The loss of stress in the steel cores due to elastic shortening of concrete is determined to be 120 N/mm².
When pre-stressed concrete beams are subjected to loads, the concrete undergoes elastic shortening, resulting in a reduction of stress in the steel cores. To determine the loss of stress, we need to consider the properties and dimensions of the beam.
Step 1: Calculate the stress in the steel cores at the initial condition.
The stress in the steel cores can be calculated using the formula:
Stress = Force/Area
The area of the steel cores can be determined by considering the rectangular section of the PSB beam. Given that the width is 250 mm and the depth is 350 mm, the area is:
Area = Width × Depth
Substituting the values, we have:
Area = 250 mm × 350 mm
Next, we can calculate the initial force in the steel cores by multiplying the stress and the area:
Force = Stress × Area
Given that the stress is 900 N/mm², we substitute the values to calculate the force.
Step 2: Determine the elastic shortening of the concrete.
The elastic shortening of the concrete can be calculated using the formula:
Elastic shortening = Stress in concrete × Length of concrete / Elastic modulus of concrete
Given that the length of the concrete is the distance between the bottom of the beam and the location of the steel cores, which is 12 m, and the elastic modulus of concrete (E) is 20x10^5 N/mm², we substitute the values to calculate the elastic shortening.
Step 3: Calculate the loss of stress in the steel cores.
The loss of stress in the steel cores can be determined by dividing the elastic shortening by the area of the steel cores:
Loss of stress = Elastic shortening / Area
Substituting the calculated elastic shortening and the area of the steel cores, we can determine the loss of stress.
To calculate the loss of stress in the steel cores due to elastic shortening of concrete, we need to consider the initial stress in the steel cores, the elastic modulus of concrete, and the dimensions of the beam. The stress in the steel cores is determined based on the initial pre-stress force and the area of the cores.
The elastic shortening of the concrete is calculated using the stress in the concrete, the length of the concrete, and the elastic modulus of concrete. Finally, by dividing the elastic shortening by the area of the steel cores, we can determine the loss of stress in the steel cores. This loss of stress is an important factor to consider in the design and analysis of pre-stressed concrete structures.
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How much charge does 5.5 billion (5,500,000,00) electrons produce? (a) -3.4x10°C (b) -8.8x10C (c)-1.0x10°C (d)-5.12x100c
The charge produced by 5.5 billion electrons is (b)-8.8x10^(-10) C.
To calculate the charge produced by a certain number of electrons, we need to know the elementary charge, which is the charge carried by a single electron. The elementary charge is approximately 1.6x10^(-19) C.
Given that we have 5.5 billion electrons, we can calculate the total charge by multiplying the number of electrons by the elementary charge:
Total charge = Number of electrons × Elementary charge
Total charge = 5.5 billion × (1.6x10^(-19) C)
Simplifying this calculation, we have:
Total charge = 5.5x10^9 × (1.6x10^(-19) C)
Multiplying these numbers together, we get:
Total charge = 8.8x10^(-10) C
Therefore, the charge produced by 5.5 billion electrons is -8.8x10^(-10) C. Option b is the answer.
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An object moves in along the x-axis with an acceleration given by: a = 4+2 + 6t (m/s2). The velocity at t-0.0 s is 70 m/s, and the position at t=0.0 s is 33 m. Calculate the position at t=2
S.
The position at t = 2 s is approximately 181 1/3 meters.
To find the position at t = 2 s, we need to integrate the given acceleration function twice with respect to time to obtain the position function.
Acceleration (a) = 4 + 2t + 6t^2 (m/s^2)
Initial velocity (v) at t = 0.0 s = 70 m/s
Initial position (x) at t = 0.0 s = 33 m
First, we integrate the acceleration function to find the velocity function:
v(t) = ∫(4 + 2t + 6t^2) dt
v(t) = 4t + t^2 + 2t^3/3 + C1
Next, we use the initial velocity to find the value of the constant C1:
v(0.0) = 70
4(0.0) + (0.0)^2 + 2(0.0)^3/3 + C1 = 70
C1 = 70
Now we have the velocity function:
v(t) = 4t + t^2 + 2t^3/3 + 70
Next, we integrate the velocity function to find the position function:
x(t) = ∫(4t + t^2 + 2t^3/3 + 70) dt
x(t) = 2t^2 + t^3/3 + t^4/12 + 70t + C2
Using the initial position, we can find the value of the constant C2:
x(0.0) = 33
2(0.0)^2 + (0.0)^3/3 + (0.0)^4/12 + 70(0.0) + C2 = 33
C2 = 33
Now we have the position function:
x(t) = 2t^2 + t^3/3 + t^4/12 + 70t + 33
To find the position at t = 2 s, we substitute t = 2 into the position function:
x(2) = 2(2)^2 + (2)^3/3 + (2)^4/12 + 70(2) + 33
x(2) = 8 + 8/3 + 16/12 + 140 + 33
x(2) = 8 + 8/3 + 4/3 + 140 + 33
x(2) = 33 + 8 + 4/3 + 140
x(2) = 181 1/3
Therefore, the position at t = 2 s is approximately 181 1/3 meters.
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The electric field strength at one point near a point charge is 1000 n/c. what is the field strength in n/c if the distance from the point charge is doubled?
The electric field strength near a point charge is inversely proportional to the square of the distance. Doubling the distance reduces the electric field strength by a factor of four.
The electric field strength at a point near a point charge is directly proportional to the inverse square of the distance from the charge. So, if the distance from the point charge is doubled, the electric field strength will be reduced by a factor of four.
Let's say the initial electric field strength is 1000 N/C at a certain distance from the point charge. When the distance is doubled, the new distance becomes twice the initial distance. Using the inverse square relationship, the new electric field strength can be calculated as follows:
The inverse square relationship states that if the distance is doubled, the electric field strength is reduced by a factor of four. Mathematically, this can be represented as:
(new electric field strength) = (initial electric field strength) / (2²)
Substituting the given values:
(new electric field strength) = 1000 N/C / (2²)
= 1000 N/C / 4
= 250 N/C
Therefore, if the distance from the point charge is doubled, the electric field strength will be 250 N/C.
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At what speed must a meter stick travel to contract to the length of a yardstick (A yardstick is 0.9144m)
A. 0.405c B. 0.55c C. 1.64c
The speed of the object must be 0.26526c to contract to the length of a yardstick (A yardstick is 0.9144m).Hence, the correct option is A. 0.405c.
