the 20-g centrifuge at nasa's ames research center in mountain view, california, is a horizontal, cylindrical tube 58.0 ft long and is represented in the figure below. assume an astronaut in training sits in a seat at one end, facing the axis of rotation 29.0 ft away. determine the rotation rate, in revolutions per second, required to give the astronaut a centripetal acceleration of 10.6g.

The value of the spring constant of the ideal spring is 106.9 N/m.

The mass suspended by the student is 0.3 kg from the ideal soring and the equilibrium displacement is 5.5 cm or 0.055 cm.

The work done by the gravity will be equal to the work done by the spring,

Mgx = 1/2Kx²

Where,

x is the equilibrium displacement,

K is the spring constant,

M is the mass,

g is acceleration due to gravity,

Putting values,

0.3 x 9.8 x 0.055 = 0.5 x K x 0.055 x 0.055

K = 106.9 N/m.

The spring constant is 106.9 N/m.

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The submerged fraction of a person when floating gently in fresh water is 0.989. The fraction of a person is submerged when floating gently in salt water with a density of 1027 kg/m³ is 0.963

fs = ρo / ρf

fs = Submerged fraction

ρo = Density of object

ρf = Density of fluid.

a ) For fresh water,

ρo = ρp = 989 kg / m³

ρf = ρw = 1000 kg / m³

fs = 989 / 1000

fs = 0.989

b ) For salt water,

ρo = ρp = 989 kg / m³

ρf = ρs = 1027 kg / m³

fs = 989 / 1027

fs = 0.963

Therefore,

a ) In fresh water, the submerged fraction is 0.989

b ) In salt water, the submerged fraction is 0.963

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1)

Circular Motion

2)

No; the direction changes.

3)

Velocity. Gravitational Pull. Force/Twist. Acceleration.

4)

The weight of the object, gravity pulling on it. The kinetic energy produced by you which caused acceleration in a certain vector direction. Location of the object.

The stick figure that is walking at a velocity of 1 m / s to the west is moving quickly relative to the ground than the stick figure that is walking at a velocity of 1 m / s to the east.

Vsg = Vsw + Vwg

Vsg = Relative velocity of stick figure wrt ground

Vsw = Relative velocity of stick figure wrt walkway

Vwg = Relative velocity of walkway wrt ground

Let the stick figure that is walking to the west be A and the stick figure that is walking to the east be B.

For A,

Vsw = - 1 m / s

Vwg = - 0.5 m / s

Vsg = - 1 - 0.5

Vsg = - 1.5 m / s

For B,

Vsw = 1 m / s

Vwg = - 0.5 m / s

Vsg = 1 - 0.5

Vsg = 0.5 m / s

The negative symbol indicates direction. So Vsg for A > Vsg for B

Therefore, the stick figure that is walking at a velocity of 1 m / s to the west is moving quickly relative to the ground than the stick figure that is walking at a velocity of 1 m / s to the east.

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The average acceleration of the dragster during this time interval is 44.57 m/s² and the average net force on the dragster during this time is 38915N.

The initial speed U of the dragster is zero while the final speed V of the dragster is 26.3m/s. The director runs for a total of time t of 0.59 seconds.

According to the equation of motion,

V = U+at

Putting values,

26.3 = 0.59a

a = 44.57 m/s².

So, the acceleration of the dragster is 44.57 m/s².

The force on the director is given by,

F = ma

m mass of the dragster and a is the acceleration of the dragster.

F = 873×44.57

F = 38915N.

So, the net average force on the dragster during this time is 38915 Newton.

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To find the collision rate, known the magnitude.

What is magnitude?

Magnitude typically refers to size or distance. By comparing the size and motion speed of the thing, we can relate magnitude to movement. The object's or quantity's size determines its magnitude.

What is mean by collision rate?

The frequency of collisions between a single particle of radius m and particles with masses ranging from (m1, m1 + m1) to (m, m1) is proportional to their concentration, n(m1) m1, where (m, m1) is the rate constant for collisions between the two particles of masses m and m1 and depends on the process. 

u=140kmph

t=7.oms

v=0

E=M(V-U)/t

⇒m(0-140)/0.007×5/18m/s

⇒5555.55 (m) N

E=(5555.55) (mass) N

Therefore, the collision lasts is 5555.55(m) N.

