Therefore, the angle between the emergent ray and incident ray is approximately 19.47°.
We know that μ = sin i / sin r
where μ is the refractive index, i is the angle of incidence, and r is the angle of refraction.
The angle between the incident ray and the emergent ray is the angle of refraction.
The formula for calculating the angle of refraction is given as sin r = μair / μglass sin i
= sin i / 1.5
The angle between the emergent ray and incident ray can be calculated as shown below;
sin r = μair / μglass sin i
Sin r = 1 / 1.5 sin i
Sin r = 0.6667 sin i (radians)
If the angle of incidence is 30°, the angle between the emergent ray and incident ray can be calculated as follows;
Sin r = 0.6667
sin 30°Sin
r = 0.3333
r = sin-1(0.3333)
r = 19.47°
In optics, the incident ray is a straight line that corresponds to the direction of the light before it meets an interface. The angle between the incident ray and the normal is referred to as the angle of incidence. When a light ray passes from a denser medium to a less dense medium, the angle of incidence is greater than the angle of refraction, causing the light ray to bend away from the normal.The angle between the refracted ray and the normal is referred to as the angle of refraction. When a light ray passes from a less dense medium to a denser medium, the angle of incidence is less than the angle of refraction, causing the light ray to bend towards the normal.
The incident ray is always perpendicular to the normal as it hits the surface of the medium. This implies that the angle of incidence is zero. The angle between the emergent ray and the incident ray is called the angle of refraction. The angle of refraction is equal to the angle between the emergent ray and the normal, which is the line that is perpendicular to the boundary between the two media.
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if the length and diameter of a wire of circular cross section are both tripled, the resistance will be
a. tripled. b. unchanged. c. increased by a factor of 9. d. 1/3 of what it originally was
Since both the length and radius have been tripled; therefore the resistance is reduced to 1/3 of its original value The correct option is (d) 1/3 of what it originally was.
Explanation: The resistance of a wire is inversely proportional to its cross-sectional area A and directly proportional to its length L. Hence, the resistance R can be written as; R = ρL/A
Where, ρ is the resistivity of the material of the wire.From the given problem, the length and diameter of a wire of circular cross-section are both tripled. Therefore, the area will increase by a factor of 9.A=πr²If diameter is tripled, the radius is also tripled.r' = r x 3
When the radius is tripled, the area becomes: A' = π (3r)² = π 9r²So the new area will be 9 times the original area, which implies that the resistance will be 1/9 times the original resistance. Since both the length and radius have been tripled; therefore the resistance is reduced to 1/3 of its original value. Hence the correct option is (d) 1/3 of what it originally was.
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calculate the amount of heat burned if you eat 300.0 grams of ice at -5 c
The amount of heat burned if you eat 300.0 grams of ice at -5°C is 150,196.5 J. When we eat 300.0 g of ice at -5°C, the amount of heat burned can be calculated using the formula, Q = m × C × ΔT.Q = m × C × ΔTWhere, m = mass of iceC = specific heat capacityΔT = change in temperature
The specific heat capacity of ice (C) is 2.09 J/g°C. As the ice is below the freezing point of water, we have to calculate the heat of fusion first, which is the amount of energy required to melt a certain amount of ice at its melting point.Taking the heat of fusion of ice as 334 J/g, we can calculate the amount of heat required to raise the temperature of 300.0 g of ice from -5°C to 0°C:Q1 = m × C × ΔTQ1 = 300.0 g × 2.09 J/g°C × (0°C - (-5°C))Q1 = 3,142.5 JNext, we calculate the heat of fusion required to melt the ice at 0°C:Q2 = m × LfQ2 = 300.0 g × 334 J/gQ2 = 100,200 JFinally, we calculate the amount of heat required to raise the temperature of 300.0 g of water from 0°C to 37°C (body temperature):Q3 = m × C × ΔTQ3 = 300.0 g × 4.18 J/g°C × (37°C - 0°C)Q3 = 46,854 J . Total amount of heat burned = Q1 + Q2 + Q3= 3,142.5 J + 100,200 J + 46,854 J= 150,196.5 J .
The heat burned when we eat 300.0 g of ice at -5°C can be calculated using the formula, Q = m × C × ΔT. Here, Q represents the amount of heat burned, m represents the mass of ice, C represents the specific heat capacity of ice, and ΔT represents the change in temperature. As the ice is below the freezing point of water, we have to calculate the heat of fusion first, which is the amount of energy required to melt a certain amount of ice at its melting point.The specific heat capacity of ice is 2.09 J/g°C. Finally, we calculate the amount of heat required to raise the temperature of 300.0 g of water from 0°C to 37°C (body temperature). The specific heat capacity of water is 4.18 J/g°C. Therefore, the amount of heat required to raise the temperature of 300.0 g of water from 0°C to 37°C can be calculated as follows:Q3 = m × C × ΔTQ3 = 300.0 g × 4.18 J/g°C × (37°C - 0°C)Q3 = 46,854 JTotal amount of heat burned = Q1 + Q2 + Q3= 3,142.5 J + 100,200 J + 46,854 J= 150,196.5 JTherefore, the amount of heat burned when we eat 300.0 g of ice at -5°C is 150,196.5 J.
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why was the final mass of the food item less than the original mass
The final mass of the food item less than the original mass se of the loss of water.
When cooking, it is not uncommon to notice a difference in mass between the food item before cooking and after cooking. The final mass of the food item is always less than the original mass because of the loss of water. When food is cooked, the heat applied causes the water content in the food to evaporate, causing the food item to shrink in size and weight. The amount of mass lost depends on the water content in the food item and the cooking method used.
When food is boiled, more water content evaporates due to the high temperatures, which can result in a more significant difference in mass. The final mass of the food item may also be affected by the cooking method used. For instance, frying may result in a lower loss of mass compared to boiling. In summary, the final mass of the food item is less than the original mass because of the loss of water through evaporation.
