Answer:
d) 0.011%
Explanation:
The probability for tunneling the barrier is given by the following formula:
[tex]P=exp(-2d\sqrt{\frac{2m_e(U_o-E)}{\hbar ^2} }\ )[/tex] ( 1 )
me: mass of the electron
Uo: energy of the barrier
E: energy of the electron
d: thickness of the barrier
By replacing the values of the parameters in (1), you obtain:
[tex]P=exp(-2(0.20*10^{-9}m)\sqrt{\frac{2(9.11*10^{-31}kg)(100eV-80eV)(1.60*10^{-19}J)}{(1.055*10^{-34}Js)^2}})\\\\P=e^{-9.15}=1.08*10^{-4}\approx0.011\%[/tex]
hence, the probability is 0.011% (answer d)
A cast-iron flywheel has a rim whose OD is 1.5 m and whose ID is 1.4 m. The flywheel weight should be chosen such that an energy fluctuation of 6.75 J will cause the angular speed to vary by no more than 240 to 260 rev/min. a.Estimate the coefficient of speed fluctuationb.If the weight of the spokes is neglected, determine the thickness of the rim
Answer:
the coefficient of speed fluctuation is 0.08
the thickness of the rim is [tex]1.423*10^{-4}\ \ m[/tex]
Explanation:
a.Estimate the coefficient of speed fluctuation
Let first determine the average speed of the flywheel by using the expression:
[tex]n = \frac{n_1+n_2}{2}[/tex]
where;
[tex]n_1 =[/tex] minimum speed = 240 rev/min
[tex]n_2 =[/tex] maximum speed = 260 rev/min
∴ [tex]n = \frac{240 +260}{2}[/tex]
n = 250 rev/ min
To find the coefficient of speed fluctuation; we have:
[tex]C_s = \frac{n_2-n_1}{n}[/tex]
[tex]C_s = \frac{260-240}{250}[/tex]
[tex]C_s = 0.08[/tex]
Hence; the coefficient of speed fluctuation is 0.08
b . If the weight of the spokes is neglected, determine the thickness of the rim
Let's start solving this process by finding the moment of inertia of the flywheel.
The moment of inertia of the fly wheel is given by the equation:
[tex]I = \frac {E_2-E_1}{C_s \omega^2}[/tex]
where ;
[tex]\omega = \frac{2 \pi *n}{60}[/tex] (since we are converting to rad/s)
[tex]\omega = \frac{2 \pi *250}{60}[/tex]
= 26.18 rad/s
[tex]E_2-E_1[/tex] = the energy fluctuation = 6.75 J
[tex]I = \frac{6.75}{0.08*26.18^2}[/tex]
= 0.123 kg.m²
To determine the weight of the flywheel ; we have the following expression;
[tex]I = \frac{W}{8g}(D^2+d^2)[/tex]
[tex]W = \frac{8gl}{D^2_o+d_i^2}[/tex]
where;
[tex]D_0[/tex] = outer diameter = 1.5 m
[tex]d_i =[/tex] inner diameter = 1.4 m
[tex]W = \frac{8*9.81*0.123}{1.5^2+1.4^2}[/tex]
W = 2.29 N
Let employ the weight density of the cast-iron flywheel [tex]w \rho[/tex] = 70575.5N/m²
Then the volume of the flywheel:
[tex]V = \frac{W}{ w \ rho}[/tex]
[tex]V = \frac{2.29}{70575.5}[/tex]
[tex]V = 3.24*10^{-5} m^3[/tex]
Let t be the thickness of the rim;
the thickness of the rim can be calculate by using the formula;
[tex]V = \frac{\pi t}{4}(D^2-d^2)[/tex]
[tex]t = \frac{4V}{\pi(D^2-d^2)}[/tex]
[tex]t = \frac{4*3.24*10^{-5}}{\pi(1.5^2-1.4^2)}[/tex]
[tex]t = 1.423*10^{-4}m[/tex]
Hence, the thickness of the rim is [tex]1.423*10^{-4}\ \ m[/tex]
A refrigerator removes heat from the freezing compartment at the rate of20 kJ per cycle and ejects 24 kJ into the room each cycle. How much energy is used in each cycle?
Answer:
Energy used = 4KJ
Explanation:
Second law of thermodynamics states that as energy is transferred or transformed, more and more of it is wasted. The Second Law also states that there is a natural tendency of any isolated system to degenerate into a more disordered state.
Now when we apply that to heat engines, we'll see that;
Heat expelled = Heat removed + Work Done
We can write it as;
Q_h = Q_c + W
We are given that;
Heat removed; Q_c = 20KJ
Heat expelled into the room in each cycle; Q_h = 24KJ
Thus; plugging these 2 values into the equation, we obtain;
24 = 20 + W
W = 24 - 20
W = 4 KJ
Work done is energy used.
Thus, energy used = 4 KJ
Final answer:
The refrigerator uses 4 kJ of energy each cycle, calculated by the work done W, which is the difference between the heat ejected Qh (24 kJ) and the heat removed Qc (20 kJ).
Explanation:
The question is calculating the energy used by a refrigerator in each cycle. The refrigerator absorbs heat Qc from the inside and ejects a larger amount of heat Qh to the room. The extra energy being ejected comes from the work W done by the refrigerator, which is the energy used by it in each cycle.
If the refrigerator removes 20 kJ (Qc) from the freezing compartment and ejects 24 kJ (Qh) into the room each cycle, the work done (energy used) W can be found using the first law of thermodynamics which states that the conservation of energy principle - the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:
W = Qh - Qc
Substituting in the given values:
W = 24 kJ - 20 kJ
W = 4 kJ
Thus, the work done (energy used) by the refrigerator in each cycle is 4 kJ.
