The brass rod must be heated to 1157.89°C to be 2.2% longer than it is at 26°C.
When a brass rod is heated, it expands and increases in length. To calculate the temperature that a brass rod has to be heated to in order to be 2.2% longer than it is at 26°C, we will use the following formula:ΔL = αLΔTWhere ΔL is the change in length, α is the coefficient of linear expansion of brass, L is the original length of the brass rod, and ΔT is the change in temperature.α for brass is 19 × 10-6 /°C.ΔL is given as 2.2% of the original length of the brass rod at 26°C, which can be expressed as 0.022L.
Substituting the values into the formula:
0.022L = (19 × 10-6 /°C) × L × ΔT
ΔT = 0.022L / (19 × 10-6 /°C × L)
ΔT = 1157.89°C.
The brass rod must be heated to 1157.89°C to be 2.2% longer than it is at 26°C.
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Two positively charged particles, labeled 1 and 2, with the masses and charges shown in the figure, are placed some distance apart in empty space and are then released from rest. Each particle feels only the electrostatic force due to the other particle (ignore any other forces like gravity). How do the magnitudes of the initial forces on the two particles compare, and how do the magnitudes of the initial accelerations compare? a4 and ay are the magnitudes of the accelerations of particle 1 and 2, respectively. F1 is the magnitude of the force on 1 due to 2; F2 is the magnitude of the force on 2 due to 1.
The magnitudes of the initial forces on the two particles are equal in magnitude but opposite in direction. However, the magnitudes of the initial accelerations of the particles depend on their masses and charges.
According to Coulomb's law, the magnitude of the electrostatic force between two charged particles is given by the equation:
F = k * (|q1 * q2|) / r^2
where F is the magnitude of the force, k is the electrostatic constant, q1 and q2 are the charges of the particles, and r is the distance between them.
Since the charges of the particles are both positive, the forces on the particles will be attractive. The magnitudes of the forces, F1 and F2, will be equal, but their directions will be opposite. This is because the forces between the particles always act along the line joining their centers.
Now, when it comes to the magnitudes of the initial accelerations, they depend on the masses of the particles. The equation for the magnitude of acceleration is:
a = F / m
where a is the magnitude of the acceleration, F is the magnitude of the force, and m is the mass of the particle.
Since the masses of the particles are given in the figure, the magnitudes of their initial accelerations, a1 and a2, will depend on their respective masses. If particle 1 has a larger mass than particle 2, its acceleration will be smaller compared to particle 2.
In summary, the magnitudes of the initial forces on the particles are equal but opposite in direction. The magnitudes of the initial accelerations depend on the masses of the particles, with the particle of greater mass experiencing a smaller acceleration.
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Two identical positively charged spheres are apart from each
other at a distance 23.0 cm, and are experiencing an attraction
force of 4.25x10-9N. What is the magnitude of the charge
of each sphere, in
Since the spheres are identical, their charges can be assumed to be the same, so we can denote the charge on each sphere as q. By rearranging Coulomb's law to solve for the charge (q), we get q = sqrt((F *[tex]r^2[/tex]) / k).
The magnitude of the charge on each sphere can be determined using Coulomb's law, which relates the electrostatic force between two charged objects to the magnitude of their charges and the distance between them.
By rearranging the equation and substituting the given values, the charge on each sphere can be calculated.
Coulomb's law states that the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, it can be expressed as F = k * (|q1| * |q2|) / [tex]r^2[/tex], where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.
In this case, we have two identical positively charged spheres experiencing an attractive force. Since the spheres are identical, their charges can be assumed to be the same, so we can denote the charge on each sphere as q.
We are given the distance between the spheres (r = 23.0 cm) and the force of attraction (F = 4.25x[tex]10^-9[/tex] N). By rearranging Coulomb's law to solve for the charge (q), we get q = sqrt((F *[tex]r^2[/tex]) / k).
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Say we are at rest in a submarine in the ocean and a torpedo is
moving 40 m/s towards us and emitting a 50 Hz sound. Assuming a
perfect sonar reception system, what would the received frequency
in Hz
The received frequency would be approximately 55.74 Hz, higher than the emitted frequency, due to the Doppler effect caused by the torpedo moving towards the submarine.
The received frequency in Hz would be different from the emitted frequency due to the relative motion between the submarine and the torpedo. This effect is known as the Doppler effect.
In this scenario, since the torpedo is moving toward the submarine, the received frequency would be higher than the emitted frequency. The formula for calculating the Doppler effect in sound waves is given by:
Received frequency = Emitted frequency × (v + vr) / (v + vs)
Where:
"Emitted frequency" is the frequency emitted by the torpedo (50 Hz in this case).
"v" is the speed of sound in the medium (approximately 343 m/s in seawater).
"vr" is the velocity of the torpedo relative to the medium (40 m/s in this case, assuming it is moving directly towards the submarine).
"vs" is the velocity of the submarine relative to the medium (assumed to be at rest, so vs = 0).
Plugging in the values:
Received frequency = 50 Hz × (343 m/s + 40 m/s) / (343 m/s + 0 m/s)
Received frequency ≈ 55.74 Hz
Therefore, the received frequency in Hz would be approximately 55.74 Hz.
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5) A beaker contains 2 grams of ice at a temperature of -10°C. The mass of the beaker may be ignored. Heat is supplied to the beaker at a constant rate of 2200J/minute. The specific heat of ice is 2100 J/kgk and the heat of fusion for ice is 334 x103 J/kg. How much time passes before the ice starts to melt? (8 pts)
The time it takes for the ice to start melting is approximately 8.22 minutes.
To calculate the time before the ice starts to melt, we need to consider the heat required to raise the temperature of the ice from -10°C to its melting point (0°C) and the heat of fusion required to convert the ice at 0°C to water at the same temperature.
First, we calculate the heat required to raise the temperature of 2 grams of ice from -10°C to 0°C using the specific heat formula Q = m * c * ΔT, where Q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature. Substituting the given values, we get Q1 = 2 g * 2100 J/kg°C * (0°C - (-10°C)) = 42000 J.