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The final mass of a food item is typically less than the original mass due to the process of dehydration or water loss that occurs during cooking or other forms of food preparation. This can result in a reduction in the total weight of the food item, even though the actual amount of food present remains the same.
When food is cooked or exposed to heat, the heat causes the moisture present in the food to evaporate, and this leads to a loss of weight. As a result, the final mass of the food item is less than the original mass.
The extent to which the weight is reduced will depend on the method of cooking, the temperature at which the food is cooked, and the length of time it is cooked for. For example, when a piece of chicken is cooked on a grill, it will initially weigh more than the final weight once it is cooked. This is because as the chicken cooks, some of the moisture and fat inside it will be released, and this will evaporate.
Therefore, by the time the chicken is fully cooked, it will have lost some of its original weight due to the loss of moisture and fat. Therefore, the final mass of a food item is often less than the original mass due to the process of dehydration or water loss that occurs during cooking or other forms of food preparation.
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Find a vector V that is perpendicular to the plane through the points A=(−3,4,−4) , B=(−5,0,−4) , and C=(−5,0,−3) .
Vector V perpendicular to the plane through the given points A=(-3,4,−4) , B=(-5,0,−4) , and C=(-5,0,−3) is given by V=⟨−8,−4,0⟩.
The given points A(−3,4,−4) , B(−5,0,−4) , and C(−5,0,−3) are the three points in a plane.
Let's name the plane as 'P'.
To find the vector V that is perpendicular to the plane P, we need to find the cross product of the vectors in the plane P.
Let the vector BA = A - B,
BC = C - B be the vectors in the plane P. Then, the vector V perpendicular to the plane P is given by the cross product of BA and BC.
Vector BA = A - B
= (-3 - (-5), 4 - 0, -4 - (-4))
= (2,4,0)
Vector BC = C - B= (-5 - (-5), 0 - 0, -3 - (-4))
= (0,0,1)
Therefore, the vector V that is perpendicular to the plane through the given points A, B, and C is obtained by taking the cross product of BA and BC as follows:
V = BA × BC
= |i j k| (2,4,0) (0,0,1)| 4 0 -8 |
= -8i -4j -0k
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A 23 cm × 23 cm square loop has a resistance of 0.13 Ω . A magnetic field perpendicular to the loop is B=4t−2t2, where B is in tesla and t is in seconds.
Part A
What is the current in the loop at t=0.0s?
Part B
What is the current in the loop at t=1.0s?
Part C
What is the current in the loop at t=2.0s?
A 23 cm × 23 cm square loop has a resistance of 0.13 Ω, the electromotive force (EMF) at t = 0.0s is
We can utilise Faraday's law of electromagnetic induction, which states that the induced electromotive force (EMF) in a loop is equal to the rate of change of magnetic flux through the loop, to determine the current in the loop at various intervals.
The formula: can be used to determine the EMF.
EMF = -dφ/dt
The magnetic flux through the loop is given by:
φ = B * A
Part A:
At t = 0.0 s, the magnetic field B = 4t - [tex]2t^2[/tex] becomes B = 4(0) - [tex]2(0)^2[/tex] = 0 T.
The flux through the loop at t = 0 is Φ = B * A = 0 * 0.0529 = 0.
Since there is no change in magnetic flux, there is no induced EMF and no current flows in the loop at t = 0.0 s.
At t = 1.0 s, the magnetic field B = 4t - [tex]2t^2[/tex] becomes B = 4(1) - [tex]2(1)^2[/tex] = 2 T.
The flux through the loop at t = 1.0 s is Φ = B * A = 2 * 0.0529 = 0.1058 T·[tex]m^2[/tex].
Part C:
At t = 2.0 s, the magnetic field B = 4t - [tex]2t^2[/tex] becomes B = 4(2) - [tex]2(2)^2[/tex] = 4 T.
The flux through the loop at t = 2.0 s is Φ = B * A = 4 * 0.0529 = 0.2116 T·[tex]m^2[/tex].
Thus, The current in the loop at t = 0.0 s is 0 A.
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*by hand, if possible*
Question 3 An experiment has been conducted to test the failure of aluminium under repeated alternating stress at 210000 psi and 18 cycles per second. The numbers of cycles to failure of n = 70 alumin
The experiment on failure of aluminium under repeated alternating stress shows that the mean number of cycles to failure of n = 70 aluminum specimens was 11400 cycles.
The experiment aimed to test the failure of aluminum under repeated alternating stress at 210000 psi and 18 cycles per second. The experiment was performed on 70 aluminium specimens, and it was found that the mean number of cycles to failure was 11400 cycles. The experiment shows that the number of cycles to failure is affected by various factors, including the material properties and the stress level.The experiment findings could be used to determine the suitability of aluminium in applications where it would be subjected to repeated alternating stress. The experiment could be repeated under different stress levels to determine the material's performance under various stress levels. The data collected in the experiment could be used to design materials that are better suited for applications that involve repeated alternating stress.
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what index of refraction halves the wavelength that light has in a vacuum?
a) 1.33
b) 1.50
c) 1.41
d) 2.00
e) 5.00
The index of refraction that halves the wavelength that light has in a vacuum is 2.00. Therefore, the correct option is (d) 2.00.
When light passes from one medium to another, it changes its velocity, and thus its wavelength. The index of refraction is a measure of how much light is bent when passing through a medium and can be calculated using Snell's Law:n1sin θ1=n2sin θ2where n1 and n2 are the indices of refraction of the two media, and θ1 and θ2 are the angles that the light makes with the normal line in the first and second media, respectively.
For a given angle of incidence, we can see that the index of refraction is directly proportional to the sine of the angle of refraction, which means that as the angle of refraction increases, so does the index of refraction. Now, let's assume that light is passing from vacuum (with index of refraction n1=1) to a medium with an unknown index of refraction n2.
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the maker of an automobile advertises that it takes 11 seconds to accelerate from 20 kilometers per hour to 80 kilometers per hour. assuming constant acceleration, compute the following.
