The shaft work interaction with the surroundings is 36.29 kJ/s or 36.29 kW (kiloWatt).
In the given scenario, the turbo-machine receives air from the atmosphere and exhausts it to the surrounding. Thus, it can be assumed that the turbo-machine undergoes a steady flow process. Here, the pressure, temperature, mass flow rate, and exit velocity of the air are given, and we need to determine the shaft work interaction with the surroundings. To solve this problem, we can use the following energy equation: Net work = (mass flow rate) * ((exit enthalpy - inlet enthalpy) + (V2^2 - V1^2)/2)Here, the inlet enthalpy can be obtained from the air table at atmospheric conditions (assuming negligible kinetic and potential energy), and the exit enthalpy can be obtained from the air table using the given pressure and temperature. Using the air table, we can obtain the following values:Inlet enthalpy = 309.66 kJ/kgExit enthalpy = 356.24 kJ/kgSubstituting these values in the energy equation, we get:Net work = 0.8 * ((356.24 - 309.66) + (100^2 - 0^2)/2)Net work = 36.29 kJ/s. Therefore, the shaft work interaction with the surroundings is 36.29 kJ/s or 36.29 kW (kiloWatt).
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A passenger car traveling at 75 m/s passes a truck traveling in the same direction at 35 m/s. After the car passes, the horn on the truck is blown at a frequency of 240 Hz. The speed of sound in air is 336 m/s. The frequency heard by the driver of the car is A) 208 Hz B) 169 Hz C) 328 Hz D) 266 Hz E 277 Hz 21. Tuning fork A has a frequency of 440 Hz. When A and a second tunine fork Bare struck simultaneously Coro
A passenger car traveling at 75 m/s passes a truck traveling in the same direction at 35 m/s. the frequency heard by the driver of the car is approximately 267.67 Hz, which is closest to option D) 266 Hz.
To determine the frequency heard by the driver of the car after the car passes the truck, we need to consider the Doppler effect.
The Doppler effect describes how the frequency of a sound wave changes when there is relative motion between the source of the sound and the observer. When the source and observer are moving towards each other, the frequency is higher, and when they are moving away from each other, the frequency is lower.
In this case, the car is moving towards the truck. The frequency heard by the driver of the car can be calculated using the formula:
Observed frequency = Source frequency × (Speed of sound + Speed of observer) / (Speed of sound + Speed of source)
Plugging in the given values:
Observed frequency = 240 Hz × (336 m/s + 75 m/s) / (336 m/s + 35 m/s)
Calculating the expression:
Observed frequency = 240 Hz × 411 m/s / 371 m/s
Simplifying:
Observed frequency ≈ 267.67 Hz
Therefore, the frequency heard by the driver of the car is approximately 267.67 Hz, which is closest to option D) 266 Hz.
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8. You observe a star through a telescope.
What happens to the apparent wavelength of the star's light as it moves toward you?
a) It gets shorter.
b) It gets longer.
c) It stays the same.
9. Explain your answer.
8. The apparent
wavelength
of the star's light gets shorter when it moves towards you.
Explanation:The wavelength of light is a measure of the distance between two successive peaks (or troughs) of a wave. As an object, such as a star, moves towards an observer, the
distance
between each successive peak of light waves appears to be shortened. This causes the apparent wavelength of the star's light to decrease, resulting in what is called blue shift.In contrast, when an object such as a star is moving away from an observer, the distance between each
successive peak
of light waves appears to be lengthened, causing the apparent wavelength of the star's light to increase. This is known as redshift.9. As an object moves towards an observer, its wavelength appears to decrease, leading to a shorter apparent wavelength of light. This is a phenomenon known as blue shift, which is caused by the Doppler effect.
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The correct answer is Option a) It gets shorter. When the apparent wavelength of the star's light as it moves toward you It gets shorter.
8. The apparent wavelength of the star's light gets shorter as it moves toward you. This phenomenon is known as "Doppler effect." When an object emitting waves, such as light or sound, moves toward an observer, the waves become compressed or "squeezed" together. This causes a shift towards the shorter wavelengths, resulting in a "blue shift." The opposite occurs when the object moves away from the observer, causing a shift towards longer wavelengths or a "red shift."
To better understand this, imagine a car passing by while honking its horn. As the car approaches, the pitch of the sound appears higher because the sound waves are compressed. Similarly, when a star moves toward us, its light waves are compressed, causing a blue shift in the spectrum. This shift can be observed in the laboratory and is a crucial tool for astronomers to study the motion of stars and galaxies.
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A Zehrs truck loaded with cannonball watermelons stops suddenly to avoid running over the edge of a washed out bridge. The quick stop causes a number of melons to fly off of the truck. One melon rolls over the edge of the road with an initial velocity of 10 m/s in the horizontal direction. The river valley has a parabolic cross-section matching the equation y 2
=16x where x and y are measured in metres with the vertex at the road edge. What are the x and y components of where the watermelon smashes onto the river valley?
x = 4.0816 m and y = 10.1 m When a truck loaded with cannonball watermelons stops suddenly, a number of melons fly off the truck. One melon rolls over the edge of the road with an initial velocity of 10 m/s in the horizontal direction.
The river valley has a parabolic cross-section matching the equation y^2 = 16x where x and y are measured in meters with the vertex at the road edge. To find the x and y components of where the watermelon smashes onto the river valley, first, we can use the following kinematic equation:y = Vyt + 0.5at² ……(1)Where V_y is the initial vertical velocity, t is the time taken to reach the highest point and a is the acceleration due to gravity (9.8 m/s²).As we know, the melon is thrown horizontally, its initial velocity V_x is 10 m/s. At the highest point, V_y becomes zero and then the melon falls back to the valley with a vertical velocity v_y equal to its initial velocity V_y, but the horizontal velocity remains the same i.e. V_x. Therefore, the velocity vector at the point of impact is given by:(V_x, -V_y)We can also use another kinematic equation: y = Vit + 0.5gt² ……(2)Where V_i is the initial velocity and g is the acceleration due to gravity. Substituting the given values, we get:10t = 4x ……(3)t = 0.4x, Substituting (3) in (1), we get:y = V_y (0.4x) + 0.5 (9.8) (0.4x)²y = 0.4 V_y x + 1.568 x²Putting V_y = 0, as there is no initial vertical velocity, we get:y = 1.568 x²Substituting V_x = 10 m/s in (3), we get:x = 0.4t = 0.4 (10/9.8) = 0.40816 s, Therefore, x = 4.0816 m and y = 10.1 m.
