are your results in complete agreement with the fundamental lens equation ? if not, to what to you attribute the discrepancies?

The amount of work done in emptying the tank by pumping the water over the top edge is 163.01* 10³ ft-lbs.

Given that, the tank is 8 feet across the top and 6 feet high

By the property of similar triangles, 4/6 = r/y

6r = 4y

r = 4/6*y = 2/3*y

Each disc is a circle with area, A = π(2/3*y)² = 4π/9*y²

The weight of each disc is m = ρw* A

m = 62.4* 4π/9*y² = 87.08*y²

The distance pumped is 6-y.

The work done in pumping the tank by pumping the water over the top edge is

W = 87.08 ∫(6-y)y² dy

W = 87.08 ∫(6y³ - y²) dy

W =  87.08 [6y⁴/4 - y³/3]

W =  87.08 [3y⁴/2- y³/3]

The limits are from 0 to 6.

W =  87.08 [3*6⁴/2 - 6³/3] = 87.08* [9*6³ - 2*36] = 87.08(1872) = 163013.76 ft-lbs

The amount of work done in emptying the tank by pumping the water over the top edge is 163013.76 ft-lbs.

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A thermodynamic process occurs in which the entropy of a system changes by −8 j/k and according to the second law of thermodynamics, the change in entropy must be equal to +8 j/k .

According to second law of thermodynamics:

Entropy change of system = − Entropy change of environment

∴ ΔS [tex]sys[/tex] = - ΔS [tex]env[/tex]

∴ ΔS [tex]sys[/tex] = - (- 8 j/k)

∴ ΔS [tex]sys[/tex] = +8 j/k

Hence , the entropy change is equal to +8 j/k .

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Knee flexion when walking is greater than knee flexion when going down stairs. is a factual assertion.

A bending action known as a flexion reduces the ratio in between segment and its proximate segment. In contrast to flexion, extension refers to a straightening motion that widens the angle between two bodily parts.

When the distance between both the bones narrows, the body flexes or bends. Flexion includes actions like raising the forearm just at elbow or bringing the hand closer to the forearm. The angle between both the vertebrae of a joint widens in extension, which is the inverse of flexion.

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The period calculated by Student a is more accurate because digital stopwatches are more precise and accurate than analog wristwatches.

What is stopwatch?
A stopwatch is a type of timepiece made to count the seconds between activation and deactivation. A stop clock is a sizable digital stopwatch made for distant viewing, such as in a sports stadium. In manual timing, a button is pressed to start and stop the clock. In a fully automatic time, sensors automatically trigger both starting and stopping. Two buttons just on case are typically used to operate the timing functions. The timer starts when the top button is pressed, and it stops when the button is pressed a second time, leaving the displayed elapsed time.

Digital stopwatches have the ability to measure time to the hundredth, or even thousandth, of a second, while analog watches measure time in seconds, minutes, and hours. The increased precision of the digital stopwatch will give a more accurate period for the pendulum oscillations.'

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Answer:

First of all mars will orbit a little faster many asteroids can hit mars due to its twice mass mars will get hotter then it is now

Momentum is about every activity that involves motion. It is an essential concept of physics and is also used in everyday life

Simply is a quantity of motion. Here quantity is measurable because if an object is moving and has mass, then it has momentum. If an object does not move then it has no momentum. However, in everyday life, it has important but many people didn’t recognize it. Momentum is just about every activity that involves motion. It is an essential concept of physics. In sports, the momentum term is commonly used. Like, if a team has momentum then it is on the move and is going to take some effort to stop. But if a team has a lot of momentum then it is really on the move and is going to be hard to stop.  

we can understand it with the help of an example, Cricket ball is much heavier than a tennis ball. Suppose we throw a cricket ball and a tennis ball, both with the same speed or velocity. It will be found that more force is required to stop the cricket ball which has more mass and less force is required to stop the tennis ball which has less mass. Therefore, we can say that the force required to stop a moving body is directly proportional to its mass.

