The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground). if an object fell 64 ft in 8 seconds, how far will it have fallen by the end of 9 seconds

Answers

Answer 1

If the distance is proportional to the square of the time, then the distance in 9 seconds will be  (9/8)²  as long as the distance in 8 seconds.

(9/8)² = 1.265625

(64 ft) · (1.265625) = 81 ft.

Answer 2

The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground). if an object fell 64 ft in 8 seconds, It will it have fallen by the end of 9 seconds at 81 feet.

What is distance?

The distance covered by a body is equal to the sum of total path covered. It is equal to the total path traveled by an object during its entire journey. This quantity is always positive. It can't be 0 or a negative number. It is defined as a scalar quantity.

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that distance, d varies directly with square of the time t, if we introduce a constant of proportionality, k, the expression becomes

d = kt²

If d = 64 when t = 8, then

64 = k × 8² = 64k

k = 64/64

k = 1

The equation becomes,

d = 1t²

Therefore, when t = 9 seconds, then

d = 1 × 9² = 81 ft

Thus, the distance can be calculated as 81 feet.

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Related Questions

Which of the following best explains why the night sky is dark?A. The universe has not always looked the way it looks today.B. The universe is not infinite in space.C. The distribution of matter in the universe is not uniform on very large scales.

Answers

Answer: The universe is not infinite in space

This question is known as the Olbers' Paradox, who in the 19th century posed a question similar to the following:

If the universe where we live is infinite, static, and uniformly populated with stars (similar to the distribution of trees in an immense forest where we would find a tree in whatever direction we observe), which have eternally existed; the light of all of them would intensely illuminate any point of space.

That is to say, we should see stars in any direction, no matter how far away they are and the celestial vault should be exaggeratedly bright.

But this is not the case, the night sky is dark and the universe too.

Why?

Well, although the standard cosmological model of the universe suggests that it is infinite, the observable universe is not.

In other words, the universe is finite.

Then, in a universe of limited size, even having a great quantity of stars and galaxies, all of them would not be enough to illuminate all the space.

In addition, there is another important point: Not only the universe is finite, also its age is; this means it had a beginning.

Hence, having a finite observable universe that is continuously expanding, distant stars and galaxies move away even further.

So, when we look at a star that is 1 million light years away, we are seeing the star as it was seen 1 million years ago.

This means that the amount of light that comes to us from distant stars decreases all the time.

Therefore the light from the most distant stars has not yet had enough time to reach us.

Answer:

It is B.

Explanation:

Which of the following properties of a mass-on-a-spring system undergoing simple harmonic motion can be changed without affecting the frequency of oscillation?
Amplitude
Spring stillness
Oscillating mass

Answers

Answer: Amplitude

If we are talking about simple harmonic motion, we are talking about waves and in this case the frequency [tex]f[/tex] is related to the period of oscillation [tex]T[/tex] in an inverse proportion.

Now, for a mass-on-a-spring system the period is given by:

[tex]T=2\pi\sqrt{\frac{m}{k}}[/tex]

Where [tex]m[/tex] is the oscillating mass and [tex]k[/tex] the spring constant, which depends on the spring stillness.

As we can see in this equation:

If we change [tex]m[/tex] and [tex]k[/tex] we will affect the period, hence the frequency.

Nevertheless, we do not see any relation with the Amplitude, this means the period (hence the frequency) does not depend on the amplitude.

Which portion of the electromagnetic spectrum is used in a television

Answers

Answer: Radio waves

Radio waves are a type of electromagnetic radiation with wavelengths between 10 m to 10,000 m. In the electromagnetic spectrum this wavelength is longer than infrared light and therefore, it goes beyond the visible spectrum.

This type of electromagnetic waves is very well reflected in the ionosphere, the layer of the atmosphere through which they travel directly or using repeaters.

In addition, they are very useful to transport information, being important in telecommunications. They are used not only for conventional radio transmissions but also in mobile telephony and TV.

It should be noted that since radio signals have large wavelengths, they can be diffracted around certain obstacles, such as hills and mountain ranges, preventing the signal from reaching its destination.

You did 130 J of work lifting a 100 N backpack. How high did you lift the backpack?