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Answer:

Explanation:

Refraction of a light ray may be defined as:

D. changing direction while crossing a boundary ​

Answer:

Radius 20 m.

Explanation:

Given:

aₙ = 1.4 m/s²

V = 5.3 m/s

___________

R - ?

Centripetal acceleration:

aₙ = V² / R

Radius:

R = V² / aₙ

R = 5.3² / 1.4 ≈ 20 m

The time taken for the train of mass 1.4 107 kg to reach the speed of 60 km/h is  362.39 seconds

Acceleration is the rate of change of the velocity of an item with appreciation to time. Accelerations are vector portions. The orientation of an item's acceleration is given by the orientation of the net pressure appearing on that object.

Calculation:-

mass of the train = 1.4 × 10⁷ kg

constant force F = 6.5  × 10⁵ N

Using Newton's second law

F = ma

a = F/m

  = 6.5  × 10⁵ N /1.4 × 10⁷ kg

  =  0.046 m/s²

This acceleration accelerates from

initial velocity u = 0

Final velocity v = 60 km/hr = 16.67 m/s

Using,

V = U + at

t = V - U/a

 = 16.67 / 0.046

 =  362.39 seconds

Acceleration is the charge at which velocity modifications with time, in terms of each speed and route. A factor or an object moving in a straight line is accelerated if it quickens or slows down. movement on a circle is extended despite the fact that the rate is consistent because the course is continually changing.

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The relationship between the generator and the energy input is the fact that the generator uses mechanic energy as input to produce electricity.

An electrical generator device is any instrument capable of generating electrical activity using any source of energy as a source for such purpose, such as the movement (motion of mechanical energy) of a turbine.

Therefore, with this data, we can see that an electricity generator device is a given instrument used to generate electricity by exploiting the mechanical energy generated through a particular process.

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The average acceleration vector of the ball is - 9.78 m/s².

When you throw a ball upward with an initial speed, it will go up until reaching its highest peak then it will go down. So the ball doing non-uniform motion. The formula for non-uniform motion including initial speed, and final speed with time is

v = u+at

v-u = at

[tex]a = \frac{v - u}{t}[/tex]

[tex]a = \frac{- 4.5 - 4.5}{0.92}[/tex]

[tex]a = \frac{- 9.0}{0.92}[/tex]

a = 9.78 m/s²

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Yes, a spectrophotometer could be used to measure the absorption of a particular wavelength of light that is not visible to a normal human eye.

Although we cannot directly observe the absorption of this light, it is quantifiable. A spectrophotometer, which measures the absorption of light at certain wavelengths (whether visible or not) by a solution, may be used to compute the concentration. The popular and accessible technique of spectrophotometry may be used to determine the concentration of compounds in a solution or the degree of light absorption.

 When a light beam is focused through the sample, each component either absorbs or transmits light of a certain wavelength. They are combined with quantifiable and visible colored byproducts. Another is that, as observed by a spectrophotometer, colorless substances generally absorb light from the region of the spectrum that is imperceptible to the human eye.

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The wool becomes positively charged because it gives up electrons to the rubber rod whereas wool is rubbed against a Nylon strip so the wool will steal electrons from the Nylon and form a negative charge.

When the woolen cloth is stroke against the plastic, both wood and plastic get electrified due to friction built while rubbing. So, plastic has greater electron affinity (ability to attract electrons) in a contrast to wool, therefore, plastic acquires a negative charge and wool obtains a positive charge. When you rub a balloon with a cloth made of wool, the balloon captures electrons from the wool, leaving the balloon with a negative charge and the wool with a positive charge. If both balloons are pat with wool, they will both have the same charge (negative) and therefore will repel each other.

So we can conclude that Wool is a conductive material, which means it readily gives away its electrons. accordingly, when you rub a balloon on wool.