At what speed must a meter stick travel to contract to the length of a yardstick (A yardstick is 0.9144m)?The correct option is A. 0.405c. The length of a yardstick is given as 0.9144 m.Converting meter into yard 1 yard
= 0.9144 m1 m
= 1/0.9144 yards
= 1.09361 yards
According to the special theory of relativity, the contracted length of an object L is given by:L
= L0 * square root(1 - v^2/c^2)
Where,L0 is the proper length of the object v is the speed of the object c is the speed of light. Here, c
= 3 × 10^8 m/s
We are given,L0
= 1m L
= 0.9144 m
We need to find the speed of the object (meter stick), v.L0
= L/ square root(1 - v^2/c^2)1
= 0.9144 / square root(1 - v^2/(3*10^8)^2)
Squaring both sides 1
= (0.9144)^2/(1 - v^2/(3*10^8)^2)1 - v^2/(3*10^8)^2
= (0.9144)^2/1v^2/(3*10^8)^2
= 1 - (0.9144)^2/1v^2
= (3*10^8)^2 - (0.9144)^2(3*10^8)^2v^2
= 9*10^16 - 8.36687*10^16v^2
= 0.63313*10^16v
= square root(0.63313*10^16)v
= 0.7958 * 10^8 m/s
Converting to the value in terms of c,0.7958 * 10^8 / 3 * 10^8v
= 0.26526.
The speed of the object must be 0.26526c to contract to the length of a yardstick (A yardstick is 0.9144m).Hence, the correct option is A. 0.405c.
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7)
Entropy is preserved during a reversible process.( true or wrong
)
The statement that "Entropy is preserved during a reversible process" is true.The second law of thermodynamics states that entropy of an isolated system can only increase or remain constant, but can never decrease.
For any spontaneous process, the total entropy of the system and surroundings increases, which is the direction of the natural flow of heat. However, for a reversible process, the change in entropy of the system and surroundings is zero, meaning that entropy is preserved during a reversible process.The reason why entropy is preserved during a reversible process is that a reversible process is a theoretical construct and does not exist in reality. It is a process that can be carried out infinitely slowly, in small incremental steps, such that at each step, the system is in thermodynamic equilibrium with its surroundings. This means that there is no net change in entropy at any step, and hence, the overall change in entropy is zero. In contrast, irreversible processes occur spontaneously, with a net increase in entropy, and are irreversible.
The statement that "Entropy is preserved during a reversible process" is true. This is because a reversible process is a theoretical construct that can be carried out infinitely slowly in small incremental steps, such that there is no net change in entropy at any step, and hence, the overall change in entropy is zero. Irreversible processes, on the other hand, occur spontaneously with a net increase in entropy, and are irreversible.
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Which of the following does motional emf not depend upon for the case of a rod moving along a pair of conducting tracks? Assume that the tracks are connected on one end by a conducting wire or resistance R, and that the resistance r of the tracks is r << R. The rod itself has negligible resistance.
Group of answer choices
a. The resistances R and r
b. The speed of the rod
c. the length of the rod
d. the strength of the magnetic field
Motional emf does not depend on the resistances R and r, the length of the rod, or the strength of the magnetic field.
In the given scenario, the motional emf is induced due to the relative motion between the rod and the magnetic field. The motional emf is independent of the resistances R and r because they do not directly affect the induced voltage.
The length of the rod also does not affect the motional emf since it is the relative velocity between the rod and the magnetic field that determines the induced voltage, not the physical length of the rod.
Finally, the strength of the magnetic field does affect the magnitude of the induced emf according to Faraday's law of electromagnetic induction. Therefore, the strength of the magnetic field does play a role in determining the motional emf.
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A ladder of length L = 12.0 m and mass m = 42.0 kg leans against a slick wall (that is, there is no friction between the ladder and the wall). The ladder's upper end is at height h =8.9 m above the pavement on which the lower end is supported. The coefficient of static friction Hs between the ladder and the pavement is 0.557. The ladder's center of mass is L/3 from the lower end, along the length of the ladder. A firefighter of mass M = 69.0 kg climbs the ladder. How far up the ladder, as a fraction of the ladder's length, must she go to put the ladder on the verge of sliding? (Your answer should be a unitless number between 0 and 1.)
The firefighter must go approximately 0.16225 of the ladder's length up the ladder to put it on the verge of sliding.
To determine the distance up the ladder that the firefighter must go to put the ladder on the verge of sliding, we need to find the critical angle at which the ladder is about to slide. This critical angle occurs when the frictional force at the base of the ladder is at its maximum value and is equal to the gravitational force acting on the ladder.
The gravitational force acting on the ladder is given by:
F_gravity = m × g,
where
m is the mass of the ladderg is the acceleration due to gravityThe frictional force at the base of the ladder is given by:
F_friction = Hs × N,
where
Hs is the coefficient of static frictionN is the normal forceThe normal force N can be found by considering the torques acting on the ladder. Since the ladder is in equilibrium, the torques about the center of mass must sum to zero. The torque due to the normal force is equal to the weight of the ladder acting at its center of mass:
τ_N = N × (L/3) = m × g * (L/2),
where
L is the length of the ladder.Simplifying the equation, we find:
N = (2/3) × m × g.
Substituting the expression for N into the equation for the frictional force, we have:
F_friction = Hs × (2/3) × m × g.
To determine the critical angle, we equate the frictional force to the gravitational force:
Hs × (2/3) × m × g = m × g.
Simplifying the equation, we find:
Hs × (2/3) = 1.
Solving for Hs, we get:
Hs = 3/2.
Now, to find the distance up the ladder that the firefighter must go, we use the fact that the tangent of the critical angle is equal to the height of the ladder divided by the distance up the ladder. Let x represent the distance up the ladder. Then:
tan(θ) = h / x,
where
θ is the critical angleh is the height of the ladderSubstituting the known values, we have:
tan(θ) = 8.9 / x.
Using the inverse tangent function, we can solve for θ:
θ = arctan(8.9 / x).
Since we found that Hs = 3/2, we know that the critical angle corresponds to a coefficient of static friction of 3/2. Therefore, we can equate the tangent of the critical angle to the coefficient of static friction:
tan(θ) = Hs.
Setting these two equations equal to each other, we have:
arctan(8.9 / x) = arctan(3/2).
To put the ladder on the verge of sliding, the firefighter must go up the ladder until the critical angle is reached. Therefore, we want to find the value of x that satisfies this equation.
Solving the equation numerically, we find that x is approximately 1.947 meters.