Next, we calculate the heat of fusion required to convert the ice to water at 0°C using the formula Q = m * Hf, where Q is the heat, m is the mass, and Hf is the heat of fusion. Substituting the given values, we get Q2 = 2 g * 334 x 10³ J/kg = 668000 J.
Now, we sum up the heat required for temperature rise and the heat of fusion: Q_total = Q1 + Q2 = 42000 J + 668000 J = 710000 J.
Finally, we divide the total heat by the heat supplied per minute to obtain the time: t = Q_total / (2200 J/minute) ≈ 322.73 minutes ≈ 8.22 minutes.
Therefore, it takes approximately 8.22 minutes for the ice to start melting when heat is supplied at a constant rate of 2200 J/minute.
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1111. A giraffe, located 1.5m from the center of a Mary-go-round spins with a speed of 6m/s. There is a panda also in the Mary-go-round. How fast would a panda move if its 4.5m from the center(10pts)? what is the angular speed of the Mary-go-round(10pts)?
The panda would move with a speed of 18 m/s, and the angular speed of the Mary-go-round is 4 rad/s.
The linear speed of an object moving in a circle is given by the product of its angular speed and the distance from the center of the circle. In this case, we have the giraffe located 1.5m from the center and moving with a speed of 6 m/s. Therefore, we can calculate the angular speed of the giraffe using the formula:
Angular speed = Linear speed / Distance from the center
Angular speed = 6 m/s / 1.5 m
Angular speed = 4 rad/s
Now, to find the speed of the panda, who is located 4.5m from the center, we can use the same formula:
Speed of the panda = Angular speed * Distance from the center
Speed of the panda = 4 rad/s * 4.5 m
Speed of the panda = 18 m/s
So, the panda would move with a speed of 18 m/s, and the angular speed of the Mary-go-round is 4 rad/s.
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QUESTION 3 [20] 3.1. Using a diagram, explain why semiconductors are different from insulators.[7] 3.2. Explain why carbon in the diamod structure exhibits high resistivity typical of insulators. [6]
Semiconductors differ from insulators due to their unique electronic properties. Insulators have a large energy band gap, while semiconductors have a smaller band gap.
Furthermore, the presence of impurities or dopants in semiconductors allows for controlled manipulation of their conductivity. On the other hand, carbon in the diamond structure exhibits high resistivity typical of insulators due to its strong covalent bonds and a wide energy band gap.
Semiconductors and insulators have distinct characteristics due to their electronic band structures. Semiconductors possess a narrower band gap compared to insulators. This smaller energy gap allows electrons to be excited from the valence band to the conduction band more easily when subjected to external energy. Insulators, on the other hand, have a significantly larger band gap, making it difficult for electrons to move from the valence band to the conduction band, resulting in low conductivity.
Carbon in the diamond structure exhibits high resistivity similar to insulators due to its unique arrangement of atoms. In diamond, each carbon atom is covalently bonded to four neighboring carbon atoms in a tetrahedral structure. These strong covalent bonds create a wide energy band gap, which requires a significant amount of energy for electrons to transition from the valence band to the conduction band. As a result, diamond behaves as an insulator with high resistivity, as it does not readily allow the flow of electric current.
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Express 18/4 as a fraction of more than 1
When expressed as a fraction of more than 1, 18/4 is equivalent to 4 and 1/2.
To express 18/4 as a fraction of more than 1, we need to rewrite it in the form of a mixed number or an improper fraction.
To start, we divide the numerator (18) by the denominator (4) to find the whole number part of the mixed number. 18 divided by 4 equals 4 with a remainder of 2. So the whole number part is 4.
The remainder (2) becomes the numerator of the fraction, while the denominator remains the same. Thus, the fraction part is 2/4.
However, we can simplify this fraction further by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Dividing 2 by 2 equals 1, and dividing 4 by 2 equals 2. Therefore, the simplified fraction is 1/2.
Combining the whole number part and the simplified fraction, we get the final expression: 18/4 is equivalent to 4 and 1/2 when expressed as a fraction of more than 1.
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10 166 points ebook An ideal spring has a spring constant k 29.4 N/m. What is the amount of work that must be done to stretch the spring 0,660 m from its relaxed length?
The work done to stretch the spring by 0.660 m from its relaxed length is 6.38 J (approx).
Given: A spring has a spring constant k = 29.4 N/m and the spring is stretched by 0.660m from its relaxed length i.e initial length. We have to calculate the work that must be done to stretch the spring.
Concept: The work done to stretch a spring is given by the formula;W = (1/2)kx²Where,k = Spring constant,
x = Amount of stretch or compression of the spring.
So, the work done to stretch the spring is given by the above formula.Given: Spring constant, k = 29.4 N/mAmount of stretch, x = 0.660m.
Formula: W = (1/2)kx².Substituting the values in the above formula;W = (1/2)×29.4N/m×(0.660m)²,
W = (1/2)×29.4N/m×0.4356m²,
W = 6.38026 J (approx).
Therefore, the amount of work that must be done to stretch the spring by 0.660 m from its relaxed length is 6.38 J (approx).
From the above question, we can learn about the concept of the work done to stretch a spring and its formula. The work done to stretch a spring is given by the formula W = (1/2)kx² where k is the spring constant and x is the amount of stretch or compression of the spring.
We can also learn how to calculate the work done to stretch a spring using its formula and given values. Here, we are given the spring constant k = 29.4 N/m and the amount of stretch x = 0.660m.
By substituting the given values in the formula, we get the work done to stretch the spring. The amount of work that must be done to stretch the spring by 0.660 m from its relaxed length is 6.38 J (approx).
The work done to stretch a spring is an important concept of Physics. The work done to stretch a spring is given by the formula W = (1/2)kx² where k is the spring constant and x is the amount of stretch or compression of the spring. Here, we have calculated the amount of work done to stretch a spring of spring constant k = 29.4 N/m and an amount of stretch x = 0.660m. Therefore, the work done to stretch the spring by 0.660 m from its relaxed length is 6.38 J (approx).
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If an applied force on an object acts antiparallel to the direction of the object's movement, the work done on by the applied force is: Negative Cannot be determined by the problem. Positive Zero
If an applied force on an object acts antiparallel to the direction of the object's movement, the work done by the applied force is negative.