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The magnitude of its acceleration is a= g ([tex]W_{B}[/tex])/( 2[tex]W_{A}[/tex] +[tex]W_{B}[/tex] )

The length of the vector is all there is to an acceleration's magnitude. To put it another way, writing the magnitude of acceleration indicates how quickly velocity varies. In the standard international (SI) system, the acceleration is measured in units of meters per second square.

Let T be the rope's tension, assuming it has no mass.

T =( 2[tex]W_{A}[/tex])a/g ------- 1

([tex]W_{B}[/tex]) - T = ([tex]W_{B}\\[/tex])a/g ------- 2

Add 1 and 2

[tex]W_{B}[/tex] =(a/g)( 2[tex]W_{A}[/tex]+ [tex]W_{B}[/tex])

a= g ([tex]W_{B}[/tex])/( 2[tex]W_{A}[/tex] +[tex]W_{B}[/tex] ).

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Mv is equal to m - 2.5 log(d/10)2. There is a minus sign in the expression because stars distant than 10 pc have Mv that is more negative than m. Make careful you provide the star's given distance in parsecs (1 pc = 3.26 ly = 206265 AU) if you use this formula.

The moon can appear to be nearly -13 magnitude bright, the moon can appear to be -6 magnitude bright, and stars can get as bright as nearly -1.5 magnitude.

The star's actual magnitude is determined by subtracting its apparent magnitude by five times the trigonometric parallax of its distance from the star.

First-magnitude stars have apparent magnitudes less than +1.50, making them the brightest stars in the night sky. In the first century B.C., Hipparchus invented the magnitude scale. He assigned first magnitude to the 20 brightest stars and sixth magnitude to the stars that are faint enough to be seen with the unaided eye.

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The maximum height travelled by the ball before returning to the ground is 8.62 m.

The maximum height travelled by the ball before returning to the ground is calculated by applying the following kinematic equation as shown below.

H = (u²sin²θ) / 2g

where;

H = (26² (sin 30)²) / (2 x 9.8)

H = 8.62 m

Thus, the maximum height travelled by a projectile depends on the initial velocity and angle of projection.

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Answer:

[tex]\textsf{a)} \quad x=\dfrac{25(7-\sqrt{13})}{3}=28.2870727\; \sf mm[/tex]

[tex]\textsf{b)} \quad V=379037.8082\; \sf mm^3[/tex]

Explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Volume of a rectangular prism}\\\\$V=w\:l\:h$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width of the base. \\ \phantom{ww}$\bullet$ $l$ is the length of the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given:

The dimensions of the rectangular prism in terms of x are:

Substitute these values into the formula for volume to create an equation in terms of x:

[tex]\begin{aligned}\implies V&=(150-2x)(200-2x)x\\&=(30000-700x+4x^2)x\\&=4x^3-700x^2+30000x\end{aligned}[/tex]

To find the value of x that will give the maximum volume, differentiate the equation for volume.

[tex]\begin{aligned}\implies \dfrac{\text{d}V}{\text{d}x}&=3 \cdot 4x^{3-1}-2 \cdot 700x^{2-1}+30000x^{1-1}\\&=12x^2-1400x+30000\end{aligned}[/tex]

Set the derivative to zero and solve for x using the quadratic formula:

[tex]\implies x=\dfrac{-(-1400) \pm \sqrt{(-1400)^2-4(12)(30000)}}{2(12)}[/tex]

[tex]\implies x=\dfrac{1400 \pm \sqrt{520000}}{24}[/tex]

[tex]\implies x=\dfrac{1400 \pm \sqrt{40000 \cdot 13}}{24}[/tex]

[tex]\implies x=\dfrac{1400 \pm \sqrt{40000}\sqrt{13}}{24}[/tex]

[tex]\implies x=\dfrac{1400 \pm 200\sqrt{13}}{24}[/tex]

[tex]\implies x=\dfrac{175\pm 25\sqrt{13}}{3}[/tex]

[tex]\implies x=\dfrac{25(7\pm\sqrt{13})}{3}[/tex]

To determine which value of x will give the maximum volume, differentiate again:

[tex]\begin{aligned}\implies \dfrac{\text{d}^2V}{\text{d}x^2}&=2 \cdot12x^{2-1}-1400x^{1-1}+0\\&=24x-1400\end{aligned}[/tex]