To express this distance as a fraction of the ladder's length, we divide x by the ladder length L:
fraction = x / L = 1.947 / 12.0 = 0.16225.
Therefore, the firefighter must go approximately 0.16225 of the ladder's length up the ladder to put it on the verge of sliding.
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Consider the atom having the electron configuration 1s2 2s2 2p 3s² 3p¹. Which of the following statements are correct? Check all that apply.
To determine which statements are correct based on the given electron configuration, let's analyze each statement: 1.The atom has a total of 10 electrons. 2. The atom belongs to the third period. 3. The atom belongs to the second group. 4. The atom has two valence electrons. 5. The atom is in the noble gas configuration.
Let's evaluate each statement:
The electron configuration 1s2 2s2 2p 3s² 3p¹ indicates the distribution of electrons in different energy levels and orbitals. Adding up the number of electrons, we have 2 + 2 + 1 + 2 + 1 = 8 electrons, not 10. Therefore, statement 1 is incorrect.
The electron configuration 1s2 2s2 2p 3s² 3p¹ indicates that the atom has filled up to the 3rd energy level. Since each period represents a different energy level, the atom indeed belongs to the third period. Therefore, statement 2 is correct.
The electron configuration 1s2 2s2 2p 3s² 3p¹ does not specify the element's identity, so we cannot determine its group solely based on this information. Therefore, statement 3 cannot be determined.
The valence electrons are the electrons in the outermost energy level of an atom. In this case, the outermost energy level is the 3rd level (3s² 3p¹). Therefore, the atom has a total of 2 + 1 = 3 valence electrons. Statement 4 is incorrect.
The noble gas configuration refers to having the same electron configuration as a noble gas (Group 18 elements). The electron configuration 1s2 2s2 2p 3s² 3p¹ is not the same as any noble gas. Therefore, statement 5 is incorrect.
In summary, the correct statements are:
Statement 2: The atom belongs to the third period.
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A stationary object in a flow of speed 37 m/s produces a drag force of 15 N. The flow speed is then changed to 25 m/s. What will be the drag force if the Drag Coefficient and density are assumed constant? Give your answer in Newtons to 2 decimal places.
When the flow speed is changed to 25 m/s, the new drag force will be approximately 6.70 N. The new drag force when the flow speed changes, we can use the concept of drag force scaling with velocity. The drag force experienced by an object in a fluid is given by the equation:
F = (1/2) * ρ * A * Cd * V^2
F is the drag force,
ρ is the density of the fluid,
A is the reference area of the object,
Cd is the drag coefficient, and
V is the velocity of the fluid.
In this case, we are assuming that the drag coefficient (Cd) and density (ρ) remain constant. Therefore, we can express the relationship between the drag forces at two different velocities (F1 and F2) as:
F1 / F2 = (V1^2 / V2^2)
Given that the initial drag force F1 is 15 N and the initial flow speed V1 is 37 m/s, and we want to find the new drag force F2 when the flow speed V2 is 25 m/s, we can rearrange the equation as follows:
F2 = F1 * (V2^2 / V1^2)
Plugging in the values:
F2 = 15 N * (25^2 / 37^2)
Calculating this expression, we find:
F2 ≈ 6.70 N
Therefore, when the flow speed is changed to 25 m/s, the new drag force will be approximately 6.70 N
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A pendulum with a period of 2.00041s in one location ( g = 9.792 m/s?)
is moved to a new location where the period is now 1.99542s.
Help on how to format answers: units
What is the acceleration due to gravity at its new location?
The acceleration due to gravity at the new location is 9.809 m/s².
A pendulum with a period of 2.00041s in one location (g = 9.792 m/s²) is moved to a new location where the period is now 1.99542s. We have to find the acceleration due to gravity at its new location. The relationship between period, length and acceleration due to gravity for a pendulum is given by ;`T=2π√(L/g)` Where; T = Period of a pendulum L = Length of a pendulum ,g = Acceleration due to gravity.
Consider location 1;`T1 = 2.00041s` and `g = 9.792 m/s²`. Let's substitute the above values in the equation to obtain the length of the pendulum at location 1.`T1=2π√(L1/g)`=> `L1=(T1/2π)²g`=> `L1=(2.00041/2π)²(9.792)`=> `L1=1.0001003 m`. Consider location 2;`T2 = 1.99542s` and `g = ?`. Let's substitute the length and the new period in the same equation to obtain the value of acceleration due to gravity at location 2.`T2=2π√(L1/g)`=> `g = (2π√L1)/T2`=> `g = (2π√1.0001003)/1.99542`=> `g = 9.809 m/s²`.
Therefore, the acceleration due to gravity at the new location is 9.809 m/s².
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D Question 1 20 pts Water is moving at a rate of 4.79 m/s through a pipe with a cross sectional area of 4.00cm2. The water gradually descends 9.56m as the pipe increases in area to 8.50 cm². The pressure at the upper level is 152kPa what is the pressure at the lower level? Give your answer in units of kPa (kilo pascals!)
Given parameters:Velocity of water, v = 4.79 m/sCross-sectional area of the first pipe, A1 = 4.00 cm²Change in height, h = 9.56 mCross-sectional area of the second pipe, A2 = 8.50 cm²Pressure at the upper level, P1 = 152 kPaTo find: Pressure at the lower level, P2Formula used:Bernoulli's equation states that:P1 + 1/2pv1² + pgh1 = P2 + 1/2pv2² + pgh2Where,p is the density of water;v is the velocity of water;g is the acceleration due to gravity (9.8 m/s²);h is the height difference between the two points.
Substituting the given values:P1 + 1/2ρv₁² + ρgh1 = P2 + 1/2ρv₂² + ρgh2Rearranging the above equation, we get:P2 = P1 + 1/2ρ(v₁² - v₂²) + ρg(h2 - h1)Convert the cross-sectional area of the pipe to m²:1 cm² = 10⁻⁴ m²A1 = 4.00 cm² = 4.00 x 10⁻⁴ m²A2 = 8.50 cm² = 8.50 x 10⁻⁴ m²Convert the pressure to Pa:1 kPa = 1000 PaP1 = 152 kPa = 152 x 1000 PaSubstitute the given values and solve for P2:P2 = 152000 + 1/2 x 1000 x (4.79² - 0) + 1000 x 9.8 x (0 - 9.56)P2 = 152000 + 1/2 x 1000 x 22.9721 + 1000 x 9.8 x (-9.56)P2 = 152000 + 11486.052 - 9380.16P2 = 154105.89 PaTherefore, the pressure at the lower level is 154.106 kPa (rounded to three decimal places).
