A ray in glass arrives at the glass-water interface at an angle of 48° with the normal. The refracted ray, in water, makes a 72° angle with the normal. The index of refraction of water is 1.33. Then the ray in glass is redirected so its new angle of incidence is 37°. What is the new angle of refraction in the water? Show all work.

The dispersion of light occurs when a beam of white light (which is compound of many wavelengths or "colors") is refracted (the different rays of light are diverted depending on their wavelengths) in some medium, leaving their constituent colors separated.

The best known case is when a beam of white light from the sun passes through a prism, thus obtaining rays of different colors like those of the rainbow.

This phenomenom was named by Isaac Newton in the  eighteenth century, who performed the experiment explained above.

Hence, the correct option is C.

Answer:

Time elapsed

Explanation:

Acceleration is a vector quantity. It is defined as:

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

where

v is the final velocity

u is the initial velocity

t is the time elapsed

Acceleration is measured in meters per second squared (m/s^2). It must be noticed that acceleration is a vector, so it also has a direction. In particular:

- when acceleration is negative, it means that the object is slowing down, so acceleration is in opposite direction to the velocity

- when acceleration is positive, it means that the object is speeding up, so acceleration is in the same direction as the velocity

Acceleration is the rate of change in velocity over a time period. It is a vector with direction and magnitude and is measured in m/s². The average acceleration is calculated by the formula 'change in velocity ÷ time interval'.

Acceleration is defined as the change in velocity divided by the time period during which this change occurs. It is the rate at which velocity changes, represented by the formula 'average acceleration = change in velocity ÷ time interval' over which it changed. This concept can be understood well with a velocity versus time graph, where the slope represents acceleration. Namely, slope = change in velocity ÷ change in time.

Acceleration is a vector, indicating it possesses both magnitude and direction. It is measured in SI units as meters per second squared or m/s², indicating how velocity changes every second. Thus, acceleration can occur due to a change in speed (magnitude of velocity), change in direction, or both.

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Answer:

Infrared

Explanation:

Answer:

Infrared

Explanation:

Explanation:

Marie Curie's notebooks, as well as all of her belongings, including her clothes, were contaminated with ionizing radiation. In fact, also those of her husband, because this couple of scientists discovered the radioactivity of several elements, helping the advance of science, but did not know about the consequences of dealing with these materials without adequate protection.  

It should be noted that Curie's notes are stored in the basements of the National Library of France, stored in thick lead boxes and those who wish to access these documents must follow the appropriate protocol to treat radioactive material, wear appropriate clothing and sign a responsibility agreement before allowing them to review the documents.

The current will drop to half of its original value.

To solve this problem, we must use Ohm's law that states that in a circuit the voltage [tex]v[/tex] across a resistor is directly proportional to the current that flows through that circuit. In other words:

[tex]v \propto Ri \\ \\ or: \\ \\ v=Ri \\ \\ It's \ also \ valid: i=\frac{v}{R}[/tex]

According to our problem, if the voltage in the circuit is held constant while the resistance double, that is [tex]R_{New}=2R \ and \ v_{New}=v[/tex]. So:

[tex]v=R_{New}i_{New} \\ \\ v=2Ri_{New} \\ \\ Isolating \ i_{New}: \\ \\ i_{New}=\frac{v}{2R} \therefore i_{New}=\frac{1}{2}\frac{v}{R} \therefore i_{New}=\frac{1}{2}i[/tex]

In conclusion, the current will drop to half of its original value.

Answer:

Because moisture and warmth are crucial to thunderstorms

Answer: 9*10^15 N

Force=kqq/r^2

F=[(9*10^9)(1)(1)]/.001^2=9.0*10^15

Answer:

The force of repulsion between the two object is 9*10¹⁵ N

Explanation:

Coulomb's law indicates that charged bodies suffer a force of attraction or repulsion when approaching. The value of said force is proportional to the product of the value of its loads and inversely proportional to the square of the distance that separates them. This is expressed mathematically by the expression:

[tex]F=K*\frac{Q*q}{r^{2} }[/tex]

where:

From this law it is possible to predict the electrostatic force of attraction or repulsion between two particles according to their electrical charge and the distance between them.