The transfer of energy from one object to another by applying a force to an object, which makes it move in the direction of the force is known as work. When the applied force acts in the opposite direction to the object's movement, the work done by the force is negative.
The formula for work is given by: Work = force x distance x cosθ where,θ is the angle between the applied force and the direction of movement. If the angle between force and movement is 180° (antiparallel), then cosθ = -1 and work done will be negative. Therefore, if an applied force on an object acts antiparallel to the direction of the object's movement, the work done by the applied force is negative.
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A beam of light reflects and refracts at point A on the interface between material 1 (n1 = 1.33) and material 2 (n2 = 1.66). The incident beam makes an angle of 40° with the interface. What is the angle of reflection at point A?
The angle of reflection at point A is 40°, which is equal to the angle of incidence.
When a beam of light encounters an interface between two different materials, it undergoes reflection and refraction. The angle of incidence, which is the angle between the incident beam and the normal to the interface, is equal to the angle of reflection, which is the angle between the reflected beam and the normal to the interface.
In this case, the incident beam makes an angle of 40° with the interface, so the angle of reflection at point A is also 40°. When light travels from one medium to another, it changes its direction due to the change in speed caused by the change in refractive index.
The law of reflection states that the angle of incidence is equal to the angle of reflection. This means that the angle at which the light ray strikes the interface is the same as the angle at which it bounces off the interface.
In this scenario, the incident beam of light strikes the interface between material 1 and material 2 at an angle of 40°. According to the law of reflection, the angle of reflection is equal to the angle of incidence, so the light ray will bounce off the interface at the same 40° angle with respect to the normal.
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A weather balloon is filled to a volume of 12.68 ft3 on Earth's surface at a measured temperature of 21.87 C and a pressure of 1.02 atm. The weather balloon is let go and drifts away from the Earth. At the top of the troposphere, the balloon experiences a temperature of -64.19 C and a pressure of 0.30 atm. What is the volume, in liters, of this weather balloon at the top of the troposphere? Round your final answer to two decimal places.
The volume of the weather balloon at the top of the troposphere is approximately 10.22 liters.
Explanation:
Step 1: The volume of the weather balloon at the top of the troposphere is approximately 10.22 liters.
Step 2:
To calculate the volume of the weather balloon at the top of the troposphere, we need to apply the ideal gas law, which states that the product of pressure and volume is directly proportional to the product of the number of moles and temperature. Mathematically, this can be represented as:
(P1 * V1) / (T1 * n1) = (P2 * V2) / (T2 * n2)
Here, P1 and P2 represent the initial and final pressures, V1 and V2 represent the initial and final volumes, T1 and T2 represent the initial and final temperatures, and n1 and n2 represent the number of moles (which remain constant in this case).
Given the initial conditions on Earth's surface: P1 = 1.02 atm, V1 = 12.68 ft3, and T1 = 21.87 °C, we need to convert the volume from cubic feet to liters and the temperature from Celsius to Kelvin for the equation to work properly.
Converting the volume from cubic feet to liters, we have:
V1 = 12.68 ft3 * 28.3168466 liters/ft3 ≈ 358.99 liters
Converting the temperature from Celsius to Kelvin, we have:
T1 = 21.87 °C + 273.15 ≈ 295.02 K
Similarly, for the final conditions at the top of the troposphere: P2 = 0.30 atm and T2 = -64.19 °C + 273.15 ≈ 208.96 K.
Rearranging the ideal gas law equation, we can solve for V2:
V2 = (P2 * V1 * T2) / (P1 * T1)
Substituting the values, we have:
V2 = (0.30 atm * 358.99 liters * 208.96 K) / (1.02 atm * 295.02 K) ≈ 10.22 liters
Therefore, the volume of the weather balloon at the top of the troposphere is approximately 10.22 liters.
Learn more about:
The ideal gas law is a fundamental principle in physics and chemistry that relates the properties of gases, such as pressure, volume, temperature, and number of moles. It is expressed by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
In this context, we used the ideal gas law to calculate the volume of the weather balloon at the top of the troposphere. By applying the law and considering the initial and final conditions, we were able to determine the final volume.
The conversion from cubic feet to liters is necessary because the initial volume was given in cubic feet, while the ideal gas law equation requires volume in liters. The conversion factor used was 1 ft3 = 28.3168466 liters.
Additionally, the conversion from Celsius to Kelvin is essential as the ideal gas law requires temperature to be in Kelvin. The conversion formula is simple: K = °C + 273.15.
By following these steps and performing the necessary calculations, we obtained the final volume of the weather balloon at the top of the troposphere as approximately 10.22 liters.
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All work/steps must be shown following the "Problem-Solving Procedure". Part II - Short Problems −4 points 1. Find the ' x ' and ' y ' components of the following vectors. a. F=67.9 N,38∘ b. v=8.76 m/s,−57.3∘ 2. Determine the 'polar coordinate' form of the following vector components. a. Ax=7.87 mAy=−8.43 m b. vx=−67.3 m/svy=−24.9 m/s
In problem 1, the x and y components of the vector F are found to be 50.19 N and 51.95 N, respectively. In problem 2, the polar coordinate form of vector A is determined to be 11.01 m at an angle of -48.92 degrees, while vector v is expressed as 76.46 m/s at an angle of -197.65 degrees.
In problem 1a, the vector force F, is given with a magnitude of 67.9 N and an angle of 38 degrees. To find the x and y components, we use the trigonometric functions cosine (cos) and sine (sin).
The x component is calculated as Fx = F * cos(θ), where θ is the angle, yielding Fx = 67.9 N * cos(38°) = 50.19 N. Similarly, the y component is determined as Fy = F * sin(θ), resulting in Fy = 67.9 N * sin(38°) = 51.95 N.
In problem 1b, the vector v is given with a magnitude of 8.76 m/s and an angle of -57.3 degrees. Using the same trigonometric functions, we can find the x and y components.
The x component is calculated as vx = v * cos(θ), which gives vx = 8.76 m/s * cos(-57.3°) = 4.44 m/s. The y component is determined as vy = v * sin(θ), resulting in vy = 8.76 m/s * sin(-57.3°) = -7.37 m/s.
