The question is incomplete. The complete question is :
Consider a composite cube made of epoxy with fibers aligned along one axis of the cube (the fibers are parallel to four of the twelve cube edges). If the cube can only be loaded in axial tension such that the force is uniformly applied over - and is normal to - a cube face, what is the lowest possible positive length change the cube can experience under this tension? The applied tensile force is 102 KN. The unloaded cube edge length is 56 mm. The glass fibers have an elastic modulus of 200 GPa. The epoxy has an elastic modulus of 38 GPa. The cube is comprised of 18 vol% epoxy (the balancing vol % is glass fiber). Hint: The loading axis is intentionally unspecified. Answer Format: Lowest possible length increase (change of length) under tension.
Solution :
Given :
[tex]$E_{glass fibre}$[/tex] = 200 GPa
[tex]$V_{glass fibre} = 82\%$[/tex]
[tex]$E_{epoxy}$[/tex] = 38 GPa
[tex]$V_{epoxy} = 82\%$[/tex]
Edge length = 56 mm
Cube is loaded in axial tension such that the force is uniformly applied over a cube face.
[tex]$E_{\text{composite}}=\frac{E_{glass fibre} \times E_{epoxy}}{(E_{glass fibre .E_{epoxy}})+(E_{fibre}.V_{glass fibre})}$[/tex]
[tex]$E_{composite} = \frac{200 \times 38}{(200 \times 0.18)+(38\times 0.82)}$[/tex]
[tex]$=113.16 $[/tex] GPa
Applied stress [tex]$=\frac{\text{applied load}}{\text{area}}$[/tex]
[tex]$\sigma=\frac{102 \times 10^3 \ N}{56 \times 56 \times 10^{-6} \ m^2}$[/tex]
= 32.5 MPa
By Hooke's law
[tex]$\sigma = E . \epsilon$[/tex]
[tex]$\sigma = E. \frac{\Delta l}{l}$[/tex]
[tex]$\Delta l = \frac{\sigma}{E}\times l$[/tex]
Length change, [tex]$\Delta l =\frac{32.5 \times 10^6 \ Pa}{113.16 \times 10^9 \ Pa}\times 56 \times 10^{-2} \ m$[/tex]
[tex]$\Delta l = \frac{32.5 \times 56}{113.16} \times 10^{-3} \ mm$[/tex]
= 0.016 mm
When a narrow laser beam passes through a fine wire mesh before arriving at the wall, it forms a complicated pattern of bright spots on the wall. This pattern of spots would not occur if you sent a flashlight beam through the mesh because light from the flashlight is not a single electromagnetic wave. cannot be sent through a single opening of the mesh. is horizontally polarized, while laser light is vertically polarized. is vertically polarized, while laser light is horizontally polarized.
Answer:
this pattern to occur there must be coherence in the light beams.
you use a flashlight, the rays are incoherent so diffraction patterns cannot occur.
Explanation:
The point pattern that appears in the wall is the result of the interference and diffraction processes through each space of the mesh, for this pattern to occur there must be coherence in the light beams.
The coherence process is that all the rays have the same constant and phase, before the appearance of the lasers, the light is stopped by a small opening and this ray is the one that passes through the slits, with the appearance of the laser this it is consistent from its production process, so opening is not necessary, with this there is much greater intensity and the measurement process is simplified.
When you use a flashlight, the rays are incoherent so diffraction patterns cannot occur.
Polarization has no effect on diffraction patterns so it does not matter if it is vertical or horizontal.
The velocity of a particle is given by v=25t2 -80t-200, where velocity is meter per second and time is seconds. Determine the velocity for the first six seconds when acceleration is zero.
Answer:
v = 220 m / s
Explanation:
This is a kinematics exercise, the expression for velocity is
v = 25 t² - 80 t - 200
asks the velocity for time t = 6 s.
let's calculate
v = 25 6² - 80 6 - 200
v = 220 m / s
The velocity for the first six seconds when acceleration is zero is -44 m/s.
What is velocity?
The velocity of an object is the rate of change displacement with time.
The velocity of the object for the first six seconds when the acceleration is zero is calculated as follows;
[tex]a = \frac{dv}{dt} \\\\a = 50t - 80\\\\0 = 50t - 80\\\\50t = 80\\\\t = 1.6 \ s[/tex]
Velocity when time = 1.6 s
[tex]v(1.6) = 25(1.6)^2 - 80(1.6) - 200\\\\v(1.6) = -264 \ m/s[/tex]
The velocity for the first six seconds when acceleration is zero.