The force will be of attraction if the charges are of opposite sign and of repulsion if they are of the same sign.

In this case:

Then:

[tex]F=9*10^{9} \frac{N*m^{2} }{C^{2} } *\frac{1 C*1C}{(0.001m)^{2} }[/tex]

So:

F=9*10¹⁵ N

The force of repulsion between the two object is 9*10¹⁵ N

Momentum

The momentum of a particle is defined as the product of the particle mass and the particle velocity as follows:

[tex]\overrightarrow{p}=m\overrightarrow{v}[/tex]

On the other hand, the impulse of a constant force is defined as:

[tex]\overrightarrow{J}=\varSigma\overrightarrow{F}(t_{2}-t_{1})=\varSigma\overrightarrow{F}\Delta t[/tex]

We also know that the net force acting on  a particle equals the rate of change  of the particle’s momentum, so:

[tex]\varSigma\overrightarrow{F}=m\overrightarrow{a}=m\frac{d}{dt}(\overrightarrow{v})=\frac{d}{dt}(m\overrightarrow{v})=\frac{d\overrightarrow{p}}{dt}[/tex]

If the force is constant, then [tex]\frac{d\overrightarrow{p}}{dt}[/tex] equals the total change in momentum over a period of time:

[tex]\varSigma\overrightarrow{F}=\frac{\overrightarrow{p_{2}}-\overrightarrow{p_{1}}}{t_{2}-t_{1}} \\ \\ \varSigma\overrightarrow{F}(t_{2}-t_{1})=\overrightarrow{p_{2}}-\overrightarrow{p_{1}} \\ \\ \boxed{\overrightarrow{J}=\Delta \overrightarrow{p}}[/tex]

The impulse experienced by a body is equivalent to its change in momentum. This principle is based on Newton's second law of motion. Impulse is the product of the force and the duration over which it is applied.

The impulse experienced by a body is equivalent to the body’s change in momentum. This principle is based on Newton's second law, which in terms of momentum states that the net force applied to a system equals the rate of change of the momentum that the force causes. In simpler terms, when a force is applied on an object for a certain amount of time, the object experiences an impulse. This impulse is the difference between the initial and final momentum of the object.

For example, consider a ball bouncing off a floor. If the force of the floor on the ball is constant over a specific duration, then the resulting impulse or change in momentum can be calculated by multiplying the force by the duration of the force application. So, an impulse can cause the object's motion to change due to the effect it has on the ball's momentum.

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Temperature is a physical quantity that reflects the amount of heat in a body or medium. This amount of heat is related to the internal energy of a system (thermodynamically speaking), according to the movement (speed) of each of the particles that compose it, this means that it is related to its kinetic energy.

Therefore, the higher the kinetic energy, the higher the thermal energy in the system and the higher the temperature.

Answer:

All matter is made up of tiny particles. These particles are always moving even if the matter they make up is stationary. Recall that the energy motion is called kinetic energy. So all particles of matter have kinetic energy. Temperature is a measure of the average kinetic energy of the individual particles in matter.

Explanation:

Answer:

D) Both do zero work

Explanation:

The work done by a force is given by:

[tex]W=Fd cos \theta[/tex]

where

F is the force applied

d is the displacement

[tex]\theta[/tex] is the angle between the direction of the force and the displacement

From the formula, we notice that work is done online when the displacement is non-zero, so when the object is moving.

In this problem, the wall is stationary: this means that the displacement is zero, d = 0, so no work is done.

Even though Person X is pushing twice as hard as Person Y, both of them are doing zero work, because the brick wall is not moving. Thus, the displacement is zero, and the work done, according to the Physics formula, is also zero.

The correct answer is D) Both do zero work.

