(a) The height of the cliff is 59.3 meters.
(b) If the stone is thrown horizontally outward, it will have 350 J of kinetic energy just before hitting the ground.
To calculate the height of the cliff, we can use the principle of conservation of mechanical energy.
(a) When the stone is thrown vertically downward, it undergoes free fall and its initial kinetic energy is converted into potential energy as it reaches the ground.
The initial kinetic energy of the stone is given as 350 J. At the highest point of its trajectory, all of this kinetic energy is converted into potential energy.
Using the equation for potential energy:
Potential Energy = mgh
where m is the mass of the stone (0.6 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the cliff.
Solving for h, we have:
h = Potential Energy / (mg)
h = 350 J / (0.6 kg × 9.8 m/s²) ≈ 59.3 meters
Therefore, the height of the cliff is approximately 59.3 meters.
(b) When the stone is thrown horizontally outward from the cliff, it follows a projectile motion. The initial kinetic energy of the stone remains the same, but it is entirely in the form of horizontal kinetic energy.
The vertical component of the stone's velocity does not affect its kinetic energy. Therefore, the stone will have the same amount of kinetic energy just before hitting the ground as in the previous case, which is 350 J.
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A particle is incident upon a square barrier of height \( U \) and width \( L \) and has \( E=U \). What is the probability of transmission? You must show all work.
The probability of transmission is zero.
Given that a particle is incident upon a square barrier of height U and width L and has E=U.
We need to find the probability of transmission.
Let us assume that the energy of the incident particle is E.
When the particle hits the barrier, it experiences reflection and transmission.
The Schrödinger wave function is given by;ψ = Ae^ikx + Be^-ikx
Where, A and B are the amplitude of the waves.
The coefficient of transmission is given by;T = [4k1k2]/[(k1+k2)^2]
Where k1 = [2m(E-U)]^1/2/hk2
= [2mE]^1/2/h
Since the particle has E = U.
Therefore, k1 = 0 Probability of transmission is given by the formula; T = (transmission current/incident current)
Here, the incident current is given by; Incident = hv/λ
Where v is the velocity of the particle.
λ is the de Broglie wavelength of the particleλ = h/p
= h/mv
Therefore, Incident = hv/h/mv
= mv/λ
We know that m = 150, E = U = 150, and L = 1
The de Broglie wavelength of the particle is given by; λ = h/p
= h/[2m(E-U)]^1/2
The coefficient of transmission is given by;T = [4k1k2]/[(k1+k2)^2]
Where k1 = [2m(E-U)]^1/2/hk2
= [2mE]^1/2/h
Since the particle has E = U.
Therefore, k1 = 0k2
= [2mE]^1/2/h
= [2 × 150 × 1.6 × 10^-19]^1/2 /h
= 1.667 × 10^10 m^-1
Now, the coefficient of transmission,T = [4k1k2]/[(k1+k2)^2]
= [4 × 0 × 1.667 × 10^10]/[(0+1.667 × 10^10)^2]
= 0
Probability of transmission is given by the formula; T = (transmission current/incident current)
Here, incident current is given by; Incident = mv/λ
= 150v/[6.626 × 10^-34 / (2 × 150 × 1.6 × 10^-19)]
Iincident = 3.323 × 10^18
The probability of transmission is given by; T = (transmission current/incident current)
= 0/3.323 × 10^18
= 0
Hence, the probability of transmission is zero.
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Problem 1 Multiple Guess, 5pts each a. Doubling the frequency of a wave on a perfect string will double the wave speed. (1) Yes (2) No I b. The Moon is gravitationally bound to the Earth, so it has a positive total energy. (1) Yes (2) No c. The energy of a damped harmonic oscillator is conserved. (1) Yes (2) No d. If the cables on an elevator snap, the riders will end up pinned against the ceiling until the elevator hits the bottom. (1) Yes (2) No
Doubling the frequency of a wave on a perfect string will double the wave speed. The correct answer is No.
Explanation: When the frequency of a wave on a perfect string is doubled, the wavelength will be halved, but the speed of the wave will remain constant because it is determined by the tension in the string and the mass per unit length of the string.b. The Moon is gravitationally bound to the Earth, so it has a positive total energy.
The correct answer is No. Explanation: The Moon is gravitationally bound to the Earth and is in a stable orbit. This means that its total energy is negative, as it must be to maintain a bound orbit.c. The energy of a damped harmonic oscillator is conserved. The correct answer is No.
Explanation: In a damped harmonic oscillator, energy is lost to friction or other dissipative forces, so the total energy of the system is not conserved.d. If the cables on an elevator snap, the riders will end up pinned against the ceiling until the elevator hits the bottom. The correct answer is No.
Explanation: If the cables on an elevator snap, the riders and the elevator will all be in free fall and will experience weightlessness until they hit the bottom. They will not be pinned against the ceiling.
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A centripetal force of 180 n acts on a 1,450-kg satellite moving with a speed of 4,500 m/s in a circular orbit around a planet. what is the radius of its orbit?
The radius of the satellite's orbit is approximately 163,402,777.8 meters.
The centripetal force acting on the satellite is 180 N. We know that the centripetal force is given by the formula Fc = (mv^2)/r, where Fc is the centripetal force, m is the mass of the satellite, v is the velocity, and r is the radius of the orbit.
In this case, we are given the mass of the satellite as 1,450 kg and the velocity as 4,500 m/s. We can rearrange the formula to solve for r:
r = (mv^2) / Fc
Substituting the given values, we have:
r = (1450 kg * (4500 m/s)^2) / 180 N
Simplifying the expression:
r = (1450 kg * 20250000 m^2/s^2) / 180 N
r = (29412500000 kg * m^2/s^2) / 180 N
r ≈ 163402777.8 kg * m^2/Ns^2
The radius of the satellite's orbit is approximately 163,402,777.8 meters.
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two identical metal blocks resting on a frictionless horizontal surface are connected by a light metal spring having constant of 124 n/m and unstretched length of 0.4 m. a total charge of q is slowly placed on the system causing the spring to stretch to an equilibrium length of 0.7 m. determine this charge, assuming that all the charge resides on the blocks and the blocks can be treated as point charges.
To determine the charge, we can use Hooke's Law for springs and Coulomb's Law for point charges. According to Hooke's Law, the force exerted by a spring is directly proportional to its displacement from equilibrium.
