In conduction, heat is transferred when two objects are brought into close proximity. Heat is transferred within the fluid when convection takes place. Heat is transferred through electromagnetic waves without the use of particles in a process known as radiation. Heat transfer occurs because of the temperature difference.
How is radiation used to transfer thermal energy?Heat is transferred via electromagnetic energy in a process known as radiation. When we sit close to a heater in the winter, radiation from the heater spreads electromagnetic energy across our bodies. Because electromagnetic waves are emitted by hot objects like heaters and do not require a medium to travel through.
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Hot water is poured into a mug and the mug gets hot. This is an example of which type of energy transfer?
A) Radiation
B) Conduction
C) Convection
D) This is not an energy transfer
Answer:
conduction i think
Explanation:
Answer:Conduction
Explanation:
protons within a nucleus are attracted to each other by group of answer choices the nuclear force. opposite charges. their energy levels. electron repulsion.
Protons within a nucleus are attracted to each other because of a)the nuclear force.So,correct option is a.
One thing that actually helps to reduce the repulsion between the protons within a nucleus is due to the presence of neutrons. Since they have no charge so, they don't add to the repulsion which is already present, and they help to separate the protons from each other so they don't feel as strong a repulsive force from any other nearby protons.Because of presence of neutons,nucleus attracts the protons with strong nuclear force.
Now two type of force are acting on proton one is repulsive force due to same charge and nuclear force due to protons.Here nuclear force are more stronger than repulsive force due to that nucleus remains stable.
Hence, correct option is a.
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(Complete question) is:
protons within a nucleus are attracted to each other by group of answer choices
a) the nuclear force.
b)opposite charges.
c) their energy levels.
d)electron repulsion.
what is the system's potential energy when its kinetic energy is equal to 34e ? view available hint(s)for part a what is the system's potential energy when its kinetic energy is equal to ? ka2 ka22 ka24 ka28
The energy that results from an object's location in relation to other things is known as potential energy. Potential energy is frequently connected to restorative forces like the force of gravity or a spring.
What happens when kinetic energy and potential energy are equal?The mechanical energy of an item is the total of its potential and kinetic energies. A falling object loses potential energy while gaining kinetic energy. The difference between the increase in kinetic energy and the reduction in potential energy is exact.
Potential energy and kinetic energy vary primarily in that one is the energy of what can be and the other is the energy of what is. In other words, stored energy is ready to be released but potential energy is immobile.
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g a spacecraft is moving at a speed of 0.800 c relative to the earth. what is the ratio of the length of the spacecraft, as viewed through a telescope on earth, to its length when measured after landing on earth? (assume that the spacecraft is moving at a right angle to the line of observation.
If the spacecraft is moving at a speed of 0.800c , then the ratio of length of spacecraft to its length after landing is 0.600 .
Speed of Spacecraft is given as = 0.800c ,
the spacecraft is viewed through telescope ,
we have to find the ratio of the lengths of the spacecraft as viewed through the telescope on earth to its length measured after landing on earth .
let length of spacecraft viewed from telescope be = L
let length of spacecraft after landing be = L₀ :
So , by formula of length: L = L₀√(1 - v²/c²)
Substituting the values of V , we get
L/L₀ = √(1 - (0.800c)²/c²)
= √(1 - 0.800²)
= 0.600 .
Therefore , the ratio of the lengths of the spacecraft is 0.600 .
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the amplitude of a lightly damped oscillator decreases by 3.72% during each cycle. what percentage of the mechanical energy of the oscillator is lost in each cycle?
The mechanical energy of the oscillator is lost in each cycle is 7.44%.
What is mechanical energy?Mechanical energy- (Kinetic energy or potential energy-) is the energy- of either an objective in motions or the energy that is stored in objects by their position. Mechanical energy is also a driver of renewables to energy. Many forms of the renewable energy relying on Mechanical energy to be the adequately produced power or converted energy.
Since the energy is proportional to the amplitudes squared,then we found the fractional changes (assumed small) is,
EE ,−E≈ E
dE=xm2dx
m2=xm2
2xmdxm=2x
mdx.m
Thus, if we approximately the fractional changes in x
mas x mdx m
then the above-mentioned calculations of shows that multiplying by this by 2 should be give them fractional energy- change. Therefore, if x
m decreases by 3.72%, then E must decreased by 7.44%.