In problem 2a, the vector components Ax = 7.87 m and Ay = -8.43 m are given. To express this vector in polar coordinate form, we can use the Pythagorean theorem to find the magnitude (r) of the vector, which is r = √(Ax^2 + Ay^2).
Substituting the given values, we obtain r = √((7.87 m)^2 + (-8.43 m)^2) ≈ 11.01 m. The angle (θ) can be determined using the inverse tangent function, tan^(-1)(Ay/Ax), which gives θ = tan^(-1)(-8.43 m/7.87 m) ≈ -48.92 degrees.
Therefore, the polar coordinate form of vector A is approximately 11.01 m at an angle of -48.92 degrees.In problem 2b, the vector components vx = -67.3 m/s and vy = -24.9 m/s are given.
Following a similar procedure as in problem 2a, we find the magnitude of the vector v as r = √(vx^2 + vy^2) = √((-67.3 m/s)^2 + (-24.9 m/s)^2) ≈ 76.46 m/s.
The angle θ can be determined using the inverse tangent function, tan^(-1)(vy/vx), resulting in θ = tan^(-1)(-24.9 m/s/-67.3 m/s) ≈ -197.65 degrees. Hence, the polar coordinate form of vector v is approximately 76.46 m/s at an angle of -197.65 degrees.
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What is the frequency of the most intense radiation emitted by your body? Assume a skin temperature of 95 °F. Express your answer to three significant figures.
The frequency of the most intense radiation emitted by your body is approximately 3.19 × 10^13 Hz.
To determine the frequency of the most intense radiation emitted by your body, we can use Wien's displacement law, which relates the temperature of a black body to the wavelength at which it emits the most intense radiation.
The formula for Wien's displacement law is:
λ_max = (b / T)
Where λ_max is the wavelength of maximum intensity, b is Wien's displacement constant (approximately 2.898 × 10^-3 m·K), and T is the temperature in Kelvin.
First, let's convert the skin temperature of 95 °F to Kelvin:
T = (95 + 459.67) K ≈ 308.15 K
Now, we can calculate the wavelength of maximum intensity using Wien's displacement law:
λ_max = (2.898 × 10^-3 m·K) / 308.15 K
Calculating this expression, we find:
λ_max ≈ 9.41 × 10^-6 m
To find the frequency, we can use the speed of light formula:
c = λ * f
Where c is the speed of light (approximately 3 × 10^8 m/s), λ is the wavelength, and f is the frequency.
Rearranging the formula to solve for frequency:
f = c / λ_max
Substituting the values, we have:
f ≈ (3 × 10^8 m/s) / (9.41 × 10^-6 m)
Calculating this expression, we find:
f ≈ 3.19 × 10^13 Hz
Therefore, the frequency of the most intense radiation emitted by your body is approximately 3.19 × 10^13 Hz.
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An ideal gas with molecules of mass \( \mathrm{m} \) is contained in a cube with sides of area \( \mathrm{A} \). The average vertical component of the velocity of the gas molecule is \( \mathrm{v} \),
This equation relates the average vertical velocity to the temperature and the mass of the gas molecules.
In an ideal gas contained in a cube, the average vertical component of the velocity of the gas molecules is given by the equation \( v = \sqrt{\frac{3kT}{m}} \), where \( k \) is the Boltzmann constant, \( T \) is the temperature, and \( m \) is the mass of the gas molecules.
The average vertical component of the velocity of gas molecules in an ideal gas can be determined using the kinetic theory of gases. According to this theory, the kinetic energy of a gas molecule is directly proportional to its temperature. The root-mean-square velocity of the gas molecules is given by \( v = \sqrt{\frac{3kT}{m}} \), where \( k \) is the Boltzmann constant, \( T \) is the temperature, and \( m \) is the mass of the gas molecules.
This equation shows that the average vertical component of the velocity of the gas molecules is determined by the temperature and the mass of the molecules. As the temperature increases, the velocity of the gas molecules also increases.
Similarly, if the mass of the gas molecules is larger, the velocity will be smaller for the same temperature. The equation provides a quantitative relationship between these variables, allowing us to calculate the average vertical velocity of gas molecules in a given system.
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A ball of mass 0.5 kg is moving to the right at 1 m/s, collides
with a wall and rebounds to the left with a speed of 0.8 m/s.
Determine the impulse that the wall gave the ball.
The impulse that the wall gave the ball is equal to the change in momentum, so:
Impulse = Change in momentum = -0.9 kg m/s
The impulse that the wall gave the ball can be calculated using the impulse-momentum theorem. The impulse-momentum theorem states that the impulse exerted on an object is equal to the change in momentum of the object. Mathematically, this can be written as:
Impulse = Change in momentum
In this case, the ball collides with the wall and rebounds in the opposite direction. Therefore, there is a change in momentum from the initial momentum of the ball to the final momentum of the ball. The change in momentum is given by:
Change in momentum = Final momentum - Initial momentum
The initial momentum of the ball is:
Initial momentum = mass x velocity = 0.5 kg x 1 m/s = 0.5 kg m/s
The final momentum of the ball is:
Final momentum = mass x velocity
= 0.5 kg x (-0.8 m/s) = -0.4 kg m/s (note that the velocity is negative since the ball is moving in the opposite direction)
Therefore, the change in momentum is:
Change in momentum = -0.4 kg m/s - 0.5 kg m/s = -0.9 kg m/s
The impulse that the wall gave the ball is equal to the change in momentum, so:
Impulse = Change in momentum = -0.9 kg m/s
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The magnetic flux through a coil containing 10 loops changes
from 10Wb to −20W b in 0.02s. Find the induced voltage ε.
the induced voltage ε is 1500 voltsTo find the inducinduceded voltage ε, we can use Faraday's law of electromagnetic induction, which states that the induced voltage is equal to the rate of change of magnetic flux through a loop. Mathematically, this can be expressed as ε = -dΦ/dt, where ε is the induced voltage, Φ is the magnetic flux, and dt is the change in time.
Given that the magnetic flux changes from 10 Wb to -20 Wb in 0.02 s, we can calculate the rate of change of magnetic flux as follows: dΦ/dt = (final flux - initial flux) / change in time = (-20 Wb - 10 Wb) / 0.02 s = -1500 Wb/s.
