The base of a box is .45 m by .65 m. It weighs 8694 N. What is the pressure exerted on the floor by the box?
Answer:
[tex]Pressure = 29723.1\ N/m^2[/tex]
Explanation:
Given
[tex]Force = 8694N[/tex]
[tex]Length = 0.45m[/tex]
[tex]Width = 0.65m[/tex]
Required
The force exerted on the floor by the box
First, calculate the area covered by the box (i.e. the base area)
[tex]Base\ Area = Length * Width[/tex]
[tex]Base\ Area = 0.45m * 0.65m[/tex]
[tex]Base\ Area = 0.2925m^2[/tex]
Pressure is calculated as:
[tex]Pressure = \frac{Force}{Area}[/tex]
[tex]Pressure = \frac{8694N}{0.2925m^2}[/tex]
[tex]Pressure = 29723.0769231\ N/m^2[/tex]
[tex]Pressure = 29723.1\ N/m^2[/tex] --- approximated
Your name is Galileo Galilei and you toss a weight upward at 20 feet per second from the top of the Leaning Tower of Pisa (height 186 ft).
(a) Neglecting air resistance, find the weight's velocity as a function of time
(b) Find the height (in feet) of the weight above the ground as a function of time.
(c) Where and when will it reach its zenith?
The height (in feet) of the weight above the ground as a function of time will be given by the equation h = -16t² + 20t + 186. The weight will reach its zenith at t = 0.625 seconds at a height of 197.125 feet above the ground.
The given problem is a classic example of projectile motion where an object is thrown from a height and lands on the ground. The height (in feet) of the weight above the ground as a function of time will be given by the equation h = -16t² + 20t + 186, where h represents the height of the weight above the ground and t represents the time in seconds.The zenith is the highest point of the weight, i.e., the point where the weight stops moving upward and starts moving downward. To find the zenith, we need to find the time when the vertical component of the weight's velocity becomes zero, i.e., when it stops moving upwards. This can be found by differentiating the equation for height with respect to time and setting it equal to zero, which gives us the time when the vertical velocity is zero. This time is t = 0.625 seconds.
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Light enters glass from air. The angle of refraction will be A) greater than the angle of incidence. B) equal to the angle of incidence.
(B) The angle of refraction when light enters glass from air will be equal to the angle of incidence. This is in accordance with Snell's law, which relates the angles and refractive indices of the media involved.
Determine what is the Snell's law?According to Snell's law, the relationship between the angle of incidence (θ₁), the angle of refraction (θ₂), and the refractive indices of the two media is given by:
n₁ sin(θ₁) = n₂ sin(θ₂),
where n₁ and n₂ are the refractive indices of the initial medium (air) and the second medium (glass), respectively.
When light travels from air to glass, the refractive index of air (n₁) is smaller than the refractive index of glass (n₂). As a result, the sine of the angle of refraction (θ₂) will be smaller than the sine of the angle of incidence (θ₁), given that the angles are measured with respect to the normal.
Since sin(θ₂) < sin(θ₁), the only way for Snell's law to hold true is if θ₂ is smaller than θ₁. Therefore, the angle of refraction will be equal to the angle of incidence, option B.
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Two protons are aimed directly toward each other by a cyclotron accelerator with speeds of 2.20×105 m/s, measured relative to the earth.
Find the maximum electrical force that these protons will exert on each other.
The maximum electrical force that these protons will exert on each other is 2.48 x 10^-13 N.
The electrical force between two charged particles can be calculated using Coulomb's Law:
F = (k * q1 * q2) / r^2
Where:
F is the electrical force,
k is the electrostatic constant (k ≈ 8.99 x 10^9 N m^2/C^2),
q1 and q2 are the charges of the particles (in this case, both are protons, so each charge is q = 1.6 x 10^-19 C),
and r is the distance between the particles (assuming they are in contact, r ≈ 2 x 10^-15 m).
To find the maximum electrical force, we need to calculate the force when the protons are closest to each other. This occurs when they are just about to collide, so their separation distance is equal to the sum of their radii (r ≈ 2 x 10^-15 m).
Plugging the values into the formula, we have:
F = (8.99 x 10^9 N m^2/C^2) * (1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (2 x 10^-15 m)^2
F ≈ 2.48 x 10^-13 N
The maximum electrical force that these protons will exert on each other is approximately 2.48 x 10^-13 N. This force arises due to the interaction between their positive charges and is inversely proportional to the square of the distance between them.
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Which of the following occurs when the fight-or-flight response is triggered?
Answer:
A or BExplanation:
The autonomic nervous system has two components, the sympathetic nervous system and the parasympathetic nervous system. The sympathetic nervous system functions like a gas pedal in a car. It triggers the fight-or-flight response, providing the body with a burst of energy so that it can respond to perceived dangers.
an airplane has a maximum velocity of 160km/h in still air. calculate its maximum velocity when it travels in air with a crosswind of 30km/h
Answer:
Velocity can be directly added or subtracted.
