A particle moving along the y-axis has the potential energy U=4y^3J, where y is in m.
A)Graph the potential energy from y=0m to y=2m.
B)What is the y-component of the force on the particle at y=0m?
C)What is the y-component of the force on the particle at y=1m?
D)What is the y-component of the force on the particle at y=2m?

Answers

Answer 1

A) The graph of the potential energy U=4y^3J from y=0m to y=2m resembles an increasing cubic function.
Graph shows an increasing cubic function.

B) The y-component of the force on the particle at y=0m is 0N, as the slope of the potential energy curve is 0 at this point.

C) The y-component of the force on the particle at y=1m is 48N, as it is equal to the negative derivative of the potential energy curve at this point.

D) The y-component of the force on the particle at y=2m is 192N, as it is equal to the negative derivative of the potential energy curve at this point.

At y=0m, the derivative of the potential energy curve is 0, indicating that there is no change in the potential energy with respect to displacement.

Thus, the force on the particle at this point is 0N, as force is the negative gradient of the potential energy.

This means that the particle is in a state of stable equilibrium, as any small displacement from this point will result in a restoring force that returns the particle back to its initial position.


At y=1m, the derivative of the potential energy curve is 48J/m, indicating that there is a change in the potential energy with respect to displacement.

This means that there is a force acting on the particle in the negative y-direction.

The y-component of this force is equal to the negative derivative of the potential energy curve at this point, which is equal to -48N.

This means that the particle is in a state of unstable equilibrium, as any small displacement from this point will result in a net force that accelerates the particle away from its initial position.


At y=2m, the derivative of the potential energy curve is 192J/m, indicating that there is a significant change in the potential energy with respect to displacement.

This means that there is a force acting on the particle in the negative y-direction.

The y-component of this force is equal to the negative derivative of the potential energy curve at this point, which is equal to -192N.

This means that the particle is in a state of unstable equilibrium, as any small displacement from this point will result in a net force that accelerates the particle away from its initial position.

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Answer 2

To graph the potential energy from y=0m to y=2m, we simply plug in values of y from 0 to 2 into the equation U=[tex]4Y^{3J}[/tex] and plot the resulting values on a graph.

The graph will have a shape similar to a cubic function, with the y-axis representing the potential energy in joules and the x-axis representing the distance in meters. To find the y-component of the force on the particle at y=0m, we take the negative gradient of the potential energy with respect to y, which gives us the force as F=-dU/dy. Evaluating this expression at y=0m gives us F=0N, since the derivative of U with respect to y is 0 at y=0m. Therefore, there is no force acting on the particle at y=0m. To find the y-component of the force on the particle at y=1m, we use the same expression F=-dU/dy and evaluate it at y=1m. Taking the derivative of U with respect to y gives us dU/dy=12y^2J/m, so plugging in y=1m gives us F=12N. To find the y-component of the force on the particle at y=2m, we use the same expression F=-dU/dy and evaluate it at y=2m. Taking the derivative of U with respect to y gives us dU/dy=96yJ/m, so plugging in y=2m gives us F=384N.

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Related Questions

find the value of x in this figure ​

Answers

Answer:

x=50

Explanation:

Answer:

vertically opposite angles are equal

Explanation:

so

2x+30=3x-20

2x-3x= -20-30

-1x= -50

so x is 50

as minus gets cancelled both sides.

HOPE IT HELPS YOU

PLS MARK ME BRAINLIEST

what is ionisation?​

Answers

Answer: Ionisation is the process of an atom gets a negative or a positive charge by gaining or losing electrons. The result is an ion.

Explanation: Thats why

pls help i’ll give brainliest if you give a correct answer!!

Answers

Normal force. Normal force is always present when there is contact between two items. Normal force is counteracting the gravitational force.

Explaining the incorrect answers:
-It’s not frictional force because friction only occurs when something is moving and also making contact. While there is contact in this scenario, the apple is not moving.
-There is no applied force; that would be something like a push.
-There is a gravitational force on the table, but it doesn’t keep the apple’s push in check. They are both pointed downwards, to the earth.

Hope this helps!

A soccer player strikes a soccer ball with a force of 550 N. If the player and the ball remain in contact for 0.03 s. What impulse was delivered to the ball by the player?

Answers

Easy my dude.
Impulse (J) is equal to the change in momentum of the ball. It is also equal to Force times Time:
J = Ft
J = (550 N)(0.03 s)
J = 16.5 Ns

Hope this helps! Please press “Thanks!”

please help with this question!!

