Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x-component Fx=kx−bx2+cx3 must be applied to the free end. Here k=100N/m, b=700N/m2, and c=12000N/m3. Note that x>0 when the spring is stretched and x<0 when it is compressed.

Answers

Answer 1

Answer:

The work done will be 0.115 J.

Explanation:

Given that,

[tex]k=100\ N/m[/tex]

[tex]b=700\ N/m^2[/tex]

[tex]c=12000\ N/m^3[/tex]

A force along the x-axis with x-component,

[tex]F(x)=kx-bx^2+cx^3[/tex]

Suppose, How much work must be done to stretch this spring by 0.050 m from its unstretched length?

We need to calculate the work done

Using formula of work done

[tex]W(x)=\int{F(x)dx}[/tex]

Put the value into the formula

[tex]W(x)=\int{(kx-bx^2+cx^3)dx}[/tex]

[tex]W(x)=\dfrac{kx^2}{2}-\dfrac{bx^3}{3}+\dfrac{cx^4}{4}[/tex]

Put the value of k,b,c and x

[tex]W(0.050)=\dfrac{100\times(0.050)^2}{2}-\dfrac{700\times(0.050)^3}{3}+\dfrac{12000\times(0.050)^4}{4}[/tex]

[tex]W(0.050)=0.115\ J[/tex]

Hence, The work done will be 0.115 J.

Answer 2

The value of spring displacement is greater than zero. Therefore, spring is stretched.

Force in spring :

  It is given as,  [tex]F=kx[/tex]

Where k is constant and x is amount of displacement.

The force function is given that,

       [tex]F(x)=kx-bx^{2}+cx^{3}[/tex]

Here given that,  [tex]k=100N/m, b=700N/m^{2} , c=12000N/m^{3} .[/tex]

Substitute all values in above equation,

           [tex]F(x)=100x-700x^{2} +12000x^{3}[/tex]

To check, the spring is stretched or it is compressed.

Substitute f(x) = 0

          We get x is greater than zero.

Thus, The value of spring displacement is greater than zero. Therefore, spring is stretched.

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Related Questions

A marble accelerates from rest at a constant rate .it travels 36 m in 12.0 sec what’s is it’s final velocity and what was the acceleration

Answers

Answer:

a = 0.50 m/s²

v = 6.0 m/s

Explanation:

Step 1: Given data

Initial velocity (u): 0 m/s (rest)Displacement of the marble (s): 36 mTime elapsed (t): 12.0 sFinal velocity (v): ?Acceleration (a): ?

Step 2: Calculate the acceleration

We will use the following suvat equation.

s = u × t + 1/2 × a × t²

s = 0 × 12.0 s + 1/2 × a × (12.0 s)²

36 m = a × 72.0 s²

a = 0.50 m/s²

Step 3: Calculate the final velocity

We will use the following suvat equation.

v = u + a × t

v = 0 + 0.50 m/s² × 12.0 s

v = 6.0 m/s

During a game of marbles, a player is trying to win a 2 g marble that is at rest. The player flicks a 1.25 g marble at a velocity of 8 at the larger marble that is sitting still. After the collision, the smaller marble has a velocity of 1 . What is the velocity of the 2 g marble after the collision? Round your answer to the nearest whole number.

Answers

Answer:

4 m/s

Explanation:jus did on edgu 2020

A delivery truck driver's round-trip route from the warehouse takes her 5 km east, then 2 km north, then 5 km west, and then 2 km south. Which of the following statements is FALSE?​

Answers

they're all right, because he just took a lap and went back to the same starting point,

What is the measure of how much a material resists the formation of an electric field?

A. Permittivity
B. Dielectric
C. Capacitance
D. Resistance

Answers

The answer is c capacitance

Answer:

C. Capacitance

Explanation:

right on EDGE2021

why would it motivate Hollywood to use more realism in special effects?

Answers

Answer:

Explanation:

the search for authenticity in films, motivated Hollywood to use more realism in special effects.

Calculate the image position of an object located 25 cm from a concave lens with a focal length 5.0 cm

Answers

2.5 cm no that’s it

stored energy and the energy of positions are ________________ energy

Answers

Answer:

Gravitational Energy

Consider a box sliding down horizontally across a straight line. Which of the following factors affects the amount of work done against friction in this situation?
A. Speed of the box
B. Time taken to move the box
C. Distance the box is moved
D. Direction of the box is moved​

Answers

Answer:

uhhh speed of box??? I think

The factor affecting the amount of work done against friction is the distance traveled by the box.

The work done against friction is energy dissipated in reducing frictional force along the horizontal surface.

The magnitude of the work done in reducing the frictional force along the horizontal surface is given as;

W = μFd

where;

μ is the coefficient of frictionF is applied horizontal forced is the horizontal distance traveled by the box

Thus, we can conclude that the factor affecting the amount of work done against friction is the distance traveled by the box.