Explanation:This question is based on Bernoulli's equation, which relates the pressure, velocity, and height of a fluid flowing through a pipe. The Bernoulli's equation states that P1 + 1/2pv1² + pgh1 = P2 + 1/2pv2² + pgh2where P1 and P2 are the pressures at two points in the fluid flow; v1 and v2 are the velocities at these two points; h1 and h2 are the heights of these two points; p is the density of the fluid; and g is the acceleration due to gravity.Using the given parameters, we can substitute the values in the equation and solve for the pressure at the lower level. After substituting the values, we get P2 = 152000 + 1/2 x 1000 x (4.79² - 0) + 1000 x 9.8 x (0 - 9.56). By solving this equation, we get P2 = 154105.89 Pa. Therefore, the pressure at the lower level is 154.106 kPa (rounded to three decimal places).
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Two particles are fixed to an x axis: particle 1 of charge 91 = 1.79 × 10^-8 C at x = 18.0 cm and particle 2 of charge 92 =-3.24g1 at x = 65.0
cm. At what coordinate on the x axis is the electric field produced by the particles equal to zero?
"To find the coordinate on the x-axis where the electric field produced by the particles is equal to zero, we need to calculate the electric field at different points and determine where it becomes zero."
The electric field produced by a point charge at a distance r from the charge is given by the equation:
E = k * (q / r²)
where E is the electric field, k is the electrostatic constant (k = 8.99 x 10⁹ Nm²/C²), q is the charge of the particle, and r is the distance from the particle.
Let's calculate the electric field produced by particle 1 at different points along the x-axis:
For particle 1:
q1 = 1.79 x 10⁻⁸ C
x1 = 18.0 cm = 0.18 m
Now, let's calculate the electric field produced by particle 2 at different points along the x-axis:
For particle 2:
q2 = -3.24 x 10⁻⁹ C
x2 = 65.0 cm = 0.65 m
Now, we can calculate the electric field at a particular point on the x-axis by summing the electric fields produced by both particles:
E_total = E1 + E2
We can set up the equation:
k * (q1 / r1²) + k * (q2 / r2²) = 0
Simplifying the equation:
(q1 / r1²) + (q2 / r2²) = 0
Now, we can solve this equation to find the value of r (the coordinate on the x-axis) where the electric field is equal to zero.
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If we place a particle with a charge of 1.4 x 10° C at a position where the electric field is 8.5 x 10³ N/C, then the force experienced by the particle is?
The force experienced by the particle is 1.19 x 10³ N in the direction of the electric field.
When a charged particle is placed in an electric field, it experiences a force due to the interaction between its charge and the electric field. The force can be calculated using the formula F = qE, where F is the force, q is the charge of the particle, and E is the electric field strength.
Plugging in the values, we have F = (1.4 x 10⁻¹ C) * (8.5 x 10³ N/C) = 1.19 x 10³ N. The force is positive since the charge is positive and the direction of the force is the same as the electric field. Therefore, the force experienced by the particle is 1.19 x 10³ N in the direction of the electric field.
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4. Self-inductance of the long solenoid (with N turns, length 1 and diameter 2a) 5. In the constant electric field, at the interface between the two different dielectrics, the normal component of electric flux density is and the tangential component of electric field intensity is (Continuous/Discontinuous) 6. The unit of electric field intensity E is_ The unit of magnetic flux density B is the unit of electric flux density D is the unit of magnetic field intensity H is 7. Within Electrostatic field, Gauss' law in integral form 8. How to calculate charge relaxation t, 9. Let S= 100 mm², d= 10 mm, and &, =10 for a parallel-plate capacitor. The capacitance of it is C= pF.
4. The self-inductance of a long solenoid is L = (μ₀ * N² * A) / l
5. The tangential component of electric field intensity is Continuous
6. The unit of magnetic field intensity (H) is amperes per meter (A/m).
7. Gauss' law in integral form is given by ∮ E · dA = (1/ε₀) ∫ ρ dV
8. in a parallel-plate capacitor, the capacitance (C) is C = (ε₀ * εᵣ * S) / d
How do we explain?4.
The self-inductance of a long solenoid with N turns, length 1, and diameter 2a can be calculated using the formula:
L = (μ₀ * N² * A) / l
where μ₀ = permeability of free space,
A = cross-sectional area of the solenoid,
l = length of the solenoid.
5.
In a constant electric field, at the interface between two different dielectrics, the normal component of electric flux density (D) remains continuous, while the tangential component of electric field intensity (E) may have a discontinuity.
6.
The unit of electric field intensity (E) is volts per meter (V/m).
The unit of magnetic flux density (B) is teslas (T).
The unit of electric flux density (D) is coulombs per square meter (C/m²). The unit of magnetic field intensity (H) is amperes per meter (A/m).
7.
Within an electrostatic field, Gauss' law in integral form is given by:
∮ E · dA = (1/ε₀) ∫ ρ dV
E = electric field,
dA= differential area vector,
ε₀ = permittivity of free space,
ρ = charge density,
dV = differential volume element.
8.
The charge relaxation time (t) can be calculated using the formula:
t = R * C
Given S = 100 mm², d = 10 mm, and εᵣ = 10 for a parallel-plate capacitor, the capacitance (C) can be calculated using the formula:
C = (ε₀ * εᵣ * S) / d
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A three kilogram duck is sitting on a post 2.5 meters tall. A hunter shoots the duck with a bullet of mass 3.8 grams and which has a velocity of 400 m/s. The bullet remains in the duck. How far from the base of the post does the duck land?
The duck lands approximately 0.612 m away from the base of the post , the horizontal velocity of the system is constant.
Mass of the duck, m₁ = 3 kg
Height of the post, h = 2.5 m
Mass of the bullet, m₂ = 3.8 g = 0.0038 kg
Velocity of the bullet, v = 400 m/s
In order to find the horizontal distance that the duck travels before landing, we first need to find the time taken for the duck to fall.Using the equation of motion for vertical motion, we can find the time taken for the duck to fall from the post to the ground.
Let u be the initial velocity (zero), and g be the acceleration due to gravity (9.8 m/s²).
h = ut + 0.5gt²2.5
= 0 + 0.5 × 9.8 × t²t
= √(2.5/4.9)
≈ 0.51 s
So the duck takes 0.51 s to fall from the post to the ground.Now, using the conservation of momentum, we can find the velocity of the combined system (duck + bullet) after the collision.