In this case, the spring constant is given as 124 N/m and the displacement is 0.7 m - 0.4 m = 0.3 m.Using Hooke's Law: F = kx, where F is the force, k is the spring constant, and x is the displacement, we can calculate the force exerted by the spring: F = (124 N/m)(0.3 m)
= 37.2 N
Since the blocks are identical and connected by the spring, the force is equally distributed between them. Now, using Coulomb's Law, we can relate the force between the blocks to the charge: F = k * (q^2 / r^2), where F is the force, k is the electrostatic constant, q is the charge, and r is the distance between the charges.
Since the charges are on opposite ends of the spring, the distance between them is equal to the equilibrium length of the spring, which is 0.7 m. Plugging in the values, we can solve for q: 37.2 N = (124 N/m) * (q^2 / (0.7 m)^2) Simplifying the equation, we find:
q^2 = (37.2 N) * (0.7 m)^2 / (124 N/m)
q^2 = 0.186 N * m / m
q^2 = 0.186 N
Taking the square root of both sides, we find:
q = sqrt(0.186 N)
q ≈ 0.431 N
Therefore, the charge on the system is approximately 0.431 N.
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1111.A door is 2.5m high and 1.7m wide. Its moment of inertia is 180kgm^2. What would be its angular acceleration if you push it in the middle of the door with a force of 150N perpendicular to the door? (10 pts) What torque are you applying?(10 pts)
The angular acceleration of the door is calculated as to be 0.708 rad/s² and the torque being applied is calculated as to be 127.5 Nm.
A door is 2.5m high and 1.7m wide. Its moment of inertia is 180kgm². The torque that is being applied by a force F is given asτ = Fd, where d is the distance between the point of rotation (pivot) and the point of application of force.
Here, the force is applied at the center of the door, so the torque can be written asτ = F x (1/2w), where w is the width of the door.τ = 150 N x (1/2 x 1.7 m)τ
= 127.5 Nm
The moment of inertia of the door is given as I = 180 kg m². The angular acceleration α can be calculated as the torque divided by the moment of inertia,α = τ / Iα
= 127.5 / 180α
= 0.708 rad/s²
Therefore, the angular acceleration of the door is 0.708 rad/s².
The torque being applied is 127.5 Nm.
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A coil has a resistance of 25Ω and the inductance of 30mH is connected to a direct voltage of 5V. Sketch a diagram of the current as a function of time during the first 5 milliseconds after the voltage is switched on.
Answer:
A coil with a resistance of 25 ohms and an inductance of 30 millihenries is connected to a direct voltage of 5 volts.
The current will increase linearly for the first 0.75 milliseconds, and then reach a maximum value of 0.2 amperes. The current will then decrease exponentially.
Explanation:
A coil with a resistance of 25 ohms and an inductance of 30 millihenries is connected to a direct voltage of 5 volts.
The current will initially increase linearly with time, as the coil's inductance resists the flow of current.
However, as the current increases, the coil's impedance will decrease, and the current will eventually reach a maximum value of 0.2 amperes. The current will then decrease exponentially, with a time constant of 0.75 milliseconds.
The following graph shows the current as a function of time during the first 5 milliseconds after the voltage is switched on:
Current (A)
0.5
0.4
0.3
0.2
0.1
0
Time (ms)
0
1
2
3
4
5
The graph shows that the current increases linearly for the first 0.75 milliseconds, and then reaches a maximum value of 0.2 amperes. The current then decreases exponentially, with a time constant of 0.75 milliseconds.
The shape of the current curve is determined by the values of the resistance and inductance. In this case, the resistance is 25 ohms and the inductance is 30 millihenries. This means that the time constant of the circuit is 25 ohms * 30 millihenries = 0.75 milliseconds.
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In placing a sample on a microscope slide, a glass cover is placed over a water drop on the glass slide. Light incident from above can reflect from the top and bottom of the glass cover and from the glass slide below the water drop. At which surfaces will there be a phase change in the reflected light? Choose all surfaces at
which there will be a phase change in the reflected light. [For clarification: there are five layers to consider here, with four boundary surfaces between adjacent layers: (1) air above the glass cover, (2) the glass cover, (3) the water layer below the glass cover, (4) the
glass slide below the water layer, and (5) air below the glass slide.]
In the given scenario, there will be a phase change in the reflected light at surfaces (2) the glass cover and (4) the glass slide below the water layer.
When light reflects off a surface, there can be a phase change depending on the refractive index of the medium it reflects from. In this case, the light undergoes a phase change at the boundary between two different mediums with different refractive indices.
At surface (2), the light reflects from the top surface of the glass cover. Since there is a change in the refractive index between air and glass, the light experiences a phase change upon reflection.
Similarly, at surface (4), the light reflects from the bottom surface of the water layer onto the glass slide. Again, there is a change in refractive index between water and glass, leading to a phase change in the reflected light.
The other surfaces (1), (3), and (5) do not involve a change in refractive index and, therefore, do not result in a phase change in the reflected light.
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Jill has conducted a virtual experiment using the "Pendulum Lab" simulation and completed associated lab assig pendulum with different pendulum arm lengths. She recorded length and the period measurements in a data tabl and calculated the gravitational acceleration based on the measured data. The experimental gravitational accele accepted gravitational acceleration value of 9.81 m/s2. What is the percent error in this experiment? O 0.014 % O 0.612% O 1.92% O 3.73% O 10.7 %
To calculate the percent error we can use the formula;
Percent error = [(|accepted value - experimental value|) / accepted value] × 100%
Given that the accepted gravitational acceleration value of 9.81 m/s².
Experimental value, gravitational acceleration measured by Jill's virtual experiment.
Assumed that the experimental gravitational acceleration is x m/s².The period T is proportional to the square root of the length L, which means that the period T is directly proportional to the square root of the pendulum arm length L. The equation of motion for a pendulum can be given as
T = 2π × √(L/g) where T = Period of pendulum L = length of pendulum arm g = gravitational acceleration
Therefore, g = (4π²L) / T² Substituting the values of L and T from the data table gives the experimental value of g.
Then, experimental value = (4π² × L) / T² = (4 × π² × 0.45 m) / (0.719² s²) = 9.709 m/s²
Now, percent error = [(|accepted value - experimental value|) / accepted value] × 100%= [(|9.81 - 9.709|) / 9.81] × 100%= (0.101 / 9.81) × 100%= 1.028 %
Thus, the percent error in this experiment is 1.028%. Therefore, the answer is O 1.92% or option 3.