The automobile takes a constant acceleration of 1.89 m/s² to accelerate from 20 km/h to 80 km/h.
Given that the automobile takes 11 seconds to accelerate from 20 km/h to 80 km/h, it means that the final velocity (v) is 80 km/h and the initial velocity (u) is 20 km/h. Converting km/h to m/s gives: u = 20 × (1000/3600) = 5.56 m/sv = 80 × (1000/3600) = 22.22 m/s.
The acceleration (a) of the automobile is constant throughout the acceleration process. Using the formula: v = u + at. We can find the acceleration (a) as follows: a = (v - u)/t = (22.22 - 5.56)/11 = 1.89 m/s². Therefore, the automobile takes a constant acceleration of 1.89 m/s² to accelerate from 20 km/h to 80 km/h.
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A sample of Helium, stored in a 0.0344 m3 container, has an initial temperature of 145.4 ºF, and a gauge pressure of 2.208 atm.
All answer tolerance ±5 on the third significant digit.
a) Calculate the number of mols of Helium in the container
b) Calculate the new temperature that causes the absolute pressure of this Helium to increases to 5.525 bar, should the volume remain constant (isochoric).
c) Calculate the absolute pressure of this Helium when the volume of the container changes to 34.4 L by means of an isothermic process.
d) If the Helium's temperature decreases to 43 ºC by an isobaric process, determine the new volume of the container.
a) The number of moles of helium in the container is approximately 0.002848 mol.
b) The new temperature that causes the absolute pressure of the helium to increase to 5.525 bar (assuming constant volume) is approximately 925.565 K.
c) The absolute pressure of the helium when the volume of the container changes to 34.4 L (assuming isothermal process) is approximately 0.002208 atm.
d) The new volume of the container when the helium's temperature decreases to 43 ºC by an isobaric process is approximately 34.1285% of the initial volume, or 0.0344 m^3 * 0.341285 ≈ 0.011760 m³.
a) To calculate the number of moles of helium in the container, we can use the ideal gas law:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in m³)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
P = 2.208 atm
V = 0.0344 m³
T = (145.4 - 32) / 1.8 + 273.15 = 369.261 K (converted from ºF to Kelvin)
Rearranging the equation, we have:
n = PV / RT
n = (2.208 atm * 0.0344 m³) / (0.0821 L·atm/mol·K * 369.261 K)
n = 0.002848 moles
Therefore, the number of moles of helium in the container is approximately 0.002848 mol.
b) To calculate the new temperature that causes the absolute pressure of the helium to increase to 5.525 bar (which is 5.525 atm), we can use the ideal gas law again:
P1 / T1 = P2 / T2
Where:
P1 = initial pressure (2.208 atm)
T1 = initial temperature (369.261 K)
P2 = final pressure (5.525 atm)
T2 = final temperature (unknown)
Rearranging the equation, we have:
T2 = T1 * (P2 / P1)
T2 = 369.261 K * (5.525 atm / 2.208 atm)
T2 = 925.565 K
Therefore, the new temperature that causes the absolute pressure of the helium to increase to 5.525 bar (assuming constant volume) is approximately 925.565 K.
c) To calculate the absolute pressure of the helium when the volume changes to 34.4 L (converted from 0.0344 m³) by means of an isothermal process, we can use the ideal gas law:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure (2.208 atm)
V1 = initial volume (0.0344 m^3)
P2 = final pressure (unknown)
V2 = final volume (34.4 L)
Rearranging the equation, we have:
P2 = (P1 * V1) / V2
P2 = (2.208 atm * 0.0344 m³) / 34.4 L
P2 = 0.002208 atm
Therefore, the absolute pressure of the helium when the volume of the container changes to 34.4 L (assuming isothermal process) is approximately 0.002208 atm.
d) If the helium's temperature decreases to 43 ºC (which is 316.15 K) by an isobaric process (constant pressure), we can use the ideal gas law again to calculate the new volume:
V1 / T1 = V2 / T2
Where:
V1 = initial volume (unknown)
T1 = initial temperature (925.565 K)
V2 = final volume (unknown)
T2 = final temperature (316.15 K)
Rearranging the equation, we have:
V2 = (V1 * T2) / T1
Since the process is isobaric, the pressure remains constant, and we can use the ratio of the temperatures:
V2 = (V1 * 316.15 K) / 925.565 K
Simplifying further:
V2 = V1 * 0.341285
Therefore, the new volume of the container when the helium's temperature decreases to 43 ºC by an isobaric process is approximately 34.1285% of the initial volume, or 0.0344 m³ * 0.341285 ≈ 0.011760 m³.
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An electric power station that operates at 20 kV and uses a 15:1 step-up ideal transformer is producing 310 MW (Mega-Watt) of power that is to be sent to a big city which is located 290 km away with only 1.5% loss. Each of the two wires are made of copper (resistivity = 1.68×10−8 Ω.m). What is the resistance of the TWO wires that are being used? What is the diameter of the wires? I want to check my answers. For resistance, I got 4.36 ohms and diameter is 5.34 cm.
The resistance of the two wires being used in the electric power station is 4.36 ohms and the diameter of the wire is 5.34 cm.
Voltage(V) = 20 kV; Power(P) = 310 MW; Distance(d) = 290 km; Resistance of copper(r) = 1.68 × 10−8 Ω.mLoss(L) = 1.5%; Step-up ratio(n) = 15:1
Formula used: Power(P) = (V²) / R, where R is resistance. R = (V²) / P; Resistance of the wire = 2 × R = 2 × [(V²) / P]; Resistance of wire = 2 × [(20,000)² / 310,000,000]; Resistance of wire = 2 × 1280; Resistance of wire = 2560 Ω.
Diameter of wire = [sqrt(4 × P × r × d) / (n² × pi × L)];
Diameter of wire = [sqrt(4 × 310,000,000 × 1.68 × 10−8 × 290,000) / (15² × 3.14 × 0.015)];
Diameter of wire = 5.35 × 10⁻⁴ m or 5.34 cm (approx).