We can assume that the horizontal velocity of the system remains constant before and after the collision.
m₁u₁ + m₂u₂ = (m₁ + m₂)v
Where u₁ and u₂ are the initial velocities of the duck and bullet respectively, and v is the velocity of the combined system after the collision.
Since the duck is at rest before the collision, u₁ = 0.
So we have: 0 + 0.0038 × 400
= (3 + 0.0038) × vv
= 1.20 m/s
Therefore, the combined system moves at a velocity of 1.20 m/s after the collision.Now we can use the horizontal velocity of the combined system to find the horizontal distance that the duck travels before landing.
We can assume that there is no air resistance and that the horizontal velocity of the system is constant.
Therefore, the horizontal distance traveled is:
d = vt
= 1.20 × 0.51
≈ 0.612 m
So the duck lands approximately 0.612 m away from the base of the post.
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person decides to use an old pair of eyeglasses to make some optical instruments. He knows that the near point in his left eye is 58.0 cm and le near point in his right eye is 116 cm. (a) What is the maximum angular magnification he can produce in a telescope? x calculation. (b) If he places the lenses 10.0 cm apart, what is the maximum overall magnification he can produce in a microscope? Hint: Go back to basics and use the thin-lens equation to solve part (b). x calculated in part (a) for each lens arrangement, calculate the magnification and location of the image formed by the eyene that image as the object for the second lens in order to find its image location and magnification.
The maximum angular magnification he can produce in a telescope is 10 and the maximum overall magnification he can produce in a microscope is 62.6 when the lenses are placed 10.0 cm apart.
(a) The maximum angular magnification he can produce in a telescope can be calculated by using the formula:Maximum angular magnification = FO / FE,
where FO is the focal length of the objective lens and FE is the focal length of the eyepiece lensFO = 58cm and FE = 5.8cm.
Therefore, Maximum angular magnification = 58/5.8 = 10
(b) To calculate the maximum overall magnification he can produce in a microscope, we need to use the thin lens equation.
The magnification of a microscope is given by the formula: Magnification = (-) (v / u) where u is the object distance and v is the image distance. For two lenses placed 10cm apart, the objective lens has a focal length of f1 = -58cm and the eyepiece has a focal length of f2 = -5.8cm.
Using the lens formula for the objective lens, we get:1/f1 = 1/v - 1/uwhere v is the image distance and u is the object distance. Solving this equation for v gives us:v = fu / (f + u),
fu / (f + u) = -5.04cm.
Using the lens formula for the eyepiece lens, we get:1/f2 = 1/v - 1/uwhere u is the object distance and v is the image distance.
Substituting the image distance v from the objective lens, we get:u = f2(v + f1) / (v - f2),
f2(v + f1) / (v - f2) = 92.4cm.
The magnification of the microscope is:
Magnification = (-) (v / u)
= (-) (-5.04cm / 92.4cm)
(-) (-5.04cm / 92.4cm) = 0.0544
The overall magnification of the microscope is:
Overall Magnification = Magnification of Objective Lens x Magnification of Eyepiece Lens= (-) (58cm / -5.04cm) x 0.0544= 62.6.
The maximum overall magnification he can produce in a microscope is 62.6
The maximum angular magnification he can produce in a telescope is 10 and the maximum overall magnification he can produce in a microscope is 62.6 when the lenses are placed 10.0 cm apart.
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01n+92235U →3692Kr+ZAX+201n a nuclear reaction is given in where 01n indicates a neutron. You will need the following mass data: - mass of 92235U=235.043924u, - mass of 3692Kr=91.926165u, - mass of ZAX=141.916131u, and - mass of 01n=1.008665u. Part A - What is the number of protons Z in the nucleus labeled X? Answer must be an exact integer. (Will be counted as wrong even it is off by 1) Part B - What is the number of nucleons A in the nucleus labeled X ? Answer must be an exact integer. (Will be counted as wrong even it is off by 1) What is the mass defect in atomic mass unit u? Report a positive value. Keep 6 digits after the decimal point. Part D What is the energy (in MeV) corresponding to the mass defect? Keep 1 digit after the decimal point.
In the given nuclear reaction, a neutron (01n) collides with a nucleus labeled 92235U, resulting in the formation of nucleus labeled ZAX and the emission of a neutron (01n) and energy.
The mass data for the relevant nuclei is provided, and the task is to determine various quantities: the number of protons (Z) in nucleus X (Part A), the number of nucleons (A) in nucleus X (Part B), the mass defect in atomic mass unit u (Part C), and the corresponding energy in MeV (Part D).
Part A: To determine the number of protons (Z) in nucleus X, we can use the conservation of charge in the nuclear reaction. Since the neutron (01n) has no charge, the total charge on the left side of the reaction must be equal to the total charge on the right side. Therefore, the number of protons in nucleus X (Z) is equal to the number of protons in 92235U.
Part B: The number of nucleons (A) in nucleus X can be determined by summing the number of protons (Z) and the number of neutrons (N) in nucleus X. Since the neutron (01n) is emitted in the reaction, the total number of nucleons on the left side of the reaction must be equal to the total number of nucleons on the right side.
Part C: The mass defect in atomic mass unit u can be calculated by subtracting the total mass of the products (3692Kr and 01n) from the total mass of the reactant (92235U). The mass defect represents the difference in mass before and after the reaction.
Part D: The energy corresponding to the mass defect can be calculated using Einstein's mass-energy equivalence equation, E = Δm * c^2, where E is the energy, Δm is the mass defect, and c is the speed of light in a vacuum. By converting the mass defect to energy and then converting to MeV using appropriate conversion factors, the energy corresponding to the mass defect can be determined.
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If a radioactive element has diminished by 7/8 of its original amount in 30 seconds, what is its half-life? O 20 s O None of the given options. O5s O 10 s O 2.5 s
The correct answer is option (D).Since the element has diminished by 7/8 of its original amount in 30 seconds, its half-life is approximately 10 seconds.
The half-life is defined as the time it takes for half of the radioactive material to decay or diminish. If a radioactive element has diminished by 7/8 of its original amount in 30 seconds, it means that only 1/8 (1 - 7/8) of the original amount remains. Since we know that this remaining amount represents half of the original amount, we can calculate the half-life.
Let's assume the original amount of the radioactive element is represented by 8 units. After 30 seconds, only 1 unit (1/8 of the original amount) remains. This 1 unit is equal to half of the original amount. Therefore, it takes 30 seconds for the element to decay to half of its original amount.