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How to calculate weight on
mars?

Answers

it takes the weight of an object on earth and converts it to Martian weight, the formula is Weight on Mars= (Weight on Earth/9.81m/s2) * 3.711m/s2. To find the Martian weight, we divide the weight on earth by the earth's force of gravity, which is 9.81m/s2. This calculates the mass of the object. Once we have the object's mass, we can find the weight by multiplying it by the gravitational force, which it is subject to. Being that Mars has a gravitational force of 3.711m/s2, we multiply the object's mass by this quanitity to calculate an object's weight on mars.

So an object or person on Mars would weigh 37.83% its weight on earth. Therefore, a person would be much lighter on mars. Conversely, a person is 62.17% heavier on earth than on Mars.

A man jumps from a 45 m cliff into a large body of water. How long will he fall before he enters the wate

Answers

Answer:

about 2.5 seconds depending on if he jumps up and out or if he jumps out.

Explanation:


A ninja applies a force of 1250-N to a piece of 4-inch solid oak with his fist. What is the size of
the force applied to the fist by the piece of oak?

Answers

Answer:

The force is 1250-N

Explanation:

Generally according to Newtons third law , which states that for every action there is an equal and opposite reaction

 Now considering the question, the action here is the force applied by the ninja while the reaction is the force applied by the oak and from Newton law both of these action are equal but opposite to each other.

Hence the force applied by the the piece of oak on the fist is 1250 N

The distance between a scalar and a vector is that a vector quantity includes what

Answers

Answer:

magnitude and direction e.g acceleration,displacement


Which two factors are used to calculate kinetic energy?
A The chemical formula for the object
B. The velocity of an object
c. The mass of an object
D. The height of an object
E . The density of an object

Answers

The velocity of an object and the mass of an object

Answer:

B. The velocity of an object

c. The mass of an object

Explanation:

I NEED HELP!!!! THIS IS DUE TODAY OCT. 14, 2020 AT 11:59 PM!!!
Keisha has two large dogs and a small dog. The dogs like to play tug-the-rope together. Each of these three diagrams shows one way that the dogs play together with the rope. Look at each arrow and the number that goes with it. They show the direction and amount of force each dog exerts on the rope. There are three illustrations of two dogs pulling at a toy rope.


The left art should show two big dogs pulling on a rope toy each pulling with a force of 20N in the opposite direction. The middle art shows a big dog on left pulling to the left on the rope toy with a force of 20N and a little dog pulling to the right with a force of 12N. The right art shows the rope toy tied to a post, with both dogs pulling on different parts of the toy and in the same direction. One large dog pulls with a force of 20 N and the small dog pulls with a force of 12 N.


Explain whether the forces shown in each diagram are balanced or unbalanced. Use math-based evidence to support your claim for each diagram.

Answers

Answer:

The answer is unbalanced

Explanation:

Though cases like these are not really how the science will be used, they illustrate the principle.

If the left art shows two big dogs pulling on a rope toy each pulling with a force of 20N in the opposite direction. The middle art shows a big dog on left pulling to the left on the rope toy with a force of 20N and a little dog pulling to the right with a force of 12N. The right art shows the rope toy tied to a post, with both dogs pulling on different parts of the toy and in the same direction. One large dog pulls with a force of 20 N and the small dog pulls with a force of 12 N. The atomic theory has been of priceless value to chemists, but it has more than once happened in the history of science that a hypothesis, after having been useful in the discovery Present and the co-ordination of knowledge, has been aban- position doned and replaced by one more in harmony with later of the discoveries

The amount of force exerted in each direction in the rope determines if the force in play is balanced or unbalanced ;

Left art : 20N = 20N (Balanced) Middle : 20N > 12N (Unbalanced) Right art : 20N > 12N (Unbalanced)

To determine if the force acting in two direction is balanced or unbalanced, we calculate the net force acting on the object.

The net force = Force 1 - Force 2

If the netforce = 0 ; then the force is balanced, if otherwise , then it is unbalanced.

Left art :

Net force = 20N - 20N = 0 N

Right art :

20N - 12N = 8N (direction of the 20N force)

Middle :

20N - 12N = 8N (direction of the 20N force)

Therefore, the value of the net force determines if the force is balanced or not.

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Why do you think the lunar cycle is longer than the time it takes the moon to orbit Earth?

Answers

Answer:

because the moon returns to the same place on the sky once every siderial period, but the sun is also moving on the sky.

Explanation:

Hope that helps!

Answer:

Because the moon returns to the same place on the sky once every siderial  period (27.3 days), but the sun is also moving on the sky.Cycle of lunar phases takes 29.5 days. This is called the SYNODIC PERIOD

Explanation:

Find the potential energy of the bowling ball from the exercise above that is sitting on a shelf 2 meters high. Remember that g = 9.8m/s. Write equation, substitute values and units into equation, and show final answer.