At the surface of Venus the average temperature is a balmy 460∘C due to the greenhouse effect (global warming!), the pressure is 92 Earth-atmospheres, and the acceleration due to gravity is 0.894 gEarthgEarth. The atmosphere is nearly all CO2 (molar mass 44.0g/m) and the temperature remains remarkably constant. We shall assume that the temperature does not change at all with altitude.
a. What is the atmospheric pressure of 2.00 km above the surface of Venus? Express your answer in Earth-atmospheres.
b. What is the atmospheric pressure of 2.00 km above the surface of Venus? Express your answer in Venus-atmospheres.
c. What is the root-mean-square speed of the CO2 molecules at the surface of Venus and at an altitude of 2.00 km?
Answer:
a) 86 atm
b) 86 atm
c) 645 m/s
Explanation:
See attachment for calculations on how i arrived at the answer
The atmospheric pressure of 2.00 km above the surface of Venus is 86 atm and the root-mean-square speed of the CO2 molecules at the surface of Venus and at an altitude of 2.00 km is 645 m/sec.
Given :
At the surface of Venus, the average temperature is a balmy 460∘C due to the greenhouse effect (global warming!), the pressure is 92 Earth-atmospheres, and the acceleration due to gravity is 0.894 g.The atmosphere is nearly all CO2 (molar mass 44.0g/m) and the temperature remains remarkably constant.a) and b) In order to determine the atmospheric pressure of 2.00 km above the surface of Venus using the formula given below:
[tex]\rm P = P_0\times L^{\frac{Mg}{\rho T}}[/tex] --- (1)
The value of the expression [tex]\rm Mg/\rho T[/tex] is given below:
[tex]\rm \dfrac{Mg}{\rho T} = \dfrac{44\times 10^{-3}\times 9.8\times 10^3}{8.314\times 733}[/tex]
[tex]\rm \dfrac{Mg}{\rho T}=0.02076[/tex]
Now, substitute the values of the known terms in the expression (1).
[tex]\rm P=92\times L^{0.02076}[/tex]
P = 86 atm
c) The root-mean-square speed of the CO2 molecules at the surface of Venus and at an altitude of 2.00 km can be calculated as given below:
[tex]\rm V_{rms}=\sqrt{\dfrac{3RT}{M}}[/tex]
Now, substitute the values of the known terms in the above formula.
[tex]\rm V_{rms}=\sqrt{\dfrac{3\times 8.314\times 733}{44\times 10^{-3}}}[/tex]
Simplify the above expression.
[tex]\rm V_{rms} = 645\;m/sec[/tex]
For more information, refer to the link given below:
https://brainly.com/question/7213287
Supervillain Prof. Marcia Grail is experimenting with energy and electric charge to better create a new doomsday weapon (and take over the world). She gathers a charge of 1.11 x 10^-10 C and places it in the center of a large empty spherical vacuum chamber of radius 250m (the place she fixes this immovable charge can be thought of as the origin of coordinates). The potential at a point 1m away in the positive y-direction is 1 V. What is the potential 1m away in the positive x-direction
Answer:
Check the explanation
Explanation:
given
charge of [tex]1.11 * 10^{-10}[/tex] C
radius 250m
The potential at a point 1m
and 1 V
mass 2 micrograms
charge of +2 Coulombs
the potential is V = K Q / r
V = 9 X 109 X 1.11 X 10-10 / 1
V = 9 X 109 X 1.11 X 10-10
V = 0.999 volt
nearly it is V = 1 v
the energy stored is U = q X V
U = 2 X 1
U = 2 J
the energy is stored in this configuration is U = 2 J
As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.15 mm apart and position your screen 3.53 m from the slits. Although Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 639 nm . How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe
Answer:[tex]y_1=1.9\ mm[/tex]
Explanation:
Given
slit width [tex]d=1.15\ mm[/tex]
Distance of screen [tex]D=3.53\ m[/tex]
wavelength [tex]\lambda =639\ nm[/tex]
Position of any bright fringe is given by
[tex]y_n=\dfrac{n\lambda D}{d}[/tex]
[tex]y_1=\frac{1\times 639\times 10^{-9}\times 3.53}{1.15\times 10^{-3}}[/tex]
[tex]y_1=0.0019\ m[/tex]
[tex]y_1=1.9\ mm[/tex]
Position of dark fringe is given by
[tex]y_D=\dfrac{(2n+1)\lambda D}{2d}[/tex]
for second dark fringe [tex]n=1[/tex]
[tex]y_D=\dfrac{1.5\times 639\times 10^{-9}\times 3.53}{1.15\times 10^{-3}}[/tex]
[tex]y_D=0.00294\ m\approx 2.94\ mm[/tex]
You throw a rock upward. The rock is moving upward, but it is slowing down. If we define the ground as the origin, the position of the rock is _____ and the velocity of the rock is _____. You throw a rock upward. The rock is moving upward, but it is slowing down. If we define the ground as the origin, the position of the rock is _____ and the velocity of the rock is _____. negative, negative positive, negative negative, positive positive, positive
Answer:
positive, positive
You throw a rock upward. The rock is moving upward, but it is slowing down. If we define the ground as the origin, the position of the rock is positive and the velocity of the rock is positive
Explanation:
Given that the ground is defined as the origin.
The position of the rock is positive since the rock is thrown upward, the position also increases with time until it reaches the maximum height. Also, since the rock is thrown upward with the ground as the origin, the velocity of the rock is positive but the velocity reduces with time (change in height per unit time as the rock moves up is positive)
The correct option for the position of the rock is positive, and for the velocity of the rock, it is positive.
