Answer:
(a) 3.23×10⁸ N/m²
(b) 1.46×10⁻³
(c) 2.21×10¹¹ N/m²
Explanation:
(a) Stress = Force/Area.
Stress = F/A................ Equation 1
But,
F = mg................. Equation 2
Where m = mass, and g = acceleration due to gravity
A = πd²/4................. Equation 3
d = diameter of the circular cross section.
Substitute equation 2 and equation 3 into equation 1
Stress = 4mg/πd²............. Equation 4
Given: m = 25.4 kg, d = 0.555 mm = 0.000555 m
Constant: g = 9.8 m/s², π = 3.142
Substitute these values into equation 4
Stress = 4(25.4)(9.8)/(3.142×0.00555²)
Stress = 995.68/(3.08×10⁻⁶)
Stress = 3.23×10⁸ N/m²
(b)
Strain = ΔL/L.............. Equation 5
Where ΔL = extension, L = Length.
Given: ΔL = 1.1 mm = 0.0011 m, L = 75.1 cm = 0.751 m
Substitute into equation 5
Strain = 0.0011/0.751
Strain = 1.46×10⁻³.
(c)
Young modulus = Stress/Strain
Young modulus = 3.23×10⁸/ 1.46×10⁻³
Young modulus = 2.21×10¹¹ N/m²
From what height must an oxygen molecule fall in a vacuum so that its kinetic energy at the bottom equals the average energy of an oxygen molecule at 300 K ?
Answer:
The value is [tex]h = 11930 \ m[/tex]
Explanation:
From the question we are told that
The temperature is [tex]T = 300 \ K[/tex]
Generally the root mean square speed of the oxygen molecules is mathematically represented as
[tex]v = \sqrt{\frac{3 * R * T }{M} } = \sqrt{ 2 * g * h }[/tex]
Here R is the gas constant with a value [tex]R = 8.314 \ J\cdot K^{-1} \cdot \ mol^{-1}[/tex]
M is the molar mass of oxygen molecule with value [tex]M = 0.032 \ kg /mol[/tex]
So
[tex]\frac{3 * 8.314 * 300 }{0.032} = 2 * 9.8 * h[/tex]
=> [tex]h = 11930 \ m[/tex]
A long, straight wire of radius R carries a steady current I that is uniformly distributed through the cross section of the wire. Calculate the magnetic field a distance r from the center of the wire in regions r ≥ R and r < R.
Answer:
a
When [tex]r \ge R[/tex]
[tex]B = \frac{ \mu_o * I}{ 2 \pi r }[/tex]
b
When [tex]r< R[/tex]
[tex]B = [\frac{\mu_o * I }{ 2 \pi R^2} ]* r[/tex]
Explanation:
From the question we are told that
The radius is R
The current is I
The distance from the center
Ampere's law is mathematically represented as
[tex]B[2 \pi r] = \mu_o * \frac{I r^2 }{R^2 }[/tex]
[tex]B = \frac{ \mu_o}{2 \pi } * \frac{r}{R^2}[/tex]
When [tex]r \ge R[/tex]
=> [tex]B = \frac{ \mu_o * I}{ 2 \pi r }[/tex]
But when [tex]r< R[/tex]
[tex]B = [\frac{\mu_o * I }{ 2 \pi R^2} ]* r[/tex]
A radio wave sent from the surface of the earth reflects from the surface of the moon and returns to the earth. The elapsed time between the generation of the wave and the detection of the reflected wave is 2.6444 s. Determine the distance from the surface of the earth to the surface of the moon. Note: The speed of light is 2.9979 ? 108 m/s.
Answer:
7.92 × 10^8 M
A radio wave sent from the surface of the earth reflects from the surface of the moon and returns to the earth. The elapsed time between the generation of the wave and the detection of the reflected wave is 2.6444s. then the distance from the surface of the earth to the surface of the moon would be 3.9632×10⁸ meters.
What is Wavelength?It can be understood in terms of the distance between any two similar successive points across any wave for example wavelength can be calculated by measuring the distance between any two successive crests.
