A student at a polymer lab conducted a stress-relaxation experiment on a polymer, whose material response can be modeled by the Maxwell model. In the experiment, a 10-cm-long bar was stretched instantly until the stress reached 200 MPa. After 2 min, the measured stress in the bar was 160 MPa. a) Calculate the relaxation time constant of the polymer. b) If the initial stress was reached by stretching the bar by 16 mm, what is the viscosity of the dashpot in the Maxwell model

Answers

Answer 1

Answer: add 10 cm plus 200 mpa divided by 2 min then caculate that into 160 bars.

Explanation:

Answer 2

a) The relaxation time constant of the polymer is approximately 8.9 min.

b) The viscosity of the dashpot in the Maxwell model is approximately 4.55 GPa s.

What is the stress-relaxation model?

The stress-relaxation response of the Maxwell model can be modeled by the following equation:

σ(t) = σ₀ exp(-t/τ)

where σ₀ is the initial stress, τ is the relaxation time constant, and t is the time.

a) The relaxation time constant of the polymer:

σ(2 min) = 160 MPa

σ₀ = 200 MPa

160 MPa = 200 MPa exp(-2 min/τ)

Taking the natural logarithm of both sides, we get:

ln(160/200) = -2 min/τ

Solving for τ, we get:

τ = -2 min / ln(160/200) ≈ 8.9 min

Therefore, the relaxation time constant of the polymer is approximately 8.9 min.

b) The displacement of the spring in the Maxwell model can be modeled by the following equation:

x(t) = (σ₀ / G) (1 - exp(-t/τ))

where G is the shear modulus of the polymer. We can use this equation and the given displacement of 16 mm to find the viscosity of the dashpot:

x(t) = 16 mm = 0.016 m

σ₀ = 200 MPa

τ = 6.09 min = 365.4 s

Assume that the shear modulus of the polymer is constant and use the given stress to find it:

G = σ₀ / γ

where γ is the strain induced by the stretching.

Since the bar was stretched by 16 mm and its original length was 10 cm (i.e., 100 mm), the strain is:

γ = 16 mm / 100 mm = 0.16

Therefore,

G = 200 MPa / 0.16 = 1250 MPa

Now we can solve for the viscosity of the dashpot:

η = σ₀τ / x(t)

= (200 MPa) (365.4 s) / (0.016 m)

≈ 4.55 GPa s

Therefore, the viscosity of the dashpot in the Maxwell model is approximately 4.55 GPa s.

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Related Questions

A spring has a spring constant of 65.5 N/m and it is
stretched with a force of 15.3 N. How far will it stretch?

Answers

0.234m !!!!!! hope this helps :)))

A 40-pF capacitor is charged to a potential difference of 500 V. Its terminals are then connected to those of an uncharged 10-pF capacitor. Calculate: (a) the original charge on the 40-pF capacitor; (b) the charge on each capacitor after the connection is made; and (c) the potential difference across the plates of each capacitor after the connection.

Answers

(a) The original charge on the 40-pF capacitor is [tex]2 .0 \ \times \ 10^{-8} \ C[/tex].

(b) The charge on each capacitor after the connection is made is [tex]4 .0 \ \times \ 10^{-9} \ C[/tex].

(c)  The potential difference across the plates of each capacitor after the connection is 100 V and 400 V.

Original charge of the capacitor

The original charge on the 40-pF capacitor is calculated as follows;

[tex]Q = CV\\\\Q = 40 \times 10^{-12} \times 500\\\\Q = 2 .0 \ \times \ 10^{-8} \ C[/tex]

Charge on each capacitor

[tex]C = \frac{C_1C_2}{C_1 + C_2} \\\\C = \frac{10 \times 10^{-12} \times 40 \times 10^{-12}}{10\times 10^{-12} \ + \ 40 \times 10^{-12}} \\\\C = 8 \times 10^{-12} \ F[/tex]

[tex]Q = Q_1 = Q_2\\\\Q = 8 \times 10^{-12} \ \times \ 500\\\\Q = 4 \times 10^{-9} \ C[/tex]

Potential difference

The potential difference across the plates of each capacitor after the connection is calculated as follows;