Answers

Answer:

1.3 m

Explanation:

The work done in lifting the backpack is equal to the change in gravitational potential energy of the backpack, so:

[tex]\Delta U=W \Delta h[/tex]

where

W = 100 N is the weight of the backpack

[tex]\Delta h[/tex] is the change in heigth of the object

In this problem, we know that

[tex]\Delta U = 130 J[/tex]

so we can re-arrange the equation to find the change in height of the backpack:

[tex]\Delta h = \frac{\Delta U}{W}=\frac{130 J}{100 N}=1.3 m[/tex]

Suppose you measure the parallax angle for a particular star to be 0.1 arcsecond. The distance to this star is
A) 10 light-years.B) 10 parsecs.C) 0.1 light-year.D) 0.1 parsec.E) impossible to determine.

Answers

Answer:

B) 10 parsecs

Explanation:

The distance of a star measured with the parallax method is given by:

[tex]d=\frac{1}{\theta}[/tex]

where

d is the distance, in Parsec

[tex]\theta[/tex] is the parallax angle, in arcseconds

For the star in the problem, the parallax angle is

[tex]\theta=0.1''[/tex]

therefore, the distance of the star is

[tex]d=\frac{1}{0.1''}=10 pc[/tex]

so, 10 parsecs.

Which of the following is a true statement about virtual images? O You cannot see a virtual image. A virtual image must be larger than the object A virtual image is formed at the position from which the rays appear to have originated A virtual image must be upside down

Answers

Answer:

A virtual image is formed at the position from which the rays appear to have originated

Explanation:

When using lenses or mirrors to produce the image of an object, two types of images can be produced:

- Real image: a real image is produced when the rays of light actually converge to a point - in this case, the image can be projected on a screen. For a lens, a real image is located on the opposite side of the lens relative to the object, while for a mirror, a real image lies on the same side of the object with respect to the mirror

- Virtual image: a virtual image is formed at the position from which the rays appear to have originated. Because of that, a virtual image cannot physically be projected on a screen. For a mirror, a virtual image is located on the opposite side of the mirror relative to the object, while for a lens, a virtual image lies on the same side of the object with respect to the lens.

Which of the following statements are true concerning the creation of magnetic fields?
Check all that apply.
Check all that apply.
A moving electric charge creates a magnetic field at all points in the surrounding region.
A single stationary electric charge creates a magnetic field at all points in the surrounding region.
An electric current in a conductor creates a magnetic field at all points in the surrounding region.
A permanent magnet creates a magnetic field at all points in the surrounding region.
A distribution of electric charges at rest creates a magnetic field at all points in the surrounding region.

Answers

Answer:

A moving electric charge creates a magnetic field at all points in the surrounding region.

An electric current in a conductor creates a magnetic field at all points in the surrounding region.

A permanent magnet creates a magnetic field at all points in the surrounding region.

Explanation:

Magnetic field can be produced by:

- moving charges (i.e. a moving electron, or a current in a conductor)

- A magnet

The strength of the magnetic field produced by a current-carrying wire is

[tex]B=\frac{\mu_0 I}{2\pi r}[/tex]

where

I is the current

r is the distance from the wire

As we see from the formula, the magnetic field is produced at all points in the surrounding region, because B becomes zero only when r becomes infinite. The same is true for the magnetic field created by a single moving charge or by a magnet.

The following choices instead are not correct:

- A single stationary electric charge creates a magnetic field at all points in the surrounding region.

- A distribution of electric charges at rest creates a magnetic field at all points in the surrounding region.

Because they involve the presence of stationary charges, and stationary charges do not produce magnetic fields.

Final answer:

The statements that are true concerning the creation of magnetic fields are: A moving electric charge creates a magnetic field; an electric current in a conductor creates a magnetic field; and a permanent magnet creates a magnetic field. Stationary electric charges, regardless if alone or in distribution, do not generate magnetic fields.

Explanation:

Regarding the creation of magnetic fields, the following statements hold true:

A moving electric charge creates a magnetic field at all points in the surrounding region. An electric current in a conductor creates a magnetic field at all points in the surrounding region. For instance, it's why wires wrapped around a nail and connected to a battery can turn the nail into a temporary magnet. A permanent magnet creates a magnetic field at all points in the surrounding region. This is exemplified by refrigerator magnets which create magnetic fields that extend outward, allowing them to stick to the fridge.

Conversely, a single stationary electric charge or a distribution of electric charges at rest do not create magnetic fields - they generate electric fields instead.

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A gas is in a sealed container.Part ABy what factor does the gas temperature change if the volume is doubled and the pressure is tripled?Part BBy what factor does the gas temperature change if the volume is halved and the pressure is tripled?