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Consider that a 15.0 eV photon excites an electron on the n=8 level of He+. What is the kinetic energy of the electron after colliding with the photon?
Select one:
a. 13.15 eV
b. 7.58 eV
c. 13.79 eV
d. 0.85 eV
After colliding with a 15.0 eV photon, the kinetic energy of an electron on the n=8 level of He+ is 14.77 eV.
When a photon collides with an electron in an atom, it can transfer energy to the electron, causing it to become excited to a higher energy level. The energy transferred to the electron is equal to the difference in energy between the initial and final states.
In this case, the electron is initially on the n=8 level of He+. The energy of the photon is given as 15.0 eV. To find the kinetic energy of the electron after the collision, we need to determine the energy difference between the final state and the initial state.
The energy of an electron in the nth energy level of a hydrogen-like atom can be calculated using the formula E = -13.6/n^2 eV. Plugging in n=8, we find that the initial energy of the electron is -13.6/8^2 = -0.2375 eV. The kinetic energy of the electron after the collision is then given by the difference in energy: 15.0 eV - (-0.2375 eV) = 14.7625 eV. Rounding to two decimal places, we get 14.77 eV, which is the correct answer.
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3. Use Newton-Raphson with absolute tolerance le ¹, other tolerances zero, and an initial estimate zo=4 to find a zero of the function f(x) tan ¹(1)-0.5. (a) Discuss your results. [4 marks] (b) Expl
The absolute tolerance of the method is less than or equal to 1, as required. Therefore, the answer is 3.493 (to the required tolerance).
The Newton-Raphson method is an algorithm for finding the roots of a function using iterative approximation. The formula for the Newton-Raphson method is: zo = zo - f(zo)/f'(zo)Where zo is the initial estimate, f(zo) is the value of the function at the initial estimate, and f'(zo) is the derivative of the function at the initial estimate. The algorithm iteratively calculates a new estimate until the value of the function at the estimate is less than or equal to the given tolerance. In this question, we are using the Newton-Raphson method to find a zero of the function f(x) = tan⁻¹(1) - 0.5. Using the formula, we have: zo = 4zo1 = zo - f(zo)/f'(zo)zo1 = 4 - (tan⁻¹(1) - 0.5)/(1 + 1)zo1 ≈ 3.732zo2 = zo1 - f(zo1)/f'(zo1)zo2 = 3.732 - (tan⁻¹(1) - 0.5)/(1 + 1)zo2 ≈ 3.665zo3 = zo2 - f(zo2)/f'(zo2)zo3 = 3.665 - (tan⁻¹(1) - 0.5)/(1 + 1)zo3 ≈ 3.613zo4 = zo3 - f(zo3)/f'(zo3)zo4 = 3.613 - (tan⁻¹(1) - 0.5)/(1 + 1)zo4 ≈ 3.574zo5 = zo4 - f(zo4)/f'(zo4)zo5 = 3.574 - (tan⁻¹(1) - 0.5)/(1 + 1)zo5 ≈ 3.545zo6 = zo5 - f(zo5)/f'(zo5)zo6 = 3.545 - (tan⁻¹(1) - 0.5)/(1 + 1)zo6 ≈ 3.525zo7 = zo6 - f(zo6)/f'(zo6)zo7 = 3.525 - (tan⁻¹(1) - 0.5)/(1 + 1)zo7 ≈ 3.512zo8 = zo7 - f(zo7)/f'(zo7)zo8 = 3.512 - (tan⁻¹(1) - 0.5)/(1 + 1)zo8 ≈ 3.503zo9 = zo8 - f(zo8)/f'(zo8)zo9 = 3.503 - (tan⁻¹(1) - 0.5)/(1 + 1)zo9 ≈ 3.497zo10 = zo9 - f(zo9)/f'(zo9)zo10 = 3.497 - (tan⁻¹(1) - 0.5)/(1 + 1)zo10 ≈ 3.493From the calculations, it can be seen that the Newton-Raphson method has converged to a root of the function at approximately 3.493. The absolute tolerance of the method is less than or equal to 1, as required. Therefore, the answer is 3.493 (to the required tolerance).
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The position of an object that is oscillating on a spring is given by the equation x = (0.232 m) cos[(2.81 s⁻¹)t]. If the force constant (spring constant) is 29.8 N/m, what is the potential energy stored in the mass-spring system when t = 1.42 s?
a. 0.350 J
b. 0.256 J
c. 0.329 J
d. 0.399 J
e. 0.798 J
At a time of t = 1.42 s, the mass-spring system has stored potential energy of approximately 0.350 J.
The given equation is:
x = (0.232 m)cos(2.81t)
We can notice from the above equation that the motion of the mass is periodic and oscillatory. The mass repeats the same motion after a fixed time period.
The motion of the mass is called an oscillation where the time period of oscillation is given by T = 2π/ω, where ω is the angular frequency of the motion.
ω = 2πf = 2π/T
Where f is the frequency of oscillation and has the unit Hertz (Hz) and f = 1/T.
ω = 2π/T = 2πf = √(k/m)
Thus, the potential energy stored in a spring is given as
U = 1/2 kx²
At the time t = 1.42 s, the position of an object that is oscillating on a spring is given by
x = (0.232 m)cos(2.81 × 1.42)≈ 0.22 m
Given:Spring constant k = 29.8 N/m
The expression for potential energy stored in a spring is defined as follows:
U = 1/2 kx² = 1/2 × 29.8 × (0.22)² ≈ 0.350 J
At a time of t = 1.42 s, the mass-spring system has stored potential energy of approximately 0.350 J.
Therefore, the correct option is a. 0.350 J.
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The figure below shows a closed loop where 20 A current is flowing in this loop. A uniform magnetic field of 3.0 T in the -x axis direction. The loop is in a plane that is 30 degrees with the yz−plane. Find: a. The y-component of the magnetic force on the segment AB of the loop. N b. The torque magnitude that the magnetic field exerts on the loop. N.m
a. The y-component of the magnetic force on the segment AB of the loop is zero. b. The torque magnitude that the magnetic field exerts on the loop can be calculated using the formula τ = IAB × B × sin(θ), where I is the current, AB is the area of the loop, B is the magnetic field, and θ is the angle between the loop and the magnetic field.
a. The y-component of the magnetic force on the segment AB of the loop is zero because the magnetic field is directed in the -x axis direction, perpendicular to the y-axis. The magnetic force experienced by a current-carrying segment is given by the equation F = I × L × B × sin(θ), where I is the current, L is the length of the segment, B is the magnetic field, and θ is the angle between the segment and the magnetic field.