[tex]V = \frac{Q}{C} \\\\V_1 = \frac{Q}{C_1} \\\\V_1 = \frac{4 \times 10^{-9}}{40 \times 10^{-12}} \\\\V_1 = 100 \ V\\\\V_2 = \frac{Q}{C_2} \\\\V_2 = \frac{4 \times 10^{-9}}{10 \times 10^{-12} } \\\\V_2 = 400 \ V[/tex]

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a sports car has a mass of 1300kg.Starting from the rest the car generates a force of 4400 N.The frictional force opposing this motion is 280 N.What is the car’s acceleration

Answers

since the car moves, the force needed to move is greater than the frictional forces opposing it

a = 3.17m/s²

The acceleration of the car with a mass of 1300 kg which starts from rest generating a force of 4400 N and having a frictional force of 280 N is 3.17 m/s²

We'll begin by calculating the net force acting on the car. This can be obtained as follow:

Force (F) = 4400 N

Frictional force (Fբ) = 280 N

Net force (Fₙ) =?

Fₙ = F – Fբ

Fₙ = 4400 – 280

Fₙ = 4120 N

Thus, the net force acting on the car is 4120 N

Finally, we shall determine the acceleration of the car. This can be obtained as follow:

Mass (m) = 1300 Kg

Net force (F) = 4120 N

Acceleration (a) =?

Force = Mass × Acceleration

4120 = 1300 × a

Divide both side by 1300

[tex]a = \frac{4120}{1300}\\\\[/tex]

a = 3.17 m/s²

Therefore, the acceleration of the car is 3.17 m/s².

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What is sin for the given right triangle?
8.6 meters
5 meters

6.99 meters
A. l0.71
B. 0.81
C. 0.58
D. 1.72

Answers

Answer:

C

Explanation:

sin of a right triangle is opposite divided by hypotenuse

in this case, that is 5/8.6 = 0.581395349

you can easily remember the trig functions with this acronym:

SOH-CAH-TOA

S: Sine

O: Opposite

H: Hypotenuse

C: Cosine

A: Adjacent

H: Hypotenuse

T: Tangent

O: Opposite

A: Adjacent

Explanation:

sin = Mp /0P

sin = 5/8,6

sin = 0,58

Object 1 has a momentum of 10 kg m/s and Object 2 has a momentum of 25 kg m/s. Will it be easier to change the direction of movement of Object 1 or of Object 2?

Answers

Answer:

I think its object 1

Explanation:

Because the object that has more weight has a greater momentum and the lightest object that has a less momentum will be easier to change because its lighter.

A basketball player jumps straight up for a ball. To do this, he lowers his body 0.250 m and then accelerates through this distance by forcefully straightening his legs. This player leaves the floor with a vertical velocity sufficient to carry him 0.960 m above the floor. (a) Calculate his velocity (in m/s) when he leaves the floor. 4.33 Correct: Your answer is correct. m/s (b) Calculate his acceleration (in m/s2) while he is straightening his legs. He goes from zero to the velocity found in part (a) in a distance of 0.250 m.

Answers

Answer:

a. 3.73 m/s b. 27.8 m/s²

Explanation:

(a) Calculate his velocity (in m/s) when he leaves the floor.

Using the conservation of energy principles,

Potential energy gained by basketball player = kinetic energy loss of basket ball player

So, ΔU + ΔK = 0

ΔU = -ΔK

mg(h' - h) = -1/2m(v'² - v²)

g(h' - h) = -1/2(v'² - v²) where g = acceleration due to gravity = 9.8 m/s², h' = 0.960 m, h = 0.250 m, v' =0 m/s (since the basketball player momentarily stops at h' = 0.960 m) and v = velocity with which the basketball player leaves the floor

Substituting the values of the variables into the equation, we have

9.8 m/s²(0.960 m - 0.250 m) = -1/2((0 m/s)² - v²)

9.8 m/s²(0.710 m) = -1/2(-v²)

6.958 m²/s² = v²/2

v² = 2 × 6.958 m²/s²

v² = 13.916 m²/s²

v = √(13.916 m²/s²)

v = 3.73 m/s

(b) Calculate his acceleration (in m/s2) while he is straightening his legs. He goes from zero to the velocity found in part (a) in a distance of 0.250 m.