[tex]v = v_{a =0} + v_6\\\\v = - 264 \ + 25(6)^2 - 80(6) - 200\\\\v = -44 \ m/s[/tex]
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What are
the main differences between cell
walls and cell membranes?
Answer:
Cell membrane helps to enclose the cell organelles and cytosol inside a cell. A cell wall is a ridgid, protective layer and it covers the cell membrane
Explanation:
A theme park creates a new kind of water wave pool with large waves caused by constructive interference. There are two wave generators in phase with each other along either side of a pool that is 24.0 m wide. A swimmer that is 9.0 m from one generator and 14.0 m from the other notices that she is in a region with almost no wave amplitude, but there are large-amplitude waves on either side of her.
What is the longest wavelength that will produce this interference pattern?
Express your answer to three significant figures and include appropriate units.
Answer:
10.0 m
Explanation:
Since there is no amplitude at the point of the swimmer, we have destructive interference.
So, the path difference ΔL = L₂ - L₁ where L₁ = swimmer's shorter distance from one generator = 9.0 m and L₂ = swimmer's longer distance from the other generator = 14.0 m. ΔL = 14.0 m - 9.0 m = 5.0 m
Also, since we have destructive interference, ΔL = (n + 1/2)λ where n = number of wavelengths and λ = wavelength of waves
For maximum wavelength, n = 0
So, ΔL = (n + 1/2)λ
ΔL = (0 + 1/2)λ
ΔL = λ/2
λ/2 = ΔL
λ = 2ΔL
λ = 2 × 5.0 m
λ = 10.0 m
So, the longest wavelength that will produce this interference pattern is λ = 10.0 m
If 84 J of work are exerted to pull a wagon, how much force does it take to pull the wagon 7.0 m? Round your answer to the nearest whole number.
Answer: It takes 12 N of force to pull the wagon.
Explanation:
A woman is driving her car due east at a velocity of 10 m/s. If the woman has a mass of 50 kg and her car has a mass of 1.000 kg, what is the magnitude of the momentum of the woman and her car?
Answer: 10,500 kg m/s
Explanation: (1,000 + 50)(10)
If a person wanted to engineer a new type of communication device, what field of study would be the most useful?
A ) electrical engineering
B ) chemical engineering
C ) optical engineering
D ) mechanical engineering
Answer: Option A: electrical engineering.
Explanation: The field of electrical engineering, sometimes called electronics engineering, mostly outside the US, is a field of engineering that covers a number of subtopics that include large scale power systems, electronics, control systems, signal processing and telecommunications. In this case the engineer would specifically have to know about electronics (computer chips), signal processing (cell signals) and telecommunications.
A spacecraft is moving past the earth at a constant speed of 0.60 times the speed of light. The astronaut measures the time interval between ticks of the spacecraft clock to be 3.2 s. What is the time interval (in seconds) that an earth observer measures
Answer:
the time interval that an earth observer measures is 4 seconds
Explanation:
Given the data in the question;
speed of the spacecraft as it moves past the is 0.6 times the speed of light
we know that speed of light c = 3 × 10⁸ m/s
so speed of spacecraft v = 0.6 × c = 0.6c
time interval between ticks of the spacecraft clock Δt₀ = 3.2 seconds
Now, from time dilation;
t = Δt₀ / √( 1 - ( v² / c² ) )
t = Δt₀ / √( 1 - ( v/c )² )
we substitute
t = 3.2 / √( 1 - ( 0.6c / c )² )
t = 3.2 / √( 1 - ( 0.6 )² )
t = 3.2 / √( 1 - 0.36 )
t = 3.2 / √0.64
t = 3.2 / 0.8
t = 4 seconds
Therefore, the time interval that an earth observer measures is 4 seconds
A child has a mass of 35 kg. The child is running across a fiend and has a speed of 3 m/s. What is the kinetic energy of the child?
Answer:
Explanation:
Given the following data;
Mass = 35 kg
Velocity = 3 m/s
To find the kinetic energy of the child;
K.E = ½mv²
Two concentric, circular wire loops of radii r1 and r2 (r1 < r2) are located in the x-y plane; each carries a current I in a clockwise direction. (a) Find the net dipole moment of this system. (b) Repeat for the reversed current in the inner loop
Answer:
a. πi(r₁² + r₂²)
b. πi(r₂²- r₁²)
Explanation:
(a) Find the net dipole moment of this system.