Answers

Answer:

Explanation:

bv

A school bus moves slower and slower. Using what you have learned about forces, explain why the bus moves slower and slower.

Answers

Explanation:

the weight of the people inside the bus

The mass of an object is 200 kg. What is it's weight on Earth

Answers

W = mass • gravity
W = 200 • 9.8
W = 1960 N

Answer:

1N=1 kg×m/s (sqaured)

Explanation:

basically if you are 225 lb u weigh 1000N. I hope I helped

Determine how far a vehicle moved if it started at 12 m/s and accelerated up to 47 m/s in a time of 34s. ​

Answers

Answer:

[tex] s = 1,003 \: m[/tex]

Explanation:

[tex]s = \frac{1}{2} (u + v)t = \frac{1}{2} (12 + 47)34 \\ s = 1,003 \: m[/tex]

Ahmet hits a baseball that has a mass of 0.14 kg and accelerates it to 600 m/s2. What is the force that was applied?

Answers

Answer:

F = 600N

Explanation:

F = m x a

F = Force

m = mass

a = acceleration

F = 0.14 x 600 = 84N

An oil drop (m = 1.6 x 10-16 kg) is suspended between plates separated by 1.8 cm. The voltage
across the plates is 125 V. Is this possible?

Answers

Answer:

E = V / d       125 V / .018 m = 6940 V/m     electric field

F = E Q       force on Q due to E

F = E n e     where n is the number of electrons in Q

m g = E n e

n = m g / E e     where n is the number of electrons e needed to support drop

n = 1.6 * 10E-16 * 9.8 / (6940 * 1.6 * 10E-19)

n = 1.41

Since n needs to be an integral number of charges, the drop would

not be suspended (motionless under these conditions).

Which three factors are used to calculate gravitational potential energy?
A. The mass of an object
B. The acceleration of an object due to gravity
C. The density of an object
D. The velocity of an object
E. The chemical formula for an object
F. The height of an object

Answers

Answer: height, mass, and acceleration.

Explanation:

Answer:

height, mass, and acceleration.

or a,b,f

Explanation:

Holden is trying to determine the velocity of his race car. He went 20 meters east, turned around, and went 40 meters west. He turned the car one more time and went 35 meters east. His car was 15 meters from the starting line. This took 5 seconds.

What is the car’s velocity?

Answers

Answer:

3 m/s east

Explanation:

I took a test a got it right

Answer:

3 m/s east

Explanation:

Click The Pros and Cons of Plastics and use the information to answer the question.

Which scenario shows an indirect environmental impact of using plastics?

Answers

Answer:

Plastics being consumed by fish and passing toxic compounds to the humans eat the fish.

Explanation:

I did that answer and got it right.

Answer:

Plastics being consumed by fish and passing toxic compounds to the humans that eat the fish.

Explanation:

HELP PLEASE
A cyclist and his bicycle have a combined mass of 88 kg and
a combined weight of 862.4 N. The cyclist accelerates at 1.2
m/s2. After 2 seconds he reaches a speed of 2.4 m/s. What is
his momentum at this point?
A. 359.3 kg.m/s
B. 105.6 kg.m/s
C. 211.2 kg-m/s
O D. 36.7 kg-m/s

Answers

The momentum of the cyclist and bicycle at this point is 211.2 kg·m/s, calculated by multiplying their combined mass (88 kg) by their velocity (2.4 m/s). The correct answer is C.

The momentum of an object is defined as the product of its mass and velocity. To find the momentum of the cyclist at this point, we can use the equation: momentum = mass × velocityFirst, let's find the mass of the cyclist and his bicycle. We are given that their combined mass is 88 kg. Next, we need to find the velocity of the cyclist. We are given that he reaches a speed of 2.4 m/s after 2 seconds, and that he accelerates at a rate of 1.2 m/s². We can use the equation of motion: velocity = initial velocity + acceleration × timeThe initial velocity is 0 m/s (since the cyclist starts from rest), the acceleration is 1.2 m/s², and the time is 2 seconds. Substituting these values into the equation, we get:
velocity = 0 + 1.2 × 2 = 2.4 m/sFinally, we can calculate the momentum by multiplying the mass and velocity:
momentum = 88 kg × 2.4 m/s = 211.2 kg·m/sTherefore, the correct answer is C. 211.2 kg·m/s.

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When you are standing in a subway train and the train suddenly stops but your body continues to move forward. Which one of Newton's laws is this?
1st law
2nd law
3rd law
4th law

Answers

Answer:

A. 1st law.

Explanation:

Newton's first law of motion states that, an object or body will continue to be at rest or experience a uniform motion in a straight line at constant speed provided there's no action of an external force. Thus, unless compelled to change its state by an external force, a body will continue to be at rest or experience a uniform motion in a straight line.