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Instructions: Answer the following questions in the space provided. Be sure to write your responses in complete sentences.
A father pushes his daughter and son on a sled down a hill.
Part A: Other than the force exerted by the father pushing the sled, identify two additional forces that act on the sled as it travels from the top of the hill to the bottom. (2 pts)
Part B: Explain how each force you identified in Part A will affect the motion of the sled. (2 pts)
(A) The two additional forces that act on the sled as it travels from the top of the hill to the bottom are friction force and weight of the children.
(B) The force of friction is opposing the motion while the weight of the children is assisting the downward motion.
What are the forces exerted on the sled?
The forces that act on the sled as it travels from the top of the hill to the bottom with either aid the downward motion or oppose the downward motion.
The forces acting on the sled include the following;
the force applied by the fatherthe weight of the children acting normal to the surface of the sledthe force of friction acting upwards to oppose the downward motionThe weight of the children is acting downwards and it will increase the motion downwards since there in the same direction.
The force of friction between the surface of the sled and the hill will oppose the downward motion of the children as the father exerts the downward force.
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a typical tendon has a strength of 16000 pounds per square inch (psi). let's assume the achilles tendon is roughly rectangular in cross section with dimension of .4 inches x .2 inches. you can use this to calculate the force at which the achilles tendon will start to fail. at what force might the achilles tendon start to fail (in pounds, lb)?
An average tendon can withstand 16000 per square inch of force (psi). The Achilles tendon may begin to fail at a force of F = 1280 pounds.
How does science define force?That meaning of the term "force" is obvious. At this point, it is quite acceptable to refer to a force as a push or possibly a pull. An item does not "have energy in it" or "encompass energy." A force is applied to one thing by another. A factor is anything that affects non-living things as well.
Inertia or a force?Inertia is what holds the cosmos together. Literally. That could prevent matter from having the electric forces necessary to produce its system layout. Vibrating particles generate heat and rotational motion, which operate to counteract inertia.
Briefing:Area of tendon 0.4×0.2
=0.08 square inch.
0.08 square inch tendon =16000×0.08
F =1280 pound.
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how much energy (in j) must the shock absorbers of a 1180 kg car dissipate in order to damp a bounce that initially has a velocity of 0.760 m/s at the equilibrium position? assume the car returns to its original vertical position.
Since linear momentum equals m v, it varies at each bounce by the same amount, r = R. For instance, if a ball bounces eighty percent of its height each time, it loses twenty percent of its energy each time.
What is the equation for energy acquired or lost?An object's heat uptake or loss and the consequent temperature variations are related by the description above and the following equation (Q = m•C•T).
We now know that heat can occasionally be acquired or lost without a corresponding change in temperature. When the material is changing states, this is what happens.
The mass and speed of an item moving determine how much kinetic energy it has.
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calculate the angle at which a-wideslit produces its first minimum for 410-nmviolet light. (b) where is the first minimum for700-nm red light?
The first minimum of an a- wideslit is produced by 410-nm ultraviolet light at an angle of 11.8, and by 700-nm red light at an angle of 20.5.
Why would someone utilize violet light?The lens and cornea are impervious to light with UV wavelengths less than 360 nm. As a result, violet light, which ranges in wavelength from 360 nanometers to 400 nanometers, is the best light for controlling myopia from both an efficacy and safety perspective.
d
sin
θ
=
n
λ
2
(
sin
θ
)
=
(
1
)
(
410
×
10
−
9
)
sin
θ
=
410
×
10
−
9
2
=
2.05
×
10
−
7
θ
=
sin
−
1
(
2.05
×
10
−
7
)
=
1.17
×
10
−
5
Thus the angle is
1.17
×
10
−
5
.
(b.)
Given data
The width of slit is
d
=
2.00
m
.
The number of minimum is
n
=
1.
The wavelength is, \lambda =700 nm
Why does violet light exist?The wavelength of violet light, which ranges from 380 to 450 nanometers, is at the higher end of the visible spectrum (in experiments, people have so far seen to 310 nm). In contrast to X-rays and gamma rays, ultraviolet light has a wavelength that is shorter than violet but greater than both of them. In general, light violet is used to compose violet items.