For example, if a boat has a velocity V in still water.
And now you put the boat in a river with a current that has a velocity V'
The total velocity of the boat in that river is just the addition of these two velocities.
Velocity in the river = V + V'
Where the only tricky part is that the velocity is a vector, so you need to take in account the directions of each vector.
In this case, we have a plane with a maximum velocity of 160km, let's assume a direction for this velocity, let's say that is in the positive x-direction.
Then we can write the velocity in the vector form:
velocity = (vel in x-axis, vel in y-axis)
The velocity of the plane can be written as:
v = (160km/h, 0)
Now we add a crosswind of 30km/h
crosswind means that it is perpendicular, then it acts on the y-axis.
Then the total velocity of the plane will be:
velocity = (160km/h, 0) + (0, 30km/h)
velocity = (160km/h, 30km/h)
Now you can compute the total velocity of the airplane as the module of that vector.
Remember that for a vector (x, y) the module is:
mod = √(x^2 + y^2)
Then the module of the velocity is:
v = √( (160km/h)^2 + (30km/h)^2) = 162.8 km/h
In comparing the camera and the human eye, the film of the camera function as the? A. retina; B. iris; C. cornea; D. pupil.
When comparing the camera and the human eye, the film of the camera functions as the retina. The correct option is A.
A camera is a device that records and captures images. A camera, whether digital or film, relies on the same basic technology to work: light enters a camera and is focused onto a photosensitive surface that converts the light into an electrical signal.
The human eye is a sensory organ that helps people to see. The eye is comprised of several components that work together to allow light to enter the eye, focus it, and create an image that is sent to the brain. The retina, the part of the eye that corresponds to the film of the camera, is responsible for capturing the image that is formed by the eye’s lens. In comparison, the film of the camera functions as the retina.
The retina is located at the back of the eye and contains photoreceptor cells that detect light and convert it into neural signals that are sent to the brain. Similarly, the film in a camera captures the image created by the camera’s lens and converts it into an image that can be viewed or printed.Both the human eye and a camera are complex systems that work together to create images.
However, the processes that occur within the eye and the camera are quite different. The human eye relies on biological processes to create images, while a camera uses electronic and mechanical processes to capture and record images. The correct option is A.
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An amusement park builds a ride in which the victim is made to spin about a pole with a rocket strapped on his seat. The rider, box and rocket have an initial total mass of 170 kg. Neglect the mass of the rod of length 6 m .What is the moment of inertia of rider, box and rocket about the pole? The acceleration of gravity is 9.8 m/s^2 . Treat the rider, box and rocket as a point mass. Answer in units of kg · m^2
B) The rocket develops a thrust of 98 N perpendicular to the path of the rider. What is the initial angular acceleration of the rider? Answer in units of rad/s^2
C)After what time t is the rider’s velocity equal to 5 m/s? Neglect the change in mass of the rocket. Answer in units of s.
D)Gas exits the rocket at vt = 390 m/s. What mass per second must leave to develop the thrust F given above? Answer in units of kg/s .
The moment of inertia of the rider, box, and rocket about the pole is 170 kg * (6 m)^2 = 6120 kg · m^2. The initial angular acceleration of the rider is 0.098 rad/s^2.
A) The moment of inertia of the rider, box, and rocket about the pole can be calculated using the formula for the moment of inertia of a point mass rotating around an axis. The moment of inertia (I) is given by the product of the mass (m) and the square of the distance (r) from the axis of rotation:
I = m * r^2
Since the mass of the rider, box, and rocket is given as 170 kg and the rod is neglected, the moment of inertia will be the same for all components. Therefore, the moment of inertia of the rider, box, and rocket about the pole is 170 kg * (6 m)^2 = 6120 kg · m^2.
B) The initial angular acceleration of the rider can be determined using Newton's second law of rotational motion, which states that the torque (τ) is equal to the moment of inertia (I) multiplied by the angular acceleration (α). The torque can be calculated as the product of the force (F) applied perpendicular to the path of the rider and the distance (r) from the axis of rotation:
τ = F * r
Rearranging the formula and substituting the given values:
α = τ / I = (98 N * 6 m) / 6120 kg · m^2 = 0.098 rad/s^2
Therefore, the initial angular acceleration of the rider is 0.098 rad/s^2.
C) The relationship between angular velocity (ω) and time (t) is given by the equation ω = α * t. Rearranging the formula to solve for time:
t = ω / α
The rider's velocity can be converted to angular velocity using the formula v = r * ω. Rearranging the formula to solve for angular velocity:
ω = v / r = 5 m/s / 6 m = 0.8333 rad/s
Substituting the values into the equation, we get:
t = 0.8333 rad/s / 0.098 rad/s^2 = 8.5 s
Therefore, the time required for the rider's velocity to reach 5 m/s is 8.5 seconds.