According to the concept of work in Physics, work is defined as the amount of energy transferred by a force over a displacement. It is given by the formula Work = Force x Distance x cosθ. Here, even though Person X is pushing twice as hard, the brick wall isn't moving (i.e., displacement is zero). When the displacement is zero, no matter how much force is applied the work done will be zero because the distance over which the force is applied is zero. Therefore, both Person X and Person Y are doing zero work.

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Answer:

A tsunami with a record run-up height of 1720 feet occurred in Lituya Bay, Alaska. On the night of July 9, 1958, an earthquake along the Fairweather Fault in the Alaska Panhandle loosened about 40 million cubic yards (30.6 million cubic meters) of rock high above the northeastern shore of Lituya Bay.

Explanation:

The largest tsunami ever recorded was a megatsunami in Lituya Bay, Alaska, reaching 1722 ft (525 m) due to a rockslide caused by a magnitude 7.8 earthquake in 1958.

The largest tsunami ever recorded occurred in Lituya Bay, Alaska, on July 9, 1958. A magnitude 7.8 earthquake triggered a massive rockslide, which caused a megatsunami, creating a wave that reached 1722 ft (525 m) above sea level. The landslide displaced a huge amount of water, which surged up the opposite side of the bay.

This is the highest wave ever known, dwarfing other catastrophic events like the Chilean earthquake tsunami of 1960 and the Tohoku-oki Earthquake tsunami in Japan in 2011. Despite the height of the 1958 megatsunami, it should be noted that the most devastating in terms of loss of life was the 2004 Indian Ocean tsunami, triggered by a magnitude 9 earthquake that took approximately 230,000 lives.

Answer:

its beacuse there are millions of species in the world, and there are still mooooore speacies we still dont know about. its impossible to study all of them it will take a great amount of time to discover and study them.but, the most mysterious place is the ocean we know more about space than we know about the ocean. the ocean is sooo HUUUUUGGGGGE and  massive it covers 70% of the world, imagine how many species will be in a place that covers 70% we still dont know about.

~batmans wife dun dun dun....

Estimating the number of species on Earth so difficult due to man not

discovering all the species on earth yet.

There is a large amount of species yet to be discovered by scientists due to

how big the earth is. The earth comprises of the land and various water

bodies. Most discoveries have been with land organisms as that is where we

live.

In water bodies such as seas, oceans there are many species yet to discover

as they are very large and humans don't live in it giving rise to less

discoveries.

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Answer:

Jason has repressed the memories

Explanation:

Answer:

Jason has amnesia.

Explanation:

Amnesia is a kind of memory loss. Some people cannot learn new things and this is known as anterograde amnesia. Some people forget events from their past and this is called as retrograde amnesia. Jason has retrograde amnesia because he has forgotten his past events. The causes for this disease are given below:

i) Brain injuries  

ii) Certain drugs and alcohol  

iii) Traumatic events  

Answer:

Frequency: [tex]2.41\cdot 10^{13}Hz[/tex], Wavelength: [tex]1.24\cdot 10^{-5}m[/tex]

Explanation:

The energy of the photon is equal to the energy required to break the bond, so 0.1 eV.

First of all, we need to convert the energy of the photon from eV to Joule:

[tex]E=0.1 eV \cdot (1.6\cdot 10^{-19}J/eV)=1.6\cdot 10^{-20} J[/tex]

The energy of the photon is related to its frequency by:

[tex]E=hf[/tex]

where h is the Planck constant and f is the frequency.

Solving for f,

[tex]f=\frac{E}{h}=\frac{1.6\cdot 10^{-20}J}{6.63\cdot 10^{-34}Js}=2.41\cdot 10^{13}Hz[/tex]

The wavelength instead is given by

[tex]\lambda=\frac{c}{f}[/tex]

where c is the speed of light. Substituting,

[tex]\lambda=\frac{3\cdot 10^8 m/s}{2.41\cdot 10^{13} Hz}=1.24\cdot 10^{-5}m[/tex]

The minimum frequency required to break a hydrogen bond in a protein molecule is approximately[tex]\(2.4 \times 10^{13}\)[/tex] Hz, and the maximum wavelength of a photon that can accomplish this is approximately[tex]\(1.2 \times 10^{-5}\)[/tex] m.