Impulse and momentum are related by the Impulse-Momentum Theorem which states that IMPULSE IS THE CHANGE IN MOMENTUM OF AN OBJECT. When we throw two cricket balls of the same mass but with different speeds or velocities then it will be found that more force is required to stop that cricket ball that is moving at a higher speed or velocity than another with a lower speed or velocity. So, we can say that the force required to stop a moving body is also directly proportional to its velocity. Thus, the quantity of motion in a body depends on the mass and velocity of the body. Momentum is a vector quantity and takes place in the direction of velocity. SI unit of momentum is kilogram meters per second or kgs-1.

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Bernoulli's principle predicts that a wing with an area of 89 m² will experience a lift of 2020656 N when air moves over its top and bottom surface with velocities aircraft 260 m/s and 180 m/s, respectively.

Engineers can use Bernoulli's Principle to safely engineer the fluid flow within and around airplanes, engines, and healthcare delivery devices by making sense of a fluid dynamics phenomenon. Bernoulli's principle, a fundamental idea in fluid dynamics, connects a fluid's pressure to its speed.

According to the Bernoulli's principle, the determined based expresses force:

[tex]P_{1} + \frac{1}{2}p(v_{1})^{2} = P_{2} + \frac{1}{2}p(v_{2})^{2}[/tex]

[tex]P_{1} - P_{2}[/tex] = (0.5) (1.29) (260)² - (0.5) (1.29) (180)²

P₁ - P₂ = 22704

F = PA = (22704) (89)

F = 2020656 N

A wingspan with either an area measuring 89 m² has a load of 2020656 N as a result.

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The magnetic moment is M = 5.40 × [tex]10^{-3} Am[/tex] and the magnitude of the Torque exerted by the magnetic field on the loop is τ = 4.32 × [tex]10^{-3}[/tex] Nm.

What does the term "magnetic moment" mean?

The measurement of an object's propensity to line up with a magnetic field is known as a magnetic moment, sometimes known as a magnetic dipole moment. The magnetic pull and direction of a magnet or other item that generates a magnetic field are known as the "Magnetic Moment" A vector quantity is the magnetic moment.

What is the magnetic moment in SI units?

Weber moment is the magnetic moment unit. Wb is used to symbolize it.

What in physics is torque?

Torque is the rotating counterpart of force in physics and mechanics. It goes by a variety of names depending on the field of research, including moment, moment of force, rotating force, and turning effect. This demonstrates how a force may alter a body's rotational motion.

Given that current through the loop is I = 17 ×[tex]10^{-3}[/tex] A,

Circumference is S = 2m

if r is the radius then S = 2πr = 2m

                                   r = 0.318m

strength of the field is B = 0.8T

a) The magnetic moment is M = I(π[tex]r^{2}[/tex])

                                                  = 5.40×[tex]10^{-3}[/tex]Am

b) Torque parallel to the coil is τ = MB

                                                      = 4.32×[tex]10^{-3}[/tex] Nm

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If a bowling ball and just a ping pong paddle both move using the same kinetic energy, then perhaps the two balls possess the same speed, in accordance with the question.

The rate at which the position of an object shifts in any direction. Speed is defined as the ratio of the amount traveled to the time required to cover that distance. Speed is indeed a scalar statistic since it just has a direction and no magnitude.

Kinetic Energy = 1/2mv²

Ping-pong balls are lighter than golf balls, hence they move faster, according to the same ball equation (KE).

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The complete question is-

If a golf ball and a ping-pong ball both I move with the same kinetic energy, which has the greater speed?

1). The two balls have the same speed.

2). The golf ball.

3). Cannot be determined.

4). The ping-pong ball.

The useful range of object distances of the lens is 1.05 m and 6.3 m.

Focal length of the camera = 175 mm

Distance of Image 1 = i₁ = 180 mm

Distance of Image 2 = i₂ = 210 mm

Since the distance between the images is positive, hence we get real images.