The magnetic dipole moment, μ = iA where i = current and A = For area
For the circular loop with radius r₁, and current i₁ in a clockwise direction, i₁ = + i positive
μ₁ = i₁A₁
= +i(πr₁²)
= πir₁²
For the circular loop with radius r₂, and current i₂ in a clockwise direction, i₂ = +i
μ₂ = i₂A₂
= +i(πr₂²)
= πir₂²
The net dipole moment, μ = μ₁ + μ₂
μ = μ₁ + μ₂
= πir₁² + πir₂²
= πi(r₁² + r₂²)
(b) Repeat for the reversed current in the inner loop
With the reversed current in the inner loop, the current is negative. So i₂ =-i
μ₁ = i₂A₁ = -i(πr₁²) = -πir₁²
So,
μ = μ₁ + μ₂
= -πir₁² + πir₂²
= πi(-r₁² + r₂²)
= πi(r₂²- r₁²)
HELP ME PLEASEEEEEEEEEEEEEE
Answer:
the vacoule in a plant is larger than that of an animal
Air(ideal gas) at 292.15k is expended by a piston from 600cm^3 to 900cm^3 at a temperature of 550k at 900kpa pressure. find the pressure before expansion.
Answer:
The pressure before expansion is 717.1 kPa.
Explanation:
We need to use the Ideal Gas equation to find the initial pressure:
[tex] PV = nRT [/tex]
Where:
P: is the pressure
V: is the volume
n: is the number of moles
R: is the gas constant
T: is the temperature
Since the number of moles does not change after the expansion, we need the following number of moles:
[tex] n = \frac{P_{f}V_{f}}{RT_{f}} [/tex] (1)
Where "f" is for final
Before the expansion, the pressure is:
[tex] P_{i} = \frac{nRT_{i}}{V_{i}} [/tex] (2)
By entering equation (1) into (2) we have:
[tex] P_{i} = (\frac{P_{f}V_{f}}{RT_{f}})(\frac{RT_{i}}{V_{i}}) [/tex]
[tex]P_{i} = \frac{P_{f}V_{f}T_{i}}{T_{f}V_{i}} = \frac{900 kPa*900 cm^{3}*292.15 K}{550 K*600 cm^{3}} = 717.1 kPa[/tex]
Therefore, the pressure before expansion is 717.1 kPa.
I hope it helps you!
The disk weights 40 lb and has a radius of gyration is 0.6 ft. A 15 lb/ft moment is applied and the spring has a spring constant of 10 lb/ft. The system was initially at rest and the disk is rolling without slipping. The spring is initially unstretched. Find the angular velocity of the wheel when disk moves to the right 0.5 ft.
Answer:
angular velocity = 2.6543 rad/s
Explanation:
To find the angular velocity of the wheel when the disk moves to the right 0.5 ft, we need to be aware that the spring will stretch twice the value of gyration with any slight change in the position or movement of gyration since the top of the wheel is holding the spring.
The work done here:
= ((distance moved by the wheel) X spring constant X (Final displacement^2 - Initial displacement^2)) + Mass (q2 – q1)
Where q2 = 0.5ft
q1 = 0.8 lb
Note that linear velocity = radius X angular velocity
= -0.5(10)(1^2 – 0) + 15(0.5/0.8) = 4.375 ft·lb
Then, the kinetic energy :
Since the spring is initially unstretched, the initial tension in the spring = 0
So the final tension = ((distance moved by the wheel) X (linear velocity)^2 X (angular velocity) ^2 + (distance moved by the wheel) X (linear velocity) X ( radius of gyration) ^2 X (angular velocity) ^2
= 0.5(40/32.2)(0.8w) ^2 + 0.5(40/32.2)(0.6)^2 X w2
final tension = 0.621 w2
So the angular velocity of the wheel when disk moves to the right 0.5 ft = The Initial workdone + Initial kinetic energy will be equal to the final workdone + the final Kinetic energy
0 + 4.375 ft·lb = 0.621 w2
angular velocity = 2.6543 rad/s
Place the balloon in a bell jar. If available also add some shaving cream and fresh marshmallows. Ask the instructor for help if you are unfamiliar with this apparatus. The motor of the vacuum pump will remove air from the bell jar when it is turned on. Make a prediction about what you think will happen to the balloon as air is removed from the bell jar.
Answer:
The balloon will collapse
Explanation:
When air is removed from the bell jar, the balloon will collapse if the internal pressure from the balloon does not balance the atmospheric pressure from the surroundings.