To calculate the minimum frequency of a photon that can break a hydrogen bond in a protein molecule, we use the energy of a photon given by the equation [tex]\(E = h \nu\),[/tex]where E is the energy of the photon, (h) is Planck's constant, and [tex]\(\nu\)[/tex] is the frequency. We can rearrange this equation to solve for the frequency:

[tex]\[\nu = \frac{E}{h}\][/tex]

Given that [tex]\(E = 0.1\) eV[/tex], we first convert this energy to joules (J), knowing that 1 eV is equivalent to[tex]\(1.602 \times 10^{-19}\) J:[/tex]

[tex]\[E = 0.1 \times 1.602 \times 10^{-19} \text{ J} = 1.602 \times 10^{-20} \text{ J}\][/tex]

Now, using Planck's constant[tex]\(h = 6.626 \times 10^{-34}\)[/tex] J·s, we can find the minimum frequency:

[tex]\[\nu = \frac{1.602 \times 10^{-20} \text{ J}}{6.626 \times 10^{-34} \text{ J}} =2.416 \times 10^{13} \text{ Hz}\][/tex]

We can rearrange this equation to solve for the wavelength:

[tex]\[\lambda = \frac{c}{\nu}\][/tex]

Using the speed of light [tex]\(c = 3 \times 10^8\) m/s,[/tex] we can find the maximum wavelength:

[tex]\[\lambda = \frac{3 \times 10^8 \text{ m/s}}{2.416 \times 10^{13} \text{ Hz}} =1.243 \times 10^{-5} \text{ m}\][/tex]

the upside down image means an inverted image and for an inverted image, magnification is negative

so the answer is -m

Answer:

C. 98 N

Explanation:

The force needed to get the skier at rest moving must be at least equal to the maximum static frictional force acting on the skier, which is given by

[tex]F=\mu W[/tex]

where

[tex]\mu = 0.14[/tex] is the coefficient of static friction

W = 700 N is the weight of the skier

Substituting into the equation, we find

[tex]F=(0.14)(700 N)=98 N[/tex]

Answer:

c

Explanation:

μ = f/N where μ is the coefficient of friction; f is the amount of force that resists motion, and N is the normal force. You must solve for f here so 700 N x .14 = 98 N.

Answer:

42 cm

Explanation:

For a converging lens, the focal length is positive:

f = +14 cm

In this problem, the distance of the object from the lens is 21 cm:

p = +21 cm

The distance of the image from the lens can be found by using the lens equation:

[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}[/tex]

where q is the image distance. Solving the formula for q and substituting the numbers, we find

[tex]\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{14 cm}-\frac{1}{21 cm}=\frac{1}{42 cm}\\q= 42 cm[/tex]

Answer:

Ammeter:

- measures current

-connected in series

-measurement expressed in amperes

-measures the amount of charge per second passing through

The rest is for voltmeter

Explanation:

Properties of an Ammeter:

Properties of a Voltmeter:

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Answer:

[tex]25.5^\circ[/tex]

Explanation:

To calculate the angle of refraction you can use Snell's law:

[tex]\text{n}_1*\sin\theta_1 = \text{n}_2*\sin\theta_2[/tex]

With what we have:

[tex]\text{n}_1 =1\\\text{n}_2= 1.33\\sin\theta_1 = 35^\circ\\sin\theta_2=x[/tex]

[tex]\therefore 1 *sin35^\circ =1.33*sin\theta_2\\\\sin\theta_2=\frac{1 *sin35^\circ}{1.33}\\\\\theta_2=\sin^{-1}(\frac{1 *sin35^\circ}{1.33})\\\\\theta_2= 25.5476^\circ\approx 25.5^\circ[/tex]

The angle of refraction of light in water can be calculated using Snell's Law, which compares the angles of incidence and refraction and the refractive indices of the two media. In this case, the angle of refraction is approximately 23 degrees.