D) To find the mass per second that must leave the rocket to develop the given thrust (F), we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (dp/dt). In this case, the force is equal to the thrust of the rocket, and the change in momentum is the mass per second leaving the rocket (dm/dt) multiplied by the exit velocity (v):
F = dm/dt * v
Rearranging the formula and substituting the given values:
dm/dt = F / v = 98 N / 390 m/s = 0.2513 kg/s
Therefore, the mass per second that must leave the rocket to develop the thrust of 98 N is 0.2513 kg/s.
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A microscope has an objective lens with a focal length of 10.0 mm . A small object is placed 0.90 mm beyond the focal point of the objective lens.
If an eyepiece with a focal length of 2.5 cm is used, with a final image at infinity, what will be the overall angular magnification of the object?
Express your answer using two significant figures.
The overall angular magnification of the object, considering two significant figures, is approximately -0.4.
To find the overall angular magnification of the object using the given parameters, we can use the formula for angular magnification:
Magnification (M) = -(focal length of the objective lens) / (focal length of the eyepiece)
Given data:
Focal length of the objective lens (f_objective) = 10.0 mm = 1.0 cm
Focal length of the eyepiece (f_eyepiece) = 2.5 cm
Substituting these values into the formula, we have:
M = -(1.0 cm) / (2.5 cm)
M = -0.4
The negative sign indicates that the image formed is inverted.
Now, to calculate the overall angular magnification, we need to consider the object distance (d_object) and the image distance (d_image) in relation to the objective lens.
Object distance from the objective lens (d_object) = 0.90 mm = 0.09 cm
Since the final image is formed at infinity, we can consider the image distance (d_image) to be at infinity.
Using the formula for angular magnification with distances:
Overall Magnification (M_overall) = M * (1 + d_image / d_object)
As d_image is infinity, we can approximate the overall magnification as:
M_overall ≈ M
Substituting the value of M, we have:
M_overall ≈ -0.4
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(root) and outer (tip) diameters of the eye region are 0.15 and 0.3 m, respectively. Use y=1.4 and Cp=1 kJ/(kg K) for this problem.
⚫ The impeller tip diameter is 0.5 m and its height is 0.05 m.
• The impeller rotates at a speed N = 200 (rev/s).
0.63π • There are a total of 12 impeller blades, where the slip factor σ = 1- , and n power input factor, , is 1.04.
• The overall isentropic efficiency is nc=0.95.
• Pressure and temperature (both static) measured at the impeller tip (station 2) are T2=400 K and P2=400 kPa, respectively.
(a) Determine the radial velocity and tangential velocity exiting from the impeller tip.
(b) Determine the stagnation temperature out of the diffuser To3.
(c) Determine the overall pressure ratio, Poз/Po1.
(d) Estimate the axial Mach number entering the eye region (use P₁= 100 kPa and To1=300 K regardless what you have found earlier). One iteration will be sufficient to estimate the density/temperature.
(a) The radial velocity and tangential velocity exiting from the impeller tip are 3.768 m/s and 10.472 m/s respectively.
(b) The stagnation temperature out of the diffuser (To₃) is 400 × [tex](P_3 / 400)^{0.4[/tex].
(c) The overall pressure ratio (Po₃/Po₁) is (P₃ / P₁) × [tex](To_3 / To_1)^{(y/(y-1))[/tex].
(d) The axial Mach number entering the eye region is √((2 / (1.4 - 1)) × [tex]((Po_1 / 100)^{((1.4-1)/1.4) - 1))[/tex]
Given:
Inner diameter (root) of the eye region: 0.15 m
Outer diameter (tip) of the eye region: 0.3 m
y = 1.4
Cp = 1 kJ/(kg K)
Impeller tip diameter: 0.5 m
Impeller height: 0.05 m
Impeller speed: N = 200 rev/s
Number of impeller blades: 12
Slip factor: σ = 1 - (0.63π / n)
Power input factor: n = 1.04
Isentropic efficiency: nc = 0.95
The static temperature at the impeller tip (station 2): T2 = 400 K
Static pressure at impeller tip (station 2): P2 = 400 kPa
Pressure at station 1 (eye region): P₁ = 100 kPa
The temperature at station 1 (eye region): To₁ = 300 K
(a) Radial velocity (Vr₂):
Vr₂ = (π × D₂ × N) / (60 × σ × n)
Vr₂ = (π × 0.5 × 200) / (60 × (1 - (0.63π / 1.04)))
Vr₂ ≈ 3.768 m/s
Tangential velocity (Vt₂):
Vt₂ = (π × D₂ × N) / 60
Vt₂ = (π × 0.5 × 200) / 60
Vt₂ ≈ 10.472 m/s
(b) Stagnation temperature out of the diffuser (To₃):
To₃ / To₂ = [tex](P_3 / P_2)^{((y-1)/y)[/tex]
To₃ / 400 = [tex](P_3 / 400)^{(0.4)[/tex]
To₃ = 400 × [tex](P_3 / 400)^{0.4[/tex]
(c) Overall pressure ratio (Po₃ / Po₁):
Po₃ / Po₁ = (P₃ / P₁) × [tex](To_3 / To_1)^{(y/(y-1))[/tex]
(d) Axial Mach number entering the eye region (M₁):
M₁ = √((2 / (y - 1)) × [tex]((Po_1 / P_1)^{((y-1)/y) - 1))[/tex]
M₁ = √((2 / (1.4 - 1)) × [tex]((Po_1 / 100)^{((1.4-1)/1.4) - 1))[/tex]
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A proton traveling due north enters a region that contains both a magnetic field and an electric field. The electric field lines point due west. It is observed that the proton continues to travel in a straight line due north. In which direction must the magnetic field lines point?
