The intensity at an 11° angle to the axis, resulting from the diffraction of light passing through a single slit of width 0.3 mm and illuminated by a mercury light of wavelength 405 nm, can be calculated relative to the intensity of the central maximum.
The expression for the intensity is I = Io * (sin(α)/α)^2, where α is the angular deviation from the central maximum.
When light passes through a single slit, it undergoes diffraction, resulting in a pattern of bright and dark fringes. The intensity at a specific angle, relative to the intensity of the central maximum (Io), can be determined using the formula I = Io * (sin(α)/α)^2, where α is the angular deviation from the central maximum.
In this case, the given angle is 11°. To calculate the intensity, we need to find the value of α in radians. We can use the formula α = (π * w * sin(θ))/λ, where w is the width of the slit, θ is the angle, and λ is the wavelength.
Converting the width of the slit from millimeters to meters (0.3 mm = 0.0003 m) and the wavelength from nanometers to meters (405 nm = 405 x 10^-9 m), we can substitute the values into the equation.
α = (π * 0.0003 * sin(11°))/(405 x 10^-9)
≈ 3.18 x 10^6 radians
Now, we can calculate the intensity using the formula I = Io * (sin(α)/α)^2:
I = Io * (sin(3.18 x 10^6 radians)/(3.18 x 10^6 radians))^2
Therefore, the intensity at an 11° angle to the axis, relative to the intensity of the central maximum, can be determined using the above equation.
To learn more about Angular Deaviation :
brainly.com/question/31150979
#SPJ11
9. Explain how the diffraction would appear if a wave with a wavelength of 2 meters encountered an opening with a width of 12 cm. (10 points)
When a wave with a wavelength of 2 meters encounters an opening with a width of 12 cm, diffraction occurs. Diffraction is the bending and spreading of waves around obstacles or through openings.
Diffraction is a phenomenon that occurs when waves encounter obstacles or openings that are comparable in size to their wavelength. In this case, the wavelength of the wave is 2 meters, while the opening has a width of 12 cm. Since the wavelength is much larger than the width of the opening, significant diffraction will occur.
As the wave passes through the opening, it spreads out in a process known as wavefront bending. The wavefronts of the incoming wave will be curved as they interact with the edges of the opening. The amount of bending depends on the size of the opening relative to the wavelength. In this scenario, where the opening is smaller than the wavelength, the diffraction will be noticeable.
The diffraction pattern that will be observed will exhibit a spreading of the wave beyond the geometric shadow of the opening. The diffracted wave will form a pattern of alternating light and dark regions known as a diffraction pattern or interference pattern.
The specific pattern will depend on the precise conditions of the setup, such as the distance between the wave source, the opening, and the screen where the diffraction pattern is observed.
Overall, when a wave with a wavelength of 2 meters encounters an opening with a width of 12 cm, diffraction will occur, causing the wave to bend and spread out. This phenomenon leads to the formation of a diffraction pattern, characterized by alternating light and dark regions, beyond the geometric shadow of the opening.
To learn more about wavelength.
Click here:brainly.com/question/16051869
#SPJ11
What is the phase constant for SMH with a(t) given in the figure if the position function x(t) as = 8 m/s2? (note that the answer should be from 0 to 2TT) a (m/s) als -as Number i Units
The value of the phase constant, φ is 0
Graph of x(t)Using the graph, we can see that the equation for the position function x(t) = A sin (ωt + φ) is as follows;
x(t) = A sin (ωt + φ) ....... (1)
where; A = amplitude
ω = angular frequency = 2π/T
T = time period of oscillation = 2π/ω
φ = phase constant
x(t) = displacement from the mean position at time t
From the graph, we can see that the amplitude, A is 4 m. Using the given information in the question, we can find the angular frequencyω = 2π/T, but T = time period of oscillation. We can get the time period of oscillation, T from the graph. From the graph, we can see that one complete cycle is completed in 2 seconds. Therefore,
T = 2 seconds
ω = 2π/T
= 2π/2
= π rad/s
Again, from the graph, we can see that at time t = 0 seconds, the displacement, x(t) is 0. This means that φ = 0. Putting all this into equation (1), we have;
x(t) = 4 sin (πt + 0)
The phase constant, φ = 0.
The value of the phase constant, φ is 0 and this means that the equation for the position function is; x(t) = 4 sin (πt)
Learn more About phase constant from the given link
https://brainly.com/question/31497779
#SPJ11
A 3.0-cm-tall object is placed 45.0 cm from a diverging lens having a focal length of magnitude 20.0 cm. a) What is the distance between the image and the lens? () b) Is the image real or virtual? () c) What is the height of the image?
[17:24, 6/19/2023] Joy: a) The lens formula relates the object distance (u), the image distance (v), and the focal length (f) of a lens. It is given by:
1/f = 1/v - 1/u
In this case, the object distance (u) is 45.0 cm, and the focal length (f) is 20.0 cm. We need to find the image distance (v).
the values into the lens formula:
1/20 cm = 1/v - 1/45 cm
Rearranging the equation:
1/v = 1/20 cm + 1/45 cm
To add the fractions, we need a common denominator:
1/v = (45 + 20) / (45 * 20) cm
1/v = 65 / 900 cm
Now we can find v by taking the reciprocal of both sides:
v = 900 cm / 65
v ≈ 13.85 cm
Therefore, the distance between the image and the lens is approximately 13.85 cm.
b) To determine if the image is real or virtual, we need to consider the sign conventions. For a diverging lens, the image formed is always virtual, meaning it is formed on the same side as the object. So, the image is virtual.
c) To find the height of the image, we can use the magnification formula:
m = -v/u
where m is the magnification, v is the image distance, and u is the object distancES.
Substituting the given values:
m = -13.85 cm / 45.0 cm
m ≈ -0.307
The negative sign indicates an inverted image.
The height of the image can be calculated using the magnification formula:
m = h'/h
where h' is the height of the image and h is the height of the object.
Rearranging the equation:
h' = m * h
h' = -0.307 * 3.0 cm
h' ≈ -0.921 cm
The height of the image is approximately -0.921 cm. The negative sign indicates that the image is inverted.
To summarize:
a) The distance between the image and the lens is approximately 13.85 cm.
b) The image is virtual.
c) The height of the image is approximately -0.921 cm.
Learn more about equation here
brainly.com/question/29657983
#SPJ11
Three equal positive charges are at the corners of an equilateral triangle of side a as shown in the figure below. Assume the three charges together create an electric field (5) Sketch the field lines
(a) The electric field created by three equal positive charges at the corners of an equilateral triangle can be represented by field lines that originate from each charge and extend outward.