Answers

A) The temperature increases by a factor 6

We can use the ideal gas equation:

[tex]pV=nRT[/tex]

where

p is the pressure

V is the volume

n is the number of moles

R is the gas constant

T is the temperature

We can also rewrite it as

[tex]\frac{pV}{T}=nR[/tex]

The gas is in a sealed container - this means the amount of gas is fixed, so n is constant. Since R is constant too, the term on the right in the equation is constant. So we can rewrite the equation as:

[tex]\frac{p_1V_1}{T_1}=\frac{p_2 V_2}{T_2}[/tex]

where in this problem we have:

[tex]V_2 = 2V_1[/tex] (the volume is doubled)

[tex]p_2 = 3 p_1[/tex] (the pressure is tripled)

re-arranging the equation, we find the change in temperature:

[tex]\frac{T_2}{T_1}=\frac{p_2 V_2}{p_1 V_1}=\frac{(3 p_1)(2 V_1)}{p_1 V_1}=6[/tex]

so, the temperature increases by a factor 6.

B) The temperature increases by a factor 1.5.

We can use again the same equation:

[tex]\frac{p_1V_1}{T_1}=\frac{p_2 V_2}{T_2}[/tex]

Where in this case:

[tex]V_2 = \frac{V_1}{2}[/tex] (the volume is halved)

[tex]p_2 = 3 p_1[/tex] (the pressure is tripled)

So, we can find the change in temperature:

[tex]\frac{T_2}{T_1}=\frac{p_2 V_2}{p_1 V_1}=\frac{(3 p_1)(\frac{V_1}{2})}{p_1 V_1}=\frac{3}{2}=1.5[/tex]

So, the temperature increases by 1.5 times.

Considering the combined law equation:

Part A: the temperature increases by a factor of 6.Part B: the temperature increases by a factor of 1.5.

Gay-Lussac's Law

Gay-Lussac's Law indicates that, as long as the volume of the container containing the gas is constant, as the temperature increases, the gas molecules move faster. Then the number of shocks against the walls increases, that is, the pressure increases. That is, the gas pressure is directly proportional to its temperature.

In summary, when there is a constant volume, as the temperature increases, the gas pressure increases. And when the temperature decreases, gas pressure decreases.

Gay-Lussac's law can be expressed mathematically as follows:

[tex]\frac{P}{T}=k[/tex]

where:

P= pressureT= temperaturek= Constant

Boyle's Law

Pressure and volume are related by Boyle's law, which says that the volume occupied by a given mass of gas at constant temperature is inversely proportional to pressure.

Boyle's law is expressed mathematically as:

P× V=k

where:

P= pressureV= volumek= Constant

Charles's Law

Finally, Charles's Law consists of the relationship that exists between the volume and the temperature of a certain amount of ideal gas, which is maintained at a constant pressure.

This law says that for a given sum of gas at constant pressure, as the temperature increases, the volume of the gas increases and as the temperature decreases, the volume of the gas decreases. That is, the volume is directly proportional to the temperature of the gas.

In summary, Charles' law is a law that says that when the amount of gas and pressure are kept constant, the ratio between volume and temperature will always have the same value:

[tex]\frac{V}{T}=k[/tex]

where:

V= volumeT= temperaturek= Constant

Combined law equation

Combined law equation is the combination of three gas laws called Boyle's, Charlie's and Gay-Lusac's law:

[tex]\frac{PxV}{T}=k[/tex]

Studying two different states, an initial state 1 and an final state 2, the following will be true:

[tex]\frac{P1xV1}{T1}=\frac{P2xV2}{T2}[/tex]

Part A

In this case, you know that:

Volume is double: V2= 2×V1Pressure is tripled: P2= 3×P1

So, replacing in the combined law equation:

[tex]\frac{P1xV1}{T1}=\frac{3xP1x2xV1}{T2}[/tex]

Solving:

[tex]\frac{P1xV1}{T1}=\frac{6xP1xV1}{T2}[/tex]

[tex]\frac{T2}{T1}=\frac{6xP1xV1}{P1xV1}[/tex]

[tex]\frac{T2}{T1}=6[/tex]

T2= 6×T1

Finally, the temperature increases by a factor of 6.