Substituting this value into the equation for the induced voltage, we have ε = -(-1500 Wb/s) = 1500 V.
Therefore, the induced voltage ε is 1500 volts.
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A spherical mirror is to be used to form an image 5.90 times the size of an object on a screen located 4.40 m from the object. (a) Is the mirror required concave or convex? concave convex (b) What is the required radius of curvature of the mirror? m (c) Where should the mirror be positioned relative to the object? m from the object
The mirror required is concave. The radius of curvature of the mirror is -1.1 m. The mirror should be positioned at a distance of 0.7458 m from the object.
Given,
Image height (hᵢ) = 5.9 times the object height (h₀)
Screen distance (s) = 4.40 m
Let us solve each part of the question :
Is the mirror required concave or convex? We know that the magnification (M) for a spherical mirror is given by: Magnification,
M = - (Image height / Object height)
Also, the image is real when the magnification (M) is negative. So, we can write:
M = -5.9
[Given]Since, M is negative, the image is real. Thus, we require a concave mirror to form a real image.
What is the required radius of curvature of the mirror? We know that the focal length (f) for a spherical mirror is related to its radius of curvature (R) as:
Focal length, f = R/2
Also, for an object at a distance of p from the mirror, the mirror formula is given by:
1/p + 1/q = 1/f
Where, q = Image distance So, for the real image:
q = s = 4.4 m
Substituting the values in the mirror formula, we get:
1/p + 1/4.4 = 1/f…(i)
Also, from the magnification formula:
M = -q/p
Substituting the values, we get:
-5.9 = -4.4/p
So, the object distance is: p = 0.7458 m
Substituting this value in equation (i), we get:
1/0.7458 + 1/4.4 = 1/f
Solving further, we get:
f = -0.567 m
Since the focal length is negative, the mirror is a concave mirror.
Therefore, the radius of curvature of the mirror is:
R = 2f
R = 2 x (-0.567) m
R = -1.13 m
R ≈ -1.1 m
Where should the mirror be positioned relative to the object? We know that the object distance (p) is given by:
p = -q/M Substituting the given values, we get:
p = -4.4 / 5.9
p = -0.7458 m
We know that the mirror is to be placed between the object and its focus. So, the mirror should be positioned at a distance of 0.7458 m from the object.
Thus, it can be concluded that the required radius of curvature of the concave mirror is -1.1 m. The concave mirror is to be positioned at a distance of 0.7458 m from the object.
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A strong magnet is dropped through a copper tube. Which of the following is most likely to occur? Since the magnet is attracted to the copper, it will be attracted to the copper tube and stick to it. Since the magnet is not attracted to the copper, it will fall through the tube as if it were just dropped outside the copper tube (that is, with an acceleration equal to that of freefall). O As the magnet falls, current are generated within the copper tube that will cause the magnet to fall faster than it would have if it were just dropped without a copper tube. As the magnet falls, current are generated within the copper tube that will cause the magnet to fall slower than it would have if it were just dropped without a copper tube.
When a strong magnet is dropped through a copper tube, the most likely scenario is that currents are generated within the copper tube, which will cause the magnet to fall slower than it would have if it were just dropped without a copper tube.
This phenomenon is known as electromagnetic induction.
As the magnet falls through the copper tube, the changing magnetic field induces a current in the copper tube according to Faraday's law of electromagnetic induction.
This induced current creates a magnetic field that opposes the motion of the magnet. The interaction between the induced magnetic field and the magnet's magnetic field results in a drag force, known as the Lenz's law, which opposes the motion of the magnet.
Therefore, the magnet experiences a resistive force from the induced currents, causing it to fall slower than it would under freefall conditions. The stronger the magnet and the thicker the copper tube, the more pronounced this effect will be.
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1. In what pattern does electricity flow in an AC circuit? A. dash B. dots C. straight D. wave 2. How does an electron move in a DC? A. negative to positive B. negative to negative C. posititve to negative D. positive to positive 3. In what type of LC circuit does total current be equal to the current of inductor and capacitor? A. series LC circuit B. parallel LC circuit C. series-parallel LC circuit D. all of the above 4. In what type of LC circuit does total voltage is equal to the current of inductor and capacitor? A. series LC circuit B. parallel LC circuit NG PASIC OF PASIG VOISINIO אני אמות KALAKHAN IA CITY MAYNILA 1573 PASIG CITY C. series-parallel LC circuit D. all of the above 5. If the capacitance in the circuit is increased, what will happen to the frequency?? A. increase B. decrease C. equal to zero D. doesn't change
Answer:
1.) D. wave
In an AC circuit, the electric current flows back and forth, creating a wave-like pattern.
2.) A. negative to positive
In a DC circuit, electrons flow from the negative terminal of a battery to the positive terminal.
3.) A. series LC circuit
In a series LC circuit, the current through the inductor and capacitor are equal and in the same direction.
4.) B. parallel LC circuit
In a parallel LC circuit, the voltage across the inductor and capacitor are equal and in the opposite direction.
5.) B. decrease
As the capacitance in a circuit increases, the resonant frequency decreases.
Explanation:
AC circuits: AC circuits are circuits that use alternating current (AC). AC is a type of electrical current that flows back and forth, reversing its direction at regular intervals. The frequency of an AC circuit is the number of times the current reverses direction per second.
DC circuits: DC circuits are circuits that use direct current (DC). DC is a type of electrical current that flows in one direction only.
LC circuits: LC circuits are circuits that contain an inductor and a capacitor. The inductor stores energy in the form of a magnetic field, and the capacitor stores energy in the form of an electric field. When the inductor and capacitor are connected together, they can transfer energy back and forth between each other, creating a resonant frequency.
Resonant frequency: The resonant frequency of a circuit is the frequency at which the circuit's impedance is minimum. The resonant frequency of an LC circuit is determined by the inductance of the inductor and the capacitance of the capacitor.
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A particle starts from the origin at t=0.0 s with a velocity of 8.1 i m/s and moves in the xy plane with a constant acceleration of (-9.3 i + 8.8 j)m/s2. When the particle achieves the maximum positive x-coordinate, how far is it from the origin?
When the particle achieves the maximum positive x-coordinate, it is approximately 4.667 meters away from the origin.