Substitute both values of x into the second derivative:

[tex]x=\dfrac{25(7+\sqrt{13})}{3} \implies \dfrac{\text{d}^2V}{\text{d}x^2}=721.1102551 > 0\implies \sf minimum[/tex]

[tex]x=\dfrac{25(7-\sqrt{13})}{3} \implies \dfrac{\text{d}^2V}{\text{d}x^2}=-721.1102551 < 0\implies \sf maximum[/tex]

Therefore, the value of x which will give the maximum volume is:

[tex]x=\dfrac{25(7-\sqrt{13})}{3}=28.2870727\; \sf mm[/tex]

To find the maximum volume of the box, substitute the found value of x into the equation for volume:

[tex]\begin{aligned}\implies V_{\sf max}&=4\left(\dfrac{25(7-\sqrt{13})}{3}\right)^3-700 \left(\dfrac{25(7-\sqrt{13})}{3}\right)^2+30000 \left (\dfrac{25(7-\sqrt{13})}{3}\right)\\\\&=379037.8082\; \sf mm^3\end{aligned}[/tex]

The dimensions of the box with maximum possible volume will be:

acceleration of the earth due to jupiter's gravitational attraction at their average separation Is 246590.053 metre/sec²

Acceleration due to gravity is the acceleration gained by an object due to gravitational force. Its SI unit is m/s 2. It has both magnitude and direction, hence, it’s a vector quantity. Acceleration due to gravity is represented by g.

Enter the mass, radius and “x” for the unknown value in the respective input field

Now click the button “Calculate the Unknown” to get the acceleration due to gravity

Finally, the gravitational acceleration will be displayed in the output field.

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The heated (brown) air is separated from the cold (blue) air bubble on the left. A(n) is the term used to describe

"Fronts" are the borders that are formed when air masses converge. Cold front in three dimensions. Temperature changes caused by a front's motion can be used to identify it. A cold front causes a warmer air mass to be replaced by a colder one. Another name for it is a "dryline" or "dry front." a line or zone between two air masses that have different densities and, as a result, are typically at different temperatures. A moving front is given a name based on the air mass that is advancing; for example, a cold front if colder air is going forward. The front is the line separating two air masses. A front typically has overcast, stormy weather. Four separate fronts exist: the Cold, Warm, Stationary, and Occluded fronts. A cold front arises when two cold air masses collide with warm air masses.

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The initial speed of the projectile launched at an angle of 30 above the horizontal from the top of a 10m high cliff is 34.2 m / s

According to equations of motion,

s = u t + 1 / 2 at²

s = Displacement

u = Initial velocity

t = Time

a = Acceleration

H = 10 m

t = 4 s

θ = 30°

g = 9.8 m / s²

Here the object is launched art an angle from a height. So,

s = - H = - 10 m

u = uy

While considering vertical motion,

a = - g = - 9.8 m / s²

- H = uy t - 1 / 2 g t²

- 10 = 4 uy - 1 / 2 * 9.8 * 4²

4 uy = 68.4

uy = 17.1 m / s

sin θ = uy / u

u = 17.1 / sin 30°

u = 34.2 m / s

Therefore, the initial speed of the projectile is 34.2 m / s

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The greater amount of energy is transferred during the first case and the difference in energies is: 84 × 10³ J

Internal energy refers to all energy within a particular system, including the kinetic energy of molecules and the energy stored in chemical bonds between molecules. The interaction of heat, work, and internal energy involves the transfer and conversion of energy whenever a change is made to the system.

The amount of heat (Q) gained or lost from the sample can be calculated using the formula Q = mcΔT. where m is the mass, c is the specific heat, and ΔT is the temperature change.

For the first case:

Q = mcΔT

Q = mc(T₁ - T₂)

m = 1 kg or 1000 g

c =  4.2 J g⁻¹/°C

T₁ = 10 °C

T₂ = -15 °C

Q₁ = 1000 × 4.2 × (10 -(-15))

Q₁ = 105 × 10³ J

For the second case:

Q = mcΔT

Q = mc(T₂ - T₁)

m = 1 kg or 1000 g

c =  4.2 J g⁻¹/°C

T₁ = 60 °C

T₂ = 65 °C

Q₂ = 1000 × 4.2 × (65 - 60)

Q₂ = 21 × 10³ J

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Work done by the system is calculated to  - 456.863 J, when pressure and volume change is given.