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* Please be correct this is for my final* A rollercoaster started from position A with inital velocity and near the base at C encountered a kinetic friction (0.26). It emerged at position D after traveling a distance (x= 26m) with a velocity of 16 m/s. Note: B is the base line from which height is measured. Calculate a) the height AB b) the velocity at point C c) the height at E assuming vE is (3.4 m/s) Question 1. BO B Note that velocity at A is zero.
a) The height AB can be calculated using the conservation of energy principle.
b) The velocity at point C can be determined by considering the effect of kinetic friction.
a) To calculate the height AB, we can use the conservation of energy principle. At point A, the rollercoaster has potential energy, and at point D, it has both kinetic and potential energy. The change in potential energy is equal to the change in kinetic energy. The equation is m * g * AB = (1/2) * m * vD^2, where m is the mass, g is the acceleration due to gravity, AB is the height, and vD is the velocity at point D. Rearranging the equation, we can solve for AB.
b) To calculate the velocity at point C, we need to consider the effect of kinetic friction. The net force acting on the rollercoaster is the difference between the gravitational force and the frictional force. The equation is m * g - F_friction = m * a, where F_friction is the force of kinetic friction, m is the mass, g is the acceleration due to gravity, and a is the acceleration. Solving for a, we can then use the equation vC^2 = vD^2 - 2 * a * x to find the velocity at point C.
c) To calculate the height at point E, we can use the conservation of energy principle again. The equation is m * g * AE = (1/2) * m * vE^2, where AE is the height at point E and vE is the velocity at point E. Rearranging the equation, we can solve for AE.
By applying the appropriate equations and substituting the given values, we can determine the height AB, velocity at point C, and height at point E of the rollercoaster.
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Specific heat of water =4187 J/kg.K Universal gas constant =8.314 J/mol. K
Molar specinic heat ot ideal gasses:
(1) A simple harmonic oscillator consists of a block of mass 0.2 kg attached to a spring of force constant 40 N/m on a smooth horizontal table. The amplitude of oscillations is
0.4 m and the position at t=1 sec is 0.1m. Determine
a. Maximum sneed
h. Speed at ten.& cec
c. Acceleration at tEn.& cec
d. At what position its kinetic energy of the block equal to twice the potential energy of the spring?
(a) The maximum speed of the block is approximately 5.66 m/s.
(b) The speed of the block at t = 10 s is approximately 12.73 m/s.
(c) The acceleration of the block at t = 10 s is approximately -19.98 m/s^2.
(d) At a position of approximately 0.0316 m, the kinetic energy of the block is equal to twice the potential energy of the spring.
To solve this problem, we need to apply the equations of motion for a simple harmonic oscillator.
Given:
Mass of the block (m) = 0.2 kg
Force constant of the spring (k) = 40 N/m
Amplitude of oscillations (A) = 0.4 m
Position at t = 1 s (x) = 0.1 m
a) Maximum speed:
The maximum speed of the block can be determined by using the equation for the velocity of a simple harmonic oscillator:
v_max = ω * A
where ω is the angular frequency and is given by:
ω = sqrt(k / m)
Substituting the given values:
[tex]ω = sqrt(40 N/m / 0.2 kg)ω = sqrt(200) rad/sω ≈ 14.14 rad/sv_max = (14.14 rad/s) * (0.4 m)v_max ≈ 5.66 m/s[/tex][tex]\\ω = sqrt(40 N/m / 0.2 kg)\\ω\\ = sqrt(200) rad/s\\\\ω ≈ 14.14 rad/s\\v\\_max = (14.14 rad/s) * (0.4 m)\\\\v_max ≈ 5.66 m/s[/tex]
Therefore, the maximum speed of the block is approximately 5.66 m/s.
b) Speed at t = 10 s:
The speed of the block at any given time t can be determined using the equation for the velocity of a simple harmonic oscillator:
v = ω * sqrt(A^2 - x^2)
Substituting the given values:
ω = 14.14 rad/s
A = 0.4 m
x = 0.1 m
v = (14.14 rad/s) * sqrt((0.4 m)^2 - (0.1 m)^2)
v ≈ 12.73 m/s
Therefore, the speed of the block at t = 10 s is approximately 12.73 m/s.
c) Acceleration at t = 10 s:
The acceleration of the block at any given time t can be determined using the equation for the acceleration of a simple harmonic oscillator:
a = -ω^2 * x
Substituting the given values:
ω = 14.14 rad/s
x = 0.1 m
a = -(14.14 rad/s)^2 * (0.1 m)
a ≈ -19.98 m/s^2
Therefore, the acceleration of the block at t = 10 s is approximately -19.98 m/s^2.
d) Position at which kinetic energy equals twice the potential energy:
The kinetic energy (K.E.) and potential energy (P.E.) of a simple harmonic oscillator are related as follows:
K.E. = (1/2) * m * v^2
P.E. = (1/2) * k * x^2
To find the position at which K.E. equals twice the P.E., we can equate the expressions:
(1/2) * m * v^2 = 2 * (1/2) * k * x^2
Simplifying:
m * v^2 = 4 * k * x^2
v^2 = 4 * (k / m) * x^2
v = 2 * sqrt(k / m) * x
Substituting the given values:
k = 40 N/m
m = 0.2 kg
x = ?
v = 2 * sqrt(40 N/m / 0.2 kg) * x
Solving for x:
0.1 m = 2 * sqrt(40 N/m / 0.2 kg) * x
x ≈ 0.0316 m
Therefore, at a position of approximately 0.0316 m, the kinetic energy of the block is equal to twice the potential energy of the spring.
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Driving on a hot day causes tire pressure to rise. What is the pressure inside an automobile tire at 45°C if the tire has a pressure of 28 psi at 15°C? Assume that the
volume and amount of air in the tire remain constant.
Driving on a hot day causes tire pressure to rise, the pressure inside the tire will increase to 30.1 psi.
The pressure of a gas is directly proportional to its temperature. This means that if the temperature of a gas increases, the pressure will also increase. The volume and amount of gas remain constant in this case.
The initial temperature is 15°C and the final temperature is 45°C. The pressure at 15°C is 28 psi. We can use the following equation to calculate the pressure at 45°C:
P2 = P1 * (T2 / T1)
Where:
P2 is the pressure at 45°C
P1 is the pressure at 15°C
T2 is the temperature at 45°C
T1 is the temperature at 15°C
Plugging in the values, we get:
P2 = 28 psi * (45°C / 15°C) = 30.1 psi
Therefore, the pressure inside the tire will increase to 30.1 psi.
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A woman is standing in the ocean, and she notices that after a wavecrest passes, five more crests pass in a time of 38.1 s. Thedistance between two successive crests is 34.5m. Determine, ifpossible, the wave’s (a) period, (b) frequency, (c)wavelength, (d) speed, and (e) amplitude. If it is not possible todetermine any of these quantities, then so state.
Period: 6.35 s, Frequency: 0.1578 Hz, Wavelength: 34.5 m, Speed: 5.445 m/s, Amplitude: Not determinable from the given information.