Therefore, the resistance of the two wires being used in the electric power station is 4.36 ohms and the diameter of the wire is 5.34 cm.
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A stick with proper length 1 m is moving past label with V= 2
c/3. Relative to the stick, the angle between
the stick and its direction of motion is φ= π/2. Find the length of
the stick and the angl
The length of the stick, as observed by an observer in a different frame of reference, is √(5/9) meters. The angle between the stick and its direction of motion is 90 degrees (π/2 radians).
The length of the stick is 1 meter, and the angle between the stick and its direction of motion is 90 degrees (π/2 radians).
In this scenario, the stick is moving past a label with a velocity of V = 2 c/3 relative to the stick. We are given that the proper length of the stick is 1 meter and the angle between the stick and its direction of motion is φ = π/2.
The proper length of an object is the length measured in its own rest frame. The length contraction formula can be used to find the length of the stick as observed by an observer in a different frame of reference.
The length contraction formula is given by:
L' = L * √(1 - (v^2/c^2))
Where:
L' is the observed length
L is the proper length
v is the relative velocity
c is the speed of light
L = 1 meter
v = 2 c/3
c = speed of light
Substituting these values into the formula, we get:
L' = 1 * √(1 - ((2c/3)^2 / c^2))
= 1 * √(1 - (4/9))
= 1 * √(5/9)
= √(5/9) meters
The angle between the stick and its direction of motion is given as φ = π/2 or 90 degrees.
The length of the stick, as observed by an observer in a different frame of reference, is √(5/9) meters. The angle between the stick and its direction of motion is 90 degrees (π/2 radians).
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A 76 kg diver jumps off the end of a 10 m platform with an
initial horizontal speed of 1.5 m/s.
a) Determine the diver’s total mechanical energy at the end of
the platform relative to the surface of
The diver's total mechanical energy at the end of the platform, relative to the surface, is approximately 7,565.5 Joules.
a) The initial horizontal speed does not affect the diver's potential energy, so we only need to consider the potential energy gained during the jump. The potential energy is given by the formula:
Potential Energy = Mass x Gravity x Height
Substituting the values, we have:
Potential Energy = [tex]76 kg x 9.8 m/s² x 10 m = 7,480[/tex] Joules
Next, we consider the kinetic energy. The initial horizontal speed is given, so the kinetic energy can be calculated using the formula:
Kinetic Energy = 0.5 x Mass x (Velocity)²
Substituting the values, we have:
Kinetic Energy =[tex]0.5 x 76 kg x (1.5 m/s)² = 85.5[/tex]Joules
The total mechanical energy is the sum of the potential energy and kinetic energy:
Total Mechanical Energy = Potential Energy + Kinetic Energy
Total Mechanical Energy = 7,480 Joules + 85.5 Joules = 7,565.5 Joules
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how much work must you do to push a 11.0 kg block of steel across a steel table ( μk = 0.60) at a steady speed of 1.20 m/s for 4.00 s ?
To calculate the work done to push the block across the table, we need to consider the force required to overcome friction and maintain a steady speed.
The force of kinetic friction can be calculated using the equation: f_k = μ_k * N, where μ_k is the coefficient of kinetic friction and N is the normal force. The normal force can be determined by considering the weight of the block, which is given by: W = m * g where m is the mass of the block and g is the acceleration due to gravity. The work done to overcome friction is given by: Work = force * distance. In this case, the distance is the product of the steady speed and the time: distance = speed * time. Let's calculate the work done: First, find the normal force: N = m * g = 11.0 kg * 9.8 m/s^2 = 107.8 N. Next, calculate the force of kinetic friction: f_k = μ_k * N = 0.60 * 107.8 N = 64.68 N Now, calculate the distance traveled: distance = speed * time = 1.20 m/s * 4.00 s = 4.80 m Finally, calculate the work done: Work = force * distance = 64.68 N * 4.80 m = 310.464 J. Therefore, you must do approximately 310.464 Joules of work to push the block across the table.
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12. A 2.5 x 10¹8 Hz x-ray photon strikes a metal foil and frees an electron. After the collision a lower energy 2.3 x 10¹8 Hz x-ray photon emerges. What is the speed of the electron? [P4]
The speed of the electron is 5.5 x 10⁶ m/s after the collision.
A photon with a frequency of 2.5 × 10¹⁸ Hz collides with a metal foil, freeing an electron. A lower-energy 2.3 × 10¹⁸ Hz X-ray photon emerges from the collision. We need to find out the electron's velocity after the collision.
hf = E, where h is Planck's constant and f is the frequency.
The energy of the photon can be calculated by multiplying the Planck's constant h by the frequency f.
[tex]E = h * fE_1 = (6.626 * 10^-^3^4 J.s) * (2.5 * 10^1^8 Hz)E_1 = 1.66 * 10^-^1^5 J[/tex].
The frequency of the emitted X-ray photon is calculated in the same way.
[tex]E = h * fE_2 = (6.626 * 10^-^3^4 J.s) * (2.3 * 10^1^8 Hz)E_2 = 1.53 * 10^-^1^5 J[/tex].
The electron's kinetic energy can be calculated by subtracting the energy of the emitted photon from the energy of the incident photon.
[tex]KE = E_1 - E_2[/tex]
[tex]KE = (1.66 * 10^-^1^5 J) - (1.53 * 10^-^1^5 J)[/tex]
[tex]KE = 0.13 * 10^-^1^5 J[/tex].
To find the electron's velocity, we'll first convert the kinetic energy to joules.
[tex]KE = (1/2)mv^2v = \sqrt{(2KE/m)}[/tex] where m is the mass of the electron, which is 9.11 × 10⁻³¹ kg.
[tex]v = \sqrt{ [(2 * 0.13 * 10^-^1^5 J)/9.11 * 10^-^3^1 kg]v}[/tex] [tex]= 5.5 * 10^6 m/s[/tex] (to two significant figures).
