Answer:
The half-life of a radioactive substance is the amount of time it takes for half of the initial amount of the substance to decay. In this case, the initial number of atoms decayed to half of the initial number after 128 days. So the half-life of the radioactive substance is 128 days.
provide an explanation on why motor vehicles use what is called a multigrade viscosity oil and explain what is meant by an oil viscosity rating such as 5W30.
Each the balls shown below carries a charge q and has a mass m. The length of each thread is l, and at equilibrium, the balls are separated by an angle 2θ . How does θ vary with q and l? Show that θ satisfies sin(θ) 2 tan(θ) = q 2 16πε0 gl2 m
The equation you provided describes the relationship between the angle θ and the various physical parameters of the system.
What does the equation explains?The equation expresses the fact that the force of tension in the threads must balance the electrostatic force between the two charged balls.
On the left side of the equation, sin(θ) represents the component of the force of tension perpendicular to the thread, while tan(θ) represents the ratio of this component to the component of the force of tension along the thread.
On the right side of the equation, q represents the charge on each ball, while 16πε0 is the electric constant and g is the acceleration due to gravity. The product of these constants and the length of the threads squared, l^2, represents the electrostatic force between the balls. Finally, m represents the mass of each ball.
By equating these two sides, we see that the angle θ satisfies the relationship between the physical parameters described by the equation. As the charge q, length of the threads l, or mass m of the balls changes, the angle θ will vary accordingly in order to maintain balance between the tension and electrostatic forces
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Imagine that you are a Greek philosopher living 2,000 years ago. If you were to lecture on the structure of the Universe to students. which of the following statements would help your students distinguish between stars and planets? Choose one or more: A. Planets make up constellations. B. Stars appear much larger in the sky than do planets. C. Planets move in complex paths independent of stars.D. Stars appear to revolve around a fuxed point. E. Stars have rays of light shooting out in all directions.
Option E, which states that stars emit light in all directions, Identify the differences between planets and stars.
In which universe is Earth located?In the Virgo Supercluster of galaxies, which contains Earth, are situated. A grouping of galaxies called a supercluster is bound by gravity. The Local Group, a smaller collection of galaxies within this supercluster, is where we are located.An object with brightness that causes it to independently reflect light is referred to be a star. In contrast, a planet is only a fixed celestial entity that rotates on its own axis and has its own orbit, but it also reflects light from other sources.Option E, which states that stars emit light in all directions, Identify the differences between planets and stars.To learn more about universe refer to:
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A positive point charge +q is at the center of a spherical shell of radius R carrying charge +2q distributed uniformly over its surface. Find an expression for the electric field as a function of position r from the center of sphere inside the shell. Use a minus sign if the field points inward. Express your answer in terms of the variables q,r, and permittivity constant ϵ 0. E insalde = W Incorrect; Try Again; 27 attempts remaining X Incorrect; Try Again; 27 attempts remaining Part B Find an expression for the electric field as a function of position r outside the shell. Use a minus sign if the field points inward. Express your answer in terms of the variables q,r, and permittivity constant ϵ0.
The electric field's formula is [tex]E_{outside} = \frac{3q}{4 \pi r^2 \epsilon_0}[/tex]
When the charge q was positioned at the centre of a spherical shell with a radius of R and the charge 2q was distributed uniformly over the surface of the shell, Gauss's law was utilised to surround the gaussian surface of radius r(rR).
According to Gauss's Law, the total electric flux leaving a closed surface equals the charge within divided by the permittivity. The electric field is multiplied by the surface area that is projected in a plane and perpendicular to the field to determine the electric flux in a given area.
through the gaussian surface.
where E is the charge that was exposed by the gaussian surface.
The circle symbolises the gaussian surface with radius r(r>r) according to Gauss's law.