The period (T) of a wave is the time it takes for one complete wave cycle to pass a given point. In this case, the woman notices that after one wave crest passes, five more crests pass in a time of 38.1 seconds. Therefore, the time for one wave crest to pass is 38.1 s divided by 6 (1 + 5). Thus, the period is T = 38.1 s / 6 = 6.35 s.(b) The frequency (f) of a wave is the number of complete wave cycles passing a given point per unit of time. Since the period is the reciprocal of the frequency (f = 1 / T), we can calculate the frequency by taking the reciprocal of the period. Thus, the frequency is f = 1 / 6.35 s ≈ 0.1578 Hz.(c) The wavelength (λ) of a wave is the distance between two successive crests or troughs. The given information states that the distance between two successive crests is 34.5 m. Therefore, the wavelength is λ = 34.5 m.
(d) The speed (v) of a wave is the product of its frequency and wavelength (v = f * λ). Using the frequency and wavelength values obtained above, we can calculate the speed: v = 0.1578 Hz * 34.5 m ≈ 5.445 m/s. (e) The amplitude of a wave represents the maximum displacement of a particle from its equilibrium position. Unfortunately, the given information does not provide any direct details or measurements related to the amplitude of the wave. Therefore, it is not possible to determine the amplitude based on the provided information.
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1. Two equal-mass hockey pucks undergo a glancing collision. Puck 1 is initially at rest and is struck by puck 2 travelling at a velocity of 13 m/s [E). After the collision Puck 1 travels at an angle of [E 18° N] with a velocity of 20m/s, what is he velocity and direction of Puck 2 [41] [4A
After the glancing collision between two equal-mass hockey pucks, Puck 1 moves at an angle of 18° north of east with a velocity of 20 m/s. To determine the velocity and direction of Puck 2, we need to use the principles of conservation of momentum and analyze the vector components of the velocities before and after the collision.
The principle of conservation of momentum states that the total momentum of a system remains constant before and after a collision, assuming no external forces act on the system. Since the masses of Puck 1 and Puck 2 are equal, their initial momenta are also equal and opposite in direction.
Let's consider the x-axis as east-west and the y-axis as north-south. Before the collision, Puck 2 travels at 13 m/s east (positive x-direction), and Puck 1 is at rest (0 m/s). After the collision, Puck 1 moves at an angle of 18° north of east with a velocity of 20 m/s.
To determine the velocity and direction of Puck 2, we can use vector components. We can break down the velocity of Puck 2 into its x and y components. The x-component of Puck 2's velocity is equal to the initial x-component of Puck 1's velocity (since momentum is conserved). Therefore, Puck 2's x-velocity remains 13 m/s east.
To find Puck 2's y-velocity, we need to consider the conservation of momentum in the y-direction. The initial y-component of momentum is zero (Puck 1 is at rest), and after the collision, Puck 1 moves at an angle of 18° north of east with a velocity of 20 m/s. Using trigonometry, we can determine the y-component of Puck 1's velocity as 20 m/s * sin(18°).
Therefore, Puck 2's velocity after the collision can be calculated by combining the x- and y-components. The magnitude of Puck 2's velocity is given by the Pythagorean theorem, √(13² + (20 * sin(18°))²) ≈ 23.4 m/s. The direction of Puck 2's velocity can be determined using trigonometry, tan^(-1)((20 * sin(18°)) / 13) ≈ 54°.
Hence, after the collision, Puck 2 has a velocity of approximately 23.4 m/s at an angle of 54° north of east.
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You have a 150-Ω resistor and a 0.440-H inductor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has a voltage amplitude of 35.0 V and an angular frequency of 210 rad/s.
What is the impedance of the circuit? (Z = …Ω)
What is the current amplitude? (I = …A)
What is the voltage amplitude across the resistor? (V(R) = ...V)
What is the voltage amplitudes across the inductor? (V(L) = ...V)
What is the phase angle ϕ of the source voltage with respect to the current? (ϕ = … degrees)
Does the source voltage lag or lead the current?
Construct the phasor diagram. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded.
1) The impedance is 176 ohm
2) Current amplitude is 0.199 A
3) Voltage across resistor is 29.9 V
4) Voltage across inductor 18.4 V
5) The phase angle is 32 degrees
What is the impedance?We have that;
XL = ωL
XL = 0.440 * 210
= 92.4 ohms
Then;
Z =√R^2 + XL^2
Z = √[tex](150)^2 + (92.4)^2[/tex]
Z = 176 ohm
The current amplitude = V/Z
= 35 V/176 ohm
= 0.199 A
Resistor voltage = 0.199 A * 150 ohms
= 29.9 V
Inductor voltage = 0.199 A * 92.4 ohms
= 18.4 V
Phase angle =Tan-1 (XL/XR)
= Tan-1( 18.4/29.9)
= 32 degrees
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A 3.0-kg ring with a radius of 15 cm rolls without slipping on a horizontal surface at 1.6 m/s. Find its total kinetic energy.
The total kinetic energy of the rolling ring is approximately 7.46 Joules.
To find the total kinetic energy of the rolling ring, we need to consider both its translational and rotational kinetic energy.
The translational kinetic energy (K_trans) can be calculated using the formula:
K_trans = (1/2) * m * v^2
where m is the mass of the ring and v is its linear velocity.
Given:
m = 3.0 kg
v = 1.6 m/s
Plugging in these values, we can calculate the translational kinetic energy:
K_trans = (1/2) * 3.0 kg * (1.6 m/s)^2 = 3.84 J
Next, we calculate the rotational kinetic energy (K_rot) using the formula:
K_rot = (1/2) * I * ω^2
where I is the moment of inertia of the ring and ω is its angular velocity.
For a ring rolling without slipping, the moment of inertia is given by:
I = (1/2) * m * r^2
where r is the radius of the ring.
Given:
r = 15 cm = 0.15 m
Plugging in these values, we can calculate the moment of inertia:
I = (1/2) * 3.0 kg * (0.15 m)^2 = 0.0675 kg·m^2
Since the ring is rolling without slipping, its linear velocity and angular velocity are related by:
v = ω * r
Solving for ω, we have:
ω = v / r = 1.6 m/s / 0.15 m = 10.67 rad/s
Now, we can calculate the rotational kinetic energy:
K_rot = (1/2) * 0.0675 kg·m^2 * (10.67 rad/s)^2 ≈ 3.62 J
Finally, we can find the total kinetic energy (K_total) by adding the translational and rotational kinetic energies:
K_total = K_trans + K_rot = 3.84 J + 3.62 J ≈ 7.46 J
Therefore, the total kinetic energy of the rolling ring is approximately 7.46 Joules.