A. East
B. West
C. Into Page
D. Out of Page
E. South
The magnetic field lines pοint tοwards the East (A).
What are magnetic field lines?Magnetic field lines are a visual representatiοn used tο depict the directiοn and strength οf the magnetic field arοund a magnet οr a current-carrying cοnductοr. They indicate the path that a hypοthetical magnetic nοrth pοle wοuld take if placed in the vicinity οf the magnetic field.
The prοtοn is a pοsitively charged particle and is traveling due nοrth. Since the electric field lines pοint due west, the electric fοrce οn the prοtοn is directed tοwards the west. In οrder fοr the prοtοn tο cοntinue traveling in a straight line due nοrth, the magnetic fοrce οn the prοtοn must be directed tοwards the east. This can be achieved if the magnetic field lines pοint tοwards the east.
Therefοre, the magnetic field lines pοint tοwards the East directiοn which is οptiοn A.
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1. Find the density of the N nucleus. 2. The binding energy per nucleon E, of the lithium isotope Li is 5.6 MeV/nucleon. Find its atomic mass of this isotope. 3. Find the energy needed to remove a proton from the nucleus of the potassium isotopek
The density of the N nucleus can be calculated by dividing its mass by its volume, the binding energy per nucleon E of the lithium isotope Li is [tex]5.6 MeV/nucleon[/tex], the energy needed to remove a proton from the nucleus of the potassium isotope K is [tex]289.77 MeV[/tex]
The mass number of N is 14 and its atomic number is 7. The number of neutrons in the N nucleus is given by [tex]14 - 7 = 7[/tex] neutrons.
The mass of one neutron is about 1.008665 atomic mass units (amu) or [tex]1.67493 \times 10^{-27} kg[/tex].
The mass of the N nucleus = [tex]7(1.008665) + 7.016004 = 14.04273 $ amu[/tex]. Thus, the density of the N nucleus can be calculated by dividing its mass by its volume.
The binding energy per nucleon E of the lithium isotope Li is 5.6 MeV/nucleon. To find its atomic mass of this isotope, the mass defect of the nucleus is calculated using the formula:
Mass defect = (Zmp + Nmn) - M
where
Z = number of protons, N = number of neutrons, mp = mass of a proton, mn = mass of a neutron, M = mass of the nucleus.The mass of a proton is approximately [tex]1.00728 amu[/tex], while the mass of a neutron is approximately [tex]1.00866 amu[/tex].
Mass defect = [tex](3 \times 1.00728 + 4 \times 1.00866) - 7.01600[/tex]Mass defect = [tex]0.126 $ amu[/tex]Atomic mass of [tex]Li-7 = 7.01600 - 0.126[/tex]Atomic mass of [tex]Li-7 = 6.89 amu[/tex]The energy needed to remove a proton from the nucleus of the potassium isotope K can be calculated using the formula:
Binding energy = [tex]E \times A[/tex]
where E is the binding energy per nucleon, A is the mass number. Binding energy of K isotope = 7.43 MeV/nucleon (given)
Mass number of K isotope = [tex]39[/tex]Binding energy = [tex]7.43 \times 39[/tex]Binding energy = [tex]289.77 MeV[/tex]Thus, the energy needed to remove a proton from the nucleus of the potassium isotope K is [tex]289.77 MeV[/tex].
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If the velocity of an object is v=-5t+30, at what time does it change direction? Ot=6 O t=5 Ot=3 Ot=2 Ot=0
Option (A) t = 6 , is the correct option .
The object changes direction at t = 6. The given velocity equation is v = -5t + 30, where v represents velocity and t represents time.
To determine when the object changes direction, we need to find the time at which the velocity becomes zero. The given velocity equation is v = -5t + 30, where v represents velocity and t represents time.
Setting the velocity equation equal to zero, we have:
-5t + 30 = 0
To solve for t, we can isolate t by subtracting 30 from both sides of the equation:
-5t = -30
Next, divide both sides of the equation by -5 to solve for t:
t = -30 / -5
t = 6
The object changes direction at t = 6. At this time, the velocity becomes zero.
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Two long, parallel wires carry currents of I1 = 27.0 A and I2 = 13.5 A in opposite directions (see figure below). Which of the following statements must be true? More than one statement may be correct.
In region I, the magnetic field is into the page and is never zero.