[tex]\int\limits E.ds=\frac{Q}{\epsilon_0}[/tex]
Here, q+2q is
[tex]E_{outside} \times 4 \pi r^2 = \frac{2q+q}{\epsilon_0}[/tex]
[tex]E_{outside} = \frac{3q}{4 \pi r^2 \epsilon_0}[/tex]
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how can you use graphs to calculate the displacement of an object
Finding the slope of both the velocity-time graph is necessary in graphs in order to compute an object's displacement.
What is a displacement illustration?When there is displacement, an object's position as relation to a stationary reference alters. For instance, when a player strikes a pool ball, it goes from one place to another. It is said to be misplaced. There is a magnitude and a direction to the vector quantity displacement.
What exactly does psychological displacement entail?A defense tactic called displacement involves someone shifting their unpleasant emotions of one thing or person to another. A person who is angry about their job, for instance, might rage at a family person in order the "take it out" on them.
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What happens after we die on earth?
Your heart stops beating, your breathing stops, and your brain stops working. According to research, brain activity may continue for several minutes after a person is declared dead.
What do people see when they die?Visual or auditory hallucinations are common during the dying process. The reappearance of deceased family members or loved ones is common. These visions are thought to be normal.
The dying may shift their focus to "another world," where they may converse with people or see things that others do not.
Thus, brain activity is not synonymous with consciousness or awareness. It does not imply that the individual is aware that they have died.
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A tennis player tosses a tennis ball straight up and then catches it after 1.57 s at the same height as the point of release.
PART A:
-9.8 m/s^2 (S)
PART B:
0 meters (N)
PART C:
≈ 7.7 (ROUNDED)
Accurate: 7.69300
PART D:
4.9 m (Δy)
Transcribed Text:
A tennis player tosses a tennis ball straight up and then catches it after 1.57 seconds at the same height as the point of release.
Required:
Acceleration of the ball while in flightVelocity of the ball at maximum heightInitial velocityMaximum height reachedUse the following kinematic equations:
[tex]v=v_o+at[/tex]
Final velocity = Initial Velocity + Acceleration × Time
Δ[tex]x=v_ot+\frac{1}{2}at^2[/tex]
Change in position (displacement) = Initial velocity × time + (0.5) (acceleration × final time)²
[tex]v^2=v_o2+2a[/tex]Δ[tex]x[/tex]
Final velocity (squared) = Initial velocity (two times) + (two times) acceleration * change in position
*A illustration shall be provided for better understanding*
Part A:
Once the tennis player releases the ball, the only force acting on that ball is the gravitational force which exerts an acceleration of -9.8 m/s^2.
Part B:
At that maximum height (as seen in the attached picture) would have a velocity of 0 for just a split moment making this the answer.
PART C: *Be aware that the PART A and B are just conceptual type questions and now we have actual calculations to figure out*.
Reviewing what we know,
Acceleration = -9.8 m/s^2
Time = 2.00 seconds
Now we have to find the initial velocity.
Reviewing the picture and the final velocity, it should turn out this way:
[tex]Vi=V_i,V=-V_o[/tex]Looking at the kinematic equations we would use:
[tex]V_f=V_i+at[/tex]
Current equation:
[tex]-V_o=V_o+(-9.8)(1.57)[/tex]
* MULTIPLY -9.8 and 1.57!!!
Now we must subtract the V(naught) from both sides.
The left and right side would become:
[tex]-2v_o=-15.38600[/tex]
Divide -2 from both sides.
Initial velocity = 7.69300
Rounded
≈ 7.7 m/s
This would make the initial velocity equal to 7.7 m/s
PART D:
In order to solve for maximum height, we must use some values we would need to find this answer.
Initial velocity = 7.69300 m/s
Acceleration = -9.8m/s^2
Final velocity (or velocity at max height) = 0 m/s
Δy = ...
The kinematic equation we would be using is:
[tex]v^2=v_o2+2a[/tex]Δ[tex]x[/tex]
Because the situation is in the vertical dimension, the 'delta x' will be changed to:
[tex]v^2=v_o2+2a[/tex]Δ[tex]y[/tex]
Subtract the initial velocity squared from both sides of the equation.