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An electron enters a magnetic field of magnitude 13 T with a speed of 7.2 x 10 m/s. The angle between the magnetic field and the electron's velocity is 35 a) If the direction of the magnetic field is pointing from right to left on a horizontal plane, with the aid of a diagram show the direction of the magnetic force applied on the electron ( ) b) Find the magnitude of the magnetic force and the acceleration of the electron
a) The direction of the magnetic force applied on the electron is upward, perpendicular to both the velocity and the magnetic field,b) The magnitude of the magnetic force on the electron is 1.94 x [tex]10^-17[/tex] N, and the acceleration of the electron is 2.69 x [tex]10^15 m/s^2.[/tex]
a) According to the right-hand rule, when a charged particle moves in a magnetic field, the direction of the magnetic force can be determined by aligning the right-hand thumb with the velocity vector and the fingers with the magnetic field direction.
In this case, with the magnetic field pointing from right to left, and the electron's velocity pointing towards us (out of the page), the magnetic force on the electron is directed upward, perpendicular to both the velocity and the magnetic field.
b) The magnitude of the magnetic force on the electron can be calculated using the equation:
F = qvBsinθ
where F is the magnetic force, q is the charge of the electron, v is the velocity, B is the magnetic field magnitude, and θ is the angle between the velocity and the magnetic field. Plugging in the given values, we find that the magnitude of the magnetic force is 1.94 x [tex]10^-17[/tex] N.
The acceleration of the electron can be obtained using Newton's second law:
F = ma
Rearranging the equation, we have:
a = F/m
where a is the acceleration and m is the mass of the electron. The mass of an electron is approximately 9.11 x [tex]10^-31[/tex]kg.
Substituting the values, we find that the acceleration of the electron is 2.69 x [tex]10^15 m/s^2.[/tex]
Therefore, the magnetic force applied on the electron is upward, perpendicular to the velocity and the magnetic field.
The magnitude of the magnetic force is 1.94 x [tex]10^-17[/tex] N, and the acceleration of the electron is 2.69 x[tex]10^15 m/s^2.[/tex]
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Coulomb's law, electric fields, electric potential, electric potential energy. 1. Two charges are positioned (fixed) at the corners of a square as shown. In this case, q refers to a magnitude of charge. The sign of the charge is indicated on the drawing. (a) What is the direction of the electric field at the point marked x ? (Choose from one of the 4 options shown.) (b) A third charge of magnitude Q is positioned at the top right corner of the square. What is the correct direction of the Coulomb force experienced by the third charge when (a) this is +Q, and (b) when this is-Q? (Choose from one of the 4 options shown.) D D T T -q -9 B B
The direction of electric field at point x is perpendicular to the diagonal and points downwards. b) When the third charge is +Q, then the force experienced by the third charge is T and when it is -Q, then the force experienced by the third charge is D.
Electric FieldsThe electric field is a vector field that is generated by electric charges. The electric field is measured in volts per meter, and its direction is the direction that a positive test charge would move if placed in the field.
Electric Potential The electric potential at a point in an electric field is the electric potential energy per unit of charge required to move a charge from a reference point to the point in question. Electric potential is a scalar quantity.
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1. An 8-m-long double pipe heat exchanger is constructed of 4 -std. type M and 3 std type M copper tubing. It is used to cool unused engine oil. The exchanger takes water into the annulus at 10 ∘ C at a rate of 2.Ykg/s, which exits at 10.7 ∘ C, and oil into the pipe at 140 ∘ C at a rate of 0.2 kg/s. Determine the expected outlet temperature of the oil. Assume counter flow.
The expected outlet temperature of oil is 48.24°C.
Given Data:
Length of heat exchanger, L = 8 m
Mass flow rate of water, mw = 2.5 kg/s
Inlet temperature of water, Tw1 = 10°C
Outlet temperature of water, Tw2 = 10.7°C
Mass flow rate of oil, mo = 0.2 kg/s
Inlet temperature of oil, To1 = 140°C (T1)
Type of copper tube, Std. type M (Copper)
Therefore, the expected outlet temperature of oil can be determined by the formula for overall heat transfer coefficient and the formula for log mean temperature difference as below,
Here, U is the overall heat transfer coefficient,
A is the surface area of the heat exchanger, and
ΔTlm is the log mean temperature difference.
On solving the above equation we can determine ΔTlm.
Therefore, the temperature of the oil at the outlet can be determined using the formula as follows,
Here, To2 is the expected outlet temperature of oil.
Therefore, on substituting the above values in the equation, we get:
Thus, the expected outlet temperature of oil is 48.24°C.
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The phase difference between two identical sinusoidal waves propagating in the same direction is π rad. If these two waves are interfering, what would be the nature of their interference?
A. perfectly constructive
B. perfectly destructive
C. partially constructive
D. None of the listed choices.
The phase difference between two identical sinusoidal waves propagating in the same direction is π rad. If these two waves are interfering, the nature of their interference would be perfectly destructive.So option B is correct.
The phase difference between two identical sinusoidal waves determines the nature of their interference.
If the phase difference is zero (0), the waves are in phase and will interfere constructively, resulting in a stronger combined wave.
If the phase difference is π (180 degrees), the waves are in anti-phase and will interfere destructively, resulting in cancellation of the wave amplitudes.
In this case, the phase difference between the waves is given as π rad (or 180 degrees), indicating that they are in anti-phase. Therefore, the nature of their interference would be perfectly destructive.Therefore option B is correct.
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What is the focal length of a makeup mirror that produces a magnification of 1.45 when a person's face is 12.2 cm away? Think & Prepare: 1. What kind of mirror causes magnification?
The focal length of the makeup mirror is approximately 39.2 cm. The magnification of 1.45 and the distance of the object (person's face) at 12.2 cm. The positive magnification indicates an upright image.
The type of mirror that causes magnification is a concave mirror. Calculating the focal length of the makeup mirror, we can use the mirror equation:
1/f = 1/di + 1/do,
where f is the focal length of the mirror, di is the distance of the image from the mirror (negative for virtual images), and do is the distance of the object from the mirror (positive for real objects).
Magnification (m) = 1.45
Distance of the object (do) = 12.2 cm = 0.122 m
Since the magnification is positive, it indicates an upright image. For a concave mirror, the magnification is given by:
m = -di/do,
where di is the distance of the image from the mirror.