In region II, the field is into the page and can be zero.
In region III, it is possible for the field to be zero.
In region I, the magnetic field is out of the page and is never zero.
There are no points where the field is zero.
The following statements are true:
- In region I, the magnetic field is into the page and is never zero.
- In region II, the field is into the page and can be zero.
- In region III, it is possible for the field to be zero.
The magnetic field produced by a current-carrying wire follows the right-hand rule. When two parallel wires carrying currents in opposite directions are considered, the magnetic field in the regions around the wires can be determined.
In region I, the magnetic field is between the two wires. According to the right-hand rule, the magnetic field produced by the current in wire I1 is into the page, while the field produced by the current in wire I2 is out of the page. These fields add up to create a net magnetic field into the page. Since the currents are non-zero, the magnetic field in region I is never zero.
In region II, the magnetic field is outside the wires. The fields produced by the currents in wires I1 and I2 are still into the page and out of the page, respectively. However, at certain points between the wires, the magnitudes of these fields can cancel each other out, resulting in a net magnetic field of zero. Therefore, in region II, the field can be zero.
In region III, which is outside both wires, the magnetic field produced by each wire individually decreases with distance. At a certain distance from the wires, the magnetic fields can cancel each other out, resulting in a net magnetic field of zero. Therefore, in region III, it is possible for the magnetic field to be zero.
In summary, in the given scenario of two long, parallel wires carrying currents in opposite directions, the magnetic field is into the page in region I and can be zero in regions II and III. This understanding is based on the right-hand rule and the superposition principle for magnetic fields.
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If a node is observed at a point 0.340 m from one end, in what mode and with what frequency is it vibrating? (Select all that apply.)
A. The frequency is the fifth state at 30.3 Hz.
B. The frequency is the third state at 18.2 Hz.
C. The frequency is the fifteenth state at 18.2 Hz.
D. The frequency is the fifth state at 15.2 Hz.
If a node is observed at a point 0.340 m from one end, in what mode and with what frequency is it vibrating . The correct answer is B. The frequency is the third state at 18.2 Hz.
To determine the mode and frequency of vibration for a node observed at a point 0.340 m from one end, we need to consider the fundamental frequency and the harmonics of the vibrating system. The fundamental frequency is the lowest natural frequency at which the system can vibrate. It corresponds to the first harmonic mode of vibration. The harmonics are integer multiples of the fundamental frequency.
To find the fundamental frequency, we can use the formula:
F₁ = v / (2L)
Where f₁ is the fundamental frequency, v is the velocity of the wave, and L is the length of the vibrating medium.
Since the node is observed at a point 0.340 m from one end, the length of the vibrating medium is twice that distance, which is 0.680 m.
Now, we need to examine the options and determine if any of them match the calculated fundamental frequency or any of its harmonics.
A. The frequency is the fifth state at 30.3 Hz: This option does not match the calculated fundamental frequency or any of its harmonics.
B. The frequency is the third state at 18.2 Hz: This option matches the calculated fundamental frequency, as it is the first harmonic or third state.
C. The frequency is the fifteenth state at 18.2 Hz: This option does not match the calculated fundamental frequency or any of its harmonics.
D. The frequency is the fifth state at 15.2 Hz: This option does not match the calculated fundamental frequency or any of its harmonics.
Therefore, the correct option is B. The frequency is the third state at 18.2 Hz, corresponding to the fundamental frequency or first harmonic of the vibrating system
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Which of the following is another name for a convex lans?
O Diverging liens
3. Converging lens
O c Shrinking lans
OD Security lans
Answer:
3. converging lens
Explanation:
When the rays of light coming parallel to principle axis after refraction through the lens passes through a point called focus, since it converge all the ray at one point, that is why it is said to be converging lens.
Virtual images exist where no light rays actually can be found.
O A. True
B. False
Answer:
its true
Explanation:
ape x
A wave created by a certain source travels from medium 1 into another medium 2. It is noticed that its velocity is faster in medium 2 than in medium 1. Three students are discussing what happens to the properties of the wave as it moves into medium 2. Student 1: The frequency of this wave increases as this wave moves into medium 2 in order to keep the equation of the velocity of a wave valid. Student 2: No, the frequency of the wave will remain the same as it is only dependent on the source, it will be the wavelength that will increase in order to keep the equation of the velocity of a wave valid. Student 3: No, you are both wrong. Both parameters will adjust in order to keep the equation of the velocity of a wave valid. Which one of these students do you agree with? Justify your response with words and or equations.
I agree with Student 2: The frequency of the wave will remain the same as it is only dependent on the source, while the wavelength will increase as the wave moves into medium 2.
The equation that relates the velocity (v), frequency (f), and wavelength (λ) of a wave is:
v = f * λ
According to this equation, if the velocity increases in medium 2 compared to medium 1, and the frequency remains constant (as stated by Student 2), then the only way to maintain the equation is for the wavelength to increase in medium 2.