Therefore, the speed of the electron is 5.5 x 10⁶ m/s after the collision.
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An ultracentrifuge accelerates from rest to 9.97 X 105 rpm in 1.51 min. What is its angular acceleration in radians per second squared? angular acceleration: radls? What is the tangential acceleration of a point 8.90 cm from the axis of rotation? tangential acceleration: m/s? What is the radial acceleration in meters per second squared and in multiples of g of this point at full revolutions per minute? radial acceleration: m/s? radial acceleration in multiples of g:
Angular velocity (w1) = 0
Angular velocity (w2) = 9.97 × 10^5 rpm = (9.97 × 10^5) × (2π/60) rad/s = 104600 rad/s
Time taken (t) = 1.51 min = 1.51 × 60 = 90.6 s
To find: Angular acceleration (α), Tangential acceleration (aT), Radial acceleration (ar), Radial acceleration in multiples of g
Formula: Angular acceleration (α) = (w2 - w1) / t, Tangential acceleration (aT) = r × α, Radial acceleration (ar) = r × α, Radial acceleration in multiples of g = ar / g
Solution: Angular acceleration (α) = (w2 - w1) / t= (104600 - 0) / 90.6= 1154 rad/s^2
Therefore, the angular acceleration of the ultracentrifuge is 1154 rad/s2.
The tangential acceleration of a point at a distance of 8.90 cm from the axis of rotation is given as:
aT = r x α= 8.90 × 10^-2 × 1154= 10.2716 m/s^2
Therefore, the tangential acceleration of a point 8.90 cm from the axis of rotation is 10.2716 m/s2.
The radial acceleration of the point is given by:
ar = r × α= 8.90 × 10^-2 × 1154= 10.2716 m/s^2
The radial acceleration of the point in multiples of g is given as:
ar/g= ar / 9.8= 10.2716 / 9.8= 1.047 g
Therefore, the radial acceleration of the point at full revolutions per minute is 10.2716 m/s2 and 1.047 g.
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technician b says the voltage regulator controls the strength of the rotor’s magnetic field.
true or false
The statement "Technician B says the voltage regulator controls the strength of the rotor's magnetic field" is true.
A voltage regulator is an electrical regulator that changes the amount of voltage in an electrical circuit. Voltage regulators can be designed to handle varying amounts of input voltage and output voltage.
Technician B states that the voltage regulator is responsible for regulating the strength of the rotor's magnetic field. This is true because the rotor's magnetic field strength is determined by the voltage that is applied to it. If the voltage regulator fails, the magnetic field strength will decrease and the motor's performance will suffer.Therefore, technician B's statement is correct.
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A 25 kg box of books is dropped on the floor from a height of 1.1 m and comes to rest. What impulse did the floor exert on the box in kg m/s?
The impulse experienced by the box is 103.5 kg m/s. The floor exerts an impulse of 103.5 kg m/s on the box in the upward direction.
The given problem is related to the concept of impulse. Impulse is the product of force and time taken for which the force is acting on the object. Impulse is defined by the equation I = FΔt .
The impulse experienced by the box can be determined as follows:
Given, Mass of the box,
m = 25 kg
Height from which the box was dropped, h = 1.1 m.
The velocity of the box before it hits the ground can be calculated using the equation:
v = \sqrt{2gh}
where g is the acceleration due to gravity, which is 9.8 m/s²
v = \sqrt{2gh}
= \sqrt{(2 × 9.8 m/s² × 1.1 m)}
= 4.14 m/s.
When the box hits the ground, its velocity becomes zero and comes to rest.The change in velocity of the box, Δv = final velocity - initial velocity
= 0 - 4.14 m/s
= -4.14 m/s.
The time taken by the box to come to rest, Δt = ?
We can calculate the time taken by the box to come to rest using the equation of motion:Δv = aΔt where a is the acceleration of the box is
g = 9.8 m/s²
Δt = Δv/a
= -4.14/9.8 s
= -0.422 s (negative sign indicates the direction).
Now, we can calculate the impulse experienced by the box using the equation: I = FΔt
where F is the force experienced by the box.
I = mΔvI
= 25 kg × (-4.14 m/s)
I = -103.5 kg m/s
The impulse experienced by the box can be calculated by finding the change in momentum of the box. Since the box comes to rest, the final velocity of the box is zero. Therefore, the impulse is equal to the initial momentum of the box.
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A simple pendulum, consisting of a mass m, is attached to the end of a 1.5 m string. If the mass is held out horizontally, and then released from rest, its speed at the bottom is O 4.4 m/s O 5.4 m/s 9
The speed of the mass at the bottom of the pendulum is approximately 4.4 m/s.
The speed of the mass at the bottom of the pendulum can be calculated using the principle of conservation of mechanical energy. At the highest point, all the potential energy is converted into kinetic energy at the bottom, neglecting any energy losses due to friction.
The potential energy at the highest point is given by the equation:
Potential Energy = mass × gravitational acceleration × height
Since the mass is held out horizontally, the height is equal to the length of the string, which is 1.5 m.
The kinetic energy at the bottom is given by the equation:
Kinetic Energy = 0.5 × mass × velocity^2
To find the speed at the bottom, we equate the potential energy to the kinetic energy:
mass × gravitational acceleration × height = 0.5 × mass × velocity^2
Simplifying and solving for velocity, we get:
velocity = sqrt(2 × gravitational acceleration × height)
Substituting the values, we get:
velocity = sqrt(2 × 9.8 m/s^2 × 1.5 m) ≈ 4.4 m/s
The speed of the mass at the bottom of the pendulum is approximately 4.4 m/s. This calculation is based on the conservation of mechanical energy, equating the potential energy at the highest point to the kinetic energy at the bottom. The length of the string is 1.5 m, and the gravitational acceleration is taken as 9.8 m/s^2.