Using thin lens equation,

= (1/f) = (1/i) + (1/o)

For image 1,

= (1/o₁) = (1/f) - (1/i₁)

= (1/o₁) = (1/175) - (1/180)

= o₁ = 6299.4 mm = 6.3 m

Similarly for image 2,

=  (1/o₂) = (1/f) - (1/i₂)

=  (1/o₂) = (1/175) - (1/210)

= o₂ = 1050 mm = 1.05 m

Thus, any object between 1.05 m and 6.3 m will be useful.

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The tension in each rope is T₁ is 130 N, T₂ is 370 N.

In order for the system to be at rest, the sum of all the forces must be zero and the torque around a point on the beam must be zero.

Let the tension in the rope 1 T₁ and in rope 2 T₂:

m*a = T₁ + T₂ -100 -400 = 0

T₁ + T₂ = 500 -------(1)

Torque around the centre point of the beam is:

τ = r × F = 5* T₁ + 3*400 - 5* T₂ = 0

T₁ - T₂ = -240 ------(2)

Solving (1) and (2), we have

T₁ = 130 N and T₂ = 370 N

Thus, the tension in rope 1 is 130N and the tension in rope 2 is 370 N.

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This is much less than the minimum value for the best vacuum as the value of pressure for the given hydrogen atom is 2.76*10-16 pascal.

What is pressure?

Pressure is defined as the amount of force applied per unit area.If the surface is high the amount of pressure applied is low and vice versa. Thus pressure seems to inversely dependent on the amount of area on which the force is applied

As  per the given information

Temperature = 20 K

Volume = 10-6 m3

PV = nRT

V = 10-6 m3

n = 1/NA ; NA = avegadro number = 6.022*1023

n = 1.66*10-24

R = 8.314 J/K/mole

T = 20K

P = 1.66*10-24*8.314*20 / 10-6  

P = 2.76*10-16 pascal

Thus the value of pressure for the given hydrogen atom is 2.76*10-16 pascal which is much less than the minimum value for the best vacuum.

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The results for the two fluids are so different because of the differences in their thermal and physical properties. Water has a much higher thermal conductivity than air, so it can transfer heat more quickly from the sphere to the fluid. Water also has a much higher density than air, so it can exert a greater drag force on the sphere.

What is atmospheric pressure?
The pressure within Earth's atmosphere is referred to as atmospheric pressure or barometric pressure (just after barometer). The definition of the standard atmosphere, or atm, is 101,325 Pa (1,013.25 hPa), which is equal to 1013.25 millibars, 760 mm Hg, 29,9212 inches Hg, or 14.696 psi. The Earth's average sea atmospheric pressure is roughly equivalent with one atm, or one atmosphere, and is measured in the atm unit. In most cases, the hydrostatic pressure brought on by the weight of the air just above measurement point is a close approximation of atmospheric pressure. Because there is less atmospheric mass at lower elevations, atmospheric pressure decreases as elevation rises.

(a) Drag Force:
The drag force on a sphere in water can be calculated using the drag equation:

F _ d = 0.5 * C _ d * ρ_f * V ^ 2 *A

Where C _ d is the drag coefficient for a sphere, ρ _ f is the fluid density, V is the fluid velocity, and A is the projected area of the sphere.

For water, C _ d = 0.47, ρ _ f = 1000 kg/m3, V = 2.5 m/s and A = 314.16 mm2.

Therefore, the drag force on the sphere is:
F _ d = 0.5 * 0.47 * 1000 * 2.5 ^ 2 * 314.16 = 371.2 N

Heat Rate:
The rate of heat transfer from the sphere to the fluid can be calculated using the following equation:
Q _ dot = h * A * ( T _ s - T _ f )

Where h is the heat transfer coefficient, A is the surface area of the sphere, T _ s is the temperature of the sphere, and T _ f is the temperature of the fluid.
For water, h = 4500 W/m2K.
Therefore, the rate of heat transfer is:
Q _ dot = 4500 * 314.16 * (60 - 30) = 4.4 x 10 ^ 6 W

(b) Drag Force:
The drag force on a sphere in air can be calculated using the same equation as for water:
F _ d = 0.5 * C _ d * ρ _ f * V ^ 2 * A

Where C _ d is the drag coefficient for a sphere, ρ _ f is the fluid density, V is the fluid velocity, and A is the projected area of the sphere.
For air, C _ d = 0.47, ρ _ f = 1.2 kg/m3, V = 2.5 m/s, and A = 314.16 mm2.