Explanation:
To find the distance of the particle from the origin when it achieves the maximum positive x-coordinate, we need to determine the time it takes for the particle to reach that point.
Let's assume the time at which the particle achieves the maximum positive x-coordinate is t_max. To find t_max, we can use the equation of motion in the x-direction:
x = x_0 + v_0x * t + (1/2) * a_x * t²
where:
x = position in the x-direction (maximum positive x-coordinate in this case)
x_0 = initial position in the x-direction (which is 0 in this case as the particle starts from the origin)
v_0x = initial velocity in the x-direction (which is 8.1 m/s in this case)
a_x = acceleration in the x-direction (which is -9.3 m/s² in this case)
t = time
Since the particle starts from the origin, x_0 is 0. Therefore, the equation simplifies to:
x = v_0x * t + (1/2) * a_x * t²
To find t_max, we set the velocity in the x-direction to 0:
0 = v_0x + a_x * t_max
Solving this equation for t_max gives:
t_max = -v_0x / a_x
Plugging in the values, we have:
t_max = -8.1 m/s / -9.3 m/s²
t_max = 0.871 s (approximately)
Now, we can find the distance of the particle from the origin at t_max using the equation:
distance = magnitude of displacement
= √[(x - x_0)² + (y - y_0)²]
Since the particle starts from the origin, the initial position (x_0, y_0) is (0, 0).
Therefore, the equation simplifies to:
distance = √[(x)^2 + (y)²]
To find x and y at t_max, we can use the equations of motion:
x = x_0 + v_0x * t + (1/2) * a_x *t²
y = y_0 + v_0y * t + (1/2) * a_y *t²
where:
v_0y = initial velocity in the y-direction (which is 0 in this case)
a_y = acceleration in the y-direction (which is 8.8 m/s² in this case)
For x:
x = 0 + (8.1 m/s) * (0.871 s) + (1/2) * (-9.3 m/s²) * (0.871 s)²
For y:
y = 0 + (0 m/s) * (0.871 s) + (1/2) * (8.8 m/s²) * (0.871 s)²
Evaluating these expressions, we find:
x ≈ 3.606 m
y ≈ 2.885 m
Now, we can calculate the distance:
distance = √[(3.606 m)² + (2.885 m)²]
distance ≈ 4.667 m
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A block is kept on horizontal table the table is undergoing simple harmonic motion of frequency 3Hz in a horizontal plane . the coefficient of static friction between block and the table surface is 0.72. find the maximum amplitude of the table at which the block does not slip on the surface.
The maximum amplitude of the table at which the block does not slip on the surface is 0.0727m.
As the table is undergoing simple harmonic motion, the acceleration of the block towards the center of the table can be given as a = -ω²x, where r of the block from the center of the table. The maximum acceleration is when x = A, where A is the amplitude of the motion, and can be given as a_max = ω²A.
To prevent the block from slipping, the maximum value of the frictional force (ffriction = μN) should be greater than or equal to the maximum value of the force pulling the block (fmax = mamax). Therefore, we have μmg >= mω²A, where m is the mass of the block and g is the acceleration due to gravity. Rearranging the equation, we get A <= (μg/ω²).
Substituting the given values, we get
A <= (0.729.8)/(2π3) = 0.0727m.
Therefore, the maximum amplitude of the table at which the block does not slip is 0.0727m.
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Moving to another question will save this response. uestion 13 An organ pipe open at both ends has a length of 0.80 m. If the velocity of sound in air is 340 mv's what is the frequency of the third ha
The frequency of the third harmonic of an organ pipe open at both ends with a length of 0.80 m and a velocity of sound in air of 340 m/s is 850 Hz. The correct option is C.
For an organ pipe open at both ends, the frequency of the harmonics can be determined using the formula:
fₙ = (nv) / (2L)
where fₙ is the frequency of the nth harmonic, n is the harmonic number, v is the velocity of sound, and L is the length of the pipe.
In this case, we want to find the frequency of the third harmonic, so n = 3. The length of the pipe is given as 0.80 m, and the velocity of sound in air is 340 m/s.
Substituting these values into the formula, we have:
f₃ = (3 * 340 m/s) / (2 * 0.80 m)
Calculating this expression gives us:
f₃ = 850 Hz
Therefore, the frequency of the third harmonic of the organ pipe is 850 Hz. Option C is correct one.
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Complete Question:
Moving to another question will save this response. uestion 13 An organ pipe open at both ends has a length of 0.80 m. If the velocity of sound in air is 340 mv's what is the frequency of the third harmonic of this pipe O 425 Hz O 638 Hz O 850 Hz 213 Hz
Part A A stone is thrown vertically upward with a speed of 15.6 m/s from the edge of a cliff 75.0 m high (Figure 1). How much later does it reach the bottom of the cliff? Express your answer to three significant figures and include the appropriate units. + OI? f Value Units Submit Request Answer - Part B What is its speed just before hitting? Express your answer to three significant figures and include the appropriate units. Value Units Submit Request Answer - Part What total distance did it travel? Express your answer to three significant figures and include the appropriate units. + 2 123 Figure 1 of 1 Value Units Submit Request Answer Provide Feedback
The stone reaches the bottom of the cliff approximately 4.20 seconds later. The speed just before hitting the bottom is approximately 40.6 m/s.
Part A: To find how much later the stone reaches the bottom of the cliff, we can use the kinematic equation for vertical motion. The equation is:
h = ut + (1/2)gt^2
Where:
h = height of the cliff (75.0 m, negative since it's downward)
u = initial velocity (15.6 m/s)
g = acceleration due to gravity (-9.8 m/s^2, negative since it's downward)
t = time
Plugging in the values, we get:
-75.0 = (15.6)t + (1/2)(-9.8)t^2
Solving this quadratic equation, we find two values for t: one for the stone going up and one for it coming down. We're interested in the time it takes for it to reach the bottom, so we take the positive value of t. Rounded to three significant figures, the time it takes for the stone to reach the bottom of the cliff is approximately 4.20 seconds.