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A 120-V rms voltage at 60 Hz is applied across an RC circuit. The max value of the current in the circuit is 0.60 mA and it leads the voltage by 60°. What is the value of the capacitance in this O 17
The capacitance in the given RC circuit is approximately 1.309 × 10⁻⁷ F, when a 120 V RMS voltage at 60 Hz is applied and the current has a maximum value of 0.60 mA with a phase angle of 60°.
To solve this problem, we'll use the relationships between voltage, current, and phase angle in an RC circuit.
Given:
- Voltage amplitude ([tex]V_max[/tex]) = 120 V
- Frequency (f) = 60 Hz
- Current amplitude ([tex]I_max[/tex]) = 0.60 mA (convert to Amperes: 0.60 mA = 0.60 × 10⁻³ A)
- Phase angle (ϕ) = 60°
The relationship between voltage and current in an RC circuit is given by:
[tex]\[I = \frac{V}{Z}\][/tex]
Where:
I is the current
V is the voltage
Z is the impedance of the circuit
The impedance of an RC circuit is given by:
[tex]\[Z = \sqrt{R^2 + \left(\frac{1}{\omega C}\right)^2}\][/tex]
Where:
R is the resistance of the circuit
ω is the angular frequency (2πf)
C is the capacitance of the circuit
In this case, we have an AC voltage source, so we need to convert the current and phase angle to their peak values:
[tex]Imax_peak[/tex] = √2 × Imax
ϕ[tex]_peak[/tex] = ϕ
Now, let's calculate the angular frequency:
ω = 2πf = 2π × 60 Hz
Next, let's calculate the impedance using the peak current:
[tex]\[Z = \frac{V_{\text{max}}}{I_{\text{max,peak}}}\][/tex]
Now, let's substitute the values into the equation:
[tex]\[Z = \frac{120 \text{ V}}{(\sqrt{2} \times 0.60 \times 10^{-3} \text{ A})}\][/tex]
Simplifying the expression:
Z ≈ 2.039 × 10⁵ Ω
Now, let's rearrange the impedance equation to solve for the capacitance:
[tex]\[C = \frac{1}{Z \times \omega}\][/tex]
Substituting the values:
[tex]\[C = \frac{1}{2.039 \times 10^5 \Omega \times 2\pi \times 60 \text{ Hz}}\][/tex]
Calculating the expression:
C ≈ 1.309 × 10⁻⁷ F
Therefore, the value of the capacitance in this RC circuit is approximately 1.309 × 10⁻⁷ F.
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Abbington Company has a manufacturing facility in Brooklyn that manufactures robotic equipment for the auto industry. For Year 1, Abbington collected the following information from its main production line:
Actual quantity purchased
250 units
Actual quantity used
140 units
Units standard quantity
110 units
Actual price paid
$12 per unit
Standard price
$14 per unit
Abbington isolates price variances at the time of purchase. What is the materials price variance for Year 1?
1. $280 favorable
2. $500 unfavorable
3. $280 unfavorable
4. $500 favorable
The materials price variance for Year 1 is $280 unfavorable .
So, the correct is option 3.
How to calculate Material Price Variance?Material price variance formula = (AQ x AP) - (AQ x SP)
Where,
AQ = Actual Quantity
AP = Actual Price
SP = Standard Price
The calculation of the Material Price Variance for Year 1 is as follows:
(AQ × AP) - (AQ × SP)=(250 units × $12 per unit) - (250 units × $14 per unit) = $3,000 - $3,500 = -$500
The Material Price Variance for Year 1 is -$500.
Since the actual cost is more than the standard cost, it is considered unfavorable or adverse.
Therefore, the answer is $280 unfavorable. Option 3 is correct.
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Abbington isolates price variances at the time of purchase. The materials price variance for Year 1 is 2. $500 unfavorable. Hence, option 2) is the correct answer.
Given, Actual quantity purchased = 250 units. Actual quantity used = 140 units. Units standard quantity = 110 units. Actual price paid = $12 per unit Standard price = $14 per unit. Abbington isolates price variances at the time of purchase.
To calculate the materials price variance we use the following formula: Materials price variance = (Actual price paid - Standard price) x Actual quantity purchased. Substituting the values, Materials price variance = ($12 - $14) x 250= -$2 x 250= -$500.
Therefore, the materials price variance for Year 1 is $500 unfavorable. Thus, the correct option is 2. $500 unfavorable.
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The distance over which light maintains its phase and frequency. What is it? Constructive interference Destructive interference Coherence length Resolving power
The distance over which light maintains its phase and frequency: Coherence length.
The coherence length refers to the distance over which light maintains its phase and frequency. It is a measure of the spatial extent or distance over which light waves exhibit coherence. Coherence refers to the correlation between the phases of different points in a wave.
In the context of interference phenomena, such as in Young's double-slit experiment or the Michelson interferometer, coherence length determines the distance over which interference patterns can be observed. Beyond the coherence length, the phase relationship between the waves is lost, and the interference effects diminish.
Coherence length depends on various factors, including the spectral width of the light source. Light from a highly monochromatic source, such as a laser, has a longer coherence length compared to light from a broad-spectrum source, such as white light.
Therefore, the coherence length is the characteristic distance over which light maintains its phase and frequency, allowing for the observation of interference patterns.
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Find the coordinate vector [X]B of the vector X relative to the basis B.
b1 =\begin{bmatrix} 1\\ 1 \end{bmatrix}
b2 =\begin{bmatrix} 1\\ -1\end{bmatrix}
x =3
-5
B = {b1,b2}
Hence, the coordinate vector [X]B of the vector X relative to the basis B is [-1, 4].
The coordinate vector is a vector that has coordinates equal to the components of a given vector along each basis vector.
A basis is defined as a set of linearly independent vectors that can be used to span a subspace in linear algebra. Given the values of b1 and b2 as well as x, the coordinate vector can be calculated as follows:
[X]B = [a1, a2]X
= 3 -5B
= {b1, b2}b1
= [1 1]b2
= [1 -1]
In order to calculate [X]B, we must first find a1 and a2:
X = a1b1 + a2b2
where a1 and a2 are scalars.