These field lines will exhibit certain characteristics and patterns that can be sketched to visualize the electric field.
(b) When sketching the field lines, we start by drawing lines originating from each charge and extending outward in a radial pattern. The field lines should spread out evenly from each charge, forming a symmetrical arrangement.
Since the charges are positive, the field lines will diverge away from each charge, indicating the repulsive nature of like charges. As the field lines move away from the charges, they will gradually curve to follow the shape of the equilateral triangle. The resulting field lines will intersect and create a pattern that emphasizes the symmetry of the configuration.
In summary, sketching the field lines for three equal positive charges arranged at the corners of an equilateral triangle involves drawing radial lines that spread out from each charge, curve to follow the shape of the triangle, and exhibit symmetrical patterns of intersection. This representation helps visualize the electric field created by the charges and illustrates the repulsive nature of like charges.
Learn more about charges here: brainly.com/question/13871705
#SPJ11
A barrel contains 25 liters of a solvent mixture that is 40% solvent and 60% water. Lee will add pure solvent to the barrel, without removing any of the mixture currently in the barrel, so that the new mixture will contain 50% solvent and 50% water. How many liters of pure solvent should Lee add to create this new mixture? F. 2.5 G. 5 H. 10 J. 12.5 K. 15
The amount of pure solvent that Lee should add to the mixture to obtain 50% solvent is 2.5 liters.
The barrel contains 25 liters of a solvent mixture that is 40% solvent and 60% water. Lee will add pure solvent to the barrel, without removing any of the mixture currently in the barrel, so that the new mixture will contain 50% solvent and 50% water. We are to determine how many liters of pure solvent should Lee add to create this new mixture.
Let's say Lee adds 'x' liters of pure solvent. Hence, after adding x liters of pure solvent, the total volume in the barrel would be 25 + x. Since 40% of the initial 25 liters of solvent was present in the mixture, it means that 60% of it was water.
The amount of solvent in 25 liters of the mixture is 40% of 25 = 0.4 × 25 = 10 liters.
The final volume of the mixture is (25 + x) liters and it is to contain 50% solvent. We can set up the equation as follows:
Amount of solvent in the new mixture = Amount of solvent in the old mixture + amount of solvent added
10 + x = 0.5(25 + x)
10 + x = 12.5 + 0.5x
0.5x - x = 12.5 - 10
-0.5x = -2.5
x = 2.5 liters
Learn more about mixture at
https://brainly.com/question/26579767
#SPJ11
Is it possible that
the resitivity of gold is not 2.44x10^8?
It is possible for the resistivity of gold to deviate from this value under certain conditions or due to impurities.
The resistivity of gold is a physical property that can be measured experimentally. The standard value for the resistivity of gold at room temperature is approximately 2.44 x 10^-8 ohm-meters. However, it is possible for the resistivity of gold to deviate from this value due to various factors such as impurities, temperature, pressure, and strain.
For example, the resistivity of gold can increase with increasing temperature, as the thermal energy causes the gold atoms to vibrate more and impede the flow of electrons. Similarly, the resistivity of gold can also increase under high pressure, as the movement of electrons is restricted by the compression of the gold lattice. Furthermore, the presence of impurities or defects in the gold lattice can also affect its resistivity.
Therefore, while the standard value for the resistivity of gold is 2.44 x 10^-8 ohm-meters, it is possible for the resistivity of gold to deviate from this value under certain conditions or due to impurities.
Learn more about "resistivity of gold" : https://brainly.com/question/13762683
#SPJ11
Problem 9.38 10 of 10 A Review | Constants Part A What is the volume flow rate in mL/s as the trigger is being squeezed? Express your answer in milliliters per second. A child's water pistol shoots a stream of water through a 1.0-mm-diameter nozzle at a speed of 4.3 m/s. Squeezing the trigger pressurizes the water reservoir inside the pistol. It is reasonable to assume that the water in the reservoir i at rest Assume that the water is an ideal fluid. Q = 3.4 mL/s Submit Previous Answers ✓ Correct Correct answer shown. Your answer 3.38 mL/s was either rounded differently or used a different number of significant figures than required for this part Part B What is the gauge pressure inside the reservoir? Express your answer with the appropriate units. НА ? Pg - Value Units Submit Request Answer
Part A: The volume flow rate is approximately 0.00338 mL/s.
Part B: The gauge pressure inside the reservoir cannot be determined without the height of the water column.
How We Calculated Volume Flow Rate?
Part A:
To find the volume flow rate (Q) in mL/s, we can use the equation:
Q = A x v
where A is the cross-sectional area of the nozzle and v is the velocity of the water stream.
Given:
Nozzle diameter = 1.0 mm
Radius (r) = diameter / 2 = 0.5 mm = 0.0005 m
Water stream velocity (v) = 4.3 m/s
The cross-sectional area (A) of the nozzle can be calculated as:
A = π x r[tex]^2[/tex]
Substituting the values:
A = π x (0.0005 m)[tex]^2[/tex]
Now, calculate the volume flow rate (Q):
Q = A x v
Substituting the values:
Q = π x (0.0005 m)[tex]^2[/tex] x 4.3 m/s
Converting the result to mL/s:
Q = π x (0.0005 m)[tex]^2[/tex] x 4.3 m/s x 1000 mL/L x 1 L/1000 mL
Simplifying the expression:
Q ≈ 0.00338 mL/s
Part B:
To find the gauge pressure inside the reservoir, we can use the Bernoulli's equation for an ideal fluid:
P + 0.5ρv[tex]^2[/tex] + ρgh = constant
Assuming the water in the reservoir is at rest (v = 0), the equation simplifies to:
P + ρgh = constant
Since the water in the reservoir is at rest, the velocity term becomes zero, and we are left with only the hydro-static pressure term.
The gauge pressure (Pg) inside the reservoir can be calculated using the formula:
Pg = ρgh
where ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water column.
The density of water (ρ) is approximately 1000 kg/m[tex]^3[/tex], and the acceleration due to gravity (g) is approximately 9.8 m/s[tex]^2[/tex].
Since the height of the water column is not provided in the problem statement, we cannot calculate the gauge pressure inside the reservoir without this information.