Part B

In this case, you know that:

Volume is halved: V2= V1÷ 2= [tex]\frac{V1}{2}[/tex]Pressure is tripled: P2= 3×P1

So, replacing in the combined law equation:

[tex]\frac{P1xV1}{T1}=\frac{3xP1x\frac{V1}{2} }{T2}[/tex]

Solving:

[tex]\frac{P1xV1}{T1}=\frac{3xP1xV1}{2T2}[/tex]

[tex]\frac{T2}{T1}=\frac{3xP1xV1}{2P1xV1}[/tex]

[tex]\frac{T2}{T1}=\frac{3}{2} =1.5[/tex]

T2= 1.5×T1

Finally, the temperature increases by a factor of 1.5.

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Will the sun ever explode as a type i supernova?

Answers

Answer:

Yes.

Explanation:

A student found the rock shown above and weighed it to determine its mass. What steps should the student take to find its density?

Answers

In order to find the density of the rock, the student should follow the steps highlighted below.

Steps in determining density of a rock

Weigh the rock using a scale to find out how heavy it is in grams. Ensure that the measurement is very precise.

Find out how much space the rock takes up: There are a few ways to figure out how big an irregularly shaped object, like a rock, is. There are two usual ways:

"Use water to measure volume: Pour water into a cylinder and write down how much there is at the start. " Gently put the rock in the water, and make sure there are no air bubbles stuck.

Find out how much water the rock is pushing out of the way now. Subtract the starting volume from the ending volume to find the volume of the rock.

Archimedes' principle: First, weigh the rock in the air. Then, weigh it again when it's completely underwater. The change in weight when a rock is in water is the same as the weight of the water that the rock pushes aside. Find the volume of the rock by dividing its weight by the density of water, which is usually 1 gram per cubic centimeter.

To find the density of a rock, divide its mass (in grams) by its volume (in cubic centimeters or milliliters). Density = Mass / Volume

Density is the amount of mass in a certain amount of space. It is calculated by dividing the amount of mass by the amount of space it takes up.

Ensure that the measurements for mass and volume are the same (like both in grams or both in kilograms, both in cubic centimeters or both in milliliters).

After calculating the density, write it in the right units. Density is usually measured in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

A 4000-? resistor is connected across a 220-V power source. What current will flow through the resistor?

Answers

Answer:

55 mA

Explanation:

Ohm's law states:

V = IR

where V is voltage, I is current, and R is resistance.

220 V = I (4000 Ω)

I = 0.055 A

I = 55 mA

When a fish expands its air bladder, the density of the fish
decreases.increases. remains the same.none of the above

Answers

Answer: decreases

Every substance, body or material has mass and volume, however the mass of different substances occupy different volumes.

This is where density  [tex]D[/tex]  appears as a  physical characteristic property of matter that establishes a relationship between the mass  [tex]m[/tex] of a body or substance and the volume  [tex]V[/tex] it occupies.

[tex]D=\frac{m}{V}[/tex]

So, according to this equation, the density is inversely ptoportional to the volume:

If the volume increases, the density decreases.

This is what a fish does to have buoyancy, since the density of a body is related to its buoyancy:

A body will float on another fluid if its density is lower.

This is what the fish does when it expands its air bladder, incrementing its volume, hence decreasing its density.

When a wave travels through a material, how do the two interact? Image: none

Answers

When a wave travels through a material, it can either reflect, refract or diffraction.

Reaction that takes place when wave travels through material

When a wave travels through a material, it interacts with the material in a number of ways, depending on the type of wave and the properties of the material. It could result into reflection, refraction and diffraction.

Reflection is the process in which light or any other wave bounces off a surface, changing its direction of propagation. When a light ray hits a smooth surface, it reflects at an angle equal to the angle of incidence. This phenomenon is used in mirrors and other reflective surfaces to form images.

Refraction is the bending of light or any other wave as it passes from one medium to another with a different refractive index. When light passes through a medium, such as air, and enters another medium, such as water, the change in speed causes the light to bend. This bending of light is responsible for phenomena such as the apparent displacement of objects when viewed through a curved surface, such as a lens or a prism.

Diffraction is the bending and spreading of waves as they encounter an obstacle or pass through an aperture. This phenomenon is most noticeable when waves encounter a slit or a barrier with a size similar to their wavelength. Diffraction is responsible for the behavior of light around edges and obstacles, such as the spreading of light around a sharp edge or the fringes of interference patterns in a double-slit experiment.

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Which resistors in the circuit must have the same amount of charge passing through each second?

Answers

Resistors 'C' and 'D' are in series.  There's only one possible route for current to flow through them.  