As given in the problem A radio wave sent from the surface of the earth reflects from the surface of the moon and returns to the earth. The elapsed time between the generation of the wave and the detection of the reflected wave is 2.6444s
the given speed of the light is 2.9979 ×10⁸ m/s
As we know that
Distance =speed ×time
Distance = 2.9979 ×10⁸× 2.6444
=7.92644× 10⁸
This is the total distance covered by both ways from the moon to earth
The actual distance of the moon from earth would be half of this distance
Thus, the distance from the surface of the earth to the surface of the moon would be 3.9632×10⁸ meters.
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A Pipe Filled with Helium A certain organ pipe, open at both ends, produces a fundamental frequency of 293 Hz in air Now consider a pipe that is stopped (i.e., closed at one end) but still has a fundamental frequency of 293 Hz in air. How does your answer to Part A, fHe, change
Complete question:
A certain organ pipe, open at both ends, produces a fundamental frequency of 293 Hz in air. If the pipe is filled with helium at the same temperature, what fundamental frequency fHe will it produce? Take the molar mass of air to be 28.97 g/mol and the molar mass of helium to be 4.00 g/mol. Now consider a pipe that is stopped (i.e., closed at one end) but still has a fundamental frequency of 293 Hz in air. How does your answer to first question, fHe, change?
Answer:
The fundamental frequency that helium produced is 788.6 Hz.
Since the fundamental frequency of air in closed pipe is still the same value as open pipe, the fundamental frequency of helium will not change.
Explanation:
The speed of sound in pipe when filled with air is given by;
[tex]v = \sqrt{\frac{\gamma RT}{M} }[/tex]
Where;
γ = 1.4
R = 8.31 J/mol.K
M = 0.02897 kg/mol
T = 20°C = 293 K
[tex]v_{air} = \sqrt{\frac{1.4* 8.31*293}{0.02897} } = 343 \ m/s[/tex]
The speed of sound in pipe when filled with helium is given by
[tex]v_{He} = \sqrt{\frac{1.4* 8.31*293}{0.004} } =923.14 \ m/s[/tex]
Now, determine the fundamental frequency Helium will it produce
v = fλ
[tex]\frac{V_{air}}{F_o{air}} = \frac{V_{He}}{F_o{He}}\\\\F_o{He} = \frac{F_o{air}*V_{He}}{V_{air}} \\\\F_o{He} = \frac{(293)*(923.14)}{343}\\\\F_o{He} = 788.6 \ Hz[/tex]
Since the fundamental frequency of air in closed pipe is still the same value as open pipe, the fundamental frequency of helium will not change.
A scientist is observing a figure under the microscope that appears to be alive, however she is not sure. The scientist observes a membrane, but after closer observation notices that the image is not clear. What additional observation could she make to support that the object that she is observing under the microscope is alive? A. Bright, vibrant colors. B. Hair that surrounds the object. C. Communicating with another organism. D. The object splitting into two parts to form two organisms. BTW it is either C or D just couldn't figure it out.
Answer:
D. The object splitting into two parts to form two organisms.
Explanation:
The splitting of cell of an organism actually shoes if it's Alive or not .
The splitting can be either mitosis or meosis for either plant or animal.
But for the fact that it's has cell membrane shoes it's either a plant or an animal.
So the splitting will confirm it's alive.
Answer:
D the correct answer is D
Explanation:
I took the test and was going to pick c but changed my mind
i have been wondering this for a long time, does higher density mean higher solidity?
Explanation:
Solidity means the quality or state of being firm or strong in structure. Density means the degree of compactness in a structure.
Suppose that the clay balls model the growth of a planetesimal at various stages during its accretion. Choose the planetesimal that is most likely
to pull in debris particle A.
Answer:2
Explanation:
Suppose that the clay balls model the growth of a planetesimal at various stages during its accretion, the planetesimal that is most likely to pull in debris particle A would be option B.
What is science?Science is the methodical, empirically-based pursuit and application of knowledge and understanding of the natural and social worlds.
Science is a way of learning about the world.
People may contribute to the development of new knowledge through science and utilize it to promote their objectives.
It is a method, a thing, and an organization all at once.
If the clay balls represent the formation of a planetesimal at different phases of its accretion, then option B represents the planetesimal that is most likely to draw in debris particle A.