When the rock is thrown upward, it moves away from the ground, which we have defined as the origin. Since the rock is above the ground, its position is positive. Although the rock is slowing down as it moves upward, it still has an upward velocity until it reaches its peak height. Therefore, the velocity of the rock is also positive because it is still moving in the upward direction, even though it is decelerating.
To summarize:
- The position of the rock is positive because it is above the origin (ground).
- The velocity of the rock is positive because it is moving upward, despite the fact that it is slowing down.
The correct answer is: positive, positive.
Brian is forced to help Stewie play on the swings at the park. He pushes Stewie until Stewie could reach a maximum height of 0.5 m above the lowest point on the swing and then stepped aside. Stewie gets scared of such a high height (considering he is very short) and decides to jump off the swings at the swings lowest point. If Stewie has a mass of 5 kg and the swing has a mass of 2 kg, what is the maximum height the swing will reach after Stewie jumps off with a velocity of 2 m/s?
Answer: 0.3 m
So basically we want to think of this situation from the perspective of conservation of energy. As in, we can derive the velocity of both the swing and Stewie at the bottom of the swing via:
mgh = 0.5m*v^2
v = (2*g*h)^0.5 = (2*9.8*0.5)^0.5 = 3.13 m/s
This represents the velocity of Stewie and the swing at the bottom of the swing's path. Now, we will think of this from the perspective of conservation of momentum. Basically, the collective momentum of Stewie and the swing is equal to the sum of their subsequent momenta:
(5+2)*3.13 = 5*2+5*v(swing); v(swing) represents the velocity of the swing following Stewie jumping.
7*3.13 = 10 + 5v
v = 2.4 m/s
Now, we return to conservation of energy and find that the kinetic energy of the swing following Stewie jumping is equivalent to its final gravitational potential energy.
Based on the easily derivable formula: h=v^2/2g, we find that h = 2.4^2/19.6,
which is: 0.3 m.
If g is supposed to be 10 or you need a different degree of precision, then you can use my method. Hope this helps.
Which letter (A, B, or C) shows where you should apply the most effort to lift the stone?
A submarine dives to a depth of 100-m beneath the surface of the Pacific Ocean. The density of sea water is 1030 kg/m3. The submarine has a hatch with an area of 2 m2 located on the top of the submarine. No need to show work. a) Calculate the gauge pressure applied on the submarine at the depth of 100 m. b) Calculate the absolute pressure applied on the submarine at the depth of 100 m. Assume the atmospheric pressure in the air above the ocean is one atmosphere. c) Calculate how much force is required in order to open the hatch from the inside of submarine. Assume that the pressure inside the submarine is one atmosphere.
Answer:
A) 1010430 pa
B) 1111755 pa
C) 2020860 N
Explanation:
Guage pressure = pgh
= 1030 kg/m3 x 9.81 m/s2 x 100 m
= 1010430 pa
Absolute pressure is Guage pressure + atmospheric pressure.
= 1010430 + 101325 = 1111755 pa
If the pressure inside submarine is 1 atm, then net pressure will be
1111755 - 101325 = 1010430 pa
Force required to open hatch against this pressure will be,
F = pghA
pgh = 1010430 pa
F = 1010430 pa x 2 m^2
F = 2020860 N
Based on the data provided:
the gauge pressure is the absolute gauge pressure is 1111755 pathe force required to open the hatch is 2020860 NWhat is the gauge pressure on the submarines at the given depth?The gauge pressure is calculating using the formula:
Guage pressure = pgh
where:
p is density of seawater = 1030 kg/m^3
g is acceleration due to gravity = 9.81 m/s^2
h is depth = 100 m
Substituting:
Gauge pressure = 1030 kg/m3 x 9.81 m/s2 x 100 m
Gauge pressure = 1010430 pa
Therefore, the gauge pressure is 1010420 pa
What is the absolute gauge pressure at this depth?The absolute gauge pressure is calculated using the formula:
Absolute pressure = Guage pressure + atmospheric pressure.
Atmospheric pressure = 1 atm = 101325 pa
Thus:
Absolute gauge pressure = 1010430 + 101325
Absolute gauge pressure = 1111755 pa
Therefore, the absolute gauge pressure is 1111755 pa
What is the force that will be applied to open the hatch from inside of the submarine?First determine the net pressure.
Pressure inside submarine = 1 atm
Net pressure = 1111755 - 101325
Net pressure = 1010430 pa
Force required to open hatch against this pressure is then calculated from the formula:
Force = net pressure × area
Force = 1010430 pa x 2 m^2
Force = 2020860 N
Therefore, the force required to open the hatch is 2020860 N
Learn more about about guage pressure and force at: https://brainly.com/question/9376763
What should Jaime do to increase the number of energy storage molecules that producers can make? You may choose more than one answer.
Decrease the amount of carbon dioxide in the ecosystem. Increase the amount of carbon dioxide in the ecosystem. Decrease the amount of sunlight in the ecosystem. Increase the amount of sunlight in the ecosystem.
Answer: Increase the amount of carbon dioxide in the ecosystem.
Explanation:
The producers are the organisms which can make their own food by conducting the process of photosynthesis. The carbon dioxide, water are the reactants and carbohydrates and oxygen are the products of photosynthesis. The entire process takes place in the presence of sunlight energy.
The carbon dioxide is the chief component for this reaction and the components of carbon are produced in the form of carbohydrates. The carbohydrates are the source of energy that are utilized by the producers for cellular metabolism and other functions. These get stored in the form of storage molecules in producers. Thus to increase the no. of storage molecules that producers can make Jaime need to increase the concentration of carbon dioxide in the ecosystem.