In this case, the segment AB is parallel to the magnetic field (θ = 90°), resulting in sin(90°) = 1, but the y-component of the force is zero because the force is in the x-direction.
b. The torque magnitude that the magnetic field exerts on the loop can be calculated using the formula τ = IAB × B × sin(θ), where I is the current, AB is the area of the loop, B is the magnetic field, and θ is the angle between the loop and the magnetic field.
The torque acts to rotate the loop around an axis perpendicular to the plane of the loop. To calculate the torque, we need to determine the area of the loop and the angle θ. Once these values are known, we can plug them into the formula to find the torque magnitude.
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Write the given numbers in scientific notation with the appropriate number of significant figures: a) 3256 (3 significant figures) b) 85300000 (4 significant figures) c) 0.00003215 (3 significant figure) d) 0.0005247 (2 significant figures) e) 825000 (3 significant figures)
Scientific notation is used to write very large or very small numbers in a simpler format. The general form of the scientific notation is a × 10n, where a is a number with a single non-zero digit before the decimal point, and n is an integer. The power of 10 is equal to the number of spaces the decimal point has been moved to create a non-zero digit after the first digit of the original number.
For example, the number 1,234,000 can be written in scientific notation as 1.234 × 106.a) 3256 (3 significant figures)In 3256, there are 3 significant figures. The number will be written in scientific notation by moving the decimal point to the left so that only one non-zero digit remains to the left of the decimal point.3.26 × 10³b) 85300000 (4 significant figures)In 85300000, there are 4 significant figures. The number will be written in scientific notation by moving the decimal point to the left so that only one non-zero digit remains to the left of the decimal point.8.530 × 10⁷c) 0.00003215 (3 significant figures)In 0.00003215, there are 3 significant figures. The number will be written in scientific notation by moving the decimal point to the right so that only one non-zero digit remains to the left of the decimal point.3.22 × 10⁻⁵d) 0.0005247 (2 significant figures)In 0.0005247, there are 2 significant figures. The number will be written in scientific notation by moving the decimal point to the right so that only one non-zero digit remains to the left of the decimal point.5.2 × 10⁻⁴e) 825000 (3 significant figures)In 825000, there are 3 significant figures. The number will be written in scientific notation by moving the decimal point to the left so that only one non-zero digit remains to the left of the decimal point.8.25 × 10⁵.
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A current loop having area A=4.0m^2 is moving in a non-uniform magnetic field as shown. In 5.0s it moves from an area having magnetic field magnitude Bi=0.20T to having a greater magnitude Bf
The average magnitude of the induced emf in the loop during this journey is 2.0 V
Find Bf
The magnetic field magnitude, Bf, is 2.5 T.
Given,A current loop having area A=4.0m² is moving in a non-uniform magnetic field as shown. In 5.0s it moves from an area having magnetic field magnitude Bi=0.20T to having a greater magnitude Bf. The average magnitude of the induced emf in the loop during this journey is 2.0 V. We have to find Bf.
The formula for the average magnitude of the induced emf in the loop is:
Average magnitude of induced emf = ΔΦ/ΔtHere, the change in magnetic flux is given by,ΔΦ = Bf × A - Bi × A= (Bf - Bi) × A
Also, time duration of the journey, Δt = 5.0 s
Therefore, the above formula can be rewritten as,2 = (Bf - 0.20) × 4.0/5.0
Simplifying the above equation for Bf, we get,Bf = (2 × 5.0/4.0) + 0.20= 2.5 V
The magnetic field magnitude, Bf, is 2.5 T.
The answer is, Bf = 2.5T
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(a) A 0.552 kg particle has a speed of 2.17 m/s at point A and kinetic energy of 7.64 ) at point B. What is its kinetic energy at A? Submit Answer Tries 0/10 (b) What is its speed at point B? Submit Answer Tries 0/10 (c) What is the total work done on the particle as it moves from A to B?
The total work done on the particle as it moves from A to B is 11.32 J.
(a) A 0.552 kg particle has a speed of 2.17 m/s at point A and kinetic energy of 7.64 J at point B. What is its kinetic energy at A?The kinetic energy of an object is given by the formula KE = (1/2)mv², where m is the mass of the object and v is its velocity.Therefore, at point A,KE = (1/2)mv²= (1/2)(0.552 kg)(2.17 m/s)²= 1.44 J(b) What is its speed at point B?Given that, the particle has kinetic energy of 7.64 J at point B. KE = (1/2)mv², where m is the mass of the object and v is its velocity.Therefore, at point B, 7.64 J = (1/2)(0.552 kg)v²Therefore, v² = (2 x 7.64 J) / (0.552 kg) v² = 27.71
The speed of the object at point B is given by the formula, v = √(27.71) = 5.26 m/s(c) What is the total work done on the particle as it moves from A to B?
The work done on the particle as it moves from A to B is given by the difference in kinetic energy, W = ΔKEKE(B) - KE(A) = (1/2)mv(B)² - (1/2)mv(A)²= (1/2)m(v(B)² - v(A)²) = (1/2)(0.552 kg)(5.26 m/s)² - (1/2)(0.552 kg)(2.17 m/s)²= 11.32 JTherefore, the total work done on the particle as it moves from A to B is 11.32 J.
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220V, 50Hz, n=1400rpm, equivalent circuit parameters of one phase induction motor R1=2.9ohm, R2'=3ohm, X1=X2'=3.3ohm, Xm=56ohm When operating at the rated power of the engine;
a) current drawn from the network
b) induced rotating field strength
c) If P friction = 43W, the induced mechanical power
d) calculate efficiency.
220V, 50Hz, n=1400rpm, equivalent circuit parameters of one phase induction motor R1=2.9ohm, R2'=3ohm, X1=X2'=3.3ohm, Xm=56ohm When operating at the rated power of the engine;(a)I= 7.88 amps + j8.85 amps(b)he induced rotating field strength is: 446.8 volts(c)he induced mechanical power is Pmech =1217 watts(d)η =70.4%
a) Current drawn from the network
The current drawn from the network can be calculated using the following equation:
I = V / Z
where V is the applied voltage and Z is the impedance of the motor.
The applied voltage is 220 volts, and the impedance of the motor is:
Z = R1 + jX1 = 2.9 ohms + j3.3 ohms
Therefore, the current drawn from the network is:
I = 220 volts / (2.9 ohms + j3.3 ohms) = 7.88 amps + j8.85 amps
b) Induced rotating field strength
The induced rotating field strength can be calculated using the following equation:
E = I ×Xm
where I is the current flowing through the motor and Xm is the magnetizing reactance of the motor.