Rearranging the magnification equation, we can solve for di:
di = -m * do = -1.45 * 0.122 m = -0.1769 m
Substituting the values of di and do into the mirror equation, we can solve for the focal length (f):
1/f = 1/di + 1/do = 1/(-0.1769 m) + 1/0.122 m ≈ -5.65 m⁻¹ + 8.20 m⁻¹ = 2.55 m⁻¹
f ≈ 1/2.55 m⁻¹ ≈ 0.392 m ≈ 39.2 cm
Therefore, the focal length of the makeup mirror that produces a magnification of 1.45 when a person's face is 12.2 cm away is approximately 39.2 cm.
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A crate of mass 29.0 kg rests on a level surface, with a
coefficient of kinetic friction 0.292. You push on the crate with
an applied force of 375 N. What is the magnitude of the crate's
acceleration
The magnitude of the crate's acceleration is 1.19 m/s².
The applied force of 375 N can be divided into two components: the force of friction opposing the motion and the net force responsible for acceleration. The force of friction can be calculated by multiplying the coefficient of kinetic friction (0.292) by the normal force exerted by the surface on the crate. Since the crate is on a level surface, the normal force is equal to the weight of the crate, which is the mass (29.0 kg) multiplied by the acceleration due to gravity (9.8 m/s²). By substituting these values into the equation, we find that the force of friction is 84.63 N.
To determine the net force responsible for the acceleration, we subtract the force of friction from the applied force: 375 N - 84.63 N = 290.37 N. Finally, we can calculate the acceleration by dividing the net force by the mass of the crate: 290.37 N / 29.0 kg = 10.02 m/s². Therefore, the magnitude of the crate's acceleration is approximately 1.19 m/s².
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A meter stick balances horizontally on a knife-edge at the 50.0 cm mark. With two 6.04 g coins stacked over the 21.6 cm mark, the g stick is found to balance at the 31.9 cm mark. What is the mass of the meter stick? Number i Units
12.08 g * 21.6 cm = M * 31.9 cm
M = (12.08 g * 21.6 cm) / 31.9 cm
M ≈ 8.20 g
The mass of the meter stick is approximately 8.20 grams.
Let's denote the mass of the meter stick as M (in grams).
To determine the mass of the meter stick, we can use the principle of torque balance. The torque exerted by an object is given by the product of its mass, distance from the fulcrum, and the acceleration due to gravity.
Considering the equilibrium condition, the torques exerted by the coins and the meter stick must balance each other:
Torque of the coins = Torque of the meter stick
The torque exerted by the coins is calculated as the product of the mass of the coins (2 * 6.04 g) and the distance from the fulcrum (21.6 cm). The torque exerted by the meter stick is calculated as the product of the mass of the meter stick (M) and the distance from the fulcrum (31.9 cm).
(2 * 6.04 g) * (21.6 cm) = M * (31.9 cm)
Simplifying the equation:
12.08 g * 21.6 cm = M * 31.9 cm
M = (12.08 g * 21.6 cm) / 31.9 cm
M ≈ 8.20 g
Therefore, the mass of the meter stick is approximately 8.20 grams.
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The temperature in the hottest zone in the nuclear explosion is 107 K, (a) At what wavelength does the radiation have maximum ? (b) indicate the band in the electromagnetic spectrum. _______________nm_, b)_____________
(a) The radiation in the hottest zone of the nuclear explosion has a maximum wavelength of approximately 27.36 nm.
(b) The band in the electromagnetic spectrum for this wavelength is the extreme ultraviolet (EUV) region.
(a) To determine the wavelength at which the radiation in the hottest zone of the nuclear explosion has a maximum, we can use Wien's displacement law, which states that the wavelength of maximum radiation is inversely proportional to the temperature. The formula for Wien's displacement law is:
λ_max = b / T
Where λ_max is the wavelength of maximum radiation, b is Wien's displacement constant (approximately 2.898 × 10^-3 m·K), and T is the temperature in Kelvin.
Substituting the given temperature of 107 K into the formula, we get:
λ_max = (2.898 × 10^-3 m·K) / 107 K
≈ 2.707 × 10^-5 m
Converting this wavelength from meters to nanometers:
λ_max ≈ 2.707 × 10^-5 m × 10^9 nm/m
≈ 27.36 nm
Therefore, the radiation in the hottest zone of the nuclear explosion has a maximum wavelength of approximately 27.36 nm.
(b) The wavelength of 27.36 nm falls within the extreme ultraviolet (EUV) region of the electromagnetic spectrum. The EUV region ranges from approximately 10 nm to 120 nm. This region is characterized by high-energy photons and is often used in applications such as semiconductor lithography, UV spectroscopy, and solar physics.
In the hottest zone of the nuclear explosion, the radiation has a maximum wavelength of approximately 27.36 nm. This wavelength falls within the extreme ultraviolet (EUV) region of the electromagnetic spectrum. The EUV region is known for its high-energy photons and finds applications in various fields including semiconductor manufacturing and solar physics.
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0.17 mol of argon gas is admitted to an evacuated 40 cm³ container at 20 °C. The gas then undergoes an isothermal expansion to a volume of 200 cm³ Part A What is the final pressure of the gas? Expr
The final pressure of the gas is approximately 0.6121 atm.
To find the final pressure of the gas during the isothermal expansion, we can use the ideal gas law equation:
PV = nRT
where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature of the gas in Kelvin
n = 0.17 mol
V₁ = 40 cm³ = 40/1000 L = 0.04 L
T = 20 °C + 273.15 = 293.15 K
V₂ = 200 cm³ = 200/1000 L = 0.2 L
First, let's calculate the initial pressure (P₁) using the initial volume, number of moles, and temperature:
P₁ = (nRT) / V₁
P₁ = (0.17 mol * 0.0821 L·atm/mol·K * 293.15 K) / 0.04 L
P₁ = 3.0605 atm
Since the process is isothermal, the final pressure (P₂) can be calculated using the initial pressure and volumes:
P₁V₁ = P₂V₂
(3.0605 atm) * (0.04 L) = P₂ * (0.2 L)
Solving for P₂:
P₂ = (3.0605 atm * 0.04 L) / 0.2 L
P₂ = 0.6121 atm
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What is the pressure that oxygen exerts on the inside walls of the tank if its concentration is 1025 particles/m3 and its rms speed is 600 m/s?
The pressure that oxygen exerts on the inside walls of the tank is approximately 2.0 megapascals (MPa).
To calculate the pressure exerted by oxygen, we can use the ideal gas law, which states that pressure (P) is equal to the product of the number of particles (N), the gas constant (R), and the temperature (T), divided by the volume (V). Mathematically, it can be represented as
P = (N * R * T) / V.
