. Question number 14 to 17 are missing.
FIRSTFOUR ( m / s² )THIRDSECONDSPEEDELEVEN ( Net F, when F's acts is opposite directions = 22 - 11 = 11 N )FORCEINERTIAIMBALANCEDACCELERATIONBALANCEDPOSITIVEINCREASENo questionNo questionNo questionNo questionDECELERATIONNEGATIVEMETERVELOCITYTEN ( m / s )NORTH / SOUTH ( Based on 17th question )
All these questions are based on Newton's three laws of motion. The first law states that an object cannot move or stop until an external force is applied. The second law states that acceleration is based on the force applied on the object. The third law states that for every action there is an equal and opposite reaction.
Therefore, the answers for the questions in the word puzzle is mentioned above in order.
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what is the index of refraction of a substance that has a critical angle of 68.4º when submerged in water (n
The refractive index of the substance for the critical angle 68.4° is found as 1.43400055
To find the index of refraction, the given values are:
Critical angle is 68.4°.
What is the refractive index?The refractive index can be defined as the ratio of the speed of light in the medium to the speed in the vacuum.
The formula of the refractive index is as follows:
Where,
n is the refractive index
c is the velocity of light in a vacuum ( 3 × 108 m/s)
v is the velocity of light in a substance
The vacuum has a refractive index of 1. The refractive index of other materials can be calculated from the formula mentioned. Higher the refractive index, the higher the optical density and slower is the speed of light.The refractive index of different media can be listed in the table below:
Material Refractive Index
Air 1.0003
Water 1.333
Diamond 2.417
Ice 1.31
Ethyl Alcohol 1.36
Now, finding the value of refractive index,
As the value of critical angle is given, θ = 68.4°,
θc = Sin ⁻¹ ([tex]\frac{n2}{n1}[/tex])
Considering the given values, n2 = 1.3333
θc = θ = 68.4°
So, n1 = ( n Water) / ( sin θc)
= 1.33333 / sin 68.4°
= 1.43400055
Thus, n1 ca be found as,1.43400055
The refractive index of the substance for the critical angle 68.4° is found as 1.43400055
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if a subway train is moving to the left and then comes to a stop, what direction is the acceleration
The subway train is moving to the left and then comes to a stop, what direction is the acceleration will be towards right and will be positive.
The train comes to a stop, this means that the velocity gradually decreases. Hence, the acceleration must be positive and points towards the right.
velocity and acceleration:
velocity is the charge of alternate inside the position of an object, at the same time as acceleration is the rate of trade of the fee. consider the movement alongside a line. If the velocity and acceleration are in the same route, then the charge constantly will growth in time. inside the meantime, if the speed and acceleration are in contrary instructions, then the rate steadily decreases to 0 speed, reverses route, and now the velocity is in the identical path of the acceleration.
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If no heat is transferred during the following compression of a gas, what is the sign of w, and does internal energy of the enclosed gas increase, decrease, or remain constant?.
Answer: increase
Explanation:
increase of compression make it hot
what is the geometric relationship between the force f and the cross-section area a under consideration?
The cross-sectional area A under consideration is parallel to the force F.
What do you mean by force?An influence that can alter an object's motion is referred to as a force in physics. An object with mass can change its velocity, or accelerate, in response to a force by moving away from rest, for example. Intuitively, pushing or pulling can be used to describe forces. As a vector quantity, a force is one that has both magnitude and direction. It is expressed as a newton in the SI system (N). F is a symbol that stands for force (formerly P). The net force exerted on an object is equal to the rate at which its momentum varies over time, according to Newton's second law in its original version.
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what celestial bodies stay close to the ecliptic (astrology)
The Sun, Moon, and planets are the celestial bodies stay close to the ecliptic.
What are called celestial bodies?Objects in space such as the sun, moon, planets, and stars are known as celestial bodies or heavenly bodies. They are typically very far away from us and are a part of the vast universe we inhabit. The heavenly bodies are primarily seven celestial bodies.