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Activity
In this activity, you will solve the following problems using the rules for adding and subtracting and multiplying and dividing with significant
figures
Part A
28.97 + 45.876
Explanation:
We need to add 28.97 and 45.876.
Here, the first no is 28.97 and other no is 45.876
Here, 28.97 is the least precise value and 45.876 is most precise.
28.97 + 45.876 = 74.846
We need to write the final answer such that there is two digit after the decimal. So, 28.97 + 45.876 = 74.85 because 6 is more than 5 i.e. we add 1 to 4.
Answer:
28.97
+ 45.876
74.846
Explanation:
Because 28.97 has only two decimal places, round off the answer to two decimal places: 74.85.
Light of wavelength 500nm shines on a pair of slits. This produces an interference pattern on a screen 2.00m behind the slits. Measuring from the center of the pattern, we find that the fifth dark spot is 4.00cm away. What is the spacing between the slits
Answer:
The value is [tex]d = 0.000125 \ m[/tex]
Explanation:
From the question we are told that
The wavelength is [tex]\lambda = 500 \ nm = 500 *10^{-9 } \ m[/tex]
The distance is of the screen is [tex]D = 2.0 \ m[/tex]
The width of the fifth dark spot is [tex]y = 4.00 \ cm = 0.04 \ m[/tex]
Generally the width of a fringe is mathematically represented as
[tex]y = \frac{ n * \lambda * D }{d }[/tex]
=> [tex]0.04 = \frac{ 5 * 500 *10^{-9} * 2 }{d}[/tex]
=> [tex]d = \frac{ 5 * 500 *10^{-9} * 2 }{0.04}[/tex]
=> [tex]d = 0.000125 \ m[/tex]
By calculating its wavelength (in nm), show that the second line in the Lyman series is UV radiation.
Answer:
λ = 102.78 nm
This radiation is in the UV range,
Explanation:
Bohr's atomic model for the hydrogen atom states that the energy is
E = - 13.606 / n²
where 13.606 eV is the ground state energy and n is an integer
an atom transition is the jump of an electron from an initial state to a final state of lesser emergy
ΔE = 13.606 (1 / [tex]n_{f}^{2}[/tex] - 1 / n_{i}^{2})
the so-called Lyman series occurs when the final state nf = 1, so the second line occurs when ni = 3, let's calculate the energy of the emitted photon
DE = 13.606 (1/1 - 1/3²)
DE = 12.094 eV
let's reduce the energy to the SI system
DE = 12.094 eV (1.6 10⁻¹⁹ J / 1 ev) = 10.35 10⁻¹⁹ J
let's find the wavelength is this energy, let's use Planck's equation to find the frequency
E = h f
f = E / h
f = 19.35 10⁻¹⁹ / 6.63 10⁻³⁴
f = 2.9186 10¹⁵ Hz
now we can look up the wavelength
c = λ f
λ = c / f
λ = 3 10⁸ / 2.9186 10¹⁵
λ = 1.0278 10⁻⁷ m
let's reduce to nm
λ = 102.78 nm
This radiation is in the UV range, which occurs for wavelengths less than 400 nm.
masses of 3kg on a smooth horizontal table.It is connected by a light string passing at the edge of the table to another mass of 2kg hanging vertically.When to the system is released from rest with what acceleration do the mass move
Answer:
aaawwwwwwwsssaaaasasss
Which step of the scientific method do you perform after you state the
problem?
O A. Collect data and observations.
B. Conduct an experiment.
C. Form a hypothesis.
D. Draw conclusions.
Answer:
form a hypothosis
Explanation:
A person travels 1.5 km in 6 minutes, how fast were they traveling in meters per second?
Answer:
4.167m/sec
Explanation:
1km=1000m
1.5km=1500m
1min=60sec
6min=360sec
In 360sec they travel 1500m
In 1 sec they travel=1500m/360
1sec=4.167m
Which of the following correctly describes the relative air pressure at the center of a hurricane, with respect to the horizontal direction? Group of answer choices low at the surface, high aloft low at the surface and aloft high at the surface and aloft high at the surface, low aloft
Explanation:
The pressure of hurricane which is high decreases gradually as we move higher . The pressure is maximum at the surface . Hence the relative air pressure is higher at the surface and low at the top . Like wise the pressure is low at the center and keeps on increasing when we move outside . Hence the answer is pressure is high at surface and low aloft.