Using v² = u² + 2as where u = initial speed of basketball player before lengthening = 0 m/s, v = final speed of basketball player after lengthening = 3.73 m/s, a = acceleration during lengthening and s = distance moved during lengthening = 0.250 m

So, making, a subject of the formula, we have

a = (v² - u²)/2s

Substituting the values of the variables into the equation, we have

a = ((3.73 m/s)² - (0 m/s)²)/(2 × 0.250 m)

a = (13.913 m²/s² - 0 m²/s²)/(0.50 m)

a = 13.913 m²/s²/(0.50 m)

a = 27.83 m/s²

a ≅ 27.8 m/s²

What is the chemical formula for magnesium sulfide?

Answers

Answer:

MgS

Explanation:

What evidence do we have that the moon is receding from Earth?

Answers

For the last few billion years the Moon's gravity has been raising tides in Earth's oceanswhich the fast spinning Earth attempts to drag ahead of the sluggishly orbiting Moon. The result is that the Moon is being pushed away from Earth by 1.6 inches (4 centimeters) per year and our planet's rotation is slowing.

Two small, identical conducting spheres repel each other with a force of 0.020 N when they are 0.35 m apart. After a conducting wire is connected between the spheres and then removed, they repel each other with a force of 0.055 N. What is the original charge on each sphere

Answers

Answer:

why does anyone need to know

Explanation:

1 plus one = 69

what is the potential energy the greatest in a roller coaster​

Answers

Answer:

Gravitational potential energy is the greatest

Explanation

It is the highest point of a roller coaster.

Yanni just turned one. He loves to play with his cars and trucks. He can also name the animals he sees in books.

In which stage of development is Yanni?

childhood
infancy
adolescence
adulthood

Answers

infancy
i think hope this helps

14. Which of the following is not an example of work being done?
A. pushing a basketball away from your body
B. holding a coffee mug
C. carrying boxes across a warehouse floor

Answers

Answer:

B. holding a coffee mug

Explanation:

Something must move a distance for work to be done.

Astronomers observe the motion of four planets that orbit a star similar to the Sun. Each planet follows an elliptical orbit around its star. The astronomers measure each planet's orbital period, as shown in the table.
Planet; Orbital Period (Earth days)
Planet W; 10
Planet X; 640
Planet Y; 80
Planet Z; 270
To determine the distance each planet is from the star, astronomers applied one of Kepler's three laws.
Kepler's first law: The path of each planet around a star is an ellipse, with the star at one focus. Kepler's second law: A planet sweeps out equal areas in equal amounts of time as it revolves around the star.
Kepler's third law: The square of the time for one revolution of a planet is proportional to the cube of the radius of its orbit.
Based on the table, identify the planet that is the farthest distance from the star, and indicate which of Kepler's three laws can be used to justify your answer. Enter your answer in the box provided.​

Answers

Answer:

planet that is farthest away is planet X

kepler's third law

Explanation:

For this exercise we can use Kepler's third law which is an application of Newton's second law to the case of the orbits of the planets

          T² = ([tex]\frac{4\pi ^2}{ G M_s}[/tex] a³ = K_s a³

           

Let's apply this equation to our case

          a = [tex]\sqrt[3]{ \frac{T^2}{K_s} }[/tex]

for this particular exercise it is not necessary to reduce the period to seconds

Plant W

             10² = K_s  [tex]a_{w}^3[/tex]

             a_w = [tex]\sqrt[3]{ \frac{100}{ K_s} }[/tex]

             a_w = [tex]\frac{1}{ \sqrt[3]{K_s} }[/tex]  4.64

Planet X

             a_x = [tex]\sqrt[3]{ \frac{640^3}{K_s} }[/tex]

             a_x = \frac{1}{ \sqrt[3]{K_s} } 74.3

Planet Y

              a_y = [tex]\sqrt[3]{ \frac{80^2}{K_s} }[/tex]

              a_y = \frac{1}{ \sqrt[3]{K_s} } 18.6

Planet z

              a_z = [tex]\sqrt[3]{ \frac{270^2}{K_s} }[/tex]

              a_z = \frac{1}{ \sqrt[3]{K_s} } 41.8

From the previous results we see that planet that is farthest away is planet X

where we have used kepler's third law

pls help its already late lol

Answers

Answer:

Temperature

Explanation:

Answer:

Gravity

Explanation:

Gravity has nothing to do with weather. Temperature means hot or cold, water is rain and thunder, and wind is if it's in the winter or something like that

a wave of frequency 10hz forms a stationary wave pattern in a medium where the velocity is 30cm/s. the distance between adjacent nodes is?​

Answers

Answer:

The ans is 1 not 2

Explanation:

The distance between two adjacent node in a stationary wave is half wavelength π/2 and not full wavelength as in π,so when solving we got 2cm as the wavelength since they ask the dist. Also adjacent nodes you will divide it by 2 and the ans will give u 1cm.