The angle of refraction of light can be calculated using Snell's Law which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media.

In this case, the angle of incidence is 35 degrees, the refractive index of air is 1.00, and the refractive index of water is 1.33.

Using the formula:

sin(angle of incidence) / sin(angle of refraction) = (refractive index of air) / (refractive index of water)

We can solve for the angle of refraction:

sin(35) / sin(angle of refraction) = 1.00 / 1.33

Simplifying the equation, we find that the angle of refraction is approximately 23 degrees.

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Answer:

I believe the answer is A. Voltage

Explanation:

Answer:

[tex]A. Voltage[/tex]

Explanation:

As we know that electric potential is defined as the work done to move a unit charge from one potential to other potential.

Here the unit charge is moved from lower potential to higher potential then in that case the work done to move the charge is stored in the form of potential energy

this is given as

[tex]V = \frac{W}{q}[/tex]

so here we can say that the correct answer for the amount of potential energy for each charge is given as

[tex]A. Voltage[/tex]

If there is no friction and no horizontal force acting on the bicycle, then the bicycle keeps rolling at a constant speed in a straight line, until the cows come home, Dante's Inferno freezes over, and the POTUS accepts some responsibility for his words, actions, and consequences.

Answer:

It would keep going at constant speed.

Explanation:

Answer:

Approximately 3 photons

Explanation:

The energy of a photon at the peak of visual sensitivity is given by:

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

where

h is the Planck constant

c is the speed of light

[tex]\lambda=550 nm = 5.5\cdot 10^{-7}m[/tex] is the wavelength of the photon

Substituting into the formula,

[tex]E_1=\frac{(6.63\cdot 10^{-34} Js)(3\cdot 10^( m/s)}{5.50\cdot 10^{-7} m}=3.6\cdot 10^{-19} J[/tex]

This is the energy of one photon. The human eye can detect an amount of energy of

[tex]E=10^{-18} J[/tex]

So the amount of photons contained in this energy is

[tex]n=\frac{E}{E_1}=\frac{10^{-18} J}{3.6\cdot 10^{-19}J}=2.8 \sim 3[/tex]

so approximately 3 photons.

Answer:

Zero

Explanation:

According to Newton's second law, the net force acting on an object is equal to the product between the object's mass and its acceleration:

F = ma

For the hockey puck, there are no forces acting on it during its motion, since ice friction and air resistance are negligible. This means that the net force is zero:

F = 0

But this means that the acceleration is also zero:

a = 0

So the hockey puck is moving already at constant velocity. Therefore, there is no need for additional forces.

Final answer:

The force required to maintain a hockey puck's constant velocity across a frictionless ice pond, where air resistance is also neglected, is zero, in accordance with Newton's first law of motion.

Explanation:

The question pertains to dynamics in classical mechanics, specifically to Newton's first law of motion which states that an object in motion will remain in motion at a constant velocity if no net external force acts upon it. Since the question specifies a scenario where air resistance and ice friction are neglected, the force required to keep the puck sliding at constant velocity is zero. This is because there are no external forces acting on the puck to change its state of motion.

In a hypothetical frictionless environment, once the hockey puck is set in motion, it does not require any additional force to maintain its velocity due to the absence of resistive forces such as friction and air resistance. Indeed, this is an idealized situation, but it helps us understand the principle that, without external forces, a moving object will continue to move at a constant speed and direction.

Answer:

false

Explanation:

veins carry blood towards the heart after blood passes through the capillaries.

Answer:

False

Explanation:

Veins are vessels that carry  deoxygenated blood back to the heart.