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8. The following 1 ⁄4 W resistors are in series: and What is the maximum voltage that can be applied across the series resistors without exceeding a power rating? Which resistor will burn out first if excessive voltage
Answer:
Explanation:
w
The maximum voltage that can be applied across the series resistors is Vtmax = 86.2 V. Resistor 5.6k Q will burn out first if the excessive voltage is applied.
What is a resistor?
A resistor is a passive two-terminal electrical component used in circuits to implement electrical resistance. Resistors have a variety of uses in electronic circuits, including lowering current flow, adjusting signal levels, dividing voltages, biasing active components, and terminating transmission lines.
Electrical parts called rheostats are constructed from resistive wire wound around a ceramic core. They were once employed to regulate the amount of power used by ovens, heaters, and motors.
The following 1 ⁄4 W resistors are in series and the voltages in each are:
1.2k - 8.02 V2.2k Q - 14.7 V3.9k 2 - 26.1 V5.6k Q - 37.4 VTherefore, the Vtmax = 86.2 V is the highest voltage that can be applied across the series resistors. The 5.6k Q resistor will burn out first if too much voltage is applied.
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The question is incomplete. Your most probably complete question is given below:
Problems related to Power in Series Circuits
Q.1 The following 1/4 W resistors are in series: 1.2k, 2.2k Q, 3.9k 2, and 5.6k Q. What is the maximum voltage that can be applied across the series resistors without exceeding a power rating? Which resistor will burn out first if excessive voltage is applied?
a system absorbs heat from the surroundings and has work done on it by the surroundings. what are the signs of qsystem and wsystem?
The sign of qsystem and qsystem are - qsystem>0 and qsystem>0.
What is q and w system?The Q-system for rock mass-containing classifications is developed by the barton, Lien, and Lunde. It expresses the quality of the rock mass-containing in the so-called Q-value, on whichs designe are based and support recommendations of the underground excavations.
systems is a portions of the Universe that had been chosen up for studying in the changed that takes places withing it in responses to varying conditions. A systematic may be complexity, such as a planet, or relatively simple, as the liquid withing a glass.
Beacuse when system gain extra heat then surrounding q is posetive and when the surrounding works on the system then w is also positive.
Thus both qsystem and
qsystem are same.
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9. A 1,500-kg Lamborghini Aventador is moving forward with a force of
5,000 N. It experiences 1,250 N of air resistance (air friction). What is the
car's acceleration? (Remember: you need the NET force first!)
1.500
Answer:
Below
Explanation:
The friction subtracts from the forward force
F = ma
(5000 - 1250) / 1500 = a = 2.5 m/s^2
the law of conservation of energy cannot be created nor destroyed, it can only change form. if this is the case, why are we worried about energy sources in our world?
Energy cannot be generated or destroyed; it can only be changed from one form of energy to another, according to the rule of conservation of energy. This implies that a system always possesses the same amount of energy, barring external energy addition.
In the event that energy cannot be generated or destroyed, why is there a crisis?According to the rule of conservation of energy, energy cannot be generated or destroyed. It can only be changed from one form to another, though. It is simply changed from a form that we can use to one that is less useful. Energy problem as a result of this
Energy efficiency is necessary to save expenses and extend the life of the resources.
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Question 16 During a rocket launch, the action force is considered the force of explosion from the burning fuel and expanding gases. Which of the following would be considered the reaction force?
The reaction force to the action force during a rocket launch would be C. the force exerted by the ground or launch pad on the rocket.
How to illustrate the force?The force that the ground or launch pad applies to the rocket during a rocket launch will act as a reaction force to the action force. The rocket is propelled upward by the force of explosion caused by the burning fuel and expanding gases. The force that keeps the rocket grounded and keeps it from moving is known as the reaction force, and it is the force that the launch pad or ground exerts in response to this action force.
Equal in magnitude but directed in the opposite direction, the action and reaction forces act on various objects. The reaction force affects the ground or launch pad, whereas the action force affects the rocket.
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Complete question
During a rocket launch, the action force is considered the force of explosion from the burning fuel and expanding gases. Which of the following would be considered the reaction force?
A. The starting force
B. The force of the explosion
C. The force exerted by the ground or launch pad on the rocket.
if a planetary body (such as a rocky body bigger than about 400 km diameter) is big enough, it will be spherical. why is this:
The larger objects are rounded essentially comes down to gravity. The gravitational pull of an object will always be directed toward its mass centre. The more massive and gravitational attraction something has, the bigger it is.