This behavior can be explained by the fact that different media have different properties, such as density and elasticity, which affect the propagation of the wave. When a wave travels from one medium to another, the speed of the wave can change. However, the frequency of the wave is determined by the source and remains constant. Therefore, in order to maintain the equation v = f * λ, the wavelength must adjust to compensate for the change in velocity.
In summary, Student 2 is correct in stating that the frequency of the wave will remain the same, while the wavelength will increase as the wave moves into medium 2 to keep the equation of the wave velocity valid.
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A 200-m radio telescope is used to investigate sources emitting a 21-cm wavelength. The
minimum angular separation resolvable for this system is
Select one:
a. 0.073°
b. 0.154°
c. 0.0013°
d. 0.0026°
e. 0.03°
The minimum angular separation resolvable for a 200-m radio telescope investigating sources emitting a 21-cm wavelength is 0.073°.
The angular resolution of a telescope is determined by the ratio of the wavelength of the radiation being observed to the diameter of the telescope. In this case, the telescope has a diameter of 200 meters, and the wavelength being observed is 21 cm (or 0.21 m).
The formula for calculating the angular resolution is given by θ = λ/D, where θ is the angular resolution, λ is the wavelength, and D is the diameter of the telescope. Substituting the given values into the formula, we get θ = 0.21 m / 200 m = 0.00105 radians.
To convert this to degrees, we multiply by (180/π), which gives us approximately 0.073°. Therefore, the minimum angular separation resolvable for this system is 0.073°.
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true/false. the sun radiates at an effective temperature of 5780 k and has a radius of about 696000 km
True. The Sun radiates at an effective temperature of 5780 K and has a radius of about 696,000 km.
The Sun's effective temperature refers to the temperature at which a black body (an idealized object that absorbs all incident radiation) would emit the same amount of radiation as the Sun. This value is approximately 5780 K, representing the temperature of the Sun's photosphere, the visible surface. Regarding the Sun's radius, it has an estimated average radius of about 696,000 km. This measurement defines the distance from the center of the Sun to its outer edge. The Sun is classified as a G-type main-sequence star, and its size is relatively large compared to other stars, making it an important reference point for understanding stellar characteristics.
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If water is flowing in a 1-inch diameter pipe with an average velocity of 3 m/s and the wall roughness is 400 microns, calculate the wall shear stress.
Answer:
Shear stress is 50.63 Pascal
Explanation:
As we know shear stress = [tex]\frac{\rho V^2 f}{8} \\[/tex]
Rho is the density
V is the velocity
f is the value from Moody's chart
We will know determine Reynolds number to determine the flow type and then the f value
[tex]R_e = \frac{ \rho*V*D}{u}[/tex]
[tex]R_e = \frac{1000*3*0.0254}{0.001} = 76200[/tex]
This is a turbulent flow and hence the roughness index is [tex]\frac{E}{D} = 0.0157[/tex], From this we get f = 0.045
Now shear stress = [tex]\frac{1000 * 3^2 * 0.045}{8} = 50.63[/tex] Pa
A quasar is observed with a redshift of z = 3.7. What will be the wavelength of the observed Lyman-alpha line from this quasar? wavelength: ___ nm
This is in the visible part of the clectromagnetic spectrum.
The wavelength of the observed Lyman-alpha line from this quasar with a redshift of z = 3.7 will be approximately 444 nm.
The formula to calculate the observed wavelength (λ_obs) of an object with redshift (z) is given by:
λ_obs = λ_rest * (1 + z)
In this case, we are interested in the Lyman-alpha line, which has a rest wavelength (λ_rest) of 121.6 nm.
Substituting the values into the formula, we have:
λ_obs = 121.6 nm * (1 + 3.7)
λ_obs = 121.6 nm * 4.7
λ_obs ≈ 570.32 nm
However, it's important to note that the Lyman-alpha line falls in the ultraviolet (UV) region of the electromagnetic spectrum, not in the visible part.
Since the question specifically mentions that it is in the visible part, it suggests a typographical error or some other contextual discrepancy.
The wavelength of the observed Lyman-alpha line from this quasar, assuming a redshift of z = 3.7, is approximately 570.32 nm.
However, the Lyman-alpha line is in the ultraviolet (UV) region, not the visible part of the electromagnetic spectrum.
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Assume a 4800 nT/min geomagnetic storm disturbance hit the United States. You are tasked with estimating the economic damage resulting from the storm. If two large power grids collapse and 130 million people are without power for 2 months, how much economic impact would that cause to the United States? Explain the assumptions you are making in your estimate.
The economic impact resulting from the collapse of two large power grids and 130 million people being without power for two months due to a 4800 nT/min geomagnetic storm disturbance in the United States would be substantial, likely amounting to billions of dollars.
1. Loss of productivity: The major factor contributing to the economic impact would be the loss of productivity during the two-month period. Without power, businesses, industries, and essential services would be severely disrupted, leading to a decline in output and economic activity.