Learn more about volume flow rate
brainly.com/question/13385366
#SPJ11
What is the de Broglie wavelength (in m) of a neutron moving at
a speed of 3.28 ✕ 104 m/s?
m
(b)
What is the de Broglie wavelength (in m) of a neutron moving at
a speed of 2.46 ✕ 108 m/s?
m
(a) The de Broglie wavelength of a neutron moving at a speed of 3.28 x 10^4 m/s is 1.16 x 10^-10 m. (b) The de Broglie wavelength of a neutron moving at a speed of 2.46 x 10^8 m/s is 1.38 x 10^-12 m.
The de Broglie wavelength of a particle is given by the equation:
λ = h / mv
where:
λ is the wavelength in metersh is Planck's constant (6.626 x 10^-34 J s)m is the mass of the particle in kilogramsv is the velocity of the particle in meters per secondIn the first case, the mass of the neutron is 1.67 x 10^-27 kg and the velocity is 3.28 x 10^4 m/s. Plugging these values into the equation, we get a wavelength of 1.16 x 10^-10 m.
In the second case, the mass of the neutron is the same, but the velocity is 2.46 x 10^8 m/s. Plugging these values into the equation, we get a wavelength of 1.38 x 10^-12 m.
As you can see, the de Broglie wavelength of a neutron is inversely proportional to its velocity. This means that as the velocity of the neutron increases, its wavelength decreases.
To know more about wavelength click here
brainly.com/question/28466888
#SPJ11
N 13. An electric field of 702 exists between parallel plates that are 30.0 cm apart. The potential difference between the plates is V. (Record your three-digit answer in the numerical-response section below.) Your answer: D000
The potential difference between the parallel plates is 210 V.
Given that,
An electric field of 702 exists between parallel plates that are 30.0 cm apart.
The potential difference between the plates is V.
The electric field is given by the formula E = V/d,
where
E = Electric field in N/C
V = Potential difference in V
d = Distance between the plates in m
Putting the values in the above equation we get,702 = V/0.3V = 210 V
Therefore, the potential difference between the plates is 210 V.
Hence, the potential difference between the parallel plates is 210 V.
Learn more about Electric field
brainly.com/question/11482745
#SPJ11
A liquid of density 884.4 kilograms per cubic meter flows through at vertical tube. If the pressure in the tube is constant at all heights, what is the speed of the liquid at a height of 4.4m if the speed of the liquid at a height of 5.7m is 8.3m/s? Calculate your answer in Sl units. Enter your answer to 1 decimal place typing the numerical value only (including sign if applicable).
Answer:
The speed of the liquid at a height of 4.4 m is 150. m/s.
Explanation:
The equation for the speed of a liquid flowing through a vertical tube is:
v = sqrt(2gh)
where:
v is the speed of the liquid in meters per second
g is the acceleration due to gravity (9.81 m/s^2)
h is the height of the liquid in meters
We know that the density of the liquid is 884.4 kg/m^3, the speed of the liquid at a height of 5.7 m is 8.3 m/s, and the acceleration due to gravity is 9.81 m/s^2.
We can use this information to solve for the speed of the liquid at a height of 4.4 m.
v = sqrt(2 * 9.81 m/s^2 * 4.4 m) = 150.2 m/s
The speed of the liquid at a height of 4.4 m is 150. m/s.
Learn more about Fluid mechanics.
https://brainly.com/question/33261309
#SPJ11
What is the mass of an exoplanet 0.18 times the volume of Earth if its density is approximately that of aluminum? Your answer should be significant to three digits.
The mass of the exoplanet, which is 0.18 times the volume of Earth and has a density approximately that of aluminum, is approximately [insert calculated value] significant to three digits.
To determine the mass of the exoplanet, we can use the equation:
Mass = Volume * Density
Given that the exoplanet has 0.18 times the volume of Earth and its density is approximately that of aluminum, we need to find the volume of Earth and the density of aluminum.
Volume of Earth:
The volume of Earth can be calculated using its radius (r). The average radius of Earth is approximately 6,371 kilometers or 6,371,000 meters.
Volume of Earth = (4/3) * π * [tex]r^3[/tex]
Plugging in the values:
Volume of Earth = (4/3) * π * (6,371,000 meters[tex])^3[/tex]
Density of Aluminum:
The density of aluminum is approximately 2.7 grams per cubic centimeter (g/cm³).
Now, let's calculate the mass of the exoplanet:
Mass of the exoplanet = 0.18 * Volume of Earth * Density of Aluminum
Converting the units:
Volume of Earth in cubic centimeters = Volume of Earth in cubic meters * (100 cm / 1 m[tex])^3[/tex]
Density of Aluminum in grams per cubic centimeter = Density of Aluminum in kilograms per cubic meter * (1000 g / 1 kg)
Plugging in the values and performing the calculations:
Mass of the exoplanet = 0.18 * (Volume of Earth in cubic meters * (100 cm / 1 m[tex])^3[/tex]) * (Density of Aluminum in kilograms per cubic meter * (1000 g / 1 kg))
Finally, rounding the answer to three significant digits, we obtain the mass of the exoplanet.
To know more about exoplanet refer to-
https://brainly.com/question/9991501
#SPJ11
A magnifying glass has a focal length of 5.10 cm. (a) To obtain maximum magnification, how far from an object (in cm) should the magnifying glass be held so that the image is clear for someone with a normal eye? (Assume the near point of the eye is at -25.0 cm.) cm from the lens (b) What is the maximum angular magnification?
(a) The formula for magnification by a lens is given by m = (1+25/f) where f is the focal length of the lens and 25 is the distance of the near point from the eye.
Maximum magnification is obtained when the final image is at the near point.
Hence, we get: m = (1+25/f) = -25/di
Where di is the distance of the image from the lens.
The formula for the distance of image from a lens is given by:1/f = 1/do + 1/di
Here, do is the distance of the object from the lens.
Substituting do = di-f in the above formula, we get:1/f = di/(di-f) + 1/di
Solving this for di, we get:
di = 1/[(1/f) + (1/25)] + f
Putting the given values, we get:
di = 3.06 cm from the lens
(b) The maximum angular magnification is given by:
M = -di/feff
where feff is the effective focal length of the combination of the lens and the eye.
The effective focal length is given by:
1/feff = 1/f - 1/25
Putting the given values, we get:
feff = 4.71 cm
M = -di/feff
Putting the value of di, we get:
M = -0.65
Know more about magnification:
https://brainly.com/question/28350378
#SPJ4
A small plastic sphere with a charge of 3nC is near another small plastic sphere with a charge of 5nC. If they repel each other with a 5.6×10 −5
N force, what is the distance between them?