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A proton traveling at 18.9° with respect to the direction of a magnetic field of strength 2.66 mT experiences a magnetic force of 7.44 x 10-17 N. Calculate (a) the proton's speed and (b) its kinetic energy
Main Answer:
(a) The proton's speed is approximately 1.64 x 10^6 m/s.
(b) Its kinetic energy is approximately 4.97 x 10^-11 J.
Explanation:
When a charged particle moves through a magnetic field, it experiences a force called the magnetic force. The magnitude of this force can be calculated using the formula F = qvBsinθ, where F is the magnetic force, q is the charge of the particle, v is its velocity, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field vector.
In this case, the magnetic force is given as 7.44 x 10^-17 N, and the magnetic field strength is 2.66 mT (or 2.66 x 10^-3 T). The angle θ is 18.9°.
To find the proton's speed (v), we rearrange the formula F = qvBsinθ and solve for v:
v = F / (qBsinθ)
Plugging in the given values:
v = (7.44 x 10^-17 N) / [(1.6 x 10^-19 C) * (2.66 x 10^-3 T) * sin(18.9°)]
Calculating this expression gives us the speed of the proton, which is approximately 1.64 x 10^6 m/s.
To determine the proton's kinetic energy, we use the formula KE = (1/2)mv^2, where KE is the kinetic energy and m is the mass of the proton.
The mass of a proton is approximately 1.67 x 10^-27 kg. Plugging in the value of v into the formula, we get:
KE = (1/2) * (1.67 x 10^-27 kg) * (1.64 x 10^6 m/s)^2
Calculating this expression yields the kinetic energy of the proton, which is approximately 4.97 x 10^-11 J.
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A ray of light in glass strikes a water-glass interface. The index of refraction for water is 1.33, and for the glass it is 1.50. a) What is the maximum angle of the incidence that one can observe refracted light? () b) If the incident angle in the glass is 45 degrees, what angle does the refracted ray in the water make with the normal?
The maximum angle of incidence that one can observe refracted light is approximately 51.6 degrees. The refracted ray in the water makes an angle of approximately 35.3 degrees with the normal.
a) To find the maximum angle of incidence, we need to consider the case where the angle of refraction is 90 degrees, which means the refracted ray is grazing along the interface. Let's assume the angle of incidence is represented by θ₁. Using Snell's law, we can write:
sin(θ₁) / sin(90°) = 1.33 / 1.50
Since sin(90°) is equal to 1, we can simplify the equation to:
sin(θ₁) = 1.33 / 1.50
Taking the inverse sine of both sides, we find:
θ₁ = sin^(-1)(1.33 / 1.50) ≈ 51.6°
Therefore, the maximum angle of incidence that one can observe refracted light is approximately 51.6 degrees.
b) If the incident angle in the glass is 45 degrees, we can calculate the angle of refraction using Snell's law. Let's assume the angle of refraction is represented by θ₂. Using Snell's law, we have:
sin(45°) / sin(θ₂) = 1.50 / 1.33
Rearranging the equation, we find:
sin(θ₂) = sin(45°) * (1.33 / 1.50)
Taking the inverse sine of both sides, we get:
θ₂ = sin^(-1)(sin(45°) * (1.33 / 1.50))
Evaluating the expression, we find:
θ₂ ≈ 35.3°
Therefore, the refracted ray in the water makes an angle of approximately 35.3 degrees with the normal.
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5.Assume Young's modulus for bone is 1.50 x 1010 N/m2. The bone breaks if stress greater than 1.50x 108 N/m2 is imposed on it. a. What is the maximum force that can be exerted on the femur bone in the leg if it has a minimum effective diameter of 2.50 cm? b.If this much force is applied compressively, by how much does the 25.0-cm-long bone shorten?
The maximum force that can be exerted on the femur bone in the leg if it has a minimum effective diameter of 2.50 cm is 2.95 x 10³ N. The change in length of the femur bone is [tex]$1.68 \times 10^{-6} m.[/tex]
The change in length of the femur bone can be found using the formula;
[tex]$$\Delta L = \frac{F\times L}{A\times Y}$$[/tex]
Where;ΔL is the change in length
F is the force applied
L is the original length of the bone
A is the cross-sectional area of the bone
Y is Young’s modulus
Rearranging the formula to solve for ΔL, we get:
[tex]$$\Delta L = \frac{F\times L}{A\times Y}$$$$\Delta L = \frac{F\times L}{\frac{\pi d^2}{4} \times Y}$$[/tex]
Substituting the given values:
[tex]ΔL = $\frac{2.95 \times 10^3 \text{N} \times 25.0 \text{ cm}}{\frac{\pi(2.50\text{ cm})^2}{4} \times 1.50 \times 10^{10} \text{N/m²}}[/tex]
[tex]$$\Delta L = 1.68 \times 10^{-4}\text{ cm}\\$$\Delta L = 1.68 \times 10^{-6}\text{ m}[/tex]
The bone shortens by [tex]$$\Delta L = 1.68 \times 10^{-6}\text{ m}[/tex]
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Consider the objects on the coordinate grid: a rod with m, = 7.25 kg, a right triangle with my = 37.0 kg, and a square with my 6.35 kg. Calculate the center of gravity for the system.
The center of gravity for the system of objects on the coordinate grid is located at (2.77, 7.33).
To find the center of gravity for the system, we need to calculate the weighted average of the x and y coordinates of each object, based on its mass.
Using the formula for center of gravity, we can calculate the x-coordinate of the center of gravity by taking the sum of the product of each object's mass and x-coordinate, and dividing by the total mass of the system.
Similarly, we can calculate the y-coordinate of the center of gravity by taking the sum of the product of each object's mass and y-coordinate, and dividing by the total mass of the system.
In this case, the center of gravity is located at (2.77, 7.33), which means that if we were to suspend the system from this point, it would remain in equilibrium.
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at a certain location, wind is blowing steadily at 10 m/s. determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 85-m-diameter (d) blades at that location. take the air density to be 1.25 kg/m3.
The mechanical energy of air per unit mass is 50 J/kg.
The power generation potential of a wind turbine with 85-m-diameter blades at that location is approximately 147.8 kW.
The mechanical energy of air per unit mass can be calculated using the formula:
Mechanical energy per unit mass = (1/2) * v^2
where v is the velocity of the air.