Therefore, the drag force on the sphere is:
F _ d = 0.5 * 0.47 * 1.2 * 2.5 ^ 2 * 314.16 = 31.2 N

Heat Rate:
The rate of heat transfer from the sphere to the fluid can be calculated using the same equation as for water:
Q _ dot = h * A *(T _ s - T _ f)

Where h is the heat transfer coefficient, A is the surface area of the sphere, T _ s is the temperature of the sphere, and T _ f is the temperature of the fluid.
For air, h = 30 W/m2K.

Therefore, the rate of heat transfer is:
Q _ dot = 30*314.16*(60 - 30) = 3.8 x 10^5 W

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Order from fastest to slowest

[tex]1\geq 2\geq 3\geq 4\geq 5[/tex]

Sort the items in order of speed. Overlap items to rank them equally.

The wheel in the is rolling to the right without slipping.

Rank in order, from fastest to slowest, the speeds of the points labaled 1 through 5.

Rank items from fastest to slowest. To rank items as equivalent, overlap them.

an sphere is pure rolling speed of context point 5 meet be zero w.r.t ground.

Hence, v-ωR=0

v=ωR

[tex]v_5_/_g\geq v_5_/_c+v_c_/_g...............(1)[/tex]

part.5

speed= 0 [tex]v_5=0[/tex]

part.2

[tex]v_2=\sqrt{v^2+v^2}[/tex]

[tex]= \sqrt{2} v[/tex]

=(1.414)v

part.3

[tex]v_3= \sqrt{v^2[/tex]ω[tex]^{2}[/tex][tex]R^2/4[/tex] = 1.118v

part. 1

[tex]v_1[/tex]=v+ωR

=2v

part. 4

[tex]v_4[/tex]=v

order from fastest to slowest

[tex]1\geq 2\geq 3\geq 4\geq 5[/tex]

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Assuming a constant angular acceleration, the linear acceleration of a point on the edge of the wheel 2.0 s after the wheel has started accelerating is equal to the angular acceleration multiplied by the radius of the wheel.

What is acceleration?
Acceleration was the last mathematical concept covered in Lesson 1. Acceleration is a frequently misunderstood concept that means something very different from what sports announcers or other people usually mean when they use it. Acceleration is described as follows: The rate that an object keeps changing its velocity is known as acceleration, a vector quantity. If an object's velocity is changing, it is accelerating. Sometimes when a person is moving quickly, sports announcers will say that the person is accelerating. But speed has nothing to with acceleration. Even when moving very quickly, a person may not be accelerating. Changing the speed at which an object is moving is what acceleration is all about.

Assuming a constant angular acceleration, the linear acceleration of a point on the edge of the wheel 2.0 s after the wheel has started accelerating is equal to the angular acceleration multiplied by the radius of the wheel.

Linear acceleration = Angular acceleration x Radius
Linear acceleration = (2π rad/s^2) x (1 meter)
Linear acceleration = 2π m/s^2

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1) The extension of the spring is 0.12 m

2) The distance is missing thus the gravitational potential energy can not be determined

3) The potential energy is given by 0.27 J

4) The energy that is missing is lost to friction.

According to the Hooke's law, the force that is exerted by an object on a spring is proportional to the extension as long as the elastic limit is not exceeded.

1) We have the following from the question and these would be used to solve the question.

F = mg =

m = mass of the object

g = acceleration due to gravity

F = 0.445 kg * 9.8 m/s^2

= 4.36 N

Thus;

F = Ke

F = force applies

K = force constant

e = extension

e = F/K

e = 4.36 N/37.5 N/m

e = 0.12 m

3) The change in the potential energy is given by;

W = 1/2Ke^2

W = 1/2 *  37.5 * ( 0.12)^2

W = 0.27 J

4) The missing energy went into heat caused by friction or work from some other external force.