A 24.0-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 225 N. For the first 11.0 m the floor is frictionless, and for the next 10.0 m the coefficient of friction is 0.20. What is the final speed of the crate after being pulled these 21.0 m?
Answer:
18.83m/s
Explanation:
In the first 11meters, we can calculate the Kinectic energy since we know that
the floor is frictionless then work done by the horizontal force= Kinectic energy gain by the block in the first 11m.
Then Kinetic Energy = wordone
But work done= Force × distance
Kinetic Energy=(225×11)= 2475J
In the next 10.0 m the coefficient of friction is 0.20, the Kinectic energy has equal value to the difference in workdone by both the horizontal and frictional force
K.E= (Force× distance) - ( mass × gravity× coefficient of friction × distance at 10 m)
K.E= [(225×10)-(.20× 9.8×10× 24)]
K.E= 2250-470.4
= 1779.6J
The addition of the Kinectic energy above give us the total Kinectic energy experience by the crate.
Total Kinectic energy= 1779.6+2475
= 4254.6J
the final speed of the crate after being pulled these 21.0 m?
Total distance= 11m + 10m = 21 m
Then the final speed can be calculated from the total Kinectic energy, since we know that
K.E= 0.5mv^2
V= √(2K.E/m)
= √(2×4254.6)/24
Final speed v = √354.55
Final speed v= 18.83m/s
Therefore, the final speed of the crate after being pulled these 21.0 m is 18.83m/s
If the period of a simple pendulum is T and you increase its length so that it is 4 times longer, what will the new period be?
Answer:
T' = 2T
Explanation:
The time period of a simple pendulum is given by the relation as follows :
[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]
l is length of the pendulum
g is acceleration due to gravity
If the length is increased four time, new length is l' = 4l
So,
New time period is :
[tex]T'=2\pi \sqrt{\dfrac{l'}{g}}\\\\T'=2\pi \sqrt{\dfrac{4l}{g}}\\\\T'=2\times 2\pi \sqrt{\dfrac{l}{g}}\\\\T'=2\times T[/tex]
So, the new time period is 2 times of the initial time period.
What is the gauge pressure in Pascals inside a honey droplet of a 0.1 cm diameter? Assume that air is surrounding this droplet and the surface tension of honey is 0.052 N/m.
Give your answer to the nearest integer (do NOT use scientific notation).
Answer:
The gauge pressure in Pascals inside a honey droplet is 416 Pa
Explanation:
Given;
diameter of the honey droplet, D = 0.1 cm
radius of the honey droplet, R = 0.05 cm = 0.0005 m
surface tension of honey, γ = 0.052 N/m
Apply Laplace's law for a spherical membrane with two surfaces
Gauge pressure = P₁ - P₀ = 2 (2γ / r)
Where;
P₀ is the atmospheric pressure
Gauge pressure = 4γ / r
Gauge pressure = 4 (0.052) / (0.0005)
Gauge pressure = 416 Pa
Therefore, the gauge pressure in Pascals inside a honey droplet is 416 Pa
a box with a weight of 555 N is sitting on the ground and the bottom of the box measures 0.55 m by 0.45. What is the pressure exerted by the box on the ground?
Explanation:
Pressure = force / area
P = 55 N / (0.55 m × 0.45 m)
P = 220 Pa
What is the magnitude of the total acceleration of point A after 2 seconds? The bar starts from rest and has a constant angular acceleration of 1.0 rad/s2 clockwise.
Answer:
a_total = 2 √ (α² + w⁴) , a_total = 2,236 m
Explanation:
The total acceleration of a body, if we use the Pythagorean theorem is
a_total² = a_T²2 + [tex]a_{c}[/tex]²
where
the centripetal acceleration is
a_{c} = v² / r = w r²
tangential acceleration
a_T = dv / dt
angular and linear acceleration are related
a_T = α r
we substitute in the first equation
a_total = √ [(α r)² + (w r² )²]
a_total = 2 √ (α² + w⁴)
Let's find the angular velocity for t = 2 s if we start from rest wo = 0
w = w₀ + α t
w = 0 + 1.0 2
w = 2.0rad / s
we substitute
a_total = r √(1² + 2²) = r √5
a_total = r 2,236
In order to finish the calculation we need the radius to point A, suppose that this point is at a distance of r = 1 m
a_total = 2,236 m
Find the lowest two frequencies that produce a maximum sound intensity at the positions of Moe and Curly.