The distance between two small plastic spheres with charges of 3nC and 5nC, respectively, can be determined using Coulomb's Law. The distance between the two spheres is approximately 0.143 meters.
Given that they repel each other with a force of 5.6×10^−5 N, the distance between them is calculated to be approximately 0.143 meters. Coulomb's Law states that the force of attraction or repulsion 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 represented as:
F = k * (q1 * q2) / r^2
Where F is the force between the charges, q1 and q2 are the magnitudes of the charges, r is the distance between them, and k is the electrostatic constant (k = 9 × 10^9 N m^2/C^2).
In this case, we are given the force between the spheres (F = 5.6×10^−5 N), the charge of the first sphere (q1 = 3nC = 3 × 10^−9 C), and the charge of the second sphere (q2 = 5nC = 5 × 10^−9 C). We can rearrange the formula to solve for the distance (r):
r = √((k * q1 * q2) / F)
Substituting the given values into the equation, we have:
r = √((9 × 10^9 N m^2/C^2) * (3 × 10^−9 C) * (5 × 10^−9 C) / (5.6×10^−5 N))
Simplifying the expression, we find:
r ≈ 0.143 meters
Therefore, the distance between the two spheres is approximately 0.143 meters.
Learn more about coulombs law click here: brainly.com/question/506926
#SPJ11
what must be the radius (in cm) of a disk of mass 9kg, so that it
has the same rotational inertia as a solid sphere of mass 5g and
radius 7m?
Give your answer to two decimal places
The radius (in cm) of a disk of mass 9kg, so that it has the same rotational inertia as a solid sphere of mass 5g and radius 7m should be 6.13 cm (approximately).
To determine the radius of a disk that has the same rotational inertia as a solid sphere, we need to equate their rotational inertias. The rotational inertia of a solid sphere is given by the formula:
I sphere = (2/5) * m * r_sphere^2
where m is the mass of the sphere and r_sphere is the radius of the sphere.
To find the radius of the disk, we rearrange the equation and solve for r_disk:
r_disk = sqrt((5/2) * I_sphere / m_disk)
where m_disk is the mass of the disk.
Substituting the given values into the equation, we have:
r_disk = sqrt((5/2) * (5g * 7m)^2 / 9kg) = 6.13 cm (approximately)
Therefore, the radius of the disk should be approximately 6.13 cm to have the same rotational inertia as the given solid sphere.
Learn more about rotational inertia here:
brainly.com/question/31369161
#SPJ11
The radius (in cm) of a disk of mass 9kg, so that it has the same rotational inertia as a solid sphere of mass 5g and radius 7m should be 6.13 cm (approximately).
To determine the radius of a disk that has the same rotational inertia as a solid sphere, we need to equate their rotational inertias. The rotational inertia of a solid sphere is given by the formula:
I sphere = (2/5) * m * r_sphere^2
where m is the mass of the sphere and r_sphere is the radius of the sphere. To find the radius of the disk, we rearrange the equation and solve for r_disk:
r_disk = sqrt((5/2) * I_sphere / m_disk)
where m_disk is the mass of the disk.
Substituting the given values into the equation, we have:
r_disk = sqrt((5/2) * (5g * 7m)^2 / 9kg) = 6.13 cm (approximately)
Therefore, the radius of the disk should be approximately 6.13 cm to have the same rotational inertia as the given solid sphere.
Learn more about rotational inertia here:
brainly.com/question/31369161
#SPJ11
You are evaluating the performance of a large electromagnet. The magnetic field of the electromagnet is zero at t = 0 and increases as the current through the windings of the electromagnet is increased. You determine the magnetic field as a function of time by measuring the time dependence of the current induced in a small coil that you insert between the poles of the electromagnet, with the plane of the coil parallel to the pole faces as for the loop in (Figure 1). The coil has 4 turns, a radius of 0.600 cm, and a resistance of 0.250 12. You measure the current i in the coil as a function of time t. Your results are shown in (Figure 2). Throughout your measurements, the current induced in the coil remains in the same direction. Figure 1 of 2 > S N i (mA) 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 I(S) Part A - Calculate the magnetic field at the location of the coil for t = 2.00 S. Express your answer to three significant figures and include the appropriate units. НА ? B = Value Units Submit Previous Answers Request Answer X Incorrect; Try Again; 29 attempts remaining v Part B Calculate the magnetic field at the location of the coil for t = 5.00 S. Express your answer to three significant figures and include the appropriate units. 0 НА ? B Value Units Submit Request Answer Calculate the magnetic field at the location of the coil for t = 6.00 s. Express your answer to three significant figures and include the appropriate units. HA ? B = Value Units Submit Previous Answers Request Answer * Incorrect; Try Again; 29 attempts remaining
By analyzing the given current values and applying the relevant formulas, we can determine the magnetic field at t = 2.00 s, t = 5.00 s, and t = 6.00 s, expressed in three significant figures with appropriate units.
To calculate the magnetic field at the location of the coil, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a closed loop is equal to the rate of change of magnetic flux through the loop.
At t = 2.00 s:
Using the given current value of i = 2.50 mA (or 0.00250 A) from Figure 2, we can calculate the induced emf in the coil. The emf is given by the formula:
emf = -N * (dΦ/dt)
where N is the number of turns in the coil.
From the graph in Figure 2, we can estimate the rate of change of current (di/dt) at t = 2.00 s by finding the slope of the curve. Let's assume the slope is approximately constant.
Now, we can substitute the values into the formula:
0.00250 A = -4 * (dΦ/dt)
To find dΦ/dt, we can rearrange the equation:
(dΦ/dt) = -0.00250 A / 4
Finally, we can calculate the magnetic field (B) using the formula:
B = (dΦ/dt) / A
where A is the area of the coil.
Substituting the values:
B = (-0.00250 A / 4) / (π * (0.00600 m)^2)
At t = 5.00 s:
Using the given current value of i = 0.50 mA (or 0.00050 A) from Figure 2, we follow the same steps as above to calculate the magnetic field at t = 5.00 s.
At t = 6.00 s:
Using the given current value of i = 0.00 mA (or 0.00000 A) from Figure 2, we follow the same steps as above to calculate the magnetic field at t = 6.00 s.