Every electron that flows through one of them has to flow through the other one.  

The current (amount of charge per second) must be the same in 'C' and 'D', no matter how many ohms of resistance either one may have. (answer-choice B)

Answer:

C & D

Explanation:

physics s2

Is the following chemical equation balanced?

4Al + 3O2 2Al2O3

yes
no

Answers

Answer:no Explanation:

Which of the following is the law of conservation of momentum?

A. The impulse acting on any object is the change in momentum that it causes.
B. The acceleration of any object is equal to the net force acting on it divided by its mass.
C. In the absence of any external force, the total momentum of a system stays the same.
D. When two objects interact within a closed system, neither one changes its momentum.

Answers

In the absence of any external force, the total momentum of a system stays the same is the law of conservation of momentum.

What is the law of conservation of momentum?

The law of conservation of momentum state that in an isolated system, the total mass of objects does not change which means that the mass of objects before collision is equal to the total mass after collision.

The formula for law of conservation of momentum is. M1V1 + M2v2 = M1V1 + M2V2

M1 is initial mass of objects

V1 initial velocity of the object.

M2 is final mass

V2 final velocity.

Therefore, In the absence of any external force, the total momentum of a system stays the same is the law of conservation momentum.

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which is the correct path of light through a reflecting telescope?


A). Primary Mirror--->eyepiece--->secondary mirror--->eye


B). Primary mirror--->secondary mirror--->eyepiece--->eye


C). Secondary Mirror--->Primary Mirror--->Eye--->Eyepiece


Eyepiece--->Primary Mirror--->Secondary Mirror--->eye

Answers

The correct path of light through a reflecting telescope will be Primary mirror--->secondary mirror--->eyepiece--->eye.

What is reflecting telescope?

A reflecting telescope (also called a reflector) is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image

it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors.

Reflecting telescopes come in many design variations and may employ extra optical elements to improve image quality or place the image in a mechanically advantageous position.

A curved primary mirror is the reflector telescope's basic optical element that creates an image at the focal plane. The distance from the mirror to the focal plane is called the focal length.

Film or a digital sensor may be located here to record the image, or a secondary mirror may be added to modify the optical characteristics and/or redirect the light to film, digital sensors, or an eyepiece for visual observation.

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A cyclist rides her bike 7 mi east, and then 2 mi north before taking a break. Then she rides 5 mi east and then 3 mi north. What are the magnitude and direction of the cyclist’s resultant displacement?



magnitude: 10.9 mi; direction: 22.6° north of east



magnitude: 10.9 mi; direction: 67.4° north of east



magnitude: 13.0 mi; direction: 67.4° north of east



magnitude: 13.0 mi; direction: 22.6° north of east


Answers

Answer:

D 13.0mi, dir 22.6° north of east

Explanation:

Total movement east is 7+5 miles, or 12 miles. Total movement north is 2+3 miles, or 5 miles. The total displacement, as the crow flies, is of [tex]\sqrt{12^2+5^2} =13[/tex]miles. The angle is the inverse tangent of north/east, or [tex]tan^{-1} \frac 5 {12} =22.62°[/tex]

Alana drew a diagram to compare the life cycles of low-mass and high-mass stars.


Which labels belong in the areas marked X, Y, and Z?

A.) X: Nuclear fusion forms hydrogen in the main sequence star.
Y: A white dwarf is part of the cycle.
Z: A supernova is part of the cycle.

B.) X: A white dwarf is part of the cycle.
Y: Nuclear fusion forms hydrogen in the main sequence star.
Z: A supernova is part of the cycle.

C.) X: A protostar is part of the cycle.
Y: It begins in a nebula.
Z: nuclear fusion forms hydrogen in the main sequence star.

D.) X: It begins in a nebula.
Y: Nuclear fusion forms hydrogen in the main sequence star.
Z: A protostar is part of the cycle.

Answers

Answer:

B

Explanation:

Both low and high mass stars begin as nebulae, then become protostars.  Both use nuclear fusion to form hydrogen in the main sequence.

The differences are that low mass stars have longer life cycles and become white dwarfs.  High mass stars have shorter life cycles and undergo supernova explosions.

Answer: b

Explanation:

Sound waves travel fastest through a A) gas. B) liquid. C) solid. D) vacuum.

Answers

Sound waves travel faster through solids than they do through gases or liquids.  (C)  They don't travel through vacuum at all.