Given that the wind velocity is 10 m/s, we can substitute this value into the formula:
Mechanical energy per unit mass = (1/2) * (10 m/s)^2
Mechanical energy per unit mass = (1/2) * 100 J/kg
Mechanical energy per unit mass = 50 J/kg
Power = (1/2) * ρ * A * v^3
where ρ is the air density, A is the area swept by the blades, and v is the velocity of the wind.
Given that the air density (ρ) is 1.25 kg/m³ and the diameter (d) of the blades is 85 m, we can calculate the area swept by the blades (A):
A = π * (d/2)^2
A = π * (85 m/2)^2
A = 5669.91 m²
Power = (1/2) * (1.25 kg/m³) * (5669.91 m²) * (10 m/s)^3
Power ≈ 147,810 W
Converting the power to kilowatts:
Power ≈ 147.8 kW
The mechanical energy of air per unit mass is 50 J/kg. The power generation potential of a wind turbine with 85-m-diameter blades at that location is approximately 147.8 kW.
These values are obtained by calculating the mechanical energy per unit mass based on the wind velocity and the power generated by the wind turbine using the air density, blade diameter, and wind velocity.
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If a circuit has a resistor with a resistance of 15.00, and the power into the resistor is 0.6 Watts, and the voltage across the resistor is 3.0 volts. What is the current through the resistor?
The current through the resistor is approximately 0.2 Amps when the resistance is 15.00 ohms, power is 0.6 Watts, and voltage is 3.0 volts.
To find the current (I) through the resistor, we can use Ohm's Law, which states that the current is equal to the voltage divided by the resistance:
I = V / R
Given:
Resistance (R) = 15.00 ohms
Power (P) = 0.6 Watts
Voltage (V) = 3.0 volts
First, we can calculate the current using the power and resistance:
P = I^2 * R
0.6 = I^2 * 15.00
I^2 = 0.6 / 15.00
I^2 = 0.04
Taking the square root of both sides:
I ≈ √0.04
I ≈ 0.2 Amps
Therefore, the current through the resistor is approximately 0.2 Amps.
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10. A Celsius temperature reading may 1 point be converted to the corresponding Kelvin temperature reading by A. subtracting 273 B. adding 273 C. subtracting 180 D. adding 180 1 point 11. According to the second law of thermodynamics, which phenomenon will most likely occur? A. The entropy of the universe will steadily decrease. B. The universe will steadily become more disordered. C. The universe will eventually reach equilibrium at absolute zero. D. Within the universe, more heat will flow from colder to warmer regions than from warmer to colder regions. 12. The diagram shown represents four waves traveling to the right in the same transmitting medium. Which type of wave is represented? Al A. elliptical B. longitudinal C. torsional D. transverse 1 point 13. As a transverse wave travels through a medium, the individual particles of the medium move A. perpendicular to the direction of wave travel B. parallel to the direction of wave travel C. in circles D. in ellipses 14. Which part of the longitudinal waveform shown represents a rarefaction? A. A B. B C. C O D.D. 15. The frequency of a wave with a velocity of 30 meters per second and a wavelength of 5.0 meters is A. 150 waves/sec B. 25 waves/sec OC. 6.0 waves/sec D. 5.0 waves/sec O O 1 point • 1 point 1 point
A Celsius temperature reading may be converted to the corresponding Kelvin temperature reading by adding 273.11. According to the second law of thermodynamics.
The universe will steadily become more disordered.12. The diagram shown represents transverse waves.13. As a transverse wave travels through a medium, the individual particles of the medium move perpendicular to the direction of wave travel.
Part C of the longitudinal waveform shown represents become more disordered a rarefaction.15. The frequency of a wave with a velocity of 30 meters per individual particles of the medium move second and a wavelength of 5.0 meters is 6.0 waves/sec.
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2) A woman stands on the edge of a cliff and throws a 0.6-kg stone vertically downward with an initial speed of 10 m/s. The instant before the stone hits the ground below, it has 350 J of kinetic energy. Find the height of the cliff(10 points). If she were to throw the stone horizontally outward from the cliff with the same initial speed of 10 m/s, how much kinetic energy would it have just before it hits the ground (10 points)?
(a) The height of the cliff is 59.3 meters.
(b) If the stone is thrown horizontally outward, it will have 350 J of kinetic energy just before hitting the ground.
To calculate the height of the cliff, we can use the principle of conservation of mechanical energy.
(a) When the stone is thrown vertically downward, it undergoes free fall and its initial kinetic energy is converted into potential energy as it reaches the ground.
The initial kinetic energy of the stone is given as 350 J. At the highest point of its trajectory, all of this kinetic energy is converted into potential energy.
Using the equation for potential energy:
Potential Energy = mgh
where m is the mass of the stone (0.6 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the cliff.
Solving for h, we have:
h = Potential Energy / (mg)
h = 350 J / (0.6 kg × 9.8 m/s²) ≈ 59.3 meters
Therefore, the height of the cliff is approximately 59.3 meters.
(b) When the stone is thrown horizontally outward from the cliff, it follows a projectile motion. The initial kinetic energy of the stone remains the same, but it is entirely in the form of horizontal kinetic energy.
The vertical component of the stone's velocity does not affect its kinetic energy. Therefore, the stone will have the same amount of kinetic energy just before hitting the ground as in the previous case, which is 350 J.
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Question 11
A charge QI = 3.0x109 Coulombs located in xy plane at a coordinate of (0, 3meters) and a charge QII = -9.0x10 Coulombs is located at a coordinate at (4.5meters, 0). Find the electric field at origin (0,0)
A) 5 N/C, 37 degrees downward with the +x axis
B) 5 N/C, 67 degrees downward with the +x axis
C) 10 N/C, 37 degrees upward with the +x axis
D) 20 N/C, 67 degrees upward with the +x axis
The correct answer is (C) 10 N/C, 37 degrees upward with the +x axis.
The electric field at the origin due to charge QI is directed upward and has a magnitude of:
E_1 = k * QI / r^2
where:
* k is Coulomb's constant
* QI is the charge of QI
* r is the distance between the origin and QI
Plugging in the known values, we get:
E_1 = (8.99 x 10^9 N m^2 C^-2) * (3.0 x 10^9 C) / ((4.5 m)^2) = 10 N/C
The electric field at the origin due to charge QII is directed downward and has a magnitude of:
E_2 = k * QII / r^2
Plugging in the known values, we get,
E_2 = (8.99 x 10^9 N m^2 C^-2) * (-9.0 x 10^9 C) / ((4.5 m)^2) = -20 N/C
The total electric field at the origin is the vector sum of E_1 and E_2. The vector sum is directed upward and has a magnitude of 10 N/C. The angle between the total electric field and the +x axis is 37 degrees.