Using evidence from the article, defend the concept that
Earth's magnetic poles have swapped places over time.
Answer: Scientists found evidence of Earth's magnetic field reversal in rocks on the ocean floor at plate boundaries. These rocks have alternating polarity due to magnetization that were during their cooling period. Using radiometric dating, scientists estimate that reversals occur approximately every several hundred thousand years.
Explanation: The earth’s magnetic field impacts into the alignment of elements like iron in rocks due to Ferro-magnetization. This causes the elements to align in a north-south direction. Accordingly scientists have studied this alignment in ancient rocks, such as in the layers of sedimentary rocks, and realized that the earth magnetic field has flipped around 200,000 to 300,000 in the last 20 million years.
Answer:
Scientists found evidence of Earth's magnetic field reversal in rocks on the ocean floor at plate boundaries. These rocks have alternating polarity due to magnetization that occurred during their cooling period. Using radiometric dating, scientists estimate that reversals occur approximately every several hundred thousand years.
Explanation:
A ski lift is used to transport people from the base of a hill to the top. If the lift leaves the
base at a velocity of 15.5 m/s and arrives at the top with a final velocity of 0 m/s, what is the height of the hill? Round the answer to the nearest tenth.
Answer:
12.3
Explanation:
Answer:
12.3
Explanation:
got it right
A traffic controller at the airport watches a commercial plane circling above at a distance of 24.0 km as the pilot waits for clearance to land. If the Moon subtends an angle of 9.89 10-3 radians at the controller's location, what is the distance the jet travels as its nose moves across the diameter of the Moon?
Answer:
The distance travelled is [tex]S = 237.36 \ m[/tex]
Explanation:
From the question we are told that
The distance of the airplane from the ground is [tex]L = 24.0\ km[/tex]
The angle subtended by the moon is [tex]\theta = 9.89*10^{-3} \ radians[/tex]
The distance traveled can be mathematically represented as
[tex]S = R \theta[/tex]
Substituting values
[tex]S = 24 *10^3 * 9.89*10^{-3}[/tex]
[tex]S = 237.36 \ m[/tex]
please help me asap!!!!!
Answer:
no, because if he was pushing the box with constant force the box would have to move with constant speed
Explanation:
A lens is formed from a plastic material that has an index of refraction of 1.59 . If the radius of curvature of one surface is 1.15 m and the radius of curvature of the other surface is 1.80 m , use the lensmaker's equation to calculate the magnitude of the focal length | f | and the power | P | of the lens.
Using the lensmaker's equation with an index of refraction of 1.59 and radii of curvature of 1.15 m and -1.80 m, we find the focal length |f| to be approximately 1.19 m and the power |P| to be about 0.84 diopters.
Explanation:To calculate the magnitude of the focal length |f| and the power |P| of the lens, we use the lensmaker's equation which is given by:
1/f = (n - 1) * (1/r1 - 1/r2)
where n is the index of refraction of the lens material, r1 and r2 are the radii of curvature of the lens surfaces. Given the index of refraction n = 1.59, and the radii of curvature r1 = 1.15 m (positive for convex surface) and r2 = -1.80 m (negative for concave surface), we can substitute these values into the equation.
Calculating |f|:
1/f = (1.59 - 1) * (1/1.15 + 1/1.80)
= 0.59(0.870 + 0.556)
= 0.59 * 1.426
= 0.841
Thus, |f| = 1/0.841 m ≈ 1.19 m.
To calculate the power of the lens P, which is given in diopters (D), we use: P = 1/f in meters. So, |P| = 1/1.19 m ≈ 0.84 D.
This calculation highlights the application of physics principles in analyzing optical systems.
This question checks that you can use the formula of the electric field due to a long, thin wire with charge on it. The field due to an infinitely long, thin wire with linear charge density LaTeX: \lambda λ is LaTeX: \vec{E} = \frac{1}{4\pi\epsilon_0}\frac{2\lambda}{r}\hat{r}E → = 1 4 π ϵ 0 2 λ r r ^. Imagine a long, thin wire with a constant charge per unit length of -6.6LaTeX: \times10^{-7}× 10 − 7 C/m. What is the magnitude of the electric field at a point 10 cm from the wire (assuming that the point is much closer to the wire's nearest point than to either of its ends)? Give your answer in units of kN/C.
Answer:
E = -118 KN / C
Explanation:
In this exercise we are given the expression of the electric field for a wire
E = 1 /4πε₀ 2λ / r
they also indicate the linear density of charge
λ = 6,6 10⁻⁷ C / m
ask to calculate the electric field at a position at r = 10 cm from the wire
k = 1 /4πε₀ = 8,988 10⁹ N m² / C²
E = 8,988 10⁹ 2 (-6.6 10⁻⁷ / 0.10)
E = -1.18 105 N / C
we reduce to KN / C
1 KN / C = 10³ N / C
E = -1.18 10² KN / C
E = -118 KN / C
the negative sign indicates that the field is directed to the charged
A string is 1.6 m long. One side of the string is attached to a force sensor and the other side is attached to a ball with a mass of 200 g. The ball is lifted to a height of 1.5 m above the ground and then released from rest. The ball swings to its lowest point where the string breaks. The ball is then in free-fall until it hits the ground. How far would the ball travel in the horizontal direction between points B and C (i.e. what is the range)?