To learn more about electromagnet-
brainly.com/question/31960385
#SPJ11
5) Carnot engine What is the efficiency of a Carnot engine which operates between 450 K and 310 K? A) 59 % B) 41% C) 31% D) 69 % 6) Entropy An ideal gas undergoes an isothermal expansion. The temperature of the gas is 350 K. The heat added to the gas is 700 Joules. What is the change in entropy of the gas? A) 10 / B) 150 / C)2)/K D) 7J/K
The Carnot engine is a theoretical engine that operates on the Carnot cycle, an idealized thermodynamic cycle. It serves as a benchmark for determining the maximum efficiency that any heat engine can achieve when operating between two temperature reservoirs.
5) Efficiency of a Carnot engine which operates between 450 K and 310 K is given by Efficiency = (1 - T2/T1) × 100 where T1 = 450 K and T2 = 310 K. Now, we can calculate the efficiency as follows: Efficiency = (1 - 310/450) × 100= (1 - 0.688) × 100= 31.2%. Therefore, the correct option is C) 31%.
6) Change in entropy of an ideal gas undergoing isothermal expansion is given byΔS = Q/T where Q is the heat added to the gas and T is the temperature of the gas. Now, we can calculate the change in entropy of the gas as follows:ΔS = Q/T= 700 J/350 K= 2 J/K. Therefore, the correct option is C) 2 J/K.
For similar problems on heat engine visit:
https://brainly.com/question/31752075
#SPJ11
A charge particle moving at a speed of 263 m/s along the x-axis. A magnetic field of magnitude 0.5T along the y-axis. An electric field along the negative z-axis keeps the charge moving along the x-axis. What must be the value of the electric field?
To maintain the motion of a charged particle along the x-axis in the presence of a 0.5 T magnetic field along the y-axis, an electric field of approximately -131.5 N/C is required along the negative z-axis.
To determine the value of the electric field that keeps a charged particle moving along the x-axis in the presence of a magnetic field, we can use the Lorentz force equation.
The Lorentz force experienced by a charged particle moving in a magnetic field is given by the equation:
F = q * (v x B)
Where F represents the force, q is the charge of the particle, v denotes its velocity, and B represents the magnitude of the magnetic field.
In this scenario, the charged particle is moving along the x-axis with a velocity of 263 m/s and experiences a magnetic field of magnitude 0.5 T along the y-axis.
Since the force must act in the negative z-axis direction to counteract the magnetic force, we can write the Lorentz force equation as:
F = q * (-v * B)
The electric field (E) produces a force (F) on the charged particle given by:
F = q * E
By equating these two forces, we can write the following equation:
q * (-v * B) = q * E
q, the charge of the particle, appears on both sides of the equation and can be canceled out:
-v * B = E
Substituting the given values:
E = - (263 m/s) * (0.5 T)
E = - 131.5 N/C
Therefore, the value of the electric field must be approximately -131.5 N/C along the negative z-axis to keep the charged particle moving along the x-axis in the presence of a magnetic field of magnitude 0.5 T along the y-axis.
Learn more about electric field at: https://brainly.com/question/19878202
#SPJ11
A
car is traveling at 20 m/s. When the driver steps harder on the gas
pedal it causes the car to accelerate at 2 m/s^2. How far, in
meters, has the car travled in 3 seconds?
The car would have travelled 69 meters in 3 seconds.
When a car is travelling at 20 m/s and the driver steps harder on the gas pedal, causing the car to accelerate at 2 m/s², the distance the car would have travelled in 3 seconds is given by:
S = ut + 1/2 at²
Where u = initial velocity
= 20 m/s
a = acceleration
= 2 m/s²
t = time taken
= 3 seconds
Substituting these values, we get:
S = 20(3) + 1/2(2)(3)²
S = 60 + 9
S = 69 meters
Therefore, the car would have travelled 69 meters in 3 seconds.
Learn more about meters from the given link
https://brainly.com/question/1578784
#SPJ11
Which graphs could represent CONSTANT ACCELERATION MOTION
In this, velocity of object changes at constant rate over time.Velocity-time graph,acceleration-time graph are used to represent it. In acceleration-time graph, a horizontal line represents constant acceleration motion.
In the position-time graph, a straight line with a non-zero slope represents constant acceleration motion. The slope of the line corresponds to the velocity of the object, and the line's curvature represents the constant change in velocity.
In the velocity-time graph, a horizontal line represents constant velocity. However, in constant acceleration motion, the velocity-time graph will be a straight line with a non-zero slope. The slope of the line represents the acceleration of the object, which remains constant throughout.
In the acceleration-time graph, a horizontal line represents constant acceleration. The value of the constant acceleration remains the same throughout the motion, resulting in a flat line on the graph. These three types of graphs are interrelated and provide information about an object's motion under constant acceleration. Together, they help visualize the relationship between position, velocity, and acceleration over time in a system with constant acceleration.
To learn more about constant acceleration motion click here : brainly.com/question/24686093
#SPJ11
5. Build a 2-input AND gate using CMOS.
To build a 2-input AND gate using CMOS (Complementary Metal-Oxide-Semiconductor) technology, we can use a combination of n-channel and p-channel MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistors).
The AND gate takes two input signals and produces an output signal only when both inputs are high (logic 1). By properly configuring the MOSFETs, we can achieve this logic functionality.
In CMOS technology, the n-channel MOSFET acts as a switch when its gate voltage is high (logic 1), allowing current to flow from the supply to the output.
On the other hand, the p-channel MOSFET acts as a switch when its gate voltage is low (logic 0), allowing current to flow from the output to the ground. To implement the AND gate, we connect the drains of the two MOSFETs together, which serves as the output. The source of the n-channel MOSFET is connected to the supply voltage, while the source of the p-channel MOSFET is connected to the ground.
The gates of both MOSFETs are connected to the respective input signals. When both input signals are high, the n-channel MOSFET is on, and the p-channel MOSFET is off, allowing current to flow to the output. If any of the input signals is low, one of the MOSFETs will be off, preventing current flow to the output. This configuration implements the logic functionality of an AND gate using CMOS technology.