Example:

Speed of sound in normal air . . . around 340 m/s

Speed of sound in water . . . around 1,480 m/s

Speed of sound in iron . . . around 5,120 m/s

explain why meteorologists compare new weather maps and weather maps that are 24 hours old​

Answers

To see which way atmospheric conditions and meteorological phenomena are moving, and how fast.

Also to see whether they were correct yesterday.

Answer:

Meteorologists would compare a new weather map with one 24 hours old to see how fast a front is moving because the United States is very large, a large number of station models help give a more complete picture of the weather and make weather forecasts more accurate.

Explanation:

100%

Why is the answer B?

Answers

Answer:

Explanation:

The center of mass lies on a line that joins position 4 of one start with position 4 of the other star.  The shortest distance between these two points will produce the largest velocity. You are using F = m v^2/R

Small R = large force.

Large Force = increased speed.

The masses don't have any effect on the outcome: they remain constant.

Someone please help. Describe how electric potential energy, kinetic energy, and work change when two charges of opposite sign are placed near each other.

Answers

Final answer:

When two charges of opposite sign are placed near each other, the electric potential energy decreases while the kinetic energy increases.

Explanation:

When two charges of opposite sign are placed near each other, the electric potential energy, kinetic energy, and work change in specific ways. Initially, the charges have potential energy due to their position in the electric field. As they move closer together, the potential energy decreases, and this decrease is converted into kinetic energy.

The work done on the charges is negative because energy is being taken away from the system. In other words, the charges are pulling on each other and you need to do work to bring them closer. Overall, the potential energy decreases, and the kinetic energy increases.

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Final answer:

When two charges of opposite sign are placed near each other, the electric potential energy decreases while the kinetic energy increases. Work is done as the charges are brought near each other.

Explanation:

When two charges of opposite sign are placed near each other, the electric potential energy changes. The potential energy decreases as the charges approach each other, resulting in a decrease in potential energy. As the potential energy decreases, the kinetic energy of the charges increases. This is because the electric field between the charges accelerates the charges, converting their potential energy into kinetic energy. Lastly, work is done when the charges are brought near each other, as the electrostatic force between the charges can do work on the charges.

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Which is true of a solute dissolved in a solvent? A)The solute raises the freezing point of the solvent. B) The solute raises the boiling point of the solvent. C)The solvent decreases the conductivity of the solute.

Answers

Answer:

Hi,

The correct answer option is (B)The solute raises the boiling point of the solvent

Explanation:

Boiling point of a solvent is affected by the number of particles in a solution.Adding a solute to a solvent increases its boiling point because it lowers the vapor pressure of the solution.This is all about colligative properties where a decrease in vapor pressure will mean more heat needed to heat the solution to a boiling point.

All the best.

Final answer:

The true statement is that a solute raises the boiling point of a solvent. This is known as boiling point elevation. In contrary a solute will decrease the freezing point of a solvent and increase its conductivity.

Explanation:

When a solute is dissolved in a solvent it affects the properties of the solvent. The true statement from the given choices is option B - The solute raises the boiling point of the solvent. The process is called boiling point elevation. It's a colligative property meaning it relies on the number of dissolved particles in solution regardless of their nature. For example, when salt (solute) is added to water (solvent) the water’s boiling point increases.

Option A is incorrect because in actuality, a solute decreases the freezing point of a solvent. The solvent does not decrease the conductivity of the solute (Option C) but instead dissolution often increases conductivity.

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A solid ball of radius rb has a uniform charge density ρ.
Part A
What is the magnitude of the electric field E(r) at a distance r>rb from the center of the ball?
Express your answer in terms of ρ, rb, r, and ϵ0.
Part B
What is the magnitude of the electric field E(r) at a distance r Express your answer in terms of ρ, r, rb, and ϵ0.
Part C
Let E(r) represent the electric field due to the charged ball throughout all of space. Which of the following statements about the electric field are true?
Check all that apply.
E(0)=0.
E(rb)=0.
limr→∞E(r)=0.
The maximum electric field occurs when r=0.
The maximum electric field occurs when r=rb.
The maximum electric field occurs as r→∞.

Answers

A) [tex]E(r) = \frac{\rho r_b^3}{3 \epsilon_0 r^2}[/tex]

In this problem we have spherical symmetry, so we can apply Gauss theorem to find the magnitude of the electric field:

[tex]\int E(r) \cdot dr = \frac{q}{\epsilon_0}[/tex]

where the term on the left is the flux of the electric field through the gaussian surface, and q is the charge contained in the surface.