The strength of the object itself opposes such force for solid objects. For instance, you are not drawn into the centre of the Earth by the downward force of gravity. The reason for this is that the ground is pushing back up at you; it is too strong to allow you to sink through it. The power of Earth has its limits, though. Imagine a massive mountain, like Mount Everest, becoming bigger and bigger as the planet's plates collide. Everest starts to sink as it gets taller due to its weight increasing. The mountain's height will be constrained as a result of the additional weight forcing it deeper into the Earth's mantle.
Hence, planets moves in fixed orbits.
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a pen placed 25cm from a concave spherical mirror produces a real image 20cm from the mirror. what is the focal length of the mirror
The focal length of the mirror is 50cm.
What is the focal length of the mirror?This refers to the distance from the lens or mirror to the focal point(F). It is measured in centimeters, cm or meters,m.
Formula for calculating the focal length of the mirror:
f = R * 2
Where,
f = focal length
R = the radius of curvature
What is a focal point (F)?
This refers to the point where by rays or waves meet after reflection or refraction, or the point from which diverging rays or waves appear to proceed.
In the question:
R = 25cm
f = R * 2
Substituting the values we have:
f = 25cm* 2
f = 50cm
Hence, the focal length of the mirror is 50cm.
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what is the relathion shop between perriod and frequency
Frequency is inversely proportional to the time period. That is, f = 1/T.
What is frequency?This refers to the number of waves that passes a fixed place in a given amount of time. Frequency is measured in hertz, this is equal to one event per second.
What is period, T ?
This refers to the time needed for one complete cycle of vibration to pass a given point. A period is measured in seconds.
Note: AS the frequency of a wave increases, the period of the wave decreases. Frequency and Period are in reciprocal relationships.
Mathematically :
f = 1/T
T =Total time,Period
f = Frequency
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What is the acceleration of a car slowing from 12 m/s to a stop in 15 s?
Type a response (show work please)
Answer:
To find the acceleration of a car slowing from 12 m/s to a stop in 15 seconds, we can use the formula a = (vf - vi) / t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time. In this case, the initial velocity is 12 m/s, the final velocity is 0 m/s (since the car is coming to a stop), and the time is 15 seconds. Plugging these values into the formula, we get a = (0 - 12) / 15 = -0.8 m/s^2. This means that the car is slowing down at a rate of 0.8 meters per second squared.
If E.M radiation has a frequency of 58,000,000 Hz, what is the wavelength?
Please include a formula to solve this!
5.16883548 m is the wavelength, if E.M radiation has a frequency of 58,000,000 Hz.
What is the relationship between frequency and wavelength ?When it comes to waves that are travelling, the frequency of a wave is associated with its wavelength and rate of motion. The number of full wave cycles that will finish in 1 second is larger for a quicker wave than for a slower wave. As a result, a wave's velocity plays a critical role in establishing its frequency.It's crucial to remember that two waves might have the same frequency even when their wavelengths are different. Assume Wave 1 has a wavelength of 1 cm, and Wave 2 has a wavelength of 2 cm. Wave 2 must move at a pace that is twice as fast as Wave 1 in order to have the same frequency. Formula of wavelength , λ = C/fGiven data :
Formula:
λ = C/f
Where,
λ (Lambda) = Wavelength in meters
c = Speed of Light (299,792,458 m/s)
f = Frequency
λ = 58,000,000 / 299,792,458 = 5.16883548
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an automobile traveling at 80.0 km/h has tires of 75.0 cm diameter. what is the angular speed of the tires about their axles? if the car is brought to a stop uniformly in 300.0 complete turns of the tires (without skidding), what is the magnitude of the angular acceleration of the wheels? how far does the car move while braking
Initial velocity=- 80km/h, the diameter of the tyre= 75cm, and revolution= 300. initial angular velocity wi= v/r (80) (5/18)/75/200= 59.26 rad/sec. so, angular acceleration is 0.93 rad/sec2.
What was the tire's angular acceleration?We must first determine the tires' angular acceleration. Let's transform the provided translational velocity to rotational velocity to do this. Thus, the tires' angular acceleration is 2.42 rad/s2 rad/s2.
How can you figure out angular velocity?The angular velocity (w), a vector quantity in a uniform circular motion, is determined by dividing the angular displacement (), also a vector quantity, by the change in time (t). Speed is equal to |w|R and is calculated by dividing the arc length traveled (S) by the change in time (t).