To estimate the economic impact, we need to consider the following factors:
a. GDP per capita: According to the World Bank, the United States' GDP per capita was approximately $63,416 in 2020.
b. Average number of working days in two months: Assuming an average of 22 working days per month, we have a total of 44 working days affected by the power outage.
c. Workforce participation rate: As of September 2021, the U.S. labor force participation rate was around 61.6%.
d. Affected population: Given that 130 million people are without power, we need to calculate the percentage of the workforce among them. Assuming the workforce participation rate remains constant, the affected workforce can be estimated as follows:
Affected workforce = Workforce participation rate * Affected population
Affected workforce = 0.616 * 130,000,000
Affected workforce ≈ 79,976,000
e. Loss of productivity per day: To estimate the loss of productivity per day per worker, we can divide the GDP per capita by the average number of working days in a year:
Loss of productivity per day per worker = GDP per capita / 365
Loss of productivity per day per worker ≈ $63,416 / 365
Loss of productivity per day per worker ≈ $173.63
f. Total loss of productivity: The total loss of productivity during the two-month period can be calculated by multiplying the loss of productivity per day per worker by the number of affected working days and the affected workforce:
Total loss of productivity = Loss of productivity per day per worker * Number of affected working days * Affected workforce
≈ $173.63 * 44 * 79,976,000
≈ $610,964,195,520
Additional costs: The economic impact would also include additional costs incurred due to the power outage, such as emergency response efforts, infrastructure repairs, and the financial burden on individuals and businesses.
Based on the calculations, the economic impact resulting from the collapse of two large power grids and 130 million people being without power for two months due to a 4800 nT/min geomagnetic storm disturbance would be estimated at approximately $610.96 billion in terms of loss of productivity alone.
This estimate does not include the additional costs associated with the power outage, which would likely further increase the economic impact.
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A tank contains 2 m3 of air at -93°C and a gage pressure Ro6 of 1.4 MPa. Determine the mass of air, in kg. The local atmospheric pressure is 1 atm
To determine the mass of air in the tank, we need to convert the given parameters and apply the ideal gas law. The mass of air in the tank is approximately 5.04 kg.
To determine the mass of air in the tank, we need to consider the ideal gas law and convert the given parameters to appropriate units.
Given:
Volume of air (V) = 2 m³
Temperature (T) = -93°C
Gauge pressure (P) = 1.4 MPa
Local atmospheric pressure (P_atm) = 1 atm
First, let's convert the temperature from Celsius to Kelvin:
T = -93°C + 273.15 = 180.15 K
Next, we need to convert the gauge pressure to absolute pressure by adding the atmospheric pressure:
P_abs = P + P_atm = 1.4 MPa + 1 atm = 2.4 MPa
Now, we can use the ideal gas law equation to calculate the mass of air (m):
PV = nRT
Where:
P = absolute pressure
V = volume
n = number of moles of air
R = ideal gas constant
T = temperature
Rearranging the equation to solve for mass (m):
m = (n * M) / N_A
Where:
M = molar mass of air
N_A = Avogadro's number
To find the number of moles (n), we can use the equation:
n = PV / RT
Given that the molar mass of air is approximately 28.97 g/mol, and the ideal gas constant R is 8.314 J/(mol·K), we can calculate the mass of air.
Calculations:
n = (P_abs * V) / (R * T)
m = (n * M) / N_A
Substituting the values:
n = (2.4 MPa * 2 m³) / (8.314 J/(mol·K) * 180.15 K)
m = (n * 28.97 g/mol) / 6.022 x 10^23 mol⁻¹
Calculating the mass of air (m):
m ≈ 5.04 kg
Therefore, the mass of air in the tank is approximately 5.04 kg.
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A simple pendulum is executing simple harmonic motion with a time period T; If the length of the pendulum. Is increased by 21%, the Increase in the time period of the pendulum of Increased length is
The increase in the time period of the pendulum with the increased length is 0.1 times or 10% of the initial time period.
What is a time period?
The time period of a periodic motion refers to the time it takes for one complete cycle or oscillation to occur. It is the time interval between two successive identical points in the motion.
The time period (T) of a simple pendulum is given by the equation:
T = 2π√(L/g)
where L is the length of the pendulum and g is the acceleration due to gravity.
Let's assume the initial length of the pendulum is L and the increased length is L + 0.21L = 1.21L (as it is increased by 21%).
The new time period (T') of the pendulum with the increased length can be calculated using the same equation:
T' = 2π√((1.21L)/g)
To find the increase in the time period, we subtract the initial time period (T) from the new time period (T'):
ΔT = T' - T
= 2π√((1.21L)/g) - 2π√(L/g)
= 2π(√(1.21L/g) - √(L/g))
= 2π(√(1.21)√(L/g) - √(L/g))
= 2π(1.1√(L/g) - √(L/g))
= 2π(0.1√(L/g))
Therefore, the increase in the time period of the pendulum with the increased length is 0.1 times the initial time period:
ΔT = 0.1T
Hence, the increase in the time period is 10% of the initial time period.