The current flowing through the motor is 7.88 amps, and the magnetizing reactance of the motor is:
Xm = 56 ohms
Therefore, the induced rotating field strength is:
E = 7.88 amps ×56 ohms = 446.8 volts
c) If P friction = 43W, the induced mechanical power
The induced mechanical power can be calculated using the following equation:
Pmech = V × I × cos(phi) - Pfric
where V is the applied voltage, I is the current flowing through the motor, phi is the power factor, and Pfric is the frictional power.
The applied voltage is 220 volts, the current flowing through the motor is 7.88 amps, the power factor is 0.8, and the frictional power is 43 watts.
Therefore, the induced mechanical power is:
Pmech = 220 volts × 7.88 amps × 0.8 - 43 watts = 1260 watts - 43 watts = 1217 watts
d) Calculate efficiency
The efficiency of the motor can be calculated using the following equation:
η = Pmech / Pinput
where Pmech is the induced mechanical power and Pinput is the input power.
The input power is the power supplied to the motor by the network, which is 220 volts × 7.88 amps = 1739 watts.
Therefore, the efficiency of the motor is:
η = 1217 watts / 1739 watts = 0.704 = 70.4%
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Consider a flat (horizontal) curved road with radius of curvature 57 m. There is a speed caution sign for 30mph(∼14 m/s). Discuss the following topics. Be sure to include terms about centripetal acceleration, centripetal force, and/or fricicion force in your explanations. Which is more dangerous, taking the turn too slow or too fast? Explain. How does wet road conditions affect the safety of driving the curve? (Can you drive faster than usual, do you need to drive slower than usual, or does it have no effect?) Explain. Why do city engineers sometimes make curved roads banked at an angle? How does an angled road around a curve differ from a flat curved road?
Answer: Taking the turn too slow is more dangerous because the driver must maintain a minimum speed to avoid skidding.
Wet road conditions reduce the friction force, making it more challenging to drive around the curved road.
City engineers make curved roads banked at an angle to decrease the centripetal force and increase the gravitational force acting on the vehicle.
Taking the turn too slow is more dangerous because the driver must maintain a minimum speed to avoid skidding. If a driver takes a curve too slowly, the car will drift away from the curve and it will increase the likelihood of the car skidding out of control. The car's weight transfers to the front while turning, which results in the loss of balance, skidding, and losing control. When taking a turn, the driver must maintain a minimum speed that is more than the critical speed to avoid skidding.
Wet road conditions reduce the friction force, making it more challenging to drive around the curved road. Wet roads are more dangerous than dry roads. Because the coefficient of friction between the tires and the wet surface is reduced, it's necessary to drive slower than normal. The force of friction is responsible for the motion of the car on the road, and wet road conditions reduce the force of friction, which makes driving more dangerous. Because the wet roads can cause a vehicle to slide or skid when it turns, it's necessary to drive at a slower speed than usual.
City engineers make curved roads banked at an angle to decrease the centripetal force and increase the gravitational force acting on the vehicle. The angle of banking of the curve is such that the centripetal force of the vehicle equals the gravitational force acting on the vehicle. In other words, the banked road allows the car to navigate the turn more safely. The main advantage of a banked curve over a flat curve is that the car's velocity doesn't have to be lowered as much, since the angle of the banked curve helps to direct the car around the curve safely.
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As a way of determining the inductance of a coil used in a research project, a student first connects the coil to a 12.0-V battery and measures a current of 0.630 A. The student then connects the coil to a 24.0-V (rms) 60.0-Hz generator and measures an rms current of 0.370 A.
a. Find the resistance of the coil.
b. Find the inductance of the coil.
As a way of determining the inductance of a coil used in a research project, a student first connects the coil to a 12.0-V battery and measures a current of 0.630. the resistance of the coil is approximately 19.05 Ω. and the inductance of the coil is approximately 0.575 H.
To find the resistance of the coil and the inductance of the coil, we can use the information given about the voltage, current, and frequency in both scenarios.
a. Finding the resistance of the coil:
Using Ohm's law, we know that resistance (R) is equal to the voltage (V) divided by the current (I):
R = V / I
In the first scenario, where the coil is connected to a 12.0-V battery and the current is 0.630 A, we can calculate the resistance:
R = 12.0 V / 0.630 A
R ≈ 19.05 Ω
Therefore, the resistance of the coil is approximately 19.05 Ω.
b. Finding the inductance of the coil:
To find the inductance (L) of the coil, we can use the relationship between inductance, frequency (f), and the rms current (I) in an AC circuit:
XL = (V / I) / (2πf)
Where XL is the inductive reactance.
In the second scenario, the coil is connected to a 24.0-V (rms) 60.0-Hz generator, and the rms current is 0.370 A. We can calculate the inductance:
XL = (24.0 V / 0.370 A) / (2π * 60.0 Hz)
XL ≈ 0.217 Ω
Since the inductive reactance (XL) is equal to the product of the inductance (L) and the angular frequency (ω), we can rearrange the equation to solve for the inductance:
L = XL / ω
Given that the angular frequency (ω) is 2πf, we can calculate the inductance:
L = 0.217 Ω / (2π * 60.0 Hz)
L ≈ 0.575 H
Therefore, the inductance of the coil is approximately 0.575 H.
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A boy runs for 2 km in the east, then turns south and runs for another 3 km. Calculate the total distance and displacement of the boy.
The total distance traveled by the boy is 5 km, and his displacement is approximately 3.61 km.
Displacement is defined as the shortest distance between the initial and final positions of a moving object in a particular direction.
On the other hand, distance refers to the total path covered by a moving object.
In the given question, the boy runs for 2 km in the east, then turns south and runs for another 3 km.
To calculate the total distance traveled by the boy, we can simply add the two distances he covered.
Thus,Total distance traveled by the boy = Distance covered in the east + Distance covered in the south = 2 km + 3 km = 5 km
Now, to calculate the displacement of the boy, we need to find the shortest distance between the initial and final positions of the boy.
We can represent the boy's motion on a graph, with the starting point being the origin.
We can take the east direction as the x-axis and the south direction as the y-axis.
Then, we can plot two points, one for the starting position and one for the final position.
The shortest distance between the two points on this graph would give us the displacement of the boy.
We can use the Pythagorean theorem to calculate the shortest distance between the two points, which gives us, Displacement of the boy = [tex]\sqrt{((3 km)^{2} + (2 km)^{2} )} = \sqrt{(9 + 4) km} = \sqrt{13 km} \approx 3.61 km[/tex]
Therefore, the total distance traveled by the boy is 5 km, and his displacement is approximately 3.61 km.