Answer:
hello your question has some missing parts below is the complete question
and the missing diagram
The two speakers emit sound that is 180° out of phase and of a single frequency,ƒ, Find the lowest two frequencies that produce a maximum sound intensity at the positions of Moe and Curly.
answer : 1316.2 hertz
Explanation:
The frequency that produce the maximum sound intensity can be calculated using the relation below
dsin ∅ = n A
where A = dsin ∅ / n when n = 1 . d = 0.800
A = 0.800 * ( 1 / 3.162 )
A = 0.253 m
speed of sound = 333 m/s
frequency = speed / A
= 333 / 0.253 = 1316.2 hertz
What factors affect the strength of forces
Speed, weight, and time between impact and stopping all are the factors that affect force.
What is force?A force is an influence in physics that can change the motion of an object. A force can cause a mass object to change its velocity, or accelerate.
Intuitively, force can be described as a push or a pull. A force is a vector quantity because it has both magnitude and direction.
The magnitude of a force expresses its strength. The magnitude of a force is expressed in Newtons, the SI unit of force.
One Newton is the force that can cause an object weighing one kilogram to move one meter per second.
The mass of the objects and the coefficient of friction between them are the two factors. The angle between them is also important.
Thus, these are some factors affecting strength of force.
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A cylindrical can of radius R is rolling across a horizontal surface without slipping.
A. After one complete revolution of the can, what is the distance that its center of mass has moved.
B. Would this distance be greater or smaller if slipping occurred?
Answer:
a) 2πR
b) greater
Explanation:
Radius of the cylinder = R
a) after one complete revolution, the center of mass would have moved a distance equal to the circumference of the radius formed by the cylinder.
distance moved = 2πR
b) If slipping occurred, there will be some distance lost during rotation, which will increase the distance that the center of mass will have to move.
The critical period is a special time of development in humans. True False
Answer:
True
Explanation:
Without proper development during the critical period, the growth of some life skills may be severely delayed or stunted.
The rate at which energy is emitted from an accelerating charge that has charge q and acceleration a is given by dE/dt= q^2 a^2/ 6πεc^3, where c is the speed of light.
Required:
a. If a proton with a kinetic energy of 5.0 MeV is travelling in a particle accelerator in a circular orbit with a radius of 0.540 m, what fraction of its energy does it radiate per second?
b. Consider an electron orbiting with the same speed and radius. What fraction of its energy does it radiate per second?
Answer:
The value of fraction of energy is [tex]2.23\times10^{-11}[/tex]
The value of fraction of energy is [tex]7.53\times10^{-5}[/tex]
Explanation:
Given that,
Charge = q
Acceleration = a
The rate at which energy is emitted from an accelerating charge
[tex]\dfrac{dE}{dt}=\dfrac{q^2a^2}{6\pi\epsilon c^3}[/tex]....(I)
We know that,
Acceleration for circular motion is
[tex]a=\dfrac{v^2}{r}[/tex]....(II)
The kinetic energy is
[tex]K.E=\dfrac{1}{2}mv^2[/tex]
[tex]v^2=\dfrac{2(K.E)}{m}[/tex]
Put the value of v in equation (II)
[tex]a=\dfrac{2(K.E)}{mr}[/tex]
Put the value of a in equation (I)
[tex]\dfrac{dE}{dt}=\dfrac{q^2(\dfrac{2(K.E)}{mr})^2}{6\pi\epsilon c^3}[/tex]
[tex]\dfrac{dE}{dt}=\dfrac{q^24(K.E)^2}{6\pi\epsilon c^3\times m^2 r^2}[/tex]
[tex]\dfrac{\dfrac{dE}{dt}}{K.E}=\dfrac{q^24(K.E)}{6\pi\epsilon c^3\times m^2 r^2}[/tex]
Suppose that,
[tex]\dfrac{\dfrac{dE}{dt}}{K.E}=R[/tex]
So,
[tex]R=\dfrac{q^2\times4(K.E)}{6\pi\epsilon c^3\times m^2 r^2}[/tex]....(III)
(a). For proton,
We need to calculate the fraction of its energy does it radiate per second
Using equation (III)