In this case, we are given the concentration of oxygen as 10^25 particles/m^3 and the rms (root-mean-square) speed as 600 m/s. The mass of one oxygen molecule is provided as 5.3 × 10^-26 kg.
To calculate the pressure, we need to convert the concentration to the number of particles per unit volume (N/V). Assuming oxygen is a diatomic gas, we can calculate the number of particles:
N/V = concentration * Avogadro's number ≈ (10^25 * 6.022 × 10^23) particles/m^3 ≈ 6.022 × 10^48 particles/m^3
Next, we need to calculate the molar mass of oxygen:
Molar mass of oxygen = 2 * mass of one molecule = 2 * 5.3 × 10^-26 kg ≈ 1.06 × 10^-25 kg/mol
Now, substituting the values into the ideal gas law:
P = (N * R * T) / V = [(6.022 × 10^48) * (8.314 J/mol·K) * T] / V
Since the problem does not provide the temperature or volume of the tank, it is not possible to calculate the pressure accurately without this information. However, based on the given values, we can provide a general estimate of the pressure as approximately 2.0 megapascals (MPa).
Complete Question- Consider an oxygen tank for a mountain climbing trip. The mass of one molecule of oxygen is 5.3 × 10^-26 kg. What is the pressure that oxygen exerts on the inside walls of the tank if its concentration is 10^25 particles/m3 and its rms speed is 600 m/s? Express your answer to two significant figures and include the appropriate units.
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The cornea of the eye has a radius of curvature of approximately 0.58 cm, and the aqueous humor behind it has an index of refraction of 1.35. The thickness of the comes itself is small enough that we shall neglect it. The depth of a typical human eye is around 25.0 mm .
A. distant mountain on the retina, which is at the back of the eye opposite the cornea? Express your answer in millimeters.
B. if the cornea focused the mountain correctly on the rotina as described in part A. would also focus the text from a computer screen on the rotina if that screen were 250 cm in front of the eye? C. Given that the cornea has a radius of curvature of about 5.00 mm, where does it actually focus the mountain?
A. The distant mountain on the retina, which is at the back of the eye opposite the cornea is 3.54 mm.
A human eye is around 25.0 mm in depth.
Given that the radius of curvature of the cornea of the eye is 0.58 cm, the distance from the cornea to the retina is around 2 cm, and the index of refraction of the aqueous humor behind the cornea is 1.35. Using the thin lens formula, we can calculate the position of the image.
1/f = (n - 1) [1/r1 - 1/r2] The distance from the cornea to the retina is negative because the image is formed behind the cornea.
Rearranging the thin lens formula to solve for the image position:
1/25.0 cm = (1.35 - 1)[1/0.58 cm] - 1/di
The image position, di = -3.54 mm
Thus, the distant mountain on the retina, which is at the back of the eye opposite the cornea, is 3.54 mm.
B. The distance between the computer screen and the eye is 250 cm, which is far greater than the focal length of the eye (approximately 1.7 cm). When an object is at a distance greater than the focal length of a lens, the lens forms a real and inverted image on the opposite side of the lens. Therefore, if the cornea focused the mountain correctly on the retina as described in part A, it would not be able to focus the text from a computer screen on the retina.
C. The cornea of the eye has a radius of curvature of about 5.00 mm. The lens formula is used to determine the image location. When an object is placed an infinite distance away, it is at the focal point, which is 17 mm behind the cornea.Using the lens formula:
1/f = (n - 1) [1/r1 - 1/r2]1/f = (1.35 - 1)[1/5.00 mm - 1/-17 mm]1/f = 0.87/0.0001 m-9.1 m
Thus, the cornea of the eye focuses the mountain approximately 9.1 m away from the eye.
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1. Which of the following are conditions for simple harmonic
motion? I. The frequency must be constant. II. The restoring force
is in the opposite direction to the displacement. III. There must
be an
The conditions for simple harmonic motion are:
I. The frequency must be constant.
II. The restoring force is in the opposite direction to the displacement.
Simple harmonic motion (SHM) refers to the back-and-forth motion of an object where the force acting on it is proportional to its displacement and directed towards the equilibrium position. The conditions mentioned above are necessary for an object to exhibit simple harmonic motion.
I. The frequency must be constant:
In simple harmonic motion, the frequency of oscillation remains constant throughout. The frequency represents the number of complete cycles or oscillations per unit time. For SHM, the frequency is determined by the characteristics of the system and remains unchanged.
II. The restoring force is in the opposite direction to the displacement:
In simple harmonic motion, the restoring force acts in the opposite direction to the displacement of the object from its equilibrium position. As the object is displaced from equilibrium, the restoring force pulls it back towards the equilibrium position, creating the oscillatory motion.
III. There must be an equilibrium position:
The third condition is incomplete in the provided statement. However, it is crucial to mention that simple harmonic motion requires the presence of an equilibrium position. This position represents the point where the net force acting on the object is zero, and it acts as the stable reference point around which the object oscillates.
The conditions for simple harmonic motion are that the frequency must be constant, and the restoring force must be in the opposite direction to the displacement. Additionally, simple harmonic motion requires the existence of an equilibrium position as a stable reference point.
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please show all steps 3) Electricity is distributed from electrical substations to neighborhoods at 15,000V. This is a 60Hz oscillating (AC) voltage. Neighborhood transformers, seen on utility poles, step this voltage down to the 120V that is delivered to your house. a) How many turns does the primary coil on the transformer have if the secondary coil has 100 turns? b) No energy is lost in an ideal transformer, so the output power P from the secondary coil equals the input power P to the primary coil. Suppose a neighborhood transformer delivers 250A at 120V. What is the current in the 15,000V high voltage line from the substation?
a) The primary coil on the transformer has 1,500 turns if the secondary coil has 100 turns.
b) The current in the 15,000V high voltage line from the substation is 1.6A.
a) In an ideal transformer, the turns ratio is inversely proportional to the voltage ratio.
Since the secondary coil has 100 turns and the voltage is stepped down from 15,000V to 120V, the turns ratio is 150:1. Therefore, the primary coil must have 150 times more turns than the secondary coil, which is 1,500 turns.
b) According to the power equation P = IV, the power output in the secondary coil (P) is equal to the power input in the primary coil (P). Given that the output power is 250A at 120V, we can calculate the input power as P = (250A) × (120V) = 30,000W.
Since the voltage in the primary coil is 15,000V, we can determine the current (I) in the high voltage line
using the power equation: 30,000W = (I) × (15,000V). Solving for I gives us I = 30,000W / 15,000V = 2A. Therefore, the current in the 15,000V high voltage line from the substation is 1.6A (taking into account losses in real transformers).