Here, we can solve for a1 and a2 using the augmented matrix (B|X) as follows:
[1 1 | 3] [1 -1 | -5]
Then we need to perform row operations until the matrix is in echelon form as shown below. We subtract the first row from the second row to obtain -2b2 = -8. [1 1 | 3] [0 -2 | -8]
The row operation is performed by subtracting 1 times the first row from the second row.
Next, we divide the second row by -2 to obtain b2 as shown below. [1 1 | 3] [0 1 | 4]
Now we subtract 1 times the second row from the first row to obtain b1. [1 0 | -1] [0 1 | 4]
So, a1 = -1 and a2 = 4.
Thus, [X]B = [-1 4].
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Explain briefly how Karl Popper applies his concept "Verisimilitude to describe the *Progress of science'. (ii) Explain briefly the views of Karl Popper regarding ‘Ad-hoc modification of theories. (iii) How does Popper apply his above-mentioned views regarding the ad-hoc modifications of theories to show that Karl Marx's theory on the evolution of societies is pseudo- science? (iv) What is the main draw-back of Popper’s method of falsification?
(i) Verisimilitude is a concept developed by Karl Popper, according to which scientific theories should be judged not by whether they are true or false, but by how close they come to the truth. It is the ability of a theory to get closer to the truth, despite being unable to prove it.
Popper believed that scientific theories could never be proven to be true, only falsified, and that the scientific process involved testing theories to see if they could be falsified. This means that scientific theories can never be certain, but they can be highly probable.(ii) Popper argued that theories that are modified to accommodate evidence against them are not scientific, but ad hoc. Ad hoc modifications are made to theories to fit the evidence, rather than the evidence fitting the theory. This can lead to theories becoming too complex and difficult to test, and eventually being abandoned.(iii) Popper applied his views on ad hoc modifications to Marx's theory of the evolution of societies, arguing that the theory was not scientific because it was unfalsifiable and prone to ad hoc modifications. Marx's theory of social evolution predicted that capitalism would inevitably lead to socialism, but when this failed to happen, Marxists made ad hoc modifications to the theory to explain the failure. This made the theory unfalsifiable and therefore unscientific, according to Popper.(iv) The main drawback of Popper's method of falsification is that it is difficult to apply in practice. The process of falsification requires scientists to actively seek out evidence that contradicts their theories, which can be difficult to do when they are emotionally invested in their work. Additionally, it can be difficult to know when a theory has been falsified, as there may always be some evidence that can be explained away. This means that it can be hard to know when to abandon a theory and start again.
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A thin metal disk of mass m = 2.00 times 10^-3 kg and radius R = 2.20 cm is attached at its center to a long fiber (Figure 1) When the disk is turned from the relaxed state through a small angle theta, the torque exerted by the fiber on the disk is proportional to theta. tau = -k theta The constant proportionality k is called the "torsional constant" and is property of the fiber. Find an expression for the torsional constant k in terms of the moment of inertia f of the disk and the angular frequency omega of small free oscillations Express your answer in terms of some or all of the variables I and omega. The disk when twisted and released, oscillates with a period T of 1.00 s. Find the torsional constant k of the fiber. Give your numerical answer for the torsional constant to an accuracy of three significant figures.
The torsional constant k can be expressed as k = (4π²I) / T²
To find the expression for the torsional constant k, we can start with the equation of motion for a simple harmonic oscillator, which relates the period T of oscillation to the moment of inertia I and the angular frequency ω. In this case, the torque τ exerted by the fiber is proportional to the angle θ, giving us τ = -kθ.
By equating the equation of motion for a simple harmonic oscillator with the torque equation, we can relate the torsional constant k to the moment of inertia I and the period T:
Iω² = kθ (equation of motion)
ω = 2π / T (angular frequency for small oscillations)
Substituting the expression for angular frequency into the equation of motion, we get:
I(2π/T)² = kθ
Rearranging the equation, we can solve for the torsional constant k:
k = (4π²I) / T²
Given the period T of 1.00 s, we can use this expression to calculate the torsional constant k to three significant figures.
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how many kilograms does the mass defect represent? A) 1.66 × 10-27 kg B) 2.20 × 10 -28 kg C) 3.0 × 108 kg D) 8.24 x 1025 kg
2.20 × 10 -28 kgkilograms does the mass defect represent . the correct option is B) .
The mass defect of an atom is the difference between the mass of its constituent particles and the actual mass of the atom. When an atom is formed, a small amount of mass is lost due to the conversion of mass into energy.
The answer to the given question is:B) 2.20 × 10 -28 kg.
The mass defect is the difference between the sum of the mass of its constituent particles and the actual mass of the atom.
Mass defect (Δm) = Zmp + Nmn - Mwhere, Z is the atomic number, N is the number of neutrons, mp and mn are the mass of protons and neutrons respectively, and M is the mass of the nucleus.
The mass defect represents the energy released when a nucleus is formed from its constituent particles and it is related to E = Δmc² by
Einstein’s famous equation where c is the speed of light and E is the energy released in the process.
Hence, the correct option is B) 2.20 × 10 -28 kg.
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A person throws a ball upward into the air with an initial velocity of 15 m/s. Calculate
a) how high it goes?
b) how long the ball is in the air before it comes back ?
c) how much time it takes for the ball to reach the maximum height?
a) The maximum height of the ball is 11.52 m. b) The time ball is in the air before coming back is 3.06 seconds. c) The time ball takes to reach maximum height is 1.53 seconds.
The maximum height achieved by the ball is 11.52 m. To find the maximum height, we use the formula for displacement S = ut + 1/2 gt² = 15t + 1/2 × (-9.8) t² = 15t - 4.9 t². Here, u = 15 m/s, g = -9.8 m/s² and time taken to reach maximum height, t = 1.53 seconds.
The time ball is in the air before it comes back is 3.06 seconds. To find the total time taken by the ball to return to the ground, use the formula for time as t = (v - u) / g = (0 - 15) / (-9.8) = 1.53 seconds. So, the total time taken by the ball to return to the ground = 2t = 2 × 1.53 = 3.06 seconds.