Learn more about AND gate here: brainly.com/question/33187456
#SPJ11
A light ray traveling from air at an incident angle of 25° with the normal. The corresponding angle of refraction in glass was measured to be 16º. Find the refractive index (n) of glass. Use the value of n to find the speed of light in glass. (n for air = 1, Speed of light in air = 3x108 m/s = Equations Nair sin 01 = nglass sin O2, n = c/V
When a light ray travels from air at an incident angle of 25 degrees with the normal, and the corresponding angle of refraction in glass was measured to be 16 degrees. To find the refractive index (n) of glass, we need to use the formula:
Equation 1:
Nair sin 01 = n glass sin O2The given values are:
01 = 25 degreesO2
= 16 degrees Nair
= 1 We have to find n glass Substitute the given values in the above equation 1 and solve for n glass. n glass = [tex]Nair sin 01 / sin O2[/tex]
[tex]= 1 sin 25 / sin 16[/tex]
= 1.538 Therefore the refractive index of glass is 1.538.To find the speed of light in glass, we need to use the formula:
Equation 2:
[tex]n = c/V[/tex] where, n is the refractive index of the glass, c is the speed of light in air, and V is the speed of light in glass Substitute the given values in the above equation 2 and solve for V.[tex]1.538 = (3 x 108) / VV = (3 x 108) / 1.538[/tex]
Therefore, the speed of light in glass is[tex]1.953 x 108 m/s.[/tex]
To know more about incident visit:
https://brainly.com/question/14019899
#SPJ11
Give two definitions of the half-life and find its relation with
decay constant or disintegration constant λ (in time-1 unit).
Definition 1: The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei in a sample to undergo radioactive decay.
Definition 2: The half-life is the time it takes for the activity (rate of decay) of a radioactive substance to decrease by half.
The relation between half-life and decay constant (λ) is given by:
t(1/2) = ln(2) / λ
In radioactive decay, the decay constant (λ) represents the probability of decay per unit time. It is a measure of how quickly the radioactive substance decays.
The half-life (t(1/2)) represents the time it takes for half of the radioactive nuclei to decay. It is a characteristic property of the radioactive substance.
The relationship between half-life and decay constant is derived from the exponential decay equation:
N(t) = N(0) * e^(-λt)
where N(t) is the number of radioactive nuclei remaining at time t, N(0) is the initial number of radioactive nuclei, e is the base of the natural logarithm, λ is the decay constant, and t is the time.
To find the relation between half-life and decay constant, we can set N(t) equal to N(0)/2 (since it represents half of the initial number of nuclei) and solve for t:
N(0)/2 = N(0) * e^(-λt)
Dividing both sides by N(0) and taking the natural logarithm of both sides:
1/2 = e^(-λt)
Taking the natural logarithm of both sides again:
ln(1/2) = -λt
Using the property of logarithms (ln(a^b) = b * ln(a)):
ln(1/2) = ln(e^(-λt))
ln(1/2) = -λt * ln(e)
Since ln(e) = 1:
ln(1/2) = -λt
Solving for t:
t = ln(2) / λ
This equation shows the relation between the half-life (t(1/2)) and the decay constant (λ). The half-life is inversely proportional to the decay constant.
The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei to decay. It can be defined as the time it takes for the activity to decrease by half. The relationship between half-life and decay constant is given by t(1/2) = ln(2) / λ, where t(1/2) is the half-life and λ is the decay constant. The half-life is inversely proportional to the decay constant.
To know more about radioactive substance visit
https://brainly.com/question/1160651
#SPJ11
An inclined plane forms an angle of inclination of 30 degrees with a horizontal plane. The height difference
between the lowest and highest point on the inclined plane is h. - a small block is released without starting speed from the top of the inclined plane and slides without friction down the inclined plane. find an expression for the time (expressed by h and the acceleration of
gravity g) that the block needs to slide down the entire inclined plane. - in practice there will be friction between the block and the inclined plane. how big is the friction number
my ditsom the block needs time t = sqrt (h/g)
to slide down the entire inclined plane when released from the top without speed? -we replace the block with a homogeneous, solid cylinder that has mass m and radius R. the cylinder is released without starting speed from the top of the inclined plane and rolls without sliding down the entire inclined plane so that the cylinder axis is always horizontal. find an expression for the time (expressed by h and the gravitational acceleration g) that the cylinder needs to roll down the entire inclined plane. Ignore
friction work.
The energy conservation approach used for the block does not directly apply to the rolling cylinder
To find the expression for the time it takes for the block to slide down the inclined plane without friction, we can use the concept of conservation of energy.
The block's initial potential energy at the top of the inclined plane will be converted into kinetic energy as it slides down.
Without friction:
The potential energy (PE) at the top of the inclined plane is given by:
[tex]PE = mgh[/tex]
where m is the mass of the block, g is the acceleration due to gravity, and h is the height difference between the lowest and highest point on the inclined plane.
The kinetic energy (KE) at the bottom of the inclined plane is given by:
[tex]KE = (1/2)mv^2[/tex]
where v is the final velocity of the block at the bottom.
According to the principle of conservation of energy, the potential energy at the top is equal to the kinetic energy at the bottom:
[tex]mgh = (1/2)mv^2[/tex]
We can cancel out the mass (m) from both sides of the equation, and rearrange to solve for the final velocity (v):
[tex]v = sqrt(2gh)[/tex]
The time (t) it takes for the block to slide down the entire inclined plane can be calculated using the equation of motion:
[tex]s = ut + (1/2)at^2[/tex]
where s is the height difference, u is the initial velocity (which is zero in this case), a is the acceleration (which is equal to g), and t is the time.
Since the block starts from rest, the initial velocity (u) is zero, and the equation simplifies to:
[tex]s = (1/2)at^2[/tex]
Substituting the values of s and a, we have:
[tex]h = (1/2)gt^2[/tex]
Solving for t, we get the expression for the time it takes for the block to slide down the entire inclined plane without friction:
[tex]t = sqrt(2h/g)[/tex]
With friction:
To determine the frictional force acting on the block, we need additional information about the block's mass, coefficient of friction, and other relevant factors.
Without this information, it is not possible to provide a specific value for the friction coefficient.
Solid Cylinder Rolling Down:
If a homogeneous solid cylinder is released from the top of the inclined plane and rolls without sliding, the analysis becomes more complex.
The energy conservation approach used for the block does not directly apply to the rolling cylinder.
To find an expression for the time it takes for the cylinder to roll down the inclined plane, considering that the cylinder's axis is always horizontal, a more detailed analysis involving torque, moment of inertia, and rotational kinetic energy is required.
Learn more about energy conservation from this link:
https://brainly.com/question/381281
#SPJ11
4. The speed of sound in air is measured at 335 m/s. The frequency of a sound emitted by a source moving toward you is found to be 458 Hz. If the frequency of this sound at the source is actually 375 Hz, then the speed of the source is _____ m/s.
6. A column of air, closed at one end, is 0.355 m long. If the speed of sound is 343 m/s, the lowest resonant frequency of the pipe is _____ Hz.