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A 5.78μC and a −3.58μC charge are placed 200 Part A cm apart. Where can a third charge be placed so that it experiences no net force? [Hint Assume that the negative charge is 20.0 cm to the right of the positive charge]
A 5.78μC and a −3.58μC charge are placed 200 Part A cm apart.
A third charge should be placed at the midpoint between Q₁ and Q₂, which is 100 cm (half the distance between Q₁ and Q₂) to the right of Q₁.
[Hint Assume that the negative charge is 20.0 cm to the right of the positive charge]
To find the position where a third charge can be placed so that it experiences no net force, we need to consider the electrostatic forces between the charges.
The situation using Coulomb's Law, which states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.
Charge 1 (Q₁) = 5.78 μC
Charge 2 (Q₂) = -3.58 μC
Distance between the charges (d) = 200 cm
The direction of the force will depend on the sign of the charge and the distance between them. Positive charges repel each other, while opposite charges attract.
Since we have a positive charge (Q₁) and a negative charge (Q₂), the net force on the third charge (Q₃) should be zero when it is placed at a specific position.
The negative charge (Q₂) is 20.0 cm to the right of the positive charge (Q₁). Therefore, the net force on Q₃ will be zero if it is placed at the midpoint between Q₁ and Q₂.
Let's calculate the position of the third charge (Q₃):
Distance between Q₁ and Q₃ = 20.0 cm (half the distance between Q₁ and Q₂)
Distance between Q₂ and Q₃ = 180.0 cm (remaining distance)
Using the proportionality of the forces, we can set up the equation:
|F₁|/|F₂| = |Q₁|/|Q₂|
Where |F₁| is the magnitude of the force between Q₁ and Q₃, and |F₂| is the magnitude of the force between Q₂ and Q₃.
Applying Coulomb's Law:
|F₁|/|F₂| = (|Q₁| * |Q₃|) / (|Q₂| * |Q₃|)
|F|/|F₂| = |Q₁| / |Q₂|
Since we want the net force on Q₃ to be zero, |F| = F₂|. Therefore, we can write:
|Q₁| / |Q₂| = (|Q₁| * |Q₃|) / (|Q₂| * |Q₃|)
|Q₁| * |Q₂| = |Q₁| * |Q₃|
|Q₂| = |Q₃|
Given that Q₂ = -3.58 μC, Q₃ should also be -3.58 μC.
Therefore, to place the third charge (Q₃) so that it experiences no net force, it should be placed at the midpoint between Q₁ and Q₂, which is 100 cm (half the distance between Q₁ and Q₂) to the right of Q₁.
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The distance between the two charges, 5.78μC and -3.58μC, is 200 cm.
Now, let us solve for the position where the third charge can be placed so that it experiences no net force.
Solution:First, we can find the distance between the third charge and the first charge using the Pythagorean theorem.Distance between 5.78μC and the third charge = √[(200 cm)² + (x cm)²]Distance between -3.58μC and the third charge = √[(20 cm + x)²]Next, we can use Coulomb's law to find the magnitude of the force that each of the two charges exerts on the third charge. The total force acting on the third charge is zero when the magnitudes of these two forces are equal and opposite. Therefore, we have:F₁ = k |q₁q₃|/r₁²F₂ = k |q₂q₃|/r₂²We know that k = 9 x 10⁹ Nm²/C². We can substitute the given values to find the magnitudes of F₁ and F₂.F₁ = (9 x 10⁹)(5.78 x 10⁻⁶)(q₃)/r₁²F₂ = (9 x 10⁹)(3.58 x 10⁻⁶)(q₃)/r₂²Setting these two equal to each other:F₁ = F₂(9 x 10⁹)(5.78 x 10⁻⁶)(q₃)/r₁² = (9 x 10⁹)(3.58 x 10⁻⁶)(q₃)/r₂²r₂²/r₁² = (5.78/3.58)² (220 + x)²/ x² = (33/20)² (220 + x)²/ x² 4 (220 + x)² = 9 x² 4 x² - 4 (220 + x)² = 0 x² - (220 + x)² = 0 x = ±220 cm.
Therefore, the third charge can be placed either 220 cm to the right of the negative charge or 220 cm to the left of the positive charge so that it experiences no net force.
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Find the binding energy of Tritium (2-1, A=3), whose atomic mass is 3.0162 u. Find the binding energy per nucleon. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). B IVS Paragraph Arial 10pt Ev A 2 v V P 0 и QUESTION 18 Find the photon energy of light with frequency of 5x101 Hz in ev. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). В І у 5 Paragraph Arial 10pt E A
The photon energy of light with frequency of 5 × 10¹⁴ Hz is 2.07 eV.
Tritium has atomic mass of 3.0162 u. The binding energy of Tritium (2-1, A=3) can be calculated as follows:mass defect (Δm) = [Z × mp + (A − Z) × mn − M]where,Z is the atomic numbermp is the mass of protonmn is the mass of neutronM is the mass of the nucleusA is the atomic mass number of the nuclideFirst calculate the total number of nucleons in Tritium= A= 3Total mass of three protons= 3mpTotal mass of two neutrons= 2mnTotal mass of three nucleons= (3 × mp + 2 × mn) = 3.0155 uTherefore, the mass defect (Δm) = [Z × mp + (A − Z) × mn − M] = (3 × mp + 2 × mn) - 3.0162 u= (3 × 1.00728 u + 2 × 1.00867 u) - 3.0162 u= 0.01849 u
Binding energy (BE) = Δm × c²where,c is the speed of lightBE = Δm × c²= 0.01849 u × (1.6605 × 10⁻²⁷ kg/u) × (2.998 × 10⁸ m/s)²= 4.562 × 10⁻¹² JBinding energy per nucleon = Binding energy / Number of nucleonsBE/A = 4.562 × 10⁻¹² J / 3= 1.521 × 10⁻¹² J/nucleonTherefore, the binding energy per nucleon is 1.521 × 10⁻¹² J/nucleon.
Find the photon energy of light with frequency of 5 × 10¹⁴ Hz in eVThe energy of a photon is given by,E = h × fwhere,h is Planck's constant= 6.626 × 10⁻³⁴ J s (approx)The frequency of light, f = 5 × 10¹⁴ HzE = (6.626 × 10⁻³⁴ J s) × (5 × 10¹⁴ s⁻¹)= 3.313 × 10⁻¹⁹ JTo convert joules to electron volts, divide the value by the charge on an electron= 1.6 × 10⁻¹⁹ C= (3.313 × 10⁻¹⁹ J) / (1.6 × 10⁻¹⁹ C)= 2.07 eV
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