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A straight wire's field only has an axile component, B parallel =l Δl Perpendicular length makes up the field's radial component.

The tangential component of such net force may be specified as the proportion of the resultant force along the perpendicular at any point during circular motion, while the radial component may be specified as the part of the equilibrium position along the radius.

Any scalar v can be expressed in the form of its parts in the e r and e directions. Consequently, Thus v=v 1 e r+v 2 e θ, where v 1=v · e r and v 2=v · e θ.The radial component is represented by component v1, while the transverse component is represented by component v2.

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The car will skid to a distance of 180 m.

Find the attachment answer

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F > W because as the boy exerts a force downward on the rope, the tension in the rope pulls up on the boy. Plus, the boy must overcome the friction in the pulley.

Solution:

m₁a + T₁ = W

Since the rope is continuous T₁ = F

m₁a + F = W

F = W - m₁a

Tension is defined as the force transmitted through a rope, cord, or wire when pulled by forces acting from opposite sides. Tension is transmitted along the length of the wire, drawing energy evenly into the bodies at both ends.

Pulling force is the force exerted on the body by a rope or cord. Ropes and cords cannot push your body. You must always draw the body. The pulling force is directed towards the rope or cord, away from the body being pulled.

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Answer :millimeter-wave

Explanation: Because, it uses low-energy non-ionizing radiation that releases thousands of times less energy than a cell phone.

The current in a 5 ω resistor connected to a battery with an internal resistance of 3 ω if the emf of the battery is 9 v is 1.13 A

Resistance is a degree of competition to current drift in an electrical circuit. Resistance is measured in ohms, symbolized by way of the Greek letter omega (Ω). Ohms are named after Georg Simon Ohm (1784-1854), a German physicist who studied the connection between voltage, modern, and resistance.

Given,

The resistance of the resistor, R=5 ω

The internal resistance of the battery, r=3ω

The emf of the battery, E=9 V

The current through the battery is given by Ohm's law. According to this,

I = E/R=r

Where I is the current through the resistor R.

On substituting the know values,

I = 9/5+3

I = 1.13 A

Resistance is precise with R and its unit is the ohm (Ω). A resistor is a tool designed to supply resistance. Resistors can be used to restrict present-day, divide voltage, or generate warmth.

Resistance serves as a hallmark that quantifies how with no trouble modern will glide in a circuit with the use of ohms (Ω) as the unit.

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In order to raise the speed by a factor of 1.90, you must increase the force you apply to the rope by a factor of 3.61. the speed of a change in an object's location in any direction.

Speed is defined as the ratio of distance to the amount of time it took to cover that distance. Due to its lack of magnitude and merely having a direction, speed is a scalar number. A moving object is said to be moving at a variable pace when it travels a varying distance at regular intervals. Speed on average: The consistent force that results from dividing the whole distance travelled by an object by the total time it takes to traverse that distance is known as average force.

Velocity = (T/m)

V1 = (T1/m)^1/2

V2 = (T2/m)^1/2

v2 =1.9v1

1.9 = (T2/T1)^1/2

T2/T1 = 3.61

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Since both conservative and non-conservative forces are involved, so the sum of all of them will be conserved. The kinetic energy, potential energy and thermal energy all together is conserved in the system.

What is non-conservative force?

All forces that rely on the direction taken because microscopic effects depend on macroscopic phenomena are categorized as non-conservative forces. A non-conservative force, in other words, changes macroscopic motion into microscopic motion.

What is Thermal energy?

Heat is the transfer of thermal energy, whereas thermal energy is the entire internal energy of a system's temperature.

Hence, the kinetic energy, potential energy and thermal energy all together is conserved in the system.

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A ball is shot from the ground straight up into the air with initial velocity of 42 ft/sec. Assuming that the air resistance can be ignored, how high does it go? The acceleration due to gravity is 32 ft per second squared.

The maximum height reached by the ball is 27.56 ft.