A) -2.0 m

Look at the ray diagram attached in the picture, where:

p identifies the location of the object

q identifies the location of the image

F identifies the focus of the mirror

Each tick represents 1 m

We have

p = 6.0 m is the distance of the object from the mirror

f = -3.0 m is the focal length

From the ray diagram, we see that q has a distance of 2.0 m from the mirror, and it's on the other side of the mirror compared to the object, so

q = -2.0 m

This can also be verified by using the mirror equation:

[tex]\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{-3.0 m}-\frac{1}{6.0 m}=-\frac{3}{6.0 cm}\\q = \frac{-6.0 cm}{3}=-2.0 cm[/tex]

B) Upright and virtual

As we see from the picture, the image is upright, since it has same orientation as the object.

Also, we notice that the image is on the other side of the mirror, compared to the object. For a mirror,

- An image is said to be real if it is on the same side of the object

- An image is said to be virtual if it is on the opposite side of the mirror

Therefore, this means that the image is virtual.

Final answer:

The image is located 2.0 m behind a convex mirror when the object is 6.0 m away, and the image will be virtual and upright.

Explanation:

To determine the location of the image formed by a convex mirror with a focal length of -3.0 m when an object is placed 6.0 m from it, we use the mirror equation:

1/f = 1/do + 1/di

Where f is the focal length, do is the object distance, and di is the image distance. Since we know that the focal length is -3.0 m and the object distance is 6.0 m, we can plug these values into the equation:

1/(-3.0) = 1/6.0 + 1/di

Calculating the image distance di, we find:

di = -2.0 m

This means the image is located 2.0 m behind the mirror, hence we use a negative value to indicate that the image is on the other side of the mirror, which corresponds to a virtual image.

For Part B), since convex mirrors always form virtual, upright images, the image formed will be upright and virtual.

Answer:

[tex]9.12\cdot 10^{-8} m[/tex]

Explanation:

The energy needed to ionize a hydrogen atom in the ground state is:

[tex]E=13.6 eV= 2.18\cdot 10^{-18}J[/tex]

The energy of the photon is related to the wavelength by

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

where

h is the Planck constant

c is the speed of light

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

Solving the formula for the wavelength, we find

[tex]\lambda=\frac{hc}{E}=\frac{(6.63\cdot 10^{-34} Js)(3\cdot 10^8 m/s)}{2.18\cdot 10^{-18}J}=9.12\cdot 10^{-8} m[/tex]

Final answer:

The longest wavelength of light that can ionize a hydrogen atom in its ground state is approximately 91.2 nanometers (nm), which falls in the ultraviolet range of the electromagnetic spectrum.

Explanation:

The longest wavelength light capable of ionizing a hydrogen atom in the ground state is associated with the energy required to remove an electron from a hydrogen atom that is in its ground state (n=1). In physics, the process of ionization involves providing enough energy to an atom to remove its electron. The energy of a photon of light is inversely proportional to its wavelength, according to the relationship E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

The energy required to ionize hydrogen from the ground state is 13.6 eV, which is the ionization energy of hydrogen. We can calculate the longest wavelength of light capable of ionizing hydrogen using the formula λ = hc/E. The constant values are h = 6.626 x 10-34 J·s, and c = 3 x 108 m/s. Therefore, the longest wavelength, λ, is given by λ = (6.626 x 10-34 J·s * 3 x 108 m/s) / (13.6 eV * 1.602 x 10-19 J/eV), which calculates to approximately 91.2 nm.

Thus, the longest wavelength of light that can ionize hydrogen in its ground state is about 91.2 nanometers (nm), which falls in the ultraviolet (UV) range of the electromagnetic spectrum.

Answer:

B!

Explanation:

(I suck at explaining things) Basically the car has friction with the road as it slows to a stop.

The option that best demonstrates friction is a car rolling to a stop at a traffic light. Thus, the correct option for this question is B.

Friction may be defined as a type of force that significantly resists or opposes the relative motion between two surfaces of objects when they come in direct contact with each other. In a more simple sense, friction is characterized as the rubbing of one body over the surface of another.