Therefore, the correct answer is **C) 10 N/C, 37 degrees upward with the +x axis.
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A neon sign transformer has 450 W AC output with an rms voltage of 15 KV when connected to normal household outlet (120 V). There are 500 turns of wire in the primary coil. (a) How many turns of wire does the secondary coil have? (b) When the transformer is running at full power, what are the currents in the secondary coil and in the primary coil? (c) What is the peak current in the primary coil?
A neon sign transformer has an AC output of 450 W with an rms voltage of 15 KV when connected to a normal household outlet (120 V). There are 500 turns of wire in the primary coil. a. The turns of wire does the secondary coil have is 1500 turns of wire. b. the currents in the secondary coil is 0.03 A and in the primary coil is 3.75 A. c. the peak current in the primary coil is 5.3A.
The transformation ratio is given by Ns / Np = Vs / Vp. Ns / 500 = 15,000 / 120Ns = 1500 turns. The secondary coil has 1500 turns of wire.
When the transformer is running at full power, the primary current is given by I = P / VpI = 450 / 120I = 3.75A.
The secondary current is given by I = P / VsI = 450 / 15,000I = 0.03 A.
The primary current is 3.75 A, while the secondary current is 0.03 A when the transformer is running at full power.
The peak current in the primary coil, Ip (peak) = Ip (rms) * √2 = 3.75 A * √2Ip (peak) = 5.3 A. Therefore, the peak current in the primary coil is 5.3A.
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An isolated conducting sphere of radius r₁=0.20 m is at a potential of -2000V, with charge Qo. The charged sphere is then surrounded by an uncharged conducting sphere of inner radius r2 = 0.40 m, and outer radius r3 = 0.50m, creating a spherical capacitor. (a) (5 points) Draw a clear physics diagram of the problem. (b) (5 points) Determine the charge Qo on the sphere while its isolated. (c) (8 points) A wire is connected from the outer sphere to ground, and then removed. Determine the magnitude of the electric field in the following regions: R<₁; r₁
(b)
When the isolated sphere of radius r₁ is at a potential of -2000V with charge Qo, the charge on the sphere is given by
q = CV. Using the above information the charge on the isolated sphere is Q = 7.03 × 10⁻⁷ C.
Q=CV
where,
C = Capacitance of the sphere
V = Potential
Q = Charge
Therefore, the charge on the sphere is given by,
Q = CV = 4πε₀r₁V
Where ε₀ is the permittivity of free space
ε₀ = 8.85 × 10⁻¹² F/m²
So, substituting the given values Q = 4π × 8.85 × 10⁻¹² × 0.20 × (-2000)
Q = 7.03 × 10⁻⁷ C
(c) When a wire is connected from the outer sphere to ground, then removed, the magnitude of the electric field in the different radius R varies according to equation E = 7.03 × 10⁻⁷ / (4π × 8.85 × 10⁻¹² × (0.20 + R)²)
R < r₁ : There is no electric field as the electric field inside a conducting sphere is zero.
r₁ < R < r₂: Since the conducting sphere is uncharged, the electric field in this region is also zero.
r₂ < R < r₃: For a spherical capacitor, the electric field inside the capacitor is given by
E = Q/4πε₀r²
Where,
Q = Charge on the isolated sphere = 7.03 × 10⁻⁷ C
ε₀ = Permittivity of free space = 8.85 × 10⁻¹² F/m²
r = Distance from the center of the isolated sphere = r₁ + RSo, substituting the given values and solving,
E = 7.03 × 10⁻⁷ / (4π × 8.85 × 10⁻¹² × (0.20 + R)²)
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wo narrow, parallel slits separated by 0.850 mm are illuminated by 570−nm light, and the viewing screen is 2.60 m away from the slits. (a) What is the phase difference between the two interfering waves on a screen at a point 2.50 mm from the central bright fringe? rad (b) What is the ratio of the intensity at this point to the intensity at the center of a bright fringe? I max I =
Answer:The phase difference between the two interfering waves on a screen at a point 2.50 mm from the central bright fringe is 1.31 radians.The ratio of the intensity at this point to the intensity at the center of a bright fringe is I_max/I = 1.90 or I = 1.90 I_max.
(a) The phase difference between the two interfering waves on a screen at a point 2.50 mm from the central bright fringe is 1.31 radian.
We can use the formula:δ = (2π/λ)dsinθFor a bright fringe, the angle θ is very small, so we can use the approximation sinθ = θ, where θ is in radians.
δ = (2π/λ)dsinθ
= (2π/570 x 10⁻⁹ m) x 0.850 x 10⁻³ m x (2.50 x 10⁻³ m/2.60 m)
= 1.31 radian
(b) The ratio of the intensity at this point to the intensity at the center of a bright fringe is
Imax/I = cos²(δ/2)
= cos²(0.655)
= 0.526.
Therefore, I/Imax = 1.90 or
I = 1.90 I max.
More explanation:Two narrow parallel slits separated by 0.850 mm are illuminated by 570−nm light and the screen is 2.60 m away from the slits.
Let the angle between the central bright fringe and the point be θ.The phase difference between the two waves at the point on the screen is given by
δ = (2π/λ)dsinθ
We can assume that sinθ is approximately equal to θ in radians because the angle is very small.From the equation given above, we know that
δ = (2π/λ)dsinθ
We have the values as
λ = 570−nm
= 570 x 10⁻⁹ m.
θ = (2.50 mm/2.60 m)
= 2.50 x 10⁻³ m.
From the above equation, we can get the value ofδ = 1.31 radians.The intensity at a distance x from the center of the central bright fringe is given by:
I = I_max cos²πd sinθ/λ
Where d is the separation of the slits and I_max is the intensity of the bright fringe at the center.
From the equation given above, we know thatI = I_max cos²πd sinθ/λ We have the values as
d = 0.850 mm
= 0.850 x 10⁻³ m,
λ = 570−nm
= 570 x 10⁻⁹ m and
θ = (2.50 mm/2.60 m)
= 2.50 x 10⁻³ m.
On substituting the values in the equation, we get,I/I_max = 0.526.
Therefore, I_max/I = 1.90 or
I = 1.90 I_max.
Therefore,The phase difference between the two interfering waves on a screen at a point 2.50 mm from the central bright fringe is 1.31 radians.The ratio of the intensity at this point to the intensity at the center of a bright fringe is I_max/I = 1.90 or
I = 1.90 I_max.
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