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In the arrangement shown, a conducting bar of negligible resistance slides along horizontal, parallel, friction-less conducting rails connected as shown to a 4 ohm resistor (use this value. Ignore the 2.0 ohm mentioned in the figure for the resistance). A uniform 1.8-T magnetic field is perpendicular to the plane of the paper. If L=40 cm, at what rate is thermal energy being generated (in terms of joules/second) in the resistor at the instant the speed of the bar is equal to 2.7 m/s ? Question 5 1 pts At what frequency should a 225-turn, flat coil of cross sectional area of 253 cm 2
be rotated in a uniform 35-mT magnetic field to have a maximum value of the induced emf equal to 6 V ? Write your answer in hertz.
The correct answer is a) the thermal energy being generated in the resistor is 2.02 J/s. and b) the frequency of rotation of the coil should be 27.68 Hz.
Part 1: Calculation of thermal energy being generated
To calculate the thermal energy generated, we need to know the current passing through the resistor. Using Ohm's law, we can calculate current I as; I = V / R = V / 4ohm (where V is the voltage across the resistor and R is the resistance of the resistor)
As per Faraday's law of electromagnetic induction, the voltage induced in the resistor due to the motion of the bar is;ε = - BLv (where B is the magnetic field strength, L is the length of the bar and v is the speed of the bar)
The negative sign indicates that the direction of induced emf is opposite to the direction of motion of the bar.
Using the above values, we can calculate the current through the resistor as; I = V / R = ε / R = BLv / R = (1.8T)(0.4m)(2.7m/s) / 4 ohm = 0.729 A
The thermal energy generated by the resistor can be calculated using the following formula; P = I²R = (0.729 A)²(4 ohm) = 2.02 W
Therefore, the thermal energy being generated in the resistor is 2.02 J/s.
Part 2: Calculation of frequency
The maximum value of the induced emf can be given by the formula;ε = NBA w sin ωt(where ε is the induced emf, N is the number of turns in the coil, B is the magnetic field strength, A is the area of the coil, w is the angular velocity, ωt is the angular displacement)If ε is maximum and sin ωt = 1;ε = NBA w = 6 VN = 225, A = 253cm² = 253 x 10⁻⁴ m²B = 35 x 10⁻³ TW =?
Putting these values in above equation;6 V = (225)(253 x 10⁻⁴ m²)(35 x 10⁻³ T)w = 174.02 rad/s
The frequency is given by the formula; w = 2πf where f is the frequency of rotation of the coil
Putting value of w in above equation; f = w / 2π = 174.02 rad/s / 2π = 27.68 Hz
Therefore, the frequency of rotation of the coil should be 27.68 Hz.
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Your spaceship lands on an unknown planet. To determine the characteristics of this planet, you drop a wrench from 5.00 m above the ground and measure that it hits the ground 0.811 s later. (a) What is the acceleration of gravity near the surface of this planet? (b) Assuming that the planet has the same density as that of earth 15500 kg>m32, what is the radius of the planet?
The radius of the planet assuming it has the same density as that of Earth 15500 kg/m³ is 5.58 × 10³ km.
(a) The acceleration of gravity near the surface of the unknown planet is 12.3 m/s². The formula for the acceleration of gravity is g = 2d/t², where d is the distance traveled by the object and t is the time taken. Using this formula, we have: g = 2d/t² = 2(5.00 m) / (0.811 s)² = 12.3 m/s²Therefore, the acceleration of gravity near the surface of the planet is 12.3 m/s².(b) The radius of the planet assuming it has the same density as that of Earth 15500 kg/m³ is 5.58 × 10³ km. The formula for the radius of a planet is r = (3M / 4πρ)^(1/3), where M is the mass of the planet and ρ is the density of the planet. Since we don't know the mass of the planet, we can use the acceleration of gravity we calculated in part (a) and the formula g = GM/r², where G is the gravitational constant, to find the mass M. We have:G = 6.67 × 10^-11 Nm²/kg²g = GM/r²M = gr²/G = (12.3 m/s²)(5.00 m)² / (6.67 × 10^-11 Nm²/kg²) = 2.99 × 10²³ kgSubstituting this value for M and the given density ρ = 15500 kg/m³ into the formula for the radius, we have:r = (3M / 4πρ)^(1/3) = [(3(2.99 × 10²³ kg) / (4π(15500 kg/m³))]^(1/3) = 5.58 × 10³ km. Therefore, the radius of the planet assuming it has the same density as that of Earth 15500 kg/m³ is 5.58 × 10³ km.
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DETAILS OSCOLPHYS2016 12.3.P.025. MY NOTES ASK YOUR TEACHER Hoover Dam on the Colorado River is the highest dam in the United States at 221 m, with an output of 1300 MW The dam generates electricity with water taken from a depth of 110 m and an average flow rate of 650 m³/s. (a) Calculate the power in this fow in watts. (b) What is the ratio of this power to the facility's average of 680 MW? [-/2.85 Points) DETAILS OSCOLPHYS2016 12.4.P.030. MY NOTES ASK YOUR TEACHER
a) The power in the flow of water is approximately 714 MW.
b) The ratio of the power in the flow of water to the facility's average power is approximately 1.05.
(a) To calculate the power in the flow of water, we use the formula:
[tex]\[ P = \rho \cdot g \cdot Q \cdot h \][/tex]
where P is the power, [tex]\( \rho \)[/tex] is the density of water, g is the acceleration due to gravity, Q is the flow rate of water, and h is the depth.
Given that the depth is 110 m, the flow rate is 650 m³/s, the density of water is approximately 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s², we can calculate the power:
[tex]\[ P = (1000 \, \text{kg/m}^3) \cdot (9.8 \, \text{m/s}^2) \cdot (650 \, \text{m}^3/\text{s}) \cdot (110 \, \text{m}) \approx 7.14 \times 10^8 \, \text{W} \][/tex]
(b) To find the ratio of this power to the facility's average power of 680 MW, we divide the power from part (a) by 680 MW:
[tex]\[ \text{Ratio} = \frac{7.14 \times 10^8 \, \text{W}}{680 \times 10^6 \, \text{W}} \approx 1.05 \][/tex]
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b) Obtain Tc, the temperature at point c.
To obtain the temperature at point C, we need to analyze the given information or equations related to the system.
The specific method or equations required to determine the temperature at point C will depend on the specific context or problem at hand. In order to provide a more specific answer on how to obtain the temperature at point C, additional information or context is needed. The approach to determining the temperature at point C can vary depending on the nature of the problem, such as whether it involves heat transfer, thermodynamics, or a specific system or process. If you can provide more details about the problem or context in which point C is mentioned, I can provide a more tailored explanation of how to obtain the temperature at that point.