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Which is denser?
The water in a swimming pool or a quarter (coin).
Answer:
The coin is denser than any of the liquids, and will sink through everything. The oil is the least dense liquid, so it will float on the water, and the syrup is the densest liquid, so it will sink below the water.
Explanation:
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° :. ° . ☆ . . • . ● .° °★ Not sure how to copy and paste? Just right click your mouse and choose copy in options, to release repeat the process and just paste it. No mouse? Select the text with your computer pad and use ctrl c to release, ctrl v. On mobile? Press on your screen and select the text, use the option copy and paste wherever you would like!
You can use the information below to calculate it :)
Density of water: 1000 kg/m3.
Density of the coin: copper 8.96 g/cm^3
nickel 8.90 g/cm^3
1 kg = 1000 g
All you have to do now is convert it and thats it
In the circuit shown, serves as an electronic switch. If Vin is very small, determine W/ such that the circuit attenuates the signal by only 5%.Assume Va = 2.1Vand R = 1750. Assume an NMOS transistor with k'=800 A/V2 and VTh=0.5V
To attenuate the signal by only 5%, the width-to-length ratio (W/L) of the NMOS transistor should be approximately 13.125.
To determine the required W/L ratio, we need to calculate the voltage gain of the circuit and find the value of W/L that corresponds to a 5% attenuation.
First, let's analyze the circuit. We have an NMOS transistor connected in a common-source configuration, where Vin is the input voltage, Va is the gate voltage, and Vout is the output voltage.
_______________
| |
Vin -------| |
| |
| |
| NMOS |------ Vout
| |
| |
| |
|_______________|
The voltage gain (Av) of the NMOS transistor in the common-source configuration can be approximated as:
Av = -k' * (W/L) * (Vin - VTh) * (1 + λ * Vout)
where k' is the transconductance parameter, W/L is the width-to-length ratio, Vin is the input voltage, VTh is the threshold voltage, λ is the channel-length modulation parameter, and Vout is the output voltage.
Since the question states that Vin is very small, we can assume that the voltage drop across R is negligible. Therefore, Va will be approximately equal to Vin.
Va = Vin
We want the circuit to attenuate the signal by only 5%. This means the output voltage (Vout) should be 95% of the input voltage (Vin).
Vout = 0.95 * Vin
Substituting Va = Vin and Vout = 0.95 * Vin into the voltage gain equation, we get:
0.95 * Vin = -k' * (W/L) * (Vin - VTh) * (1 + λ * 0.95 * Vin)
Rearranging the equation, we have:
-k' * (W/L) * (Vin - VTh) * (1 + λ * 0.95 * Vin) = 0.95 * Vin
Simplifying, we get:
-k' * (W/L) * (1 + λ * 0.95 * Vin) = 0.95
Since Vin is very small, we can assume that λ * 0.95 * Vin is negligible compared to 1. Therefore, we can approximate the equation as:
-k' * (W/L) = 0.95
Now, let's substitute the given values:
k' = 800 A/V^2
VTh = 0.5 V
-800 * (W/L) = 0.95
Solving for W/L, we find:
W/L = 0.95 / -800 ≈ -0.0011875
The W/L ratio cannot be negative, so we take the absolute value:
W/L ≈ 0.0011875
Finally, we can calculate the width (W) for a given length (L). Assuming L = 1 (arbitrary units), we have:
W = (W/L) * L ≈ 0.0011875 * 1 ≈ 0.0011875
To attenuate the signal by only 5%, the width-to-length ratio (W/L) of the NMOS transistor should be approximately 0.0011875 (or 13.125 if the length is assumed to be 1 unit).
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An entertainer pulls a table cloth off a table leaving behind the plates and sliverware undisturbed is an example of
A.
the law of balanced forces
B.
Newton's second law
C.
Newton's third law
D.
Newton's first law
Answer:
D. Newton's first law
Explanation:
Newton's first law of inertia says that an object will remain how it is, unless affected by an outside force. In this case, the plates want to remain stationary(not moving). Therefore, if you pull the table cloth fast enough, the force of friction produced will be small enough so that the Inertia of the plates will overcome the force of friction.
A mother sees that her child’s contact lens prescription is 0.750 D. What is the child’s near point?
To determine the child's near point, we need to use the formula: Near Point = 100 cm / (Lens Power in Diopters) Given that the child's contact lens prescription is 0.750 D, we can substitute it into the formula
To determine the child's near point, we need to use the formula:
Near Point = 100 cm / (Lens Power in Diopters)
Given that the child's contact lens prescription is 0.750 D, we can substitute it into the formula:
Near Point = 100 cm / 0.750 D
Near Point ≈ 133.33 cm
Therefore, the child's near point is approximately 133.33 cm.
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light of wavelength 610 nm illuminates a diffraction grating. the second-order maximum is at angle 36.5∘.
How many lines per millimeter does this grating have?
Please who each step for full point rating
Thanks