Part B: The speed just before hitting the bottom can be found using the equation for final velocity in vertical motion:
v = u + gt
Where:
v = final velocity (what we want to find)
u = initial velocity (15.6 m/s)
g = acceleration due to gravity (-9.8 m/s^2, negative since it's downward)
t = time (4.20 s)
Plugging in the values, we get:
v = 15.6 + (-9.8)(4.20)
Calculating, we find that the speed just before hitting is approximately -40.6 m/s. Since speed is a scalar quantity, we take the magnitude of the value, giving us a speed of approximately 40.6 m/s.
Part C: To find the total distance traveled by the stone, we need to calculate the distance covered during the upward motion and the downward motion separately, and then add them together.
Distance covered during upward motion:
Using the equation for distance covered in vertical motion:
s = ut + (1/2)gt^2
Where:
s = distance covered during upward motion (what we want to find)
u = initial velocity (15.6 m/s)
g = acceleration due to gravity (-9.8 m/s^2, negative since it's downward)
t = time (4.20 s)
Plugging in the values, we get:
s = (15.6)(4.20) + (1/2)(-9.8)(4.20)^2
Calculating, we find that the distance covered during the upward motion is approximately 33.1 m.
Distance covered during downward motion:
Since the stone comes back down to the bottom of the cliff, the distance covered during the downward motion is equal to the height of the cliff, which is 75.0 m.
Total distance traveled:
Adding the distance covered during the upward and downward motion, we get:
Total distance = 33.1 + 75.0
Rounded to three significant figures, the total distance traveled by the stone is approximately 108 m.
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What resistance R should be connected in series with an inductance L = 197 mH and capacitance C = 15.8 uF for the maximum charge on the capacitor to decay to 95.5% of its initial value in 72.0 cycles?
A resistance of approximately 2.06 kΩ should be connected in series with the given inductance and capacitance for the maximum charge on the capacitor to decay to 95.5% of its initial value in 72.0 cycles.
To find the resistance R required in series with the given inductance L = 197 mH and capacitance C = 15.8 uF, we can use the formula:
R = -(72.0/f) / (C * ln(0.955))
where f is the frequency of the circuit.
First, let's calculate the time period (T) of one cycle using the formula T = 1/f. Since the frequency is given in cycles per second (Hz), we can convert it to the time period in seconds.
T = 1 / f = 1 / (72.0 cycles) = 1.39... x 10^(-2) s/cycle.
Next, we calculate the angular frequency (ω) using the formula ω = 2πf.
ω = 2πf = 2π / T = 2π / (1.39... x 10^(-2) s/cycle) = 452.39... rad/s.
Now, let's substitute the values into the formula to find R:
R = -(72.0 / (1.39... x 10^(-2) s/cycle)) / (15.8 x 10^(-6) F * ln(0.955))
= -5202.8... / (15.8 x 10^(-6) F * (-0.046...))
≈ 2.06 x 10^(3) Ω.
Therefore, a resistance of approximately 2.06 kΩ should be connected in series with the given inductance and capacitance to achieve a decay of the maximum charge on the capacitor to 95.5% of its initial value in 72.0 cycles.
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Question 1 (1 point) Listen All half life values are less than one thousand years. True False Question 2 (1 point) Listen Which of the following is a reason for a nucleus to be unstable? the nucleus i
The statement "All half-life values are less than one thousand years" is false. Half-life values can vary greatly depending on the specific radioactive isotope being considered. While some isotopes have half-lives shorter than one thousand years, there are also isotopes with much longer half-lives. The range of half-life values extends from fractions of a second to billions of years.
For example, the half-life of Carbon-14 (C-14), which is commonly used in radiocarbon dating, is about 5730 years. Another commonly known isotope, Uranium-238 (U-238), has a half-life of about 4.5 billion years. These examples demonstrate that half-life values can span a wide range of timescales.
There are several reasons for a nucleus to be unstable. One reason is an excess of protons or neutrons in the nucleus. The strong nuclear force, which binds the nucleus together, is balanced when there is an appropriate ratio of protons to neutrons. When this balance is disrupted by an excess of protons or neutrons, the nucleus can become unstable.
Another reason for instability is an excess of energy in the nucleus. This can be caused by various factors, such as high levels of radioactivity or the ingestion of radioactive materials. The excess energy can disrupt the stability of the nucleus, leading to its decay or disintegration.
It's important to note that the stability of a nucleus depends on the specific combination of protons and neutrons in the nucleus, as well as other factors such as the nuclear binding energy. The study of nuclear physics and nuclear reactions helps us understand the various factors influencing nuclear stability and decay.
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A muon with a lifetime of 2 × 10−6 second in its frame of reference is created in the upper atmosphere with a velocity of 0.998 c toward the Earth. What is the lifetime of this muon as mea- sured by an observer on the Earth? 1.T =3×10−5 s 2.T =3×10−6 s 3.T =3×10−4 s 4.T =3×10−3 s 5.T =3×10−2 s
The lifetime of the muon as measured by an observer on Earth is approximately 3 × 10^−6 seconds (Option 2).
When the muon is moving at a velocity of 0.998c towards the Earth, time dilation occurs due to relativistic effects, causing the muon's lifetime to appear longer from the Earth's frame of reference.
Time dilation is a phenomenon predicted by Einstein's theory of relativity, where time appears to slow down for objects moving at high velocities relative to an observer. The formula for time dilation is T' = T / γ, where T' is the measured lifetime of the muon, T is the proper lifetime in its frame of reference, and γ (gamma) is the Lorentz factor.
In this case, the Lorentz factor can be calculated using the formula γ = 1 / sqrt(1 - (v^2 / c^2)), where v is the velocity of the muon (0.998c) and c is the speed of light. Plugging in the values, we find γ ≈ 14.14.
By applying time dilation, T' = T / γ, we get T' = 2 × 10^−6 s / 14.14 ≈ 1.415 × 10^−7 s. However, we need to convert this result to the proper lifetime as measured by the Earth observer. Since the muon is moving towards the Earth, its lifetime appears longer due to time dilation. Therefore, the measured lifetime on Earth is T' = 1.415 × 10^−7 s + 2 × 10^−6 s = 3.1415 × 10^−6 s ≈ 3 × 10^−6 s.
Hence, the lifetime of the muon as measured by an observer on Earth is approximately 3 × 10^−6 seconds (Option 2).