Complete Question
The diagram for this question is shown on the first uploaded image
Answer:
The distance traveled in horizontal direction is [tex]D = 1.38 m[/tex]
Explanation:
From the question we are told that
The length of the string is [tex]L = 1.6 \ m[/tex]
The mass of the ball is [tex]m = 200 g = \frac{200}{1000} = 0.2 \ kg[/tex]
The height of ball is [tex]h = 1.5 \ m[/tex]
Generally the work energy theorem can be mathematically represented as
[tex]PE = KE[/tex]
Where PE is the loss in potential energy which is mathematically represented as
[tex]PE =mgh[/tex]
Where h is the difference height of ball at A and at B which is mathematically represented as
[tex]h = y_A - y_B[/tex]
So [tex]PE =mg(y_A - y_B)[/tex]
While KE is the gain in kinetic energy which is mathematically represented as
[tex]KE = \frac{1}{2 } (v_b ^2 - 0)[/tex]
Where [tex]v_b[/tex] is the velocity of the of the ball
Therefore we have from above that
[tex]PE =KE \equiv mg (y_A - y_B) = \frac{1}{2} m (v_b ^2 - 0)[/tex]
Making [tex]v_b[/tex] the subject we have
[tex]v_b = \sqrt{2g (y_A - y_B)}[/tex]
substituting values
[tex]v_b = \sqrt{2g (1.5 - 0.40)}[/tex]
[tex]v_b = 4.6 \ m/s[/tex]
Considering velocity of the ball when it hits the floor in terms of its vertical and horizontal component we have
[tex]v_x = 4.6 m/s \ while \ v_y = 0 m/s[/tex]
The time taken to travel vertically from the point the ball broke loose can be obtained using the equation of motion
[tex]s = v_y t - \frac{1}{2} g t^2[/tex]
Where s is distance traveled vertically which given in the diagram as [tex]s = -0.4[/tex]
The negative sign is because it is moving downward
Substituting values
[tex]-0.4 = 0 -\frac{1}{2} * 9.8 * t^2[/tex]
solving for t we have
[tex]t = 0.3 \ sec[/tex]
Now the distance traveled on the horizontal is mathematically evaluated as
[tex]D = v_b * t[/tex]
[tex]D = 4.6 * 0.3[/tex]
[tex]D = 1.38 m[/tex]
Answer:
bjknbjk;jln
Explanation:
a cross section of three parallel wires each carrying a current of 20 A. The current in wire B is out of the paper, while that in wires A and C are into the paper. If the distance R = 15.0 mm,
what is the magnitude of the force on a 200 cm length of wire C?
Complete Question
The diagram for this question is shown on the first uploaded image
Answer:
The magnitude of force is [tex]F_R} = 5.33 \ m N[/tex]
Explanation:
From the question we are told that
The current in wire A , B and C are [tex]I _a = I_b =I_c = I= 20 A[/tex]
The distance is [tex]R = 15.0mm = \frac{15}{1000} = 0.015m[/tex]
The length of wire C is [tex]L_c = 200cm = \frac{200}{100} = 2 m[/tex]
Generally the force exerted per unit length that is acting in between two current carrying conductors can be mathematically represented as
[tex]\frac{F}{L} = \frac{\mu_o }{2 \pi} \cdot \frac{I_1 I_2 }{R}[/tex]
Where [tex]\mu_o[/tex] is the permeability of free space with a constant value of
[tex]\mu_o = 4 \pi * 10^{-7} N/A^2[/tex]
When the current in the wire are of the same direction the force is positive and when they are in opposite direction the force is negative
Considering force between A and C
[tex]F_{A -C} = \frac{\mu_o }{2 \pi} \cdot \frac{I_a I_c }{2R} * L[/tex]
Considering force between B and C
[tex]F_{B -C} = \frac{\mu_o }{2 \pi} \cdot \frac{I_b I_c }{R} * L[/tex]
The resultant force is
[tex]F_R = F_{B -C} - F_{A -C} = \frac{\mu_o }{2 \pi} \cdot \frac{I_a I_c }{2R} * L - \frac{\mu_o }{2 \pi} \cdot \frac{I_b I_c }{R} * L[/tex]
[tex]F_R} = \frac{\mu_o }{2 \pi} \cdot \frac{I * I }{R} * L * ({1 - \frac{1}{2} })[/tex]
Substituting values
[tex]F_R} = \frac{4 \pi * 10^{-7}}{2 * 3.142} \cdot \frac{ 20*20 }{0.015} * 2 ({\frac{1}{2} })[/tex]
[tex]F_R} = 5.33 *10^{-3} N[/tex]
[tex]F_R} = 5.33 \ m N[/tex]
9) A bug of mass 0.020 kg is at rest on the edge of a solid cylindrical disk (M = 0.10 kg, R = 0.10 m) rotating in a horizontal plane around the vertical axis through its center. The disk is rotating at 10.0 rad/s. The bug crawls to the center of the disk. (a) What is the new angular velocity of the disk? (b) What is the change in the kinetic energy of the system? (c) What is the cause of the increase and decrease of kinetic energy?
The bug moving toward the center of the disk changes the moment of inertia and the angular velocity, resulting in a change in the rotational kinetic energy of the system. The principles of conservation of angular momentum and calculations of kinetic energy apply here.
Explanation:This problem involves the principle of conservation of angular momentum. Initially, when the bug is at the edge of the disk, the system's angular momentum (L) is conserved. The initial angular momentum (L_initial) is the sum of the angular momenta of the bug and the disk. It can be calculated as L_initial = I_bug(ω) + I_disk(ω) where I_bug = m*R², I_disk = (1/2)*M*R², m is the mass of the bug, M is the mass of the disk, R is the radius of the disk, and ω is the initial angular velocity.
When the bug moves to the center of the disk, the angular velocity will change but the total angular momentum will still remain conserved as L_final = I_bug(ω') + I_disk(ω') where ω' is the final angular velocity and I_bug is now 0 because the bug is at the center. From the conservation of angular momentum, we can solve for ω'.