A spring is hung from the ceiling. When a block is attached to its end, it stretches 2.6 cm before reaching its new equilibrium length. The block is then pulled down slightly and released. What is the frequency of oscillation?
Answer:
f = 3.09 Hz
Explanation:
This is a simple harmonic motion exercise where the angular velocity is
w² = [tex]\frac{k}{m}[/tex]
to find the constant (k) of the spring, we use Hooke's law with the initial data
F = - kx
where the force is the weight of the body that is hanging
F = W = m g
we substitute
m g = - k x
k = [tex]- \frac{m g}{x}[/tex]
we calculate
k = [tex]- \frac{9.8 m}{- 2.6 \ 10^{-2}}[/tex]
k = 3.769 10² m
we substitute in the first equation
w² = [tex]\frac{ 3.769 \ 10^2 \ m }{m}[/tex]
w = 19.415 rad / s
angular velocity and frequency are related
w = 2πf
f = [tex]\frac{w}{2\pi }[/tex]
f = 19.415 / 2pi
f = 3.09 Hz
Which element has 1 valence electron in its outer shell and will react with a
group 17 element in a 1:1 ratio?
A. Strontium
B. Silicon
C. Lithium
D. Sulfur
Answer: C. Lithium
Explanation: Quizzed
C. Lithium has 1 valence electron in its outer shell and so will react with a group 17 element in a 1:1 ratio.
The last number of group that an element belongs to on the periodic table tells the number of valence electrons that it will have.
Lithium is in group 1 of the periodic table which means that it has only a single electron in its valence shell.Group 17 elements have seven valence electrons and so need one more to achieve stability which is why they will react with Lithium (which has that one electron) in a 1:1 ratio.
Some of those elements include:
Fluorine ChlorineBromineIodineIn conclusion therefore, Lithium has 1 valence electron and will react with group 17 elements in a 1:1 ratio.
Find out more at https://brainly.com/question/20516188.
If you lived on Saturn, which planets would exhibit retrograde motion like that observed for Mars from Earth? (Select all that apply.)
Mercury
Venus
Earth
Mars
Jupiter
Uranus
Neptune
Answer:
earth , mercury , and neptune
Explanation:
pls mark brainless
True or False - Water changing between states of matter is an example of a physical change.
true. true is the correct answer
Drag the tiles to the correct boxes. Not all tiles will be used.
Match the molecular shapes to the correct Lewis structures.
trigonal pyramidal
trigonal planar
bent
tetrahedral
linear
Answer
1) AlH3= trigonal planar
2) CH2F2= tetrahedral
3) PH3= trigonal pyramidal
4) O3= bent
Explanation:
I took the test
Science questions!! Please help!!
Post Assessment on Investigating the Immune System
please help!! Please choose the right answers!! Dont guess if you dont know the answers!!
Answer: i think it is for 16, Infectious diseases commonly spread through the direct transfer of bacteria. for 17 i think In biology, immunity is the capability of multicellular organisms to resist harmful microorganisms. i dont have a clue about the others but i hope this is right or atleast helps
Explanation:
the density of brick is 1,600 kg/m3. what is the mass of a brick with a volume of 0.0006 m3? WILL MARK BRAINLIEST
Answer:
.0000004
Explanation:
The mass of a brick with a volume of 0.0006 m³ and a density of 1600 kg/m³ is 0.96kg.
HOW TO CALCULATE MASS?The mass of a substance can be calculated by multiplying the density of the substance by its volume. That is;
Mass = density × volume
According to this question, the density of brick is 1,600 kg/m3 and it has a volume of 0.0006m³. The mass is calculated as follows:
Mass = 0.0006 × 1600
Mass = 0.96kg
Therefore, the mass of a brick with a volume of 0.0006m³ and a density of 1600 kg/m³ is 0.96kg.
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Hi!!! Please help me, 25 points!! :D
Which material refracts the light rays the least: air, water, or glass?
Answer:
air
Explanation:
water is a liquid and can be refracted.
glass is a solid which can also be refracted.
however,
air you can't see just see mainly.
air is the answer.
hope this helps :)
As wavelength decreases the frequency of a wave _______
Question (Fill-In-the Blank):
As wavelength decreases the frequency of a wave _______
Answer:
Increases
Explanation:
When waves travel from one medium to another the frequency never changes. As waves travel into the denser medium, they slow down and wavelength decreases. Part of the wave travels faster for longer causing the wave to turn. The wave is slower but the wavelength is shorter meaning frequency remains the same.