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calculate the acceleration of a 250000- kgkg jumbo jet just before takeoff when the thrust on the aircraft is 80000 nn .
0.32 m/s² the acceleration of a 250000 kg jumbo jet just before takeoff when the thrust on the aircraft is 80000 nn.
What is a acceleration explain?Acceleration the rate at which the speed and direction of a moving object vary over time. A point or object going straight forward is accelerated when it accelerates or decelerates. Even though the speed remains constant, motion on a circle accelerates because the directions is always shifting. Due to the fact that it includes both magnitude and direction, velocity is a quantity. As the rate at which velocity changes, acceleration is likewise a vector quantity.
Briefing:The formula may be used to determine an object's acceleration given its mass and the force acting on it.
a= f/m
f is the force
m is the mass
a = 80000 / 250000
a = 0.32 m/s²
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a stone was dropped off a cliff and hit the ground with a speed of 120 ft/s. what is the height of the cliff?
If the stone is dropped off a cliff and hit the ground with speed of 120 ft/sec , then the height of the cliff is 225 feet .
a stone is dropped off a cliff ,
the speed at which the stone hit the ground is = 120 ft/s ;
the Kinematic Equation states that , v - u = 2gh ;
since the stone was at rest when it was dropped off cliff ,
the initial velocity (u) is = 0 ;
it hit the ground with speed 120 ft/sec , so the final velocity (v) is = 120 .
the acceleration due to gravity (g) is taken as 32 ft/s² .
substituting the values in the kinematic equation ,
we get ;
120² - 0² = 2*32*h
14400 = 64*h ;
h = 14400/64 ;
So , h = 225 ft .
Therefore , the height of the cliff is 225 ft .
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according to the uncertainty principle, the more we know about a particle's momentum, the less we know about its group of answer choices location or position. mass kinetic energy. speed. none of these
The correct answer is option a. According to the uncertainty principle, the more we know about a particle's momentum, the less we know about its location or position.
The uncertainty principle is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know both the exact position and momentum of a particle. This is because any attempt to measure the position of a particle with high accuracy will inevitably disturb its momentum and vice versa.
The uncertainty principle is a consequence of the wave-particle duality of quantum mechanics, which states that all particles exhibit both wave-like and particle-like behavior. When we measure the position or momentum of a particle, we are essentially measuring the wave-like properties of the particle, which are inherently uncertain. This uncertainty is inherent in the nature of the universe and cannot be overcome, no matter how advanced our measurement technologies become.
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calculate the time in seconds it would take for a radio frequency signal to travel round-trip between earth and an meo satellite at 20,000 km.
The speed of light is 299,792,458 m/s.
What is speed of light?
The speed of light is a fundamental physical constant denoted by the letter c. It is the speed at which light propagates through empty space, a vacuum. In the International System of Units (SI), the speed of light is given as exactly 299,792,458 meters per second. This is the speed of light in a vacuum, and because light does not travel at the same speed through different substances, the speed of light in a material is always less than this value.
This means that it takes 1 second for light to travel 299,792,458 m.
Therefore, it would take (20,000,000,000 m / 299,792,458 m/s) = 66.66 seconds for a radio frequency signal to travel round-trip between earth and a MEO satellite at 20,000 km.
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a student needs to find the mass of an atom. the numbers of which atomic particles determines the mass of the atom?
Answer:
Together, the number of protons and the number of neutrons determine an element's mass number: mass number = protons + neutrons. If you want to calculate how many neutrons an atom has, you can simply subtract the number of protons, or atomic number, from the mass number.
Explanation:
A particle with a charge of 11.2 μC moves with a velocity of 11.7 m/s toward geographic West (BE = 5.01 × 10–5 T). If the Lorentz force on the particle is9.12 × 10–9 N, what is the magnitude and direction of the electric field?
The magnitude of electric field is 5.08×10^-4 N/C in North direction.
What is Lorentz force?The electromagnetic field-induced magnetic and electric forces acting on a point charge are referred to as the Lorentz force. It is also referred to as electromagnetic force and is employed in electromagnetism.
Given that: charge of the particle: q = 11.2 μC.
Velocity of the particle in the west direction: v = 11.7 m/s.