The change in kinetic energy can be calculated from the difference between the initial kinetic energy and the final kinetic energy of the system. An increase or decrease in kinetic energy in this scenario is due to the displacement of the bug from the edge to the center of the disk, which changes the moment of inertia of the system and thus, the rotational kinetic energy.
Learn more about Conservation of Angular Momentum here:https://brainly.com/question/1597483
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Final answer:
The explanation covers the new angular velocity of the disk, the change in kinetic energy, and the causes for the increase and decrease in kinetic energy.
Explanation:
A: The new angular velocity of the disk can be calculated using the principle of conservation of angular momentum. The bug crawling towards the center decreases the moment of inertia, resulting in an increase in angular velocity.
B: The change in kinetic energy of the system can be determined by calculating the initial and final kinetic energies and finding their difference.
C: The increase in kinetic energy is due to the bug moving towards the center, reducing the moment of inertia. The decrease in kinetic energy occurs due to the redistribution of mass towards the center of rotation.
Polarizers #1 and #3 are "crossed" such that their transmission axes are perpendicular to each other. Polarizer #2 is placed between the polarizers #1 and #3 with its transmission axis at 60◦ with respect to the transmission axis of the polarizer #1 (see the sketch). #1 #2 #3 60◦ After passing through polarizer #2 the intensity I2 (in terms of the intermediate intensity I1) is
The intensity I2 after light passes through polarizer #2, oriented at 60° to polarizer #1, is 25% of the intermediate intensity I1.
To determine the intensity [tex]I_2[/tex] after light passes through the second polarizer, we use Malus's Law. Malus's Law states that when polarized light passes through a polarizing filter, the intensity of the transmitted light is given by:
[tex]I = I_0 * cos^2(\theta),[/tex]
where I0 is the initial intensity and θ is the angle between the light’s polarization direction and the axis of the polarizer.
In this case:
The light initially passes through polarizer #1, aligning its polarization with polarizer #1.When the light reaches polarizer #2 set at 60° to polarizer #1, the intensity I2 can be found using Malus's Law:[tex]I_2 = I_1 * cos^2(60^o)[/tex]Since [tex]cos(60^o) = 0.5:[/tex]
[tex]I_2 = I_1 * (0.5)^2= I_1 * 0.25[/tex]
Hence, the intensity [tex]I_2[/tex] is 25% of [tex]I_1[/tex].
A laser beam is incident at an angle of 30.2° to the vertical onto a solution of corn syrup in water. (a) If the beam is refracted to 18.82° to the vertical, what is the index of refraction of the syrup solution? (b) Suppose the light is red, with wavelength 632.8 nm in a vacuum. Find its wavelength in the solution. nm (c) Find its frequency in the solution. Hz (d) Find its speed in the solution.
Answer:
a) n2 = 1.55
b) 408.25 nm
c) 4.74*10^14 Hz
d) 1.93*10^8 m/s
Explanation:
a) To find the index of refraction of the syrup solution you use the Snell's law:
[tex]n_1sin\theta_1=n_2sin\theta_2[/tex] (1)
n1: index of refraction of air
n2: index of syrup solution
angle1: incidence angle
angle2: refraction angle
You replace the values of the parameter in (1) and calculate n2:
[tex]n_2=\frac{n_1sin\theta_1}{sin\theta_2}=\frac{(1)(sin30.2\°)}{sin18.82\°}=1.55[/tex]
b) To fond the wavelength in the solution you use:
[tex]\frac{\lambda_2}{\lambda_1}=\frac{n_1}{n_2}\\\\\lambda_2=\lambda_1\frac{n_1}{n_2}=(632.8nm)\frac{1.00}{1.55}=408.25nm[/tex]
c) The frequency of the wave in the solution is:
[tex]v=\lambda_2 f_2\\\\f_2=\frac{v}{\lambda_2}=\frac{c}{n_2\lambda_2}=\frac{3*10^8m/s}{(1.55)(408.25*10^{-9}m)}=4.74*10^{14}\ Hz[/tex]
d) The speed in the solution is given by:
[tex]v=\frac{c}{n_2}=\frac{3*10^8m/s}{1.55}=1.93*10^8m/s[/tex]
the personality test that presents an ambiguous stimulus picture to which the person may respond as he or she wishes is a ___.
A blob of clay is thrown at a basketball while it's in the air, and the clay sticks to the basketball. What is true about the momentum and energy of this system before and after this collision? If more than one response is correct, select all correct responses to get credit for this question.
a. Momentum is conserved
b. Kinetic energy is conserved
c. Some kinetic energy is converted into thermal energy
d. Total energy is conserved
Answer:
- Momentum is conserved
- Some kinetic energy is converted into thermal energy
Explanation:
Collision occurs when an object exert force on another. Collision can either be elastic or inelastic depending on whether the bodies stick together or separates after collision.
For elastic collision, the bodies separates after collision and due to this both their momentum and energy are conserved. Both separated object doesn't loose energy as such during collision and they possesses greater momentum.
In inelastic collision, the bodies stick together after collision. Their momentum is conserved but not their kinetic energy since they are not free to move independently.