Answers

Answer:

A.9.0 A

Explanation:

This is multiplication then add.

3*2+3=9.0

And that is how we get the answer.

1. We expect a conductor to be a constant voltage throughout. The conductive surface (silver marks) is mostly a constant voltage, but sometimes you may observe a millivolts-ish difference between different points on it. What does this mean about said conductive surface?

Answers

Answer:

Answer is explained in the explanation section below.

Explanation:

If the conductor has developed the potential difference. It simply means it is charged.

A conductor can be charged in different scenarios, let's discuss some of it and try to deduce the appropriate meaning for this question.

A conductor can be charged due to ions or

A conductor can be charged if it come across any current carrying conductor, so as to gain induced emf.

So, In both of these case, both can be very reasons for its potential difference.

Your are on a boat on a lake with no current. The lake is full of sharks that will eat you if you put your hands too close to the water, and your paddle has been eaten by those sharks. However, you do have a big bucket of grapefruit in the boat. How will you get to shore? Your answer must reference Newton's third law.

Answers

Answer:

throw the lakes to make a current maybe?

Explanation:

Why can’t the high-quality energy released from a lump of burning coal be recycled?

Answers

Answer:

when energy changes from one form to another, it always goes from a more useful to a less useful form. This means that people can't recycle or reuse high quality energy to perform useful work.

When energy changes from one form to another, it always transitions from a more helpful to a less useful one. Because of this, people are unable to reuse or recycle high-quality energy to complete crucial tasks.

What is the term of burning coal?

Coal is most frequently and significantly used in combustion, where heat is produced to create steam, which in turn powers the turbines that generate electricity. All living things, including humans, are composed of carbon. However, as coal burns, its oxygen reacts with airborne oxygen to generate carbon dioxide. Although dioxide (CO2) is an odourless, colourless gas, it is one of numerous gases found in the atmosphere that can retain the heat from the planet.

Why is burning coal a problem?

It's a major issue for climate change since it produces more carbon dioxide when burned than oil or gas. In addition to producing microscopic soot particles and hazardous substances like arsenic and mercury, coal also contributes to air pollution.

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list 10 uses of metals​

Answers

Answer:

Shiny metals such as copper, silver, and gold are often used for decorative arts, jewelry, and coins.

Strong metals such as iron and metal alloys such as stainless steel are used to build structures, ships, and vehicles including cars, trains, and trucks.

Some metals have specific qualities that dictate their use. For example, copper is a good choice for wiring because it is particularly good at conducting electricity. Tungsten is used for the filaments of light bulbs because it glows white-hot without melting.

Nonmetals are plentiful and useful. These are among the most commonly used:

Oxygen, a gas, is absolutely essential to human life. Not only do we breathe it and use it for medical purposes, but we also use it as an important element in combustion.

Sulfur is valued for its medical properties and as an important ingredient in many chemical solutions. Sulfuric acid is an important tool for industry, used in batteries and manufacturing.

Chlorine is a powerful disinfectant. It is used to purify water for drinking and fill swimming pools.

Explanation:

The carbon atom with 12 protons and 12 electrons has a charge of:
a. 1 C
b. +12 C
c. -1 C
d. 0 C
e. -12 C

Answers

Answer:

Isotopes are the elements having the same atomic number i.e same number of protons which in turn is equal to same number of electrons. Number of protons and electrons are equal as the atom is electrically neutral. So, the only option is A.

I hope it helps you !

Jenny is studying a compound that has two oxygen atoms and one nitrogen atom. Which statement describes the subscripts she will use to write the chemical formula? She will use one 2 as a subscript. She will use one 2 and one 1 as subscripts. She will use one 3 as a subscript. She will use two 2s and one 1 as subscripts.

Answers

Answer:

She will use one 2 as a subscript.

Explanation:

Nitrogen is a chemical element with the symbol "N" and has an atomic number of 7. Thus, it is found in group (5) of the periodic table and as such it has 5 electrons in its outermost shell. Therefore, nitrogen has two (5) valence electrons.

On the other hand, oxygen has an atomic number of 8 and with the symbol "O."

When nitrogen and oxygen react chemically, they produce a compound known as nitrogen dioxide [tex] NO_{2} [/tex]

In this scenario, Jenny is studying a compound that has two oxygen atoms and one nitrogen atom. Therefore, the statement which describes the subscripts she will use to write the chemical formula is, she will use one 2 as a subscript.