Here we are analyzing the field at a distance [tex]r>r_B[/tex], so outside the solid ball. If we take a gaussian sphere with radius r, we can rewrite the equation above as:

[tex]E(r) \cdot 4 \pi r^2 = \frac{q}{\epsilon_0}[/tex] (1)

where [tex]4 \pi r^2[/tex] is the surface of the sphere.

The charge contained in the sphere, q, is equal to the charge density [tex]\rho[/tex] times the volume of the solid ball, [tex]\frac{4}{3}\pi r_b^3[/tex]:

[tex]q= \rho (\frac{4}{3}\pi r_b^3)[/tex] (2)

Combining (1) and (2), we find

[tex]E(r) \cdot 4 \pi r^2 = \frac{4\rho \pi r_b^3}{3 \epsilon_0}\\E(r) = \frac{\rho r_b^3}{3 \epsilon_0 r^2}[/tex]

And we see that the electric field strength is inversely proportional to the square of the distance, r.

B) [tex]\frac{\rho r}{3 \epsilon_0}[/tex]

Now we are inside the solid ball: [tex]r<r_B[/tex]. By taking a gaussian sphere with radius r, the Gauss theorem becomes

[tex]E(r) \cdot 4 \pi r^2 = \frac{q}{\epsilon_0}[/tex] (1)

But this time, the charge q is only the charge inside the gaussian sphere of radius r, so

[tex]q= \rho (\frac{4}{3}\pi r^3)[/tex] (2)

Combining (1) and (2), we find

[tex]E(r) \cdot 4 \pi r^2 = \frac{4\rho \pi r^3}{3 \epsilon_0}\\E(r) = \frac{\rho r}{3 \epsilon_0}[/tex]

And we see that this time the electric field strength is proportional to r.

C)

E(0)=0.

limr→∞E(r)=0.

The maximum electric field occurs when r=rb.

Explanation:

From part A) and B), we observed that

- The electric field inside the solid ball ([tex]r<r_B[/tex]) is

[tex]\frac{\rho r}{3 \epsilon_0}[/tex] (1)

so it increases linearly with r

- The electric field outside the solid ball ([tex]r>r_B[/tex]) is

[tex]E(r) = \frac{\rho r_b^3}{3 \epsilon_0 r^2}[/tex] (2)

so it decreases quadratically with r

--> This implies that:

1) At r=0, the electric field is 0, because if we substitute r=0 inside eq.(1), we find E(0)=0

2) For r→∞, the electric field tends to zero as well, because according to eq.(2), the electric field strength decreases with the distance r

3) The maximum electric field occur for [tex]r=r_B[/tex], i.e. on the surface of the solid ball: in fact, for [tex]r<r_B[/tex] the electric field increases with distance, while for [tex]r>r_B[/tex] the field decreases with distance, so the maximum value of the field is for [tex]r=r_B[/tex].

Final answer:

The magnitude of the electric field E(r) at a distance r>rb and r from the center of a solid ball with uniform charge density can be calculated using the same formula. The electric field is zero at the center and surface of the ball, and approaches zero as r tends to infinity.

Explanation:

Part A:

The magnitude of the electric field E(r) at a distance r>rb from the center of the ball can be calculated using the formula:

E(r) = (ρ * (4/3) * π * rb³) / (4 * π * ϵ0 * r²)

Part B:

The magnitude of the electric field E(r) at a distance r from the center of the ball can be calculated using the formula:

E(r) = (ρ * (4/3) * π * rb³) / (4 * π * ϵ0 * r²)

Part C:

Based on the formulas provided, the following statements about the electric field are true:

E(0)=0 is true. The electric field at the center of the ball is zero.E(rb)=0 is true. The electric field at the surface of the ball is zero.limr→∞E(r)=0 is true. The electric field approaches zero as r tends to infinity.

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1. Which biome has a large canopy?

2. Which biome contains mostly deciduous trees?

3. Which biome is also known as a prairie?

4. Which biome has cold, dark winters, and sunny cool summers?

Answers

1) Tropical rain forest

2) Temperate deciduous forest

3) Temperate grassland

4) Temperate grassland

What is the energy in joules of a mole of photons associated with visible light of wavelength 486 nm?