Based on the question, the type of collision that occur is an inelastic collision since they stick together in air after collision. Some of the kinetic energy of the particles are turned into vibrational energy of the atoms leading to heating effect. Based on this, the following are true
- Their momentum before and after collision is conserved
- Some kinetic energy is converted into thermal energy(heat)
A fully penetrating well in a 33 m thick confined aquifer pumps at a constant rate of 2000 m3/day for a long time. If the head in an observation well located160 m from the well is 249 m and the undisturbed head calculated at 453 m radius of influence is 250 m, determine the aquifer’s hydraulic conductivity (in m/d), transmissivity, and the drawdown 100 m away from the well. Problem
Answer:
the aquifer’s hydraulic conductivity is K = 10.039 m/day
transmissivity T = 331.287 m/day
the drawdown 100 m away from the well is s = 1.452 m
Explanation:
Given that :
The constant pumps rate Q = 2000 m³/day
R₁ =160 m → H₁ = 249 m
R₂ = 453 m → H₂ = 250 m
The confined aquifer B is 33 m thick
The hydraulic conductivity K = [tex]\frac{Q*In (\frac{R_1}{R_2}) }{2 \pi B(H_2-H_1)}[/tex]
K = [tex]\frac{2000*In (\frac{160}{453}) }{2 \pi *33(250-249)}[/tex]
K = [tex]\frac{2081.43662}{207.3451151}[/tex]
K = 10.039 m/day
Transmissivity T = K × B
T = 10.039×33
T = 331.287 m/day
TO find the drawdown 100 m away from the well; we have:
K = [tex]\frac{Q* In(\frac{R_2}{R_1} )}{2 \pi B (H_2-H_1)} =\frac{Q* In(\frac{R_2}{R_3} )}{2 \pi B (H_2-H_3)}[/tex]
[tex]\frac{ In(\frac{453}{160} )}{(250-249)} =\frac{ In(\frac{453}{100} )}{ (250-H_3)}[/tex]
H₃ = 248.548 m
Drawdown (s) = H₂ - H₃
s = (250 - 248.548)m
s = 1.452 m
What is heat?
A. A measure of the movement of molecules inside an object
B. The transfer of energy from a hot object to a cold object
C. The force exerted on an area by an object
D. A measure of mass per unit volume of an object
Answer:
B. The transfer of energy from a hot object to a cold object
Explanation:
Answer:
The answer is option B
Explanation:
PART ONE
A steel railroad track has a length of 28 m
when the temperature is 2◦C.
What is the increase in the length of the
rail on a hot day when the temperature is
35 ◦C? The linear expansion coefficient of
steel is 11 × 10^−6(◦C)^−1
.
Answer in units of m
PART TWO
Suppose the ends of the rail are rigidly
clamped at 2◦C to prevent expansion.
Calculate the thermal stress in the rail if
its temperature is raised to 35 ◦C. Young’s
modulus for steel is 20 × 10^10 N/m^2
Answer in units of N/m^2
Answer:[tex]\Delta L=0.0101\ m[/tex]
Explanation:
Given
Length of track [tex]L_o=28\ m[/tex] when
[tex]T_o=2^{\circ}C[/tex]
Coefficient of linear expansion [tex]\alpha =11\times 10^{-6}\ ^{\circ}C^{-1}[/tex]
When Temperature rises to [tex]T=35^{\circ}C[/tex]
[tex]\Delta T=35-2=33^{\circ}C[/tex]
and we know length expand on increasing temperature
[tex]L=L_o[1+\alpha \Delta T][/tex]
[tex]L-L_o=L_o\alpha \Delta T[/tex]
[tex]\Delta L=28\times 11\times 10^{-6}\times (33)[/tex]
[tex]\Delta L=0.0101=10.164\ mm[/tex]
(b)When rails are clamped thermal stress induced
we know [tex]E=\frac{stress}{strain}[/tex]
[tex]Stress=E\times strain[/tex]
[tex]Stress=20\times 10^{10}\times \frac{\Delta L}{L_o}[/tex]
[tex]Stress=20\times 10^{10}\times \frac{0.0101}{28}[/tex]
[tex]Stress=72.14\ MPa[/tex]
[tex]Stress=72.14\times 10^{6}\ N/m^2[/tex]
A 20 kg object is pushed with a force of 100 N. What is the resulting acceleration of the
object to the nearest hundredth of a m/s
Answer:
Acceleration, [tex]a=5\ m/s^2[/tex]
Explanation:
We have,
Mass of the object is 20 kg
Force acting on the object is 100 N
It is required to find the resulting acceleration of the object. Let a is the acceleration. The force acting on object is given by :
[tex]F=ma[/tex]
a is acceleration
[tex]a=\dfrac{F}{m}\\\\a=\dfrac{100\ N}{20\ kg}\\\\a=5\ m/s^2[/tex]
So, the resulting acceleration of the object is [tex]5\ m/s^2[/tex].
A 94.0 kg ice hockey player hits a 0.150 kg puck, giving the puck a velocity of 44.0 m/s. If both are initially at rest and if the ice is frictionless,
how far does the player recoil in the time it takes the puck to reach the goal 16.5 m away?
Answer:
0.026 meter
Explanation:
using distance time equation to determine the time for the puck to move 16.5 meters.
distance 'd' = velocity'v' x time't'
16.5 = 44 x t
t =0.375 second
Here momentum is conserved. Since both objects are initially at rest, the initial momentum is 0.
Next is to determine the puck’s momentum.
Momemtum 'p' = m x v => 0.15 x 44 = 6.6kg⋅m/s
The player momentum is -6.6kg⋅m/s .
In order to determine the player’s velocity, we'll use p=mv
-6.6 = 94v
v= -0.0702 m/s
The above negative sign represents that the player is moving in the opposite direction of the puck.
Lastly, how far does the player recoil in the time it takes the puck to reach the goal 16.5 m away?
d = v x t = 0.0702 x 0.375= 0.026 meter
Final answer:
The recoil velocity of the ice hockey player is 0.07021 m/s, and the time it takes for the puck to reach the goal is 0.375 s. Therefore, the player recoils a distance of 2.633 cm in the time the puck takes to reach the goal 16.5 m away.