Magnetic field acting on it: B = 5.01 × 10^–5 T.
Lorentz force on the particle is: F = 9.12 × 10^–9 N.
Let the electric field = E.
So, Lorentz force on the particle is: F = q (V×B + E)
9.12 × 10^–9 = 11.2 × 10^-6 ( 11.7 × 5.01 × 10^–5 × sin90° + E)
⇒ 11.7 × 5.01 × 10^–5 ×1 + E = 7.79×10^-5
⇒ E = 7.79×10^-5 - 11.7 × 5.01 × 10^–5 ×1
⇒ E = - 5.08×10^-4 N/C
Hence, the electric field is 5.08×10^-4 N/C in North direction as magnetic force is acting south direction according to cork screw law.
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A train is travelling along its railroad tracks. It slows down, goes around a turn, speeds back up, coasts at a constant velocity for awhile, then slows down again.
How many times did the train accelerate?
Responses
1
2
3
4A train is travelling along its railroad tracks. It slows down, goes around a turn, speeds back up, coasts at a constant velocity for awhile, then slows down again.
How many times did the train accelerate?
Responses
1
2
3
4
The number of times the train accelerated is 3 times.
option 3 is the correct answer.
How many times did the train accelerate?
The number of times the train accelerates in the given scenario depends on the speed or velocity of the train at every given time.
a = Δv / Δt
where;
Δv is change in velocity of the trainΔt is the change in time of motionFrom the formula given above, the train will only accelerate whenever there is a change in the velocity of the train. If the velocity of the train is constant, then the acceleration of the train will be zero.
The number of acceleration of the train in the given scenario is determined as follows;
when the train slows downspeeds back upthen slows down againThus, from the illustration given above, the train change its speed three times and accelerated in those situation.
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a) what are the s and n axes on an s-n diagram, and what does the region to the left and below the plotted line indicate?
N is the total number of full load cycles, and S is the stress change. The area to the left and below the line represents cyclic stress and cycle count combinations for which no fatigue failure is anticipated to happen.
What do you mean by cyclic stress?The distribution of forces, often known as stresses, under cyclic stress changes repeatedly throughout time. Imagine one of the huge wheels that propels an aerial lift, like a ski lift, as an illustration.
How do you define a cyclic stress-strain curve?The plot of every one of these numbers is known as the cyclic stress-strain curve. Following plastic deformation, the material behaves as described by the curve. Typically, this activity differs from the initial action that is assessed in a conventional tensile test.
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Which of the following identifies a treatment method developed after the discovery of germ theory?
O Perform a bloodletting procedure.
O Recommend frequent hand washing.
O Induce the patient to vomit.
O Treat the infection with an antibiotic.
Recommend frequent hand washing are the treatment method developed after the discovery of germ theory.
What is the importance and benefits of proper handwashing?Handwashing reduces the spread of contagious diseases: Contaminated hands can transmit a variety of contagious illnesses from one person to another. These illnesses include respiratory infections like the flu, colds, and coronavirus (COVID-19), as well as gastrointestinal infections like salmonellosis.The simplest and most reliable approach we all have to stop the transmission of illnesses spread through touch is to practise good hygiene. Our hands are home to more than 150 different types of germs. Additionally, compared to men, women's hands often have more germs on them.Thus, eliminating germs by handwashing aids in the prevention of diarrhoea, respiratory infections, and maybe even skin and eye diseases.Learn more about steps of proper handwashing refer to :
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a planet has 1/2 the mass of earth and 2 times the radius of earth. what is the acceleration due to gravity?
The acceleration due to gravity on a planet with 1/2 the mass of Earth and 2 times the radius of Earth would be one fourth of the acceleration due to gravity on Earth.
What is accelaration?Acceleration is the rate of change of velocity in a given direction. It is a vector quantity, meaning it has both a magnitude (or amount) and a direction associated with it. Acceleration is caused by forces, such as gravity, friction, engine thrust, or any other unbalanced force. It is measured in meters per second squared (m/s2). Acceleration can also be negative, meaning that it is in the opposite direction of the velocity. When an object is accelerating, its speed is increasing but its direction can be changing or staying the same.
This is because the acceleration due to gravity is inversely proportional to the square of the radius, and directly proportional to the mass. Therefore, the acceleration due to gravity on the planet would be (1/2)(1/4) = 1/8 of Earth's gravity.
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