Answers

Answer:

[tex]2.46\cdot 10^5 J[/tex]

Explanation:

The enegy of a single photon is given by:

[tex]E=\frac{hc}{\lambda}[/tex]

where

h is the Planck costant

c is the speed of light

[tex]\lambda[/tex] is the wavelength of the photon

In this problem,

[tex]\lambda=486 nm=4.86\cdot 10^{-7}m[/tex]

so the energy of one photon is

[tex]E_1=\frac{(6.63\cdot 10^{-34} Js)(3\cdot 10^8 m/s)}{4.86\cdot 10^{-7}m}=4.09\cdot 10^{-19} J[/tex]

1 mole of photons contains a number of Avogadro of photons:

[tex]N_A = 6.022\cdot 10^{23}[/tex]

therefore, the total energy of 1 mole of these photons will be

[tex]E=N_A E_1 = (6.022\cdot 10^{23})(4.09\cdot 10^{-19} J)=2.46\cdot 10^5 J[/tex]

Final answer:

The energy of a mole of photons with a wavelength of 486 nm is 2.462 x 10^5 joules, calculated by applying Planck's equation and using Avogadro's number.

Explanation:

The energy in joules of a mole of photons associated with visible light of wavelength 486 nm can be calculated using Planck's equation, E = hc/\u03bb, where h is Planck's constant (6.626 x 10-34 J·s), c is the speed of light (3.00 x 108 m/s), and \u03bb is the wavelength of the light (486 nm or 486 x 10-9 m). To find the energy per mole of photons, we also use Avogadro's number (6.022 x 1023 photons/mole).

First, calculate the energy of one photon:

E = hc/\u03bb = (6.626 x 10-34 J·s) (3.00 x 108 m/s) / (486 x 10-9 m) = 4.09 x 10-19 J/photon

Then, calculate the energy per mole of photons:

Emole = E · Avogadro's number = 4.09 x 10-19 J/photon x 6.022 x 1023 photons/mole = 2.462 x 105 J/mole

Therefore, the energy of a mole of photons at 486 nm is 2.462 x 105 joules.

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t is correct to say that impulse is equal toA) momentum.B) the change in momentum.C) the force multiplied by the distance the force acts.D) all of these.E) none of these.

Answers

B is the correct answer

Hope this helps:)

In general, why does a toy car change direction when crossing a boundary between two surfaces, such as hard plastic and a carpet, on which its speed is different? Choose the best explanation based on what you’ve learned in this extension. Select one: a. The wheels of the car move at a different speeds on each surface, so the direction they move in is different. b. Between the time the first wheel crosses the boundary and the last wheel of the car does so, the car wheels are moving at different speeds. This causes the car to turn either left or right. c. Between the time the first wheel of each axle of the car crosses the boundary and last wheel of each axle does so, the wheels on the same axle on moving at different speeds. This causes the car to turn left or right. d. The car turns slightly crossing the boundary because the amount of friction the car experiences on each surface is different, so the interaction between the car and the surface changes, which pushes the car slightly to the left or right.

Answers

Answer:

D

Explanation:

The car turns slightly crossing the boundary because the amount of friction the car experiences on each surface is different, so the interaction between the car and the surface changes, which pushes the car slightly to the left or right. Hence, option (d) is correct.

What is speed?

Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.

What is friction?

The resistance provided by surfaces in touch as they move past one another is known as friction. To walk without slipping, traction is provided by friction. In most situations, friction is advantageous. They do, however, give a strong amount of opposition to the move.

When the  toy car change direction when crossing a boundary between two surfaces, such as hard plastic and a carpet, the frictional force get changed. So, the interaction between the car and the surface changes, which pushes the car slightly to the left or right. Hence option (D) is correct.

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A 70 kg person running at 4 m/s what is the kinetic energy

Answers

Let:

m = mass (kg)

v = velocity (m/s)

KE = 0.5m(v^2)

KE = 0.5(70)(4^2)

KE = 560 Joules.

Final answer:

The kinetic energy of a 70 kg person running at 4 m/s, calculated using the formula KE = 0.5 * m * v^2, is 560 Joules.

Explanation:

The kinetic energy of a body can be calculated using the formula KE = 0.5 * m * v^2, where KE represents kinetic energy, m represents mass, and v represents velocity. In this case, we have a person with a mass of 70 kg who is running at a speed of 4 m/s. Substituting these values into the formula yields: KE = 0.5 * 70 kg * (4 m/s)^2 = 560 Joules. Hence, the kinetic energy of the person running at 4 m/s is 560 Joules.

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