For a gas, work is the product of the pressure and the volume during a volume change. Relationship between pressure and volume can be found out by Boyle's Law. As the pressure on a gas increases then the volume of the gas decreases because the gas particles are forced closer together.

W= -p ΔV

p is pressure and ΔV is volume change

Given that volume changes from 0.160 liters to 0.570 liters

ΔV = 0.570 - 0.160

= 0.41 L

Given p = 11 atm

Now, W = -11 * 0.41

As 1 atm L = 101.3 J

Hence W=  -11 * 0.41 * 101.3

Work = - 456.863 J (work done by system)

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Yes, a spectrophotometer can be used to measure the absorption of a particular wavelength of light that is not visible to the human eye.

A spectrophotometer is an instrument used to measure the intensity of electromagnetic radiation at different wavelengths.

Spectrophotometry is a standard biological technique used to measure light absorption or the amount of chemicals in a solution. This technique uses a light beam which passes through the sample, and each compound in the solution absorbs or transmits light over a certain wavelength.

Spectrophotometry is the quantitative analysis of electromagnetic spectra by use of a spectrophotometer; especially in order to determine the structure or quantity of a substance.

Using the spectrophotometer, absorption of light can be measured, even if we cannot observe it unaided.

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According to the idea behind active galactic nuclei, heated plasma in an accretion disc that revolves around the black hole is principally responsible for the active galactic nucleus' high luminosity.

An active galactic nucleus (AGN) is a compact area at the Centre of a galaxy that exhibits features that indicate the luminosity is not coming from stars and is substantially brighter than usual over at least some of the electromagnetic spectrum. Is called active galactic nucleus.

A light-emitting object's radiant power, which is measured in absolute terms as luminosity, is the electromagnetic power that it radiates out over time. The total quantity of electromagnetic energy released by a star, galaxy, or other celestial object in a given amount of time is measured as luminosity in astronomy.

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The force would have to work on the block till a distance of 15.66m farther to have 56 joules of kinetic energy.

The work done is given by the product of the force applied and the distance covered along the direction of force.

So we can write,

W = F.s

Where w is the work done if is the force and S is the distance covered.

According to work energy theorem, the work done is equal to the change in kinetic energy.

The force applied in this case is 3 Newton and the body has no till a distance of 3m. Let us assume that the block is moved till a distance x in order to achieve a kinetic energy of 56 joules.

So, it can be written,

3(3+x) = 56

Solving,

9+3x = 56

3x = 47

x = 15.66 m.

So, it is required to move the body by a distance of 15.66 m.

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More force is exerted by the table against her finger than she exerts against the surface.

Active power is the force behind motion or change that is exerted or brought to bear. the elements of nature

The term "force" has a clear definition in science. It is quite acceptable to refer to a force of this level as a push or a pull. An object does not "have in it" or "contain" a force. One thing is subject to a force from another. There is no distinction between living and non-living things in the concept of a force.

The newton  is the SI unit of force. As they relate to force, the base units are: The symbol for the length measurement known as the meter is m. The symbol for the kilogram, a unit of mass the sign s represents the second, a unit of time.

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The number of electrons transported is 8.1 x 10²² electrons.

The variety of electrons in a neutral atom is identical to the number of protons. The mass wide variety of the atom is the same as the sum of the range of protons and neutrons inside the nucleus. The number of neutrons is equal to the difference between the mass number of the atom and the atomic wide variety. The reduction half-response includes a -electron gain.

The LCM is consequently 6. The net equation is a six-electron transfer. The wide variety of electrons in an atom is identical to the atomic quantity of an element for neutrally charged species. this means the number of electrons and the number of protons in an element are identical. consequently, the variety of electrons in oxygen is 8. Ionic bonds are shaped among or extra atoms by using the switch of one or extra electrons among atoms.

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