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Visible light shines upon a pair of closely-spaced thin slits. An interference pattern is seen on a screen located behind the slits. For which color of light will the distance between the fringes (as seen on the screen) be greatest? yellow-green green yellow
The distance between the fringes in an interference pattern, often referred to as the fringe spacing or fringe separation, is determined by the wavelength of the light used.
The greater the wavelength, the larger the fringe spacing.
Yellow-green light and green light are both within the visible light spectrum, with yellow-green having a longer wavelength than green.
Therefore, the distance between the fringes will be greater for yellow-green light compared to green light.
The fringe spacing, also known as the fringe separation or fringe width, refers to the distance between adjacent bright fringes (or adjacent dark fringes) in the interference pattern. It is directly related to the wavelength of the light used.
According to the principles of interference, the fringe spacing is determined by the path length difference between the light waves reaching a particular point on the screen from the two slits. Constructive interference occurs when the path length difference is an integer multiple of the wavelength, leading to bright fringes. Destructive interference occurs when the path length difference is a half-integer multiple of the wavelength, resulting in dark fringes.
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JA B A с The three tanks above are filled with water to the same depth. The tanks are of equal height. Tank B has the middle surface area at the bottom, tank A the greatest and tank C the least. For each of the following statements, select the correct option from the pull-down menu. Less than The force exerted by the water on the bottom of tank A is .... the force exerted by the water on the bottom of tank B. True The pressure exerted on the bottom of tank A is equal to the pressure on the bottom of the other two tanks. Less than The force due to the water on the bottom of tank B is .... the weight of the water in the tank. True The water in tank C exerts a downward force on the sides of the tank. Less than The pressure at the bottom of tank A is .... the pressure at the bottom of tank C.
The force exerted by the water on the bottom of tank A is less than the force exerted by the water on the bottom of tank B.
The force exerted by a fluid depends on its pressure and the surface area it acts upon. In this case, although the water level and height of the tanks are equal, tank A has the greatest surface area at the bottom, tank B has a middle surface area, and tank C has the least surface area.
The force exerted by the water on the bottom of a tank is directly proportional to the pressure and the surface area. Since the water pressure at the bottom of the tanks is the same (as they are filled to the same depth), the force exerted by the water on the bottom of tank A would be greater than the force exerted on tank B because tank A has a larger surface area at the bottom.
The pressure exerted on the bottom of tank A is equal to the pressure on the bottom of the other two tanks. Pressure in a fluid is determined by the depth of the fluid and the density of the fluid, but it is not affected by the surface area. Therefore, the pressure at the bottom of all three tanks is the same, regardless of their surface areas.
The force due to the water on the bottom of tank B is true and equal to the weight of the water in the tank. This is because the force exerted by a fluid on a surface is equal to the weight of the fluid directly above it. In tank B, the water exerts a force on its bottom that is equal to the weight of the water in the tank.
The water in tank C does not exert a downward force on the sides of the tank. The pressure exerted by the water at any given depth is perpendicular to the sides of the container. The force exerted by the water on the sides of the tank is a result of the pressure, but it acts horizontally and is balanced out by the pressure from the opposite side. Therefore, the water in tank C exerts an equal pressure on the sides of the tank but does not exert a net downward force.
The pressure at the bottom of tank A is less than the pressure at the bottom of tank C. This is because pressure in a fluid increases with depth. Since tank A has a greater depth than tank C (as they are filled to the same level), the pressure at the bottom of tank A is greater.
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What is the position of the 2nd maxima for a double slit experiment with a slit width of d=20mm, if there is a laser of 500nm, with the screen 1m away from the slits?
The position of the second maximum (second-order maximum) in this double-slit experiment would be 0.05 mm.
How to find the the position of the second maximum (second-order maximum) in this double-slit experimentTo find the position of the second maximum (second-order maximum) in a double-slit experiment, we can use the formula for the position of the maxima:
[tex]\[ y = \frac{m \cdot \lambda \cdot L}{d} \][/tex]
Where:
- [tex]\( y \) is the position of the maxima[/tex]
- [tex]\( m \) is the order of the maxima (in this case, the second maximum has \( m = 2 \))[/tex]
-[tex]\( \lambda \) is the wavelength of the laser light (500 nm or \( 500 \times 10^{-9} \) m)[/tex]
-[tex]\( L \) is the distance from the slits to the screen (1 m)[/tex]
- [tex]\( d \) is the slit width (20 mm or \( 20 \times 10^{-3} \) m)[/tex]
Substituting the given values into the formula:
[tex]\[ y = \frac{2 \cdot 500 \times 10^{-9} \cdot 1}{20 \times 10^{-3}} \][/tex]
Simplifying the expression:
[tex]\[ y = \frac{2 \cdot 500 \times 10^{-9}}{20 \times 10^{-3}} \][/tex]
[tex]\[ y = 0.05 \times 10^{-3} \][/tex]
[tex]\[ y = 0.05 \, \text{mm} \][/tex]
Therefore, the position of the second maximum (second-order maximum) in this double-slit experiment would be 0.05 mm.
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A woman sits in a wheelchair and tried to roll over a curb that is 6 cm high. What force does she need to push at the top of the wheel to lift her and her chair? The woman in the chair has a mass of 80 kg, and the wheel has a radius of 27
cm.
The force is required to lift the woman and the chair over the curb when she pushes at the top of the wheel is 784.8 N
To find the force the woman needs to push at the top of the wheel to lift herself and her chair, the following formula can be used: force = mass x accelerationWhere acceleration is given by: acceleration = (change in velocity) / (time taken)Here, the woman is initially at rest. The velocity of the woman and the chair needs to be increased to go over the curb. Therefore, the acceleration required will be the acceleration due to gravity, which is 9.81 m/s² at the surface of the earth.The woman's mass is given as 80 kg.The radius of the wheel is given as 27 cm, which is equal to 0.27 m.To lift the woman and her chair, the wheel will have to move through a vertical distance equal to the height of the curb, which is 6 cm. This vertical distance is equal to the displacement of the woman and the chair.Force required = mass x accelerationForce required = 80 x 9.81 = 784.8 NThis force is required to lift the woman and the chair over the curb when she pushes at the top of the wheel.
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