[tex] N + O_{2} ------> NO_{2} [/tex]

Where: 2 represents the subscript of oxygen.

Answer:

A- she will use 2 as a subscript

Explanation: because im doing the test rn and i got it right on edg2021

if a town was 90 miles away and you travel at 45 mph how long would it take to get there

Answers

Answer:

t = 2 hours

Explanation:

Given that,

Distance of the town, d = 90 miles

Speed, v = 45 mph

We need to find the time to get there. The speed of an object is given by :

[tex]v=\dfrac{d}{t}[/tex]

Where

t is time

[tex]t=\dfrac{d}{v}\\\\t=\dfrac{90}{45}\\\\t=2\ h[/tex]

So, the required time is 2 hours.

PLEASE HURRY
What does the investigation of Earth's layers reveal about the history of the
formation of our planet?

Answers

Answer:

there's a center of the earth..and there is every later of it..just like in a movie...it is true

Answer:

The layers of rock at Earth ’s surface contain evidence of the evolutionary processes undergone by these components of the terrestrial environment during the times at which each layer was formed. By studying this rock record from the very beginning, it is thus possible to trace their development and the resultant changes through time.

an atom has 5 protons, 6 neutrons, and 5 electrons. what is the atomic mass?​

Answers

Answer:

the atomic mass is 11

Explanation:

the atomic mass is basically how many protons and neutrons there are so for this all you have to do is some simple math:

5 + 6 = 11

and boom, ur atomic mass is equal to 11!

plzzz answer with explnation!!!
the value of acceleration due to gravity (g) will be maximum at:
a) 1/2 of the radius of earth
b) 1/4 of the radius of earth
c) 1/8 of the radius of earth

Answers

Answer:

a. 1/2 of the radius of earth

Explanation:

g= GM/r²

thus g is inversely proportional to radius

This guy has the correct explanation but is correct. See my comment on the other post!

(V) What are the objectives of the space mission?​

Answers

Explanation:

I hope this helps, I got this from another person

is an increase in speed in a certain time .

a. Acceleration
b. ActionReaction Pairs
c. Force
d. Inertia

Answers

It's Acceleration

We can calculate the average speed by finding the total distance traveled divided by the elapsed time: Average speed=–s=Total distanceElapsed time. Average speed = s – = Total distance Elapsed time.

do you weigh yourself regularly?what the things you do to adjust if your weight starts to slip upward or downward?​

Answers

Answer:

start a healthy diet. But starting a healthy diet doesn't mean only eating greens, you should minimize the amount of regular food you take and eat a balanced diet.

Weight is the measure of the mass of the body. Mass is the amount of matter a body contains.

Personally, I do weigh myself regularly in order to determine the action to take if the weight either slips upward or downwards.

If the weight slips upward, what I do is to reduce the amount of calorie intake and also exercise. Reduction in calorie intake and regular exercise can drastically reduce the weight of a body considerably.

If otherwise, I ensure I regularly consume a balanced diet and energy-giving foods.

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compare the liquid pressure at the surface of a swimming pool and the bottom of the swimming pool

Answers

Answer:

The pressure difference is equal to the product of density , height and g

Given that h is height difference between bottom and surface of a pool

P  

b

​  

−P  

s

​  

=dgh

Density d of water is 1

So we get P  

b

​  

−P  

s

​  

=gh

Therefore option A is correct

Explanation:

How do you know that Earth is affected by the gravitational pull of the sun ? Explain how you would be affected if you were able to safely move farther and farther away from Earth . Support your ideas

Answers

Answer:

The Sun's gravity pulls on the planets, just as Earth's gravity pulls down anything that is not held up by some other force and keeps you and me on the ground.

Explanation: Newton realized that the reason the planets orbit the Sun is related to why objects fall to Earth when we drop them. I am so sorry if I get this wrong, I'm in 5th grade! ♥

The Sun provides rotational motion to Earth by gravitational pull and if we get farther and farther, we will experience decreased gravitational force.

The Earth is continuously orbiting around the Sun, that is why we are experiencing the day and night everyday. And this orbiting is caused by the gravitational full by Sun on Earth, which is given as,

[tex]F = \dfrac{G \times M \times M'}{R^{2}}[/tex]

Here, G is the universal gravitational constant, M is the mass of Earth and M' is the mass of Sun. And R is the distance between the Earth and Sun.

If we suppose to move farther and farther away from the Earth then the strength of gravitational pull by Earth will decrease with the increasing distance. Because the gravitational pull is inversely proportional to square of distance.