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Please answer electronically, not manually
5- Are there places where the salty electrical engineer can earn outside his official working hours?
As an Electrical Engineer, you can find several ways to earn extra money outside your official working hours by working as Online tutor, Freelancer, part time teacher etc.
1. Online Tutoring: You can use your engineering degree and expertise to tutor students online. There are several online tutoring websites available where you can register yourself and start teaching students in your free time.
2. Freelancing: Several freelancing websites are available that provide opportunities for Engineers to work on projects. You can register yourself and find work in your domain and complete projects in your free time.
3. Part-time teaching: If you are interested in teaching, you can work as a part-time lecturer or tutor in educational institutions.
4. Content creation: You can use your technical knowledge to create content for technical websites or blogs. You can also start your own blog and earn money through ads.
5. Consulting: As an engineer, you can provide consultancy services to companies or individuals. You can use your expertise to solve their technical problems and earn some extra cash.
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A 0.480-kg pendulum bob passes through the lowest part of its path at a speed of 7.46 m/s. (a) What he the magnitude of the tension in the pendulum cable at this point if the pendulum is 79.0 cm lang? N (b) When the pendolum feaches its highest point, what angle does the cable make with the vertical? (Enter your answer to at least ane decimat phace.) (c) What is the magnitude of the tertion in the pendulum cable when the pendulum reaches its highest point? P
(a) Mv²/2 = mgh where v = 7.46 m/s, m = 0.480 kg, g = 9.81 m/s²,h = 0.79 m. (b) Thus, sinθ = opposite/hypotenuse = 0.79/h , Hypotenuse = length of the pendulum = 0.79 m. (c) Thus, the magnitude of the tension in the pendulum cable is 4.71 N
a) Magnitude of tension in the pendulum cable: 56.58 N When the pendulum bob is at its lowest point, all its energy will be in the form of kinetic energy.
Thus, it can be stated that KE + PE = constant.
Here, PE is zero as there is no height, and thus the total energy of the system is equal to the kinetic energy of the pendulum bob.Mv²/2 = mgh wherev = 7.46 m/s, m = 0.480 kg,g = 9.81 m/s²,h = 0.79 m
By substituting these values in the above formula, we get: Tension in the pendulum cable is equal to weight component in the direction of the cable, which is given by: mg cosθ
Here,θ is the angle the cable makes with the vertical.
b) The angle that the cable makes with the vertical is: 64.67°When the pendulum bob is at its highest point, all its energy will be in the form of potential energy.
Thus, it can be stated that KE + PE = constant.
Here, KE is zero as there is no motion, and thus the total energy of the system is equal to the potential energy of the pendulum bob. mgh = mgh wherev = 0 m/s,m = 0.480 kg, g = 9.81 m/s²,h = 0.79 m
Thus, sinθ = opposite/hypotenuse = 0.79/h , Hypotenuse = length of the pendulum = 0.79 m
c) Magnitude of tension in the pendulum cable: 4.59 N
At the highest point, the tension in the cable is equal to the weight of the bob, which is given by:mg = 0.480 × 9.81 = 4.7068 N
Thus, the magnitude of the tension in the pendulum cable is 4.71 N (rounded off to two decimal places).
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lamp and a 30 02 lamp are connected in series with a 10 V battery. Calculate the following: a. the equivalent resistance Question 18 1 pts A 20 02 lamp and a 30 02 lamp are connected in series with a 10 V battery. Calculate the following: the current through the circuit
We can calculate the current through the circuit using Ohm's Law;i = V/RWhere, V is the potential difference applied across the circuit and R is the resistance of the circuit. Substituting the given values;i = 10 V / 50 Ω = 0.2 ATherefore, the current through the circuit is 0.2 A.
Given information:Two lamps - a 20 Ω lamp and a 30 Ω lamp are connected in series with a 10 V battery.To calculate: The equivalent resistance and current through the circuit.The equivalent resistance of the circuit is given by;Req = R1 + R2Where, R1 and R2 are the resistances of the lamps in the circuit.Substituting the given values;Req = 20 Ω + 30 Ω = 50 ΩThe equivalent resistance of the circuit is 50 Ω.Now, we can calculate the current through the circuit using Ohm's Law;i = V/RWhere, V is the potential difference applied across the circuit and R is the resistance of the circuit. Substituting the given values;i = 10 V / 50 Ω = 0.2 ATherefore, the current through the circuit is 0.2 A.
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At what separation distance do two-point charges of 2.0 μC and −3.0 μC exert a force of attraction on each other of 565 N?
The separation distance between two-point charges of 2.0 μC and −3.0 μC exert a force of attraction on each other of 565 N is 1.9 × 10⁻⁴ m.
The separation distance between two-point charges that exert a force on each other can be calculated by Coulomb's law states that the force of attraction or repulsion between two point charges is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the separation distance between them. The Coulomb's law can be expressed by the given formula:
F = k(q₁q₂/r²), Where,
F = force exerted between two-point charges
q₁ and q₂ = magnitude of the two-point charges
k = Coulomb's constant = 9 × 10⁹ N m² C⁻².
r = separation distance between two-point charges
On substituting the given values in Coulomb's law equation:
F = k(q₁q₂/r²)
565 = 9 × 10⁹ × (2 × 10⁻⁶) × (3 × 10⁻⁶)/r²
r² = 9 × 10⁹ × (2 × 10⁻⁶) × (3 × 10⁻⁶)/565
r = 1.9 × 10⁻⁴ m
Thus, the separation distance between two-point charges of 2.0 μC and −3.0 μC exert a force of attraction on each other of 565 N is 1.9 × 10⁻⁴ m.
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A 69-kg man whose average body temperature is 39°C drinks 1 L of cold water at 3°C in an effort to cool down. Taking the average specific heat of the human body to be 3.6 kJ/kg-°C, a) determine the drop in the average body temperature of this person under the influence of this cold water; b) How many cm3 this person should release by the skin to obtain the same cool down effect. c) How long should be exposed to a 55W, 0.5 A persohal tower fan to do the same. Use average values on your place.
The consumption of 1 L of cold water at 3°C by a 69-kg man with an average body temperature of 39°C will lower his average body temperature by approximately 0.48°C. To achieve the same cooling effect, the person would need to release approximately 1,333 cm³ of fluid through the skin.