Celestial bodies in our solar system :The Sun, our star, and just about everything gravitationally connected to it, including the planets Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune, dwarf planets like Pluto, dozens of moons, and millions of asteroids, comets, and meteoroids, compose our solar system.
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Suppose you take trips that covers180km and take 3hours to make your average speed is
Explanation:
average speed= distance/time
=180÷3
=60 km/h
for the same percentage error in each of the three quantities, mass, diameter, and length, which would contribute the most to the error in the density
For the same percentage error in each of the three quantities, mass, diameter, and length, mass would contribute the most to the error in the density.
A substance's density is defined as its mass per unit of volume. Density is most frequently represented by the symbol, however Latin letter D may also be used. The formula for density is mass divided by volume:
ρ = m / v
The error's absolute value is multiplied by 100%, divided by the accepted value, and then converted to a percent.
Since, the mass is directly related to density so the mass would contribute more to the error in density out of the three quantities, mass, diameter, and length.
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a) find the velocity, in feet per second, at time : (b) find the velocity (in ft/sec) of the particle at time . (c) find all values of for which the particle is at rest. (if there are no such values, enter none . if there are more than one value, list them separated by commas.)
The velocity of a particle at time t is 4t³- 7, at time t = 3 is 101 ft/sec, and at rest is ∛7/4 sec.
The position of a particle at time t is
s(t) = t⁴ - 7t + 22, where t > 0
(A) Velocity at time t is
V(t) = s'(t)
Or, V(t) = 4t³ - 7 × 1 + 0
Or, V(t) = 4t³- 7
Hence, the velocity at time t is 4t³- 7.
B) Velocity ar time t = 3 is
V(3) = 4(3)³- 7
Or, V(3) = 101 ft/sec
Hence, the velocity at time t = 3 is 101 ft/sec.
(C) When particle is at rest, V(t) = 0
Then, 4t³ - 7 = 0
Or, t³ = 7/4
Or, t = ∛7/4 sec
Therefore, the velocity at rest is ∛7/4 sec.
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a baseball player is dashing toward home plate with a speed of 4.7 m/s when she decides to hit the dirt. she slides for 1.5 s , just reaching the plate as she stops (safe, of course).
She decides to hit the dirt in -2.64 m/s in First equation and 2.59m in second equation.
Using 1st equation of motion,
V = u + at
-3.7 = 0 + a x 1.4
Acceleration,
a = - 2.64 m/s^2
Using 2nd equation of motion,
D = ut + 0.5 at^2
D = (3.7 x 1.4) - (0.5 x 2.64 x 1.4^2)
= 2.59 m
How is speed measured in baseball?Sprint Speed, a Stat cast metric that was first used in the 2017 season, counts the number of feet per second a player covers in his quickest one-second span.
Currently, "qualifying runs" from these two groups are included in the metric:
• Runs from second base following an extra-base hit but eliminating runs of two bases or more on non-homers.
• Runs scored from first base to home on "tipped" or "weakly hit" balls.
A player's seasonal average is calculated using the best third of these runs on average.
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At the surface of jupiter’s moon io, the acceleration due to gravity is g = 1.81 m>s 2 . a watermelon weighs 44.0 n at the surface of the earth. (a) what is the watermelon’s mass on the earth’s surface? (b) what would be its mass and weight on the surface of io?
Complete question
At the surface of jupiter’s moon io, the acceleration due to gravity is g = 1.81 m>s 2 . a watermelon weighs 44.0 n at the surface of the earth. (a) what is the watermelon’s mass on the earth’s surface? (b) what would be its mass and weight on the surface of ?
Gravitational acceleration at the surface of Jupiter's moon Io is g = 1.81 [tex]\frac{m}{s^{2} }[/tex]. On the surface of the Earth, a watermelon weighs 44.0 N. The watermelon has a mass of 4.485 kg on the surface of Earth thus, it would have a mass of 4.485 kg and a weight of 8.117 N on the surface of Io.