The given parameters;

initial velocity of the ball, u = 42 ft/s

acceleration of the ball, a = 32 ft/s²

The maximum height reached by the ball is calculated as follows;

v² = u²- 2gh

where;

v is the velocity of the ball at maximum height = 0

0 = u² - 2gh

2gh = u²

h = u^2/2g

h = (42)^2 / 2*32

h = 27.56 ft

Acceleration, price at which velocity modifications with time, in terms of both speed and route. A factor or an object transferring in a immediately line is elevated if it accelerates or slows down.

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Because of their compact, rocky surfaces akin to Earth's terra firma, Mercury, Venus, Earth, and Mars are together referred to as terrestrial planets.The four planets closest to the sun are those that make up the terrestrial planets.

The four innermost planets are known called terrestrial planets and have features like a moon, valleys, volcanoes, and craters, as well as a liquid heavy-metal core and at least one moon.

Because of their compact, rocky surfaces akin to Earth's terra firma, the planets Mercury, Venus, Earth, and Mars are referred to as terrestrial.

The four planets closest to the sun are the terrestrial planets.

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The speed of the book as it slides away from the spring is 2 m/s.

What is speed?

Speed is the fastest movement.

The Potential energy of the compressed spring is also the energy needed for the book to slide away.

Using,

ke²/2 = mv²/2

ke² = mv²................. equation 1

Where k = spring constant, e = compression, m = mass of the book, v = speed of the book at which it slides.

make v the subject of the equation

v = √(ke²/m)........... Equation 2

From the question,

Given: k = 1250 N/m, e = 4 cm = 0.04 m, m = 500 g = 0.5 kg

Substitute these values into equation 2

v = √(1250×0.04²/0.5)

v = √(4)

v = 2 m/s

Hence, The speed of the book as it slides away from the spring is 2 m/s.

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A rigid assembly consists of three identical uniform bars with an extra mass attached to one of them and the system's angular momentum is zero between locations A and B.

The rigid assembly conserves angular momentum because it can freely spin in the vertical plane about the point connecting the bars. Unless an external tension is applied, angular momentum, a vector quantity, is conserved.

The assembly's initial angular momentum is zero when it is in position A of rest since its linear momentum and distance from the axis of rotation are also zero.

Because there is no external torque operating on the system, when the extra mass experiences very little disturbance and the assembly moves to position B, its angular momentum stays constant.

As a result, the system's angular momentum is zero between locations A and B.

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A magnetic field near the ceiling points up and is increasing, looking up at the ceiling, the non-Coulomb electric field curl  in the counter-clockwise

With the help of the right-hand thumb rule, where the thumb indicates the direction of the electric field, the middle finger indicates propagation and the index finger indicates the magnetic field, here the  Non-coulomb electric field also is the rate of change of magnetic flux in a loop closed ( with a negative sign ). Since the here magnetic since  here points upward so m the values of the  electric field ( ε ) are increasing, which The direction of the electric field will be  in a counter-clockwise direction.

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Colder clouds are less resistant to gravity and therefore can collapse more easily because pressure is greater in heat & lower in cold stuff.

Temperature is a unit used to represent hotness or coolness on any of a number of scales, include Fahrenheit and Celsius. Temperature shows the direction of spontaneous heat transfer, which is from a region of high temperature to a cooler body.

People frequently cite a 2010 study that concluded the highest limit of safety would be a humid temperature of 35 C, or 95 F at 100% humidity or 115 F at 50% humidity.

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Given refraction by Siller, angular refraction for first order, for light with a wave length of 613 nanometers

When waves move from one medium to another, they can change direction, which is known as refraction. Wavelength and speed changes usually occur with refraction. The bending of waves around gaps and obstructions is known as diffraction. With increasing wavelength, more diffraction occurs.

Diffraction, a term, is the change that light goes through, especially as it passes by the edges of opaque bodies or through small apertures, giving the impression that the rays are being deflected. additionally: a corresponding change of other waves (like sound waves) or of moving particles (such as electrons).

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