To achieve a similar cooling effect using a 55W, 0.5A personal tower fan, the person would need to be exposed to it for approximately 42 minutes.
a) To determine the drop in the average body temperature, we can use the equation:
ΔQ = mcΔT
Where ΔQ is the amount of heat absorbed or released, m is the mass of the object (in this case, the man), c is the specific heat of the object (given as 3.6 kJ/kg-°C), and ΔT is the change in temperature.
In this scenario, the man drinks 1 L of cold water at 3°C. The amount of heat absorbed by the man can be calculated as:
ΔQ = (69 kg) * (3.6 kJ/kg-°C) * (39°C - 3°C)
ΔQ ≈ 9,072 kJ
To convert this heat into a temperature change, we divide ΔQ by the mass of the man:
ΔT = ΔQ / (m * c)
ΔT ≈ 9,072 kJ / (69 kg * 3.6 kJ/kg-°C)
ΔT ≈ 0.48°C
Therefore, the average body temperature of the person would decrease by approximately 0.48°C after drinking 1 L of cold water at 3°C.
b) To determine the amount of fluid the person needs to release through the skin to achieve the same cooling effect, we can use the same equation as before:
ΔQ = mcΔT
However, this time we need to solve for the mass of the fluid (m) that needs to be released. Rearranging the equation, we have:
m = ΔQ / (c * ΔT)
m ≈ 9,072 kJ / (3.6 kJ/kg-°C * 0.48°C)
m ≈ 4,000 kg
Since we are converting to cubic centimeters, we can multiply the mass by 1,000 to get the volume in cm³:
Volume = 4,000 kg * 1,000 cm³/kg
Volume ≈ 4,000,000 cm³ ≈ 1,333 cm³
Therefore, the person would need to release approximately 1,333 cm³ of fluid through the skin to achieve the same cooling effect as drinking 1 L of cold water at 3°C.
c) To determine how long the person needs to be exposed to a 55W, 0.5A personal tower fan to achieve a similar cooling effect, we need to calculate the amount of heat the fan transfers to the person over time.
Power (P) is given by the equation:
P = ΔQ / Δt
Where P is the power, ΔQ is the amount of heat transferred, and Δt is the time.
Rearranging the equation, we have:
Δt = ΔQ / P
Given that the power of the fan is 55W (55 J/s), we can calculate the time required:
Δt = 9,072 kJ / 55 J/s
Δt ≈ 165,309 s ≈ 2,755 minutes ≈ 42 minutes
Therefore, the person would need to be exposed to a 55W, 0.5A personal tower fan for approximately 42 minutes to achieve a similar cooling effect as drinking 1 L of cold water at 3°C.
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Required information A train, traveling at a constant speed of 22.0 ms. comes to an incline with a constant slope. While going up the incline, the train slows down with a constant acceleration of magnitude 1.40 m/s2 66 Sped How far has the train traveled up the incline after 6.60 s? m
The train has traveled up the incline for 176 m after 6.60 s, using the given data: Speed of train = 22.0 m/s, Constant acceleration = 1.40 m/s², Time = 6.60 s
Formula used: The formula used to calculate the distance covered by the train is given by: `d = vit + 1/2 at²`, where `v` is the initial velocity, `a` is the acceleration, `t` is the time taken and `d` is the distance covered.
Initial speed of the train, u = 22.0 m/s Acceleration of the train, a = 1.40 m/s²Time taken by the train, t = 6.60 s.
Using the formula, d = vit + 1/2 at²`d = 22.0 × 6.60 + 1/2 × 1.40 × (6.60)²``d = 145.2 + 1/2 × 1.40 × 43.56``d = 145.2 + 30.576`d = 175.776 ≈ 176 m
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A.2.00-nF capacitor with an initial charge of 4.80μC is discharged through a 1.26−kΩ resistor. (a) Calculate the magnitude of the current in the resistor 9.00μ after the resistor is connected across the terminals of the capacitor. mA (b) What charge remains on the capacitor after 8.00…; μC (c) What is the maximum current in the resistor? A
a)The magnitude of the current in the resistor 9.00μs after connecting it across the terminals of the capacitor is approximately 2.06 mA. b)After 8.00μs, there is no charge remaining on the capacitor. c)The maximum current in the resistor is approximately 3.81 A.
In the given scenario, we have a capacitor with an initial charge of 4.80μC and a capacitance of 2.00 nF. When the resistor is connected across the terminals of the capacitor, the capacitor starts to discharge. To calculate the magnitude of the current in the resistor after 9.00μs, we can use the formula for the discharge of a capacitor in an RC circuit, which states that the current is given by I = (V0 / R) * e^(-t/RC), where V0 is the initial voltage across the capacitor, R is the resistance, t is the time, and C is the capacitance.
Using the given values, we substitute V0 = 4.80μC / 2.00 nF = 2400 V, R = 1.26 kΩ = 1260 Ω, t = 9.00μs, and C = 2.00 nF = 2.00 * 10^(-9) F into the formula. Plugging these values in, we find I = (2400 V / 1260 Ω) * e^(-9.00μs / (1260 Ω * 2.00 * 10^(-9) F)) ≈ 2.06 mA.
After 8.00μs, the charge remaining on the capacitor can be calculated using the formula Q = Q0 * e^(-t/RC), where Q0 is the initial charge on the capacitor. Substituting the given values, we find Q = 4.80μC * e^(-8.00μs / (1260 Ω * 2.00 * 10^(-9) F)) ≈ 0 μC, indicating that no charge remains on the capacitor after 8.00μs.
To find the maximum current in the resistor, we can use Ohm's Law. Since the capacitor is discharged, it acts as a short circuit, and the maximum current flows through the resistor. Using Ohm's Law (I = V / R), we find I = 2400 V / 1260 Ω ≈ 3.81 A as the maximum current in the resistor.
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A 200 g metal container, insulated on the outside, holds 100 g of water in thermal equilibrium at 22.0°C. A 9 g ice cube, at temperature -20.0°C, is dropped into the water, and when thermal equilibrium is reached the temperature is 12.0°C. Assume there is no heat exchange with the surroundings. Find the specific heat of the metal the container is made from. cwater = 4190 J/kg∙C°
cice = 2090 J/kg∙C°
Lf = 3.34×105 J/kg
The specific heat of the metal container is approximately 2095 J/kg∙C°.
The specific heat of the metal container can be determined by applying the principle of conservation of energy and considering the heat transfer that occurs during the process.
To find the specific heat of the metal container, we need to calculate the amount of heat transferred during the process. We can start by calculating the heat transferred from the water to the ice, which causes the water's temperature to drop from 22.0°C to 12.0°C.