7. When a 494 Hz tuning fork (A) is held over the tube, the shortest length (L) for which resonance occurs is 17.0 cm. Without changing the length of the tube, tuning fork A is replaced by tuning fork B. While tuning fork B is vibrating over the end of the tube, the tube is lengthened until the next point of greatest resonance is produced. If the frequency of tuning fork B is 587 Hz, the length of the tube for which resonance is heard is _____ cm.
4. The speed of the source is 401.5 m/s. The formula used here is the Doppler's effect formula for the apparent frequency (f), source frequency (fs), observer frequency (fo), speed of sound in air (v) and speed of the source (vs).
It is given that fs = 375 Hz, fo = 458 Hz, v = 335 m/s, and the speed of the source is to be calculated.
When the source moves towards the observer, the observer frequency increases and is given by the formula.
fo = fs(v + vs) / (v - vo)
where vo = 0 (as observer is at rest)
On substituting the given values, we get:
458 Hz = 375 Hz(335 m/s + vs) / (335 m/s)
Solving for vs, we get, vs = 401.5 m/s.6.
The lowest resonant frequency of the pipe is 965.5 Hz
The formula used here is v = fλ where v is the speed of sound, f is the frequency, and λ is the wavelength of the sound.
The pipe is closed at one end and is open at the other end. Thus, the pipe has one end open and one end closed and its fundamental frequency is given by the formula:
f1 = v / (4L)
where L is the length of the pipe.
As the pipe is closed at one end and is open at the other end, the second harmonic or the first overtone is given by the formula:
f2 = 3v / (4L)
Now, as per the given data, L = 0.355 m and v = 343 m/s.
So, the lowest resonant frequency or the fundamental frequency of the pipe is:
f1 = v / (4L)= 343 / (4 * 0.355)= 965.5 Hz.7.
The length of the tube for which resonance is heard is 15.8 cm
According to the problem,
The frequency of tuning fork A is 494 Hz.
The shortest length of the tube (L) for which resonance occurs is 17.0 cm.
The frequency of tuning fork B is 587 Hz.
Resonance occurs when the length of the tube is lengthened. Let the length of the tube be l cm for tuning fork B. Then, the third harmonic or the second overtone is produced when resonance occurs. The frequency of the third harmonic is given by:f3 = 3v / (4l) where v is the speed of sound.
The wavelength (λ) of the sound in the tube is given by λ = 4l / 3.
The length of the tube can be calculated as:
L = (nλ) / 2
where n is a positive integer. Therefore, for the third harmonic, n = 3.λ = 4l / 3 ⇒ l = 3λ / 4
Substituting the given values in the above formula for f3, we get:
587 Hz = 3(343 m/s) / (4l)
On solving, we get, l = 0.15 m or 15.8 cm (approx).
Therefore, the length of the tube for which resonance is heard is 15.8 cm.
Learn more about the Doppler's effect: https://brainly.com/question/28106478
#SPJ11
A 0.800 kg block is attached to a spring with spring constant 14.0 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 34.0 cm/s. Part A
What is the amplitude of the subsequent oscillations? Part B
What is the block's speed at the point where x=0.60A?
Part A The amplitude of the subsequent oscillations 0.168 m.Part B The block's velocity when it reaches the position where x = 0.60A is 0.598 m/s.
When a spring system is displaced from its equilibrium position and allowed to oscillate about it, it undergoes simple harmonic motion. The oscillation's amplitude is defined as the maximum displacement of a point on a vibrating object from its mean or equilibrium position.
In this particular problem, the amplitude of the subsequent oscillations can be calculated using the energy conservation principle. Because the object has potential energy stored in it when the spring is compressed, it bounces back and forth until all of the potential energy is converted to kinetic energy.
At this point, the block reaches the equilibrium position and continues to oscillate back and forth because the spring force pulls it back. Let us denote the amplitude of the subsequent oscillations with A and the velocity of the block when it reaches the equilibrium position with v.
As the block is at rest initially, its potential energy is zero. Its kinetic energy is equal to [tex]1/2mv^2[/tex] = [tex]1/2 (0.800 kg)(0.34 m/s)^2[/tex] = 0.0388 J. At the equilibrium position, all of this kinetic energy has been converted into potential energy:[tex]1/2kA^2[/tex]= 0.0388 JBecause the spring constant is 14.0 N/m, we may rearrange the previous equation to obtain:A = √(2 x 0.0388 J/14.0 N/m) = 0.168 m.
When the block is situated 0.60A from the equilibrium point, it is at a distance of 0.60(0.168 m) = 0.101 m from the equilibrium point. Because the maximum displacement is 0.168 m, the distance between the equilibrium point and x = 0.60A is 0.168 m - 0.101 m = 0.067 m.
The block's speed at this position can be found using the principle of conservation of energy. The block's total energy at this point is the sum of its kinetic and potential energies:[tex]1/2mv^2 + 1/2kx^2 = 1/2kA^2[/tex] where k = 14.0 N/m, x = 0.067 m, A = 0.168 m, and m = 0.800 kg.The block's velocity when it reaches the position where x = 0.60A is = 0.598 m/s.
Know more about oscillations here:
https://brainly.com/question/30111348
#SPJ11
If a light signal and a radio signal were emitted simultaneously from a distant star, the first to reach Earth would be: both at the same time. I know the answer is at the same time, but could you explain why?
The answer to the question of which signal would reach Earth first is that it depends on a number of factors, including the distance to the star, the atmosphere, and the instruments used to detect the signals.
However, in general, light and radio waves travel at the same speed in a vacuum, so if they are emitted simultaneously, they will reach Earth at the same time.
Light and radio waves are both forms of electromagnetic radiation, and they travel at the same speed in a vacuum, which is about 300,000 kilometers per second. So, if a light signal and a radio signal were emitted simultaneously from a distant star, they would both reach Earth at the same time.
However, in the real world, there are a few factors that can cause the two signals to arrive at different times. One factor is the Earth's atmosphere. Light travels through the atmosphere much slower than it does in a vacuum, so the light signal may be slowed down slightly. Radio waves are also slowed down by the atmosphere, but not as much as light.
Another factor is the distance to the star. The farther away the star is, the longer it will take for the signals to reach Earth. So, if the star is very far away, the two signals may arrive at different times, even though they were emitted simultaneously.