[tex] \boxed{ \boxed{ \huge\mathrm{Answer࿐}}}[/tex]
[tex] \mathrm{wavelength \: \: \dfrac{1}{ \propto} \: \: frequency }[/tex]
So, As wavelength decreases the frequency of a wave Increases.
_____________________________
[tex]\mathrm{ \#TeeNForeveR}[/tex]
Hello guys sana ok lng kau
sssssssssssss
Explanation:
Answer:
hello how are you
have a great day
a boy takes 20 minutes to cover 3.2 km on a bicycle find the speed in km/hr
Answer:
9.6 km/h
Explanation:
20 minutes=1/3 minute.
The speed of the bicycle: 3.2:1/3=9.6 km/h.
Answer: 9.6 km/h
What are the parts of a torch light name them
Answer: Batteries,the case of the torch,reflector,contacts,switch and lens and the light/bulb Hope i helped :)
13. For an object to appear transparent, what interaction must occur between light waves and the object they hit?
A. They are refracted.
C. They are diffracted
B. They are absorbed.
D. They are transmitted
Answer:
The answer is B
Explanation:
The absorption happens when photons from light hit atoms and molecules, and they vibrate because of that specific interaction. Then the heat ejects from the object in the format of thermal energy.
For an object to appear transparent, light waves must be transmitted through the object. Option D is correct.
What are light waves?Light waves are a type of electromagnetic radiation that can be perceived by the human eye.
Here,
For an object to appear transparent, light waves must be transmitted through the object. Therefore, the correct answer is D. When light waves are transmitted, they pass through the object without being absorbed or reflected, allowing us to see through the object. The degree to which light is transmitted through an object is related to the object's optical properties, such as its refractive index, which determines how much the light is bent as it passes through the object.
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Please help to Calculate the lower and upper bound for 3.2 + 4.6
Answer:
i think it is 7.10Explanation:
I dont have an explenation
Plz help w answer 1:/ confused ash
Answer:
I would say d I had the same question yesterday and I got it correct so hope that helps
A main-sequence star at a distance of 20 pc is barely visible through a certain telescope. The star subsequently ascends the giant branch, during which time its temperature drops by a factor of three and its radius increases a hundredfold. What is the new maximum distance at which the star would still be visible in the same telescope?
Answer:
Explanation:
The surface area of a star estimated by the energy emitted per sq meter yields the overall luminosity, which can be represented mathematically as:
[tex]L= 4 \pi R^2 \sigma T^4 --- (1)[/tex]
where;
L ∝ R²T⁴
and;
R = radius of the sphere
σ = Stefans constant
T = temperature
Also; The following showcase the relationship between flux density as well as illuminated surface area as:
[tex]F = \dfrac{L}{A}[/tex]
where
A = 4πd² and L ∝ R²T⁴
[tex]F = \dfrac{R^2T^4}{4 \pi d^2} \\ \\ F \alpha \dfrac{R^2T^4}{ d^2} --- (2)[/tex]
Given that:
distance d₁ = 20 pc
Then, using equation (2)
[tex]F_1 \ \alpha \ \dfrac{R^2_1T^4_1}{ d^2_1}[/tex]
However, we are also being told that there is a temp. drop by a factor of 3;
So, the final temp. [tex]T_2 = \dfrac{T_1}{3}[/tex]; and the final radius is [tex]R_2 = 100R_1[/tex] since there is increment by 100 folds.
Now;
[tex]F_2 \ \alpha \ \dfrac{R^2_2T^4_2}{ d^2_2}[/tex]
SInce;
[tex]F_1 = F_2[/tex]
It implies that:
[tex]\dfrac{R^2_1T^4_1}{ d^2_1 } = \dfrac{R^2_2T^4_2}{ d^2_2} \\ \\ d_2 = \sqrt{\dfrac{R_2^2T_2^4}{R_1^2T_1^4}}(d_1)[/tex]
Replacing all our values, we have:
[tex]d_2 = \sqrt{\dfrac{(100R_1)^2 \times (\dfrac{T_1}{3})^4}{R_1^2T_1^4}}(20 ) \\ \\ d_2 = \sqrt{\dfrac{(100)^2 }{3^4}}(20 ) \\ \\ d_2 = \sqrt{\dfrac{(100)^2 }{3^4}}(20 ) \\ \\ d_2 =222 \ pc[/tex]