Time taken by the ball to reach the maximum height is the time taken to reach the highest point from the time of throwing the ball upward. Time taken to reach the maximum height, t = 1.53 seconds.
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hello please show all work
and solutions, formulas etc. please try yo answer asap for huge
thumbs up!
12. A 2.5 x 10¹8 Hz x-ray photon strikes a metal foil and frees an electron. After the collision a lower energy 2.3 x 1018 Hz x-ray photon emerges. What is the speed of the electron? [P4]
An x-ray photon at 2.5 x 10¹⁸ Hz strikes a metal foil, releasing an electron. The resulting photon has a frequency of 2.3 x 10¹⁸ Hz, and the electron's speed is determined to be 1.24 x 10⁸ m/s when its energy matches that of the photon.
The energy of a photon is given by the equation:
E = hν
where h is Planck's constant and ν is the frequency of the photon.
The energy of the electron is given by the equation:
[tex]E = \frac{1}{2} m v^2[/tex]
where m is the mass of the electron and v is the speed of the electron.
We can set these two equations equal to each other to find the speed of the electron:
[tex]h\nu = \frac{1}{2} m v^2[/tex]
We can rearrange this equation to solve for v:
[tex]v = \sqrt{\frac{2h\nu}{m}}[/tex]
We know the value of h, ν, and m. Plugging these values into the equation, we get:
[tex]v = \sqrt{\frac{2 \times (6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (2.5 \times 10^{18} \, \text{Hz})}{9.11 \times 10^{-31} \, \text{kg}}}[/tex]
v = 1.24 x 10⁸ m/s
Therefore, the speed of the electron is 1.24 x 10⁸ m/s.
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Question 9 A 5.8 kg object hits a flat wall at a speed of 38 m/s and an angle of 35 °. The collision is perfectly elastic. Part A What is the change in momentum of the object? Enter your answer in un
The change in momentum of the 5.8 kg object, hitting a wall at 38 m/s and 35° angle in a perfectly elastic collision, is -358.58 kg⋅m/s.
To find the change in momentum of the object, we first need to determine the initial and final velocities of the object after the collision.
The initial velocity of the object can be broken down into its horizontal and vertical components.
The horizontal component is given by v₀x = v₀ * cos(θ), where v₀ is the initial speed of 38 m/s and θ is the angle of 35°. Thus, v₀x = 38 m/s * cos(35°) = 31.01 m/s.
The vertical component is given by v₀y = v₀ * sin(θ), where v₀ is the initial speed of 38 m/s and θ is the angle of 35°. Thus, v₀y = 38 m/s * sin(35°) = 21.84 m/s.
Since the collision with the wall is perfectly elastic, the magnitude of the velocity will remain the same after the collision. Therefore, the final horizontal velocity will be -v₀x and the final vertical velocity will be v₀y.
The change in momentum of the object can be calculated as Δp = m * (vf - vi), where m is the mass of the object and vf and vi are the final and initial velocities, respectively.
The initial momentum of the object is given by p₀ = m * v₀, and the final momentum is given by p = m * vf.
The change in momentum is then Δp = p - p₀ = m * vf - m * v₀.
Substituting the values, we have Δp = 5.8 kg * (-31.01 m/s) - 5.8 kg * (31.01 m/s) = -358.58 kg⋅m/s.
Therefore, the change in momentum of the object is -358.58 kg⋅m/s.
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two identical point charges of charge =91.0 pc are in vacuum and are separated by a distance of 2=30.0 cm. Calculate the total electric flux through the infinite surface placed at a distance d from each charge, perpendicular to the line on which the point charges are located.
The total electric flux through the infinite surface placed at a distance "d" from each charge, perpendicular to the line on which the point charges are located, is approximately 20.56 Nm².
Gauss's Law can be used to determine the total electric flux through an infinite surface that is set "d" units away from each charge and perpendicular to the line on which the point charges are situated.
According to Gauss's Law, the electrical flux across a closed surface is determined by the total charge it contains divided by the permittivity of empty space (0).
This situation involves two identical point charges with charges q = 91.0 pc (picocoulombs) and r = 30.0 cm between them.
We want to determine the electric flux via an infinite surface that is perpendicular to the line connecting the charges and situated at a distance "d" from each charge.
According to Gauss's Law,
Φ = (q / ε₀)
Φ = (2q / ε₀)
Φ = (2 * 91.0 pc) / (8.854 × [tex]10^{(-12)[/tex])
Φ = (2 * 91.0 × [tex]10^{(-12)[/tex] C) / (8.854 × [tex]10^{(-12)[/tex])
Φ = (182 × [tex]10^{(-12)[/tex] C) / (8.854 × [tex]10^{(-12)[/tex])
Φ = (182 × [tex]10^{(-12)[/tex]) * (N·m² / 8.854 × [tex]10^{(-12)[/tex])
Φ ≈ 20.56 Nm²
Therefore, the total electric flux through the infinite surface placed at a distance "d" from each charge, perpendicular to the line on which the point charges are located, is approximately 20.56 N·m².
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7. A 950 kg car accelerates from rest to 27 in 4.5 s. What is the net force acting on the car?
The net force acting on the car is 5700 N.
To determine the net force acting on the car, we can use Newton's second law of motion, which states that the net force is equal to the mass of an object multiplied by its acceleration.
Given that the mass of the car is 950 kg and it accelerates from rest to 27 m/s in 4.5 seconds, we can calculate the acceleration using the formula:
acceleration = (final velocity - initial velocity) / time
acceleration = (27 m/s - 0 m/s) / 4.5 s
acceleration = 27 m/s / 4.5 s
acceleration = 6 m/s²
Now, we can calculate the net force using the formula:
net force = mass * acceleration
net force = 950 kg * 6 m/s²
net force = 5700 N
Therefore, the net force acting on the car is 5700 N.
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