[tex]R=\dfrac{4\times(1.6\times10^{-19})^2\times5.0\times1.6\times10^{-19}\times10^{6}\times6\times10^{9}}{(3\times10^{8})^3\times(1.67\times10^{-27})^2\times(0.540)^2}[/tex]
[tex]R=2.23\times10^{-11}[/tex]
(b). For electron,
We need to calculate the fraction of its energy does it radiate per second
Using equation (III)
[tex]R=\dfrac{4\times(1.6\times10^{-19})^2\times5.0\times1.6\times10^{-19}\times10^{6}\times6\times10^{9}}{(3\times10^{8})^3\times(9.1\times10^{-31})^2\times(0.540)^2}[/tex]
[tex]R=0.0000753[/tex]
Hence, The value of fraction of energy is [tex]2.23\times10^{-11}[/tex]
The value of fraction of energy is [tex]7.53\times10^{-5}[/tex]
The average speed of a snail is 0.020 miles/hour and that of a Leopard is 70 miles/hour. Convert these speeds in SI units.
Gulls are often observed dropping clams and other shellfish from a height to the rocks below, as a means of opening the shells. If a seagull drops a shell from rest at a height of 16 m, how fast is the shell moving when it hits the rocks
Answer:
v = 17.71 m / s
Explanation:
We can work this exercise with the kinematics equations. In general the body is released so that its initial velocity is zero, the acceleration of the acceleration of gravity
v² = v₀² - 2 g (y -y₀)
v² = 0 - 2g (y -y₀)
when it hits the stone the height is zero and part of the height of the seagull I
v² = 2g y₀
v = Ra (2g i)
let's calculate
v =√ (2 9.8 16)
v = 17.71 m / s
Firecracker A is 300 m from you. Firecracker B is 600 m from you in the same direction. You see both explode at the same time. Define event 1 to be "firecracker A explodes" and event 2 to be "firecracker B explodes." Does.event 1 occur before, after, or at the same time as event 2? Explain.
Answer:
e see that the distances are different, the only way that the two beams of light approach simultaneously is that event 2 (farthest) occurs first than event 1
Explanation:
This is an ejercise in special relativity, where the speed of light is constant.
Let's carefully analyze the approach, we see the two events at the same time.
The closest event time is
c = (x₁-300) / t
t = (x₁-300) / c
The time for the other event is
t = (x₂- 600) / c
since they tell us that we see the events simultaneously, we can equalize
(x₁ -300) / c = (x₂ -600) / c
x₁ = x₂ - 300
We see that the distances are different, the only way that the two beams of light approach simultaneously is that event 2 (farthest) occurs first than event 1
Which of the following best describes the position of the Sun in the geocentric model? A. It is at the center of the Universe. B. It orbits Earth. C. It is at the center of the Milky Way Galaxy. D. It orbits another star.
Answer:
option B is correct
Explanation:
in geocentric model earth is at the center of the universe and sun,moon star etc orbited the earth thats why option B is correct
Average speed is calculated by dividing distance traveled by
time. How is average velocity calculated?
Answer:
The average velocity of an object is its total displacement divided by the total time taken. In other words, it is the rate at which an object changes its position from one place to another. Average velocity is a vector quantity. The SI unit is meters per second.
hope this helps you
Answer:
displacement divided by time
Explanation:
Suppose you attempt to pour out 100 g of salt, using a pan balance for measurements, while an elevator that is accelerating upward. Will the quantity (weight) of salt be too much, too little, or the correct amount? Explain
Answer:
the correct amount
Explanation:
The pan balance has two pans . When the elevator is accelerating upward , the apparent weight of both objects placed on either pan increase . The net effect is that they cancel out the effect of accelerating elevator . Hence the apparent weight of salt remains same as and equal to its real weight.
In case of spring balance, its apparent weight would have increased . Its apparent weight would have measured more than its true weight.