Hope this helps.

A cyclist exerts a 15.0 N force while riding 251 m in 30.0 s. What power does the cyclist develop?

Answers

Answer:

P=126W

Explanation:

Sorry if im wrong!

Answer:

125.5 watts

Explanation:

P=work/time

work=F*d

P=(F*d)/t

P=(15*251)/30

P=125.5 watts

amount of force times the distance it moves object

Answers

work=force×distance this is the formula

During a normal reaction to a stressful event, muscles are moved to their maximum capacity, and sensitivity is

Answers

Answer:

The paper focuses on the biology of stress and resilience and their biomarkers in humans from the system science perspective. A stressor pushes the physiological system away from its baseline state toward a lower utility state. The physiological system may return toward the original state in one attractor basin but may be shifted to a state in another, lower utility attractor basin. While some physiological changes induced by stressors may benefit health, there is often a chronic wear and tear cost due to implementing changes to enable the return of the system to its baseline state and maintain itself in the high utility baseline attractor basin following repeated perturbations. This cost, also called allostatic load, is the utility reduction associated with both a change in state and with alterations in the attractor basin that affect system responses following future perturbations. This added cost can increase the time course of the return to baseline or the likelihood of moving into a different attractor basin following a perturbation. Opposite to this is the system's resilience which influences its ability to return to the high utility attractor basin following a perturbation by increasing the likelihood and/or speed of returning to the baseline state following a stressor. This review paper is a qualitative systematic review; it covers areas most relevant for moving the stress and resilience field forward from a more quantitative and neuroscientific perspective.

Explanation:

During a normal reaction to a stressful event, muscles are moved to their maximum capacity, and sensitivity is increased.

What is Sensitivity?

This is defined as the ability of an organism to respond to stimuli such as touch, sensation etc.

During exercise, sensitivity to substances such as insulin when glucose transport wears off helps to balance energy supply.

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If 155 g of sugar can be dissolve in 100g of water at 20 degree than how much sugar will be dissolved in 300 g of water at same temperature if someone do I will make you brainly

Answers

Answer:

465 grams of sugar.

Explanation:

I'm not sure this is true: is the relationship linear?

If it is then 300 grams of water should be able told 3*155 grams of sugar

3 * 155 = 465  grams of sugar in 300 grams of water.

Is the speed of light constant throughout the universe.?

Answers

Answer:

It is a basic postulate of the theory of relativity that the speed of light is constant. This can be broken down into two parts: The speed of light is independent of the motion of the observer. The speed of light does not vary with time or place.

Explanation:

A woman stands still holding a 350 Newton bag (about 80 pounds) 2 meters off the ground. How much work does the woman do?

Answers

Answer:

700 Joules

Explanation:

What we know:

Force = 350 Newton

Distance = 2 meters

Work = ?

The formula for work is:

Work = force x distance

Plugging values into equation:

Work = 350 Newtons x 2 meters

Work = 700 Joules

I had the same question on the homework assignment with the answers provided:

a) It depends on how long she holds the bag

b) 350 Joules

c) none

d) 350 Newtons

The final answer would be c) none. The work done is 700 Joules. Hope this helps!

Find the momentum of a 15 kg object traveling at 7 m/s

What is the momentum?

What equation did you use to solve?

Answers

Answer:

105 kg*m/s

Explanation:

p=mv

momentum=mass*velocity

momentum=15kg*7m/s

momentum=105kg*m/s

Lichen grows on the surface of hornblende granite and causes it to breakdown at a faster rate. This is an example of. _______ Weathering

Answers

Answer:

Chemical.

Explanation:

Weathering can be defined as the physical and chemical breakdown of rock into smaller pieces called sediment. Weathering can be classified into two categories namely;

I. Physical weathering : it is the process of breaking rocks into pieces without affecting its chemical composition e.g temperature, abrasion and frost action.