Given data:
F = mg
Mass on the earth's surface
[tex]m = \frac{F}{g}[/tex]
[tex]m = \frac{44}{9.81}[/tex]
m = 4.485 kg
Mass will not vary from earth to moon(Io).
m = 4.485 kg
F = ma
Weight on the moon(Io's) surface
F = 4.485 × 1.81
F = 8.117 N
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a house that is losing heat at a rate of 35,000 kj/h when the outside temperature drops to 4°c is to be heated by electric resistance heaters. if the house is to be maintained at 25°c at all times, determine the re
Q(l) = 35,000 kj/h
T° = 4° c = 277k
T(H) = 298 k
given that house is to be maintained at 25° c at all times
hence internal energy is zero. du=0
now, using first law of thermodyanamics
dq= du+dw
dq= dw ( because du = 0)
hence, heat lost by house is equal to the work input for system
Q(l)= w (input)
w (input) =35,000 kj/hr
now, coefficient of performance for reversible heat pump = cop ( rev,hp)
cop ( rev,hp) = = 14.9
cop ( rev,hp) = Q(l)/w (input)
14.9 = 35,000/ (win)rev
(win)rev = 2349 kj/h ( reversible work input)
Irreversibility of process = I
I = (win) - (win)rev
I = 35000- 2349
I = 32651 KJ/hr
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A ball is thrown with an initial speed of 20 m/s at an angle of 60° to the ground. If air resistance is negligible, what is the ball’s speed at the instant it reaches its maximum height from the ground?.
The speed of the ball when it reaches its maximum height from the ground is 5.02 m/s.
The initial speed of the ball = 20 m/s
Angle to the at which the ball is thrown = 60°
Gravity = 9.81 m/s²
Resistance of the air = 0.
The maximum height reached by the ball above the ground is,
[tex]H = \frac{u ^{2 }sin ^{2}θ} {2g}[/tex]
[tex]H = \frac{20 ^{2 }sin ^{2}60°} {2 \times 9.81}[/tex]
[tex]H = \frac{ 20 \times 20 \times \sqrt{3} }{2 \times 9.81 \times 2}[/tex]
[tex] = 17.6 \: m[/tex]
Thus, the maximum height reached by the ball above the ground is 17.6 m.
The flight time of the ball is,
[tex]t = \frac{2usinθ}{g} [/tex]
[tex]t = \frac{2 \times 20 \times sin60°}{9.81} [/tex]
[tex]t = \frac{2 \times 20 \times \sqrt{3} }{9.81 \times 2} [/tex]
[tex]t = 3.5 \: s[/tex]
Thus, the flight time of the ball is 3.5 s.
The speed of the ball when it reaches it reaches the maximum height from the ground is,
[tex]Speed = \frac{ Distance }{Time}[/tex]
[tex]Speed = \frac{17.6}{3.5} [/tex]
[tex]Speed = 5.02 \: m/s[/tex]
Therefore, the speed of the ball when it reaches its maximum height from the ground is 5.02 m/s.
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Find a unit vector with a negative i component that is orthogonal to both i + j and i + k.
The correct answer is ±(- 1/√3, 1/√3, 1/√3)
a=i+j=<1,1,0)
b=i+j=<1,0,1>
c=+<(cos α, cos , cos γ)> are the unit vectors orthogonal to a and b (moving in the opposite direction).
Scalar product c.a=cos α+cos β=0
Similarly c.b=cos α+cosγ =0
c=±<-cos α, cos α, cos α>
The directions in each octant (the 2nd OX'YZ and 8th OXY'Z') are equally inclined to the axis.
cos α=± 1/√3
Thus the answer is ±(- 1/√3, 1/√3, 1/√3)
What is unit vector?
Both magnitude and direction are present in vector units. Sometimes, though, one is simply concerned with the direction and not the magnitude. In this situation, vectors are frequently regarded as having unit length. A scalar coefficient provides the magnitude, and these unit vectors are typically employed to express direction. Unit vector and scalar coefficients can be used to sum a vector decomposition.
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