The Newton's first law of motion is also known as the law of inertia; which is the tendency of a body to be at rest unless acted upon by an external force.

In this scenario, you are standing in a subway train and the train suddenly stops but your body continues to move forward. This is in accordance with Newton's first law of motion.

Hence, the sudden stoppage of the train generates a force which acts on the body thereby causing the passenger to tip or move forward.

Whats the difference between a solar eclipse and a lunar eclipse?

Answers

Answer:

A solar eclipse results when the moon passes in between the earth and the sun hiding the sun fully or partly for some time. A lunar eclipse occurs when the earth passes in between the moon and the sun casting its shadow on the moon and thus hiding it fully or partly for some time.

Explanation:

your welcome

A car accelerates from 15 m/s to 25 m/s for 6 seconds. What is the car's displacement? (use: d=>(); + v) ) ​

Answers

Answer:

hope this helps  : )

Explanation:

brainliest plz

1 HELP PLEASE I'LL GIVE BRAINLIST AND POINTS!!!
Do some research on digital vs. analog recording, and decide which you think gives the most accurate and best quality sound. State the advantages and disadvantages of each in a paragraph. Be sure to back up your opinions with facts, and state your sources.

have 2-6 paragraphs pleasee

Answers

Answer:

The question of analog vs. digital audio is one of the more hotly debated questions in the world of music, film and media today. Does digital sound better? Does analog sound better? Is there even a noticeable difference?

It’s impossible to understand the difference completely without understanding what distinguishes analog audio from digital audio. A full discussion of these terms is best left to your curriculum and discussions with your mentor in the studio. For now, though, here’s a brief explanation of what these two words mean, and the differences between them.

Analog refers to a continuously changing representation of a continuously variable quantity. Digital, however, refers to representing these variable quantities in terms of actual numbers, or digits. The last two sentences seem a bit complex, but let’s try to simplify them with an example. If you consider the numbers 1 and 2 on a number line, there are actually an infinite number of points between 1 and 2. This is what analog represents—the infinite number of possibilities between 1 and 2. Digital, on the other hand, only looks at certain number of fixed points along the line between 1 and 2 (for example, 1 ¼, 1 ½, 1 ¾, and 2).

Can you see the difference? Digital takes a few “snapshots” of the number line, while analog takes the whole line into account.

As another example, think of analog vs. digital as the difference between seeing something in real life and watching it on film. When we see something happen in real life, there are no “spaces” between what we see, so we’re watching it happen in analog. Film, however, is actually a series of still photographs that are taken in rapid-fire intervals, and when we see them in succession, it tricks our minds into thinking we’re seeing a continuous flow of movement. So in a manner of speaking, when we watch the event happen on film, we’re watching it digitally, because we’re watching increments of the event, rather than the whole thing in fluid motion. (Not to be confused with digital video vs. film, which is another discussion completely!)

Let’s bring this idea into audio, music, and the studio. Sound occurs naturally in analog–that is to say, sound occurs in a continuous set of waves that we hear with the human ear. (Think of it as a “wavy” line with an infinite number of points along it.) When we capture that sound in a way that represents all the possible frequencies, we’re recording in analog; when we use computers to translate the sound into a series of numbers that approximate what we’re hearing, we’re recording in digital.

Thus, a purely analog recording would be something that was recorded on tape and produced using manual equipment to mix, master and press into a vinyl LP. A purely digital recording would be recorded on a computer program such as Pro Tools, mixed, mastered and produced digitally, and eventually burned onto a CD as an MP3 or audio file.

The most ironic aspect of the debate about digital vs. analog recording is that nowadays a lot of music is a combination of the two.  For example, you might record a song onto analog tape, but mix and master it digitally, or release it on the Internet as an MP3.

So what’s the difference in quality between analog and digital? The idea between digital recording is that our ears and brains technically can’t determine the spaces between the digital values, just like our brains interpret film as continuous motion. However, to many people, analog sound tends to be warmer, has more texture and is thought to capture a truer representation of the actual sound. Digital is felt to be somewhat cold, technical and perhaps lacking in analog’s nuance.

However digital is much cheaper. Recording an album with analog technology can require a whole studio full of equipment, but with digital recording technology, it’s possible to record a whole album in a bedroom on a laptop. And whereas analog technology can wear out or be damaged, digital media can last for an indefinite length of time.

Today many recording artists, both major and independent, record using a mixture of digital and analog techniques. While analog audio does give warmth and a truer sound quality, digital is cheaper to work with and offers more control over the finished product.

Which of these consumers is an herbivore? *

1. lion

2. deer

3. spider

4. snake

Answers

Answer:

2. deer

Explanation:

The lion, spider, and snake eat meat or to an extent.

Deer don't eat meat

Answer:

deer :)

Explanation:

The rest are basically carnivores

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