II. Chemical weathering : it is the process of breaking rocks into pieces by chemical action which leads to changes in its chemical composition e.g carbonation, hydration, plant acid and oxidation.

In this scenario, Lichen grows on the surface of hornblende granite and causes it to breakdown at a faster rate. Thus, this is an example of chemical weathering

If you increase the frequency of a sound wave four times, what will happen to its speed?
А
The speed will increase four times.
B.
The speed will decrease four times,
C. The speed will remain the same.
D.
The speed will increase twice.
E.
The speed will decrease twice.

Answers

The answer is C wave frequency does not affect wave speed

In 1976, a 53 kg helicopter was built in Denmark. Suppose this helicopter flew east with a speed of 60.0 m/s and the total momentum of the helicopter and pilot was 7,200 kg∙m/s to the east. What was the mass of the pilot?

Answers

Answer:

67 kg.

Explanation:

From the question,

Total momentum = (mass of the pilot+ mass of the helicopter)×velocity.

I = (m+M)v............................... Equation 1

Where I = Total momentum of the pilot and the helicopter, m = mass of the pilot, M = mass of the helicopter, v = velocity.

make m the subject of the equation

m = (I/v)-M.............................. Equation 2

Given: I = 7200 kg.m/s, v = 60 m/s, M = 53 kg.

Substitute these values into equation 2

m = (7200/60)-53

m = 120-53

m = 67 kg.

Hence the mass of the pilot is 67 kg

In which scenario is the greatest amount of work done on a wagon?

A force of 55 N moves it 8 m.
A force of 60 N moves it 6 m.
A force of 50 N moves it 5 m.
A force of 40 N moves it 10 m.

Answers

Answer:

The first scenario!

Explanation:

W=F*d

a) 55*8= 440J

b) 60*6= 360J

c) 50*5= 250J

d) 40*10= 400J

The scenario with the greatest amount of work done on a wagon is "A force of 55 N moves it 8 m" and the Work done is 440N.m.

What is Work done?

Work done is simply defined as the energy transfer that takes place when an object is either pushed or pulled over a certain distance by an external force. It is expressed as;

W = F × d

Where F is force applied and d is distance travelled.

From the question;

A force of 55 N moves it 8 m

W = 55N×8m = 440N.m

A force of 60 N moves it 6 m.

W = 60N×6m = 360N.m

A force of 50 N moves it 5 m.

W = 50N×5m = 250N

A force of 40 N moves it 10 m.

W = 40N×10m = 400N.m

Therefore, the scenario with the greatest amount of work done on a wagon is "A force of 55 N moves it 8 m" and the Work done is 440N.m.

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In what order were the following energy sources
discovered by humans

Answers

There’s no order to go off of...

Select the correct answer.

A pair of pliers is an example of a simple machine with two levers. Which part of the pliers is the fulcrum?



A. A
B. B
C. C
D. D
E. E

Answers

Answer:

There isnt enough in your question to answer the question bro, like we need a picture or something bro.

Explanation:

You don't have a image attached

****PLEASE HELP**** WILL MARK BRAINLIEST
Assuming that voltage remains constant, what happens to the current in a
wire if the length of the wire increases?
O A. The current decreases.
OB. The current alternates between high and low values.
O C. The current increases.
O D. The current is not affected by a change in wire length.

Answers

Answer:

The Current decreases

Explanation:

HOPE THIS HELPS!

You are riding in the passenger seat of a car as it goes around a tight turn. You slide across the seat to the passenger side door. Which statement below properly describes what is happening? a. You are exerting a centripetal force on the door. b. The door and seat are exerting a centripetal force on you that balances the centrifugal force of the turn. c. The car seat exerts a centripetal force on you, but not enough to keep you in place, so the door exerts the rest. d. The centrifugal force is greater than the force of friction between you and the seat, so you slide outward.

Answers

Answer:

Explanation:

answer C looks good

there isn't really a "centrifugal " force. :/    when we are pushed "back" in a car seat.. it's not because there is a force pushing us backwards... but a force pushing us forwards.. just like when turning too,   a force pushes us into the corner,  not a force pushing out of the corner.  :)  

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