Explanation:
When a hockey player hits a puck on frictionless ice, this scenario is an excellent example of the conservation of momentum where the total momentum before and after the event must be equal. Since the player and the puck are initially at rest, their combined momentum is zero. Thus, when the player imparts a velocity to the puck, the player must recoil with a momentum equal in magnitude and opposite in direction to preserve the momentum balance.
To find the recoil speed of the player, we set the momentum of the puck equal to the momentum of the recoiling player:
Momentum of puck = mass of puck \\( imes\\) velocity of puckMomentum of player = mass of player \\( imes\\) recoil velocity of playerSo, \\(0.150 kg\\) \\( imes\\) 44.0 m/s = \\(94.0 kg\\) \\( imes\\) recoil velocity of player
Recoil velocity of player = \\((0.150 kg \\( imes\\) 44.0 m/s) / 94.0 kg)
Recoil velocity of player = 0.07021 m/s
To find the distance the player recoils, you first calculate the time it takes for the puck to reach the goal. Since velocity = distance / time, we rearrange to find time = distance / velocity.
Time for puck to reach the goal = Distance to goal / Speed of puck
Time for puck to reach the goal = 16.5 m / 44.0 m/s = 0.375 s
Then, we find the distance the player recoils by using the recoil velocity we found earlier:
Distance player recoils = Recoil velocity of player \\( imes\\) Time for puck to reach the goal
Distance player recoils = 0.07021 m/s \\( imes\\) 0.375 s
Distance player recoils = 0.02633 m, or 2.633 cm
Determine the magnetic flux density at a point on the axis of a solenoid with radius b and length L, and with a current I in its N turns of closely wound coil. Show that the result reduces to that given in equation 6-14 when L approaches infinity.
Answer:
See explaination
Explanation:
Magnetic flux density definition, a vector quantity used as a measure of a magnetic field.
It can be defined as the amount of magnetic flux in an area taken perpendicular to the magnetic flux's direction.
See attached file for detailed solution of the given problem.
The magnetic flux density inside a solenoid can be derived using the formula B = μ₀(NI)/L. As L approaches infinity, this simplifies to B = μ₀nI, aligning with the standard magnetic field expression for a long solenoid.
To find the magnetic flux density at a point on the axis of a solenoid with radius b, length L, a current I, and N turns of closely wound coil, use the following steps:
Step 1 : Consider an infinitesimal element dz of the solenoid. The element is located at a distance z from the center of the solenoid. The magnetic field contribution ( dB ) from this element at point ( P ) is given by the Biot-Savart law as -
[tex]\[ dB = \frac{\mu_0 I d\ell}{4\pi} \frac{1}{r^2} \][/tex]
Step 2 : For a solenoid, considering a differential element, the distance r from the element to the point P on the axis is -
[tex]\( \sqrt{b^2 + (z - x)^2} \).[/tex]
Step 3 : For a small segment dz, the current element is -
[tex]\[ dB = \frac{\mu_0 (n I dz)}{4\pi} \frac{1}{(b^2 + (z - x)^2)^{3/2}} \][/tex]
Step 4 : Integrate dB from -L/2 to L/2 :
[tex]\[ B = \int_{-L/2}^{L/2} \frac{\mu_0 (n I dz)}{4\pi} \frac{1}{(b^2 + (z - x)^2)^{3/2}} \][/tex]
Substitute, [tex]\( n = \frac{N}{L}[/tex]
[tex]\[ B = \frac{\mu_0 I N}{4\pi L} \int_{-L/2}^{L/2} \frac{dz}{(b^2 + (z - x)^2)^{3/2}} \][/tex]
Solving the integral part -
[tex]\[ \int_{-L/2}^{L/2} \frac{dz}{(b^2 + (z - x)^2)^{3/2}} = \frac{z}{b^2 \sqrt{b^2 + (z - x)^2}} \Bigg|_{-L/2}^{L/2} \][/tex]
[tex]\[ \left[ \frac{L/2}{b^2 \sqrt{b^2 + (L/2 - x)^2}} - \frac{-L/2}{b^2 \sqrt{b^2 + (-L/2 - x)^2}} \right] \][/tex]
Step 5: When L is very large, the ends of the solenoid are far away, and we can approximate:
[tex]\[ \frac{L/2 - x}{b^2 \sqrt{b^2 + (L/2 - x)^2}} \approx \frac{1}{b^2} \quad \text{and} \quad \frac{-L/2 - x}{b^2 \sqrt{b^2 + (-L/2 - x)^2}} \approx -\frac{1}{b^2} \][/tex]
This simplifies the result to -
[tex]\[ \left[ \frac{L/2 - x}{b^2 (L/2 - x)} - \frac{-L/2 - x}{b^2 (L/2 + x)} \right] = \left[ \frac{1}{b^2} - \left(-\frac{1}{b^2}\right) \right] = \frac{2}{b^2} \][/tex]
Conclusion, For a very long solenoid:
[tex]\[B = \mu_0 \frac{N}{L} I\][/tex]
Which simplifies to,
[tex]\[B = \mu_0 n I\][/tex]
Thus, for a very long soleniod the magnetic flux density can be approximated to [tex]\[B = \mu_0 n I\][/tex].
Which part of the electromagnetic Spectrum is nearest to X-rays?
microwaves
infrared light
gamma rays
radio waves
Answer:gamma rays
Explanation:
Out of all these spectrum listed in The question , gamma rays is closest to x-ray in The electromagnetic spectrum