Thus, we can conclude that the Sun provides rotational motion to Earth by gravitational pull and if we get farther and farther, we will experience decreased gravitational force.

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After Sophia eats her body breaks down the food to use as an engery source when she runs this is an example of which type of engery conversion

Answers

Answer:

cannibalism

Explanation:

because she is eating her body!

Canabilism as stated above

convex mirror is used as a rear view mirror in vehicles why give reasons

Answers

Answer: We prefer a convex mirror as a rear-view mirror in vehicles because it gives a wider field of view, which allows the driver to see most of the traffic behind him. Convex mirrors always form a virtual, erect, and diminished image of the objects placed in front of it.

Bronco the skydiver, whose mass is 80 kg experiences 200 N of air resistance and gravity pulls on him with 800 N What is the acceleration of his fall?

Answers

H E R E I S T H E A N S W E R

Bronco the skydiver, whose mass is 80 kg experiences 200 N of air resistance and gravity pulls on him with 800 N. The acceleration of his fall  7.5 m/sec².

What is force?

A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

To find the acceleration,

   F = mg

   F = 80.(10)

   F = 800 N

   air resistance = 200 N

   Net force = F - air resistance

                = 800 - 200

                =  600 N

   600 = mass . acceleration

   600 = 80 . acceleration

   acceleration = 7.5 m/sec²

Bronco the skydiver, whose mass is 80 kg experiences 200 N of air resistance and gravity pulls on him with 800 N. The acceleration of his fall  7.5 m/sec².

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4. Find the valency of atoms of chlorine, sulphur and magnesium.​

Answers

Answer:

1. Chlorine = 7 valence electrons.

2. Sulphur = 6 valence electrons.

3. Magnesium = 2 valence electrons.

Explanation:

In Chemistry, valence electrons can be defined as the number of electrons present in the outermost shell of an atom. Valence electrons are used to determine whether an atom or group of elements found in a periodic table can bond with others. Thus, this property is typically used to determine the chemical properties of elements.

1. Chlorine = it is an element found in group (7) of the periodic table known as halogens and as such it has 7 electrons in its outermost shell. Therefore, Chlorine has seven (7) valence electrons.

Sulphur = this element is found in group (6) of the periodic table and as such it has 6 electrons in its outermost shell. Therefore, Sulphur has six (6) valence electrons.

Magnesium = this element is found in group (2) of the periodic table and as such it has 2 electrons in its outermost shell. Therefore, Magnesium has two (2) valence electrons.

if anyone has course hero could you send me the Gizmo Fan Cart Physics?

Answers

Answer:

I might be able to help, but I also might not. I need to check if I can get you the answer.

Explanation:

explain budding (8marks)​

Answers

Answer: Budding is one of the methods of asexual reproduction in organisms.

Explanation:

The asexual reproduction is the process in which new organisms are produced from the parent organism without the formation of gametes. The budding is one of the methods of asexual reproduction in which from a mature organism a bud develops as an outgrowth. The bud obtains the nutrition from the parent organism and increase in size. On maturity the bud dissociate or detach from the parent organism and lives as separate individual organism. Budding can be seen in the case of Hydra, and Yeast.

Anyone who answer will get brainlest

Answers

Answer:

D

Explanation:

work = Force x distance

work = 2000 x 2 = 4000

power = work÷ time

4000/.8 = 5000W

Answer:

The answer is D 5000w

Explanation:

work = Force x distance

work = 2000 x 2 = 4000

power = work÷ time

4000/.8 = 5000W

White light is an _____________ mixture of all the colors.
a) observable b) unequal c) equal

Answers

Answer:

unequal

Explanation:

White light is a combination of all colors in the color spectrum.

Answer: C) equal

If you use a glass prism, you can split white light into a rainbow which shows all of the colors along a spectrum. Each little color slice is the same width. In other words, something like green doesn't dominate the spectrum and take up a wider portion compared to other colors.

Which situation involves kinetic energy being transformed into sound energy?

Answers

Answer:

c

Explanation:

this is because you move ( kinetic energy) your hands and clap the other person's hand, you will definitely hear sound right.

Answer:

c

Explanation:

When they move their hands together their energy transforms to sound energy.

Pls answer quick will mark brainlest and 5 stars

Answers

Answer:A

Explanation:

It’s bigger I am not sure

Answer:

For the first question, the answer is

B. Kettle

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