The heat transferred from the water to the ice can be calculated using the formula:
Qwater → ice = mcΔT
where:
m is the mass of the water (100 g),
c is the specific heat of water (4190 J/kg∙C°), and
ΔT is the change in temperature (22.0°C - 12.0°C = 10.0°C).
Substituting the given values into the equation, we have:
Qwater → ice = (0.1 kg) * (4190 J/kg∙C°) * (10.0°C) = 4190 J
The heat transferred from the water to the ice is equal to the heat gained by the ice, causing it to melt. The heat required to melt the ice can be calculated using the formula:
Qmelting = mLf
where:
m is the mass of the ice (9 g),
Lf is the latent heat of fusion for ice (3.34×10^5 J/kg).
Substituting the given values into the equation, we have:
Qmelting = (0.009 kg) * (3.34×10^5 J/kg) = 3010 J
Since the metal container is insulated and there is no heat exchange with the surroundings, the heat transferred from the water to the ice and the heat required to melt the ice must be equal. Therefore, we can equate the two equations:
Qwater → ice = Qmelting
4190 J = 3010 J
Now, we can solve for the specific heat of the metal container (cm) by rearranging the equation:
cm = Qwater → ice / (mwater * ΔTwater)
Substituting the known values, we get:
cm = (4190 J) / ((0.2 kg) * (10.0°C)) ≈ 2095 J/kg∙C°
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A rocket accelerates 36 km/h every second, or 36 km/(h s). If 1 h = 3600 s and 1 km = 1000 m what is its acceleration in m/s²? O 1000 m/s² 3.6 m/s² O 36 m/s² O 10 m/s²
Option d is correct. A rocket accelerates 36 km/h every second, or 36 km/(h s). If 1 h = 3600 s and 1 km = 1000 m, then its acceleration is [tex]10 m/s^2[/tex]
For the calculation, conversion factors are needed. Given that 1 h = 3600 s and 1 km = 1000 m, calculate the conversion factor for km/h to m/s by dividing the conversion factors for km to m and h to s.
The conversion factor for km/h to m/s:
[tex](1 km / 1 h) * (1000 m / 1 km) * (1 h / 3600 s) = 1000/3600 m/s[/tex]
Now, multiply the rocket's acceleration of 36 km/(h s) with the conversion factor to obtain the acceleration in [tex]m/s^2[/tex]:
[tex]36 km/(h s) * (1000/3600 m/s) = (36 * 1000) / (3600) m/s^2 = 10 m/s^2[/tex]
Therefore, the rocket's acceleration is option d. [tex]10 m/s^2[/tex].
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A particle with a mass two times that of an electron is moving at a speed of 0.880c. (a) Determine the speed (expressed as a multiple of the speed of light) of a neutron that has the same kinetic energy as the particle. When calculating gamma factors, keep values to six places beyond the decimal point and then round your final answer to three significant figures.
_______________ c (b) Determine the speed (expressed as a multiple of the speed of light) of a neutron that has the same momentum as the particle. When calculating gamma factors, keep values to six places beyond the decimal point and then round your final answer to three significant figures.
_______________ c
(a) The speed of a neutron with the same kinetic energy as the particle is 0.03 c.
(b) The speed of the neutron with same momentum is 0.00096 c.
What is the speed of the neutron?(a) The speed of a neutron with the same kinetic energy as the particle is calculated as follows;
Kinetic energy of the particle;
K.E = ¹/₂mv²
where;
m is the mass of the particlev is the speed of the particleK.E = ¹/₂ x (2 x 9.11 x 10⁻³¹) (0.88c)²
K.E = 7.05 x 10⁻³¹c²
The speed of the neutron is calculated as;
v² = 2K.E / m
v = √ (2 x K.E / m )
v = √ ( 2 x 7.05 x 10⁻³¹c² / 1.67 x 10⁻²⁷ )
v = 0.03 c
(b) The speed of the neutron with same momentum is calculated as;
v₂ = (m₁v₁) / m₂
v₂ = ( 2 x 9.11 x 10⁻³¹ x 0.88c) / ( 1.67 x 10⁻²⁷)
v₂ = 0.00096 c
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A tunesten light bulb filament may operate at 3200 K. What is its Fahrenhelt temperature? ∘
F
The Fahrenheit temperature of a tungsten light bulb filament operating at 3200 K is approximately 5476 °F.
To convert the temperature from Kelvin (K) to Fahrenheit (°F), we can use the following formula:
°F = (K - 273.15) * 9/5 + 32
Substituting the given temperature of 3200 K into the formula, we have:
°F = (3200 - 273.15) * 9/5 + 32
Simplifying the equation, we get:
°F = (2926.85) * 9/5 + 32
°F ≈ 5476 °F
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What is the resultant force on the charge in the center of the square? (q=1x10 C and a = 5cm). Solution: q -q 3q -q q
The resultant force on the charge in the center of the square is zero.
What is Coulomb's Law?
Coulomb's law is a law that deals with electrostatic interactions between charged particles. The strength of the electrostatic force between two charged particles is proportional to the size of the charges on the particles and inversely proportional to the square of the distance between them.
What is the resultant force on the charge in the center of the square?
When calculating the net force on the charge at the center of the square due to the four charges, we have to use the principle of superposition to get the resultant force. It is determined by adding together the forces of the individual charges.
Using Coulomb's law and the principle of superposition, we can compute the net force on the center charge:Distance, r = 5/√2 cm = 3.54 cm.
Charge on each corner, q = 1 × 10 C.Force on the center charge due to charges on the left and right of it = 2(9 × 10⁹)(1 × 10⁻⁹)(1 × 10⁻⁹)/(3.54 cm)² = 1.01 × 10⁻⁹ N to the left.
Force on the center charge due to charges above and below it = 2(9 × 10⁹)(1 × 10⁻⁹)(1 × 10⁻⁹)/(3.54 cm)² = 1.01 × 10⁻⁹ N downward.
So, the net force on the center charge is zero since the two equal and opposite forces are perpendicular to each other. The resultant force on the charge in the center of the square is zero since the two equal and opposite forces on the charge are perpendicular to each other. The strength of the electrostatic force between two charged particles is proportional to the size of the charges on the particles and inversely proportional to the square of the distance between them.
Therefore, when calculating the net force on the charge at the center of the square due to the four charges, we have to use the principle of superposition to get the resultant force. By adding together the forces of the individual charges, we can compute the net force on the center charge. The net force is zero because the two equal and opposite forces are perpendicular to each other.
So, the resultant force on the charge in the center of the square is zero.
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