This would give us:
[tex]v^2-v_0^2=2a[/tex]Δ[tex]y[/tex]
Divide both sides by 2a.
By finding this we can find the vertical displacement.
[tex]\frac{v^2-u^2}{2a}[/tex]=Δ[tex]y[/tex]
Let plug in the known values
[tex]\frac{(0)^2-(9.8)^2}{2(-9.8^2)} = 4.9m[/tex]
Done
I'll GIVE ALL MY POINTS: 30!!!!! hurrryyyyy
Survey Testing the Perceived Usability of the New E-mail System
Instructions: Please indicate the degree to which you agree with the following statements using the scale below:
1
2
3
4
Strongly Agree
Agree
Somewhat Agree
Disagree
1. Using the new e-mail system in my work group allows me to complete work more quickly and effectively.
2. Using the new e-mail system ameliorates the execution of phenomenal behavior in the room within which work takes place.
3. Using the new e-mail system for my work increases my productivity so that I can receive a good rating from my supervisor.
5. Using the new e-mail system makes it easier to prepare for meetings and finish my work on time.
There are about eight things wrong with the survey above. Below, name six things you would change based on the lesson commentary recommendations. Number your answers.
Usability of the New E-mail System 1. Substitute a more descriptive scale, such as "Strongly Agree," "Agree," "Somewhat Agree," "Somewhat Disagree," "Disagree," and "Strongly Disagree" for the numerical scale.
Simply remove the numerical scale and insert the more descriptive scale in its place to do this. The first sentence, for instance, may be altered to read "I can work more quickly and efficiently in my work group since we use the new e-mail system. Use the following scale to indicate your level of agreement with this statement: Strongly Agree, Agree, Somewhat Agree, Somewhat Disagree, Disagree, Strongly Disagree."
2. Ensure that the questions are precise and short.
You must make sure the questions are simple to grasp, not too long or difficult to answer, and plain and succinct. For instance, you could reword the survey's second statement to read, "Does using the new e-mail system boost my work performance?"
3. Check if the survey's questions are pertinent to the subject at hand.
The survey topic should be addressed by the questions. The survey in this instance concerns how usable people believe the new email system to be. Therefore, this subject should be the subject of all queries. The third statement in the survey has to be changed or removed because it has nothing to do with the subject matter.
4. Only posit inquiries that can be fully answered.
The questions ought to be created in a way that allows for truthful responses. The inquiries must to be clear and devoid of any possibility for interpretation. The fourth line, for instance, may be changed to read, "Using the new e-mail system makes it easier for me to prepare for meetings and finish my work on time?"
5. If necessary, give the questions context.
It could occasionally be required to provide the questions background. How simple is it for you to use the new e-mail system to get ready for meetings and finish your work on time, for instance, is how the fifth sentence may be phrased.
6. Lower the overall number of inquiries.
It's crucial to limit the overall number of inquiries to minimum.
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A slingshot fires a pebble from the top of a building at a speed of 13.0 m/s. The building is 22.0 m tall. Ignoring air resistance, find the speed with which the pebble strikes the ground when the pebble is fired (a) horizontally, (b) vertically straight up, and (c) vertically straight down.
In a compound microscope the objective and the eyepiece have focal lengths of 0.95 cm and 5 cm respectively, and are kept at a distance of 20 cm. The last image is formed at a distance of 25 cm from the eyepiece.The position of object and the total magnification are
a. 95/94 cm in front of field lens 94
b. 80/79 cm in front of the field lense, 93
c. 70/65 cm in front of the field lense, 65
d. 60/55cm in front of the field lense, 50
A) In a compound microscope, the focal lengths of the objective and eyepiece are 2.0 cm and 3.0 cm, respectively.
The eyepiece's final picture is formed at infinity and the objective and eyepiece are separated by 15.0 cm. Both lenses are quite narrow.
f \s0 \s \s =0.95cm
f \se \s \s =5cm
L=20cm
v \se \s \s =25cm
U \s0 \s \s =? M=?