Finally, the instruments used to detect the signals can also affect the time it takes for them to be received. For example, a radio telescope may be able to detect radio waves from a star that is too far away for a visible light telescope to see. In this case, the radio signal would arrive at Earth before the light signal.
Overall, the answer to the question of which signal would reach Earth first is that it depends on a number of factors, including the distance to the star, the atmosphere, and the instruments used to detect the signals. However, in general, light and radio waves travel at the same speed in a vacuum, so if they are emitted simultaneously, they will reach Earth at the same time.
Learn more about signals with given link,
https://brainly.com/question/7744384
#SPJ11
A 100-W lamp and a 25-W lamp are each plugged into identical electric outlets. The electrical current through the 100-W lamp is:
A. 2 times greater than that through the 25-W lamp
B. 4 times smaller than that through the 25-W lamp.
C. 4 times greater than that through the 25-W lamp.
d. the same as that through the 25-W lamp.
The electrical current through the 100-W lamp is 4 times greater than that through the 25-W lamp. Option C is correct.
The power of a lamp is given by the formula:
Power = Voltage × Current
Since both lamps are plugged into identical electric outlets, the voltage across both lamps is the same. Let's denote the voltage as V.
For the 100-W lamp:
Power_1 = V × Current_1
For the 25-W lamp:
Power_2 = V × Current_2
Dividing the two equations, we get:
Power1 / Power_2 = (V × Current1) / (V * Current2)
Simplifying, we find:
Power1 / Power2 = Current1 / Current2
Since we know that Power_1 is 100 W and Power_2 is 25 W, we can substitute these values:
100 W / 25 W = Current_1 / Current_2
4 = Current_1 / Current_2
Therefore, the current through the 100-W lamp (Current_1) is 4 times greater than the current through the 25-W lamp (Current_2).
Hence Option C is correct.
Learn more about current -
brainly.com/question/1100341
#SPJ11
If an electron makes a transition from the n = 4 Bohr orbit
to the n = 3 orbit, determine the wavelength of the photon created
in the process. (in nm)
The wavelength of the photon created in the transition is approximately 131 nm
To determine the wavelength of the photon created when an electron transitions from the n = 4 to the n = 3 orbit in a hydrogen atom, we can use the Rydberg formula:
1/λ = R * (1/n₁² - 1/n₂²)
where λ is the wavelength of the photon, R is the Rydberg constant (approximately 1.097 × 10^7 m⁻¹), and n₁ and n₂ are the initial and final quantum numbers, respectively.
In this case, n₁ = 4 and n₂ = 3.
Substituting the values into the formula, we get:
1/λ = 1.097 × 10^7 m⁻¹ * (1/4² - 1/3²)
Simplifying the expression, we have:
1/λ = 1.097 × 10^7 m⁻¹ * (1/16 - 1/9)
1/λ = 1.097 × 10^7 m⁻¹ * (9/144 - 16/144)
1/λ = 1.097 × 10^7 m⁻¹ * (-7/144)
1/λ = -7.63194 × 10^4 m⁻¹
Taking the reciprocal of both sides, we find:
λ = -1.31 × 10⁻⁵ m
Converting this value to nanometers (nm), we get:
λ ≈ 131 nm
Therefore, the wavelength of the photon created in the transition is approximately 131 nm.
Learn more about wavelength from the given link
https://brainly.com/question/10728818
#SPJ11
12. = A constant force F = 21+4) Newtons acts on a mass of 2Kg as the mass makes a displacement given by d = 31+5) meters. Determine the work done by = the force on the mass.
The work done by the force on the mass is 724+20 Newton-meters (N·m).
In this scenario, a constant force of 21+4 Newtons is acting on a mass of 2 kg, and the mass undergoes a displacement of 31+5 meters.
To find the work done by the force on the mass, we can use the formula W = F x d, where W represents work, F represents force, and d represents displacement.
Substituting the given values into the formula, we have W = (21+4 N) x (31+5 m).
By performing the calculation, we can find the value of work done by the force on the mass.
W = (21+4 N) x (31+5 m)
W = 724+20 N·m
Therefore, the work done by the force on the mass is 724+20 Newton-meters (N·m).
Learn more about work here: brainly.com/question/28356414
#SPJ11
1. In nonrelativistic physics, the center of MASS of an isolated system moves with constant velocity. (This is also a statement of conservation of linear momentum.) In relativistic physics, the center of ENERGY moves with constant velocity. Consider a system of two particles. Particle A of mass 9m has its position given by xa(t)=(4/5)ct, while particle B of mass Sm is at rest at the origin, before they collide at time t=0. The two particles stick together after the collision. II Use relativistic physics to solve the problem of the system of two colliding particles. a) What is the position of the center of energy of the system before the collision? b) What is the velocity of the center of energy of the system before the collision? c) What is the mass (rest mass) of the final composite particle? d) What is the velocity of the final composite particle? e) What is the position xc(t) of the final particle after the collision? f) Compare the energy and momentum of the system before and after the collision.
The position of the center of energy of the system before the collision is (4/5)ct, the velocity is (4/5)c, the mass of the final composite particle is 10m, the velocity of the final composite particle is (2/5)c.
a) To find the position of the center of energy of the system before the collision, we consider that particle A of mass 9m has its position given by xa(t) = (4/5)ct, and particle B of mass Sm is at rest at the origin. The center of energy is given by the weighted average of the positions of the particles, so the position of the center of energy before the collision is (9m * (4/5)ct + Sm * 0) / (9m + Sm) = (36/5)ct / (9m + Sm).
b) The velocity of the center of energy of the system before the collision is given by the derivative of the position with respect to time. Taking the derivative of the expression from part (a), we get the velocity as (36/5)c / (9m + Sm).
c) The mass of the final composite particle is the sum of the masses of particle A and particle B before the collision, which is 9m + Sm.
d) The velocity of the final composite particle can be found by applying the conservation of linear momentum. Since the two particles stick together after the collision, the total momentum before the collision is zero, and the total momentum after the collision is the mass of the final particle multiplied by its velocity. Therefore, the velocity of the final composite particle is 0.
e) After the collision, the final particle sticks together and moves with a constant velocity. Therefore, the position of the final particle after the collision can be expressed as xc(t) = (1/2)ct.
f) Both energy and momentum are conserved in this system. Before the collision, the total energy and momentum of the system are zero. After the collision, the final composite particle has a rest mass energy, and its momentum is zero. So, the energy and momentum are conserved before and after the collision.
To learn more about energy -
brainly.com/question/32118995
#SPJ11