Option C and option D do not involve the contact of one body with the surface of another. So, both these options are eliminated. In option A, an ice skater slides across the ice, but it is not noticeably slowing down, so friction is zero.

Therefore, the option that best demonstrates friction is a car rolling to a stop at a traffic light. Thus, the correct option for this question is B.

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B the chicken pox is the infectious agent

Answer:

5.10 m/s

Explanation:

The volumetric flow rate for an incompressible fluid through a pipe is constant, so we can write:

[tex]A_1 v_1 = A_2 v_2[/tex] (1)

where

[tex]A_1[/tex] is the cross-sectional area of the first part of the pipe

[tex]A_2[/tex] is the cross-sectional area of the second part of the pipe

[tex]v_1[/tex] is the speed of the fluid in the first part of the pipe

[tex]v_2[/tex] is the speed of the fluid in the second part of the pipe

Here we have:

[tex]v_1 = 1.28 m/s[/tex]

[tex]r_1 = \frac{8.0 cm}{2}=4.0 cm = 0.04 m[/tex] is the radius in the first part of the pipe, so the area is

[tex]A_1 = \pi r_1^2 = \pi (0.04 m)^2 =5.02\cdot 10^{-3}m^2[/tex]

[tex]r_2 = \frac{4.0 cm}{2}=2.0 cm = 0.02 m[/tex] is the radius in the first part of the pipe, so the area is

[tex]A_2 = \pi r_2^2 = \pi (0.02 m)^2 =1.26\cdot 10^{-3}m^2[/tex]

Using eq.(1), we find the fluid speed at the second location:

[tex]v_2 = \frac{A_1 v_1}{A_2}=\frac{(5.02\cdot 10^{-3} m^2)(1.28 m/s)}{1.26\cdot 10^{-3} m^2}=5.10 m/s[/tex]

The fluid speed at a location where the diameter has narrowed to 4.0 cm is 5.12 m/s

[tex]\texttt{ }[/tex]

The basic formula of pressure that needs to be recalled is:

Pressure = Force / Cross-sectional Area

or symbolized:

[tex]\large {\boxed {P = F \div A} }[/tex]

P = Pressure (Pa)

F = Force (N)

A = Cross-sectional Area (m²)

Let us now tackle the problem !

[tex]\texttt{ }[/tex]

Given:

diameter of pipe at location 1 = d₁ = 8.0 cm

speed of fluid at location 1 = v₁ = 1.28 m/s

diameter of pipe at location 2 = d₂ = 4.0 cm

Asked:

speed of fluid at location 2 = v₂ = ?

Solution:

We will use Continuity Equation as follows:

[tex]A_1 v_1 = A_2 v_2[/tex]

[tex]\frac{1}{4}\pi (d_1)^2 v_1 = \frac{1}{4} \pi (d_2)^2 v_2[/tex]

[tex](d_1)^2 v_1 = (d_2)^2 v_2[/tex]

[tex]v_2 = (\frac{d_1}{d_2})^2 v_1[/tex]

[tex]v_2 = (\frac{8}{4})^2 \times 1.28[/tex]

[tex]v_2 = 2^2 \times 1.28[/tex]

[tex]v_2 = 4 \times 1.28[/tex]

[tex]v_2 = 5.12 \texttt{ m/s}[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Physics

Chapter: Pressure

[tex]\texttt{ }[/tex]

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant , Liquid , Pressure

Answer:

Mercury

Explanation:

The force of gravity is equal to the mass times the centripetal acceleration:

Fg = m v² / r

Also, the force of gravity is defined by Newton's law of universal gravitation, which states the Fg = mMG / r², where m and M are the masses of the objects, G is the universal constant of gravitation, and r is the distance between the objects.

mMG / r² = m v²/ r

MG / r = v²

This means the square of the orbital velocity is equal to the mass of the sun times the universal constant of gravity divided by the orbital radius.  So whichever planet has the smallest orbital radius will have the highest orbital velocity.  Of the four options, that would be Mercury.