L D =v 0 + D+fe Dfe
20=v \s0 \s \s + \s \s30 \s6
25× \s \s5
6 \s95 \s \s =v \s0 \s
95 \s6 \s \s − \sv \s0
1 \s \s = \s95 \s100
− \sv \s0 \s
1 \s \s = \s95 \s94
v \s0 \s \s =− \s94 \s95 \s \s cm
M \sD \s \s = \sv \s0 \s
v \s0 \s
\s (1+ \sfe \sD \s \s )
M \sD \s \s = \s94 \s95
6 \s95
\s (1+ \s5 \s25 \s \s )
= \s6×98 \s95×94 \s \s ×6
=94
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a positive point charge q is at the center of a spherical shell of radius r carrying charge 2q distributed uniformly over its surface. find an expression for the electric field as a function of position r from the center of sphere inside the shell. use a minus sign if the field points inward
The total electric field at a point inside the shell is, [tex]E = \dfrac{kq}{r^{2}}[/tex].
Consider the point P placed inside the shell. As shown in the figure above, the Gaussian surface is said to have a radius r. The Gaussian surface contains no charge inside it.
Hence, q = 0
Therefore,
E = 0
It can be conclude that the field inside the spherical shell is always zero.
The electric field due to point charge q placed at the center at a point which is at a distance r from the center (inside the shell) is given by,
[tex]E = \dfrac{kq}{r^{2}}[/tex]
where, k is the permittivity of free space.
Hence, the total electric field at a point inside the shell is,
[tex]E = \dfrac{kq}{r^{2}}[/tex]
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What is Emmy's velocity at a time of 3.73 s?
Answer:
Below
Explanation:
From the top graph her acceleration is -3 m/s^2 at the point in question
From the lower graph at time t = 3 s her velocity = 5 m/s
vf = vo + at
= 5 m/s + (-3)(.73) <====3.73 s is .73 s past the 3 s mark
= 2.81 m/s
Which of the following best describes why you can analyze this event using the conservation of momentum?a. The throwing action is quick enough that external forces may be ignored.b. There are no external forces acting on the system.c. External forces don't act on the system during the jump.d. Conservation of momentum is always the best way to analyze motion.
The option that best describes why you can analyze this event using conservation of momentum, is The throwing action is quick enough that external forces may be ignored. The best answer is A.
This is because the conservation of momentum is only applicable when the external forces acting on a system are negligible. In this case, the external forces can be ignored, so the conservation of momentum can be used to analyze the motion.
The conservation of momentum is a fundamental law of physics that states that the total momentum of a system is conserved, which means that the total momentum of a system remains constant. This means that if there are no external forces acting on the system, the momentum of the system will not change. This law is particularly useful for analyzing the motion of objects, and can be used to calculate the velocity, acceleration, and other parameters of an object's motion.
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A 900 kg car traveling 11.2 m/s crashes into a pile of hay and comes to a stop in 4.6 s. Calculate the force.
Answer:To calculate the force, we can use the formula:
force = mass x acceleration
In this case, the car starts at a velocity of 11.2 m/s and comes to a stop in 4.6 seconds, so the acceleration is:
(0 m/s - 11.2 m/s) / 4.6 s = -2.4 m/s^2
We can then use this to calculate the force:
force = 900 kg x (-2.4 m/s^2) = -2160 N
Note that the negative sign indicates that the force is in the opposite direction of the car's motion. This makes sense, as the force is acting to stop the car.
Answer:
-2,187 N
Explanation:
Please find the attachment for detail
the correct number of significant figures.)
(a)
(b) the product 0.0055 ✕ 445.3
(c) the product 18.10 ✕
a) The sum of 545, 36.2, 0.080, and 9.0 is 590.280. The correct number of significant figures is 590.280 (5).
b) The product of 0.0055 and 445.3 is 2.46015. The correct number of significant figures is 2.46 (3).
c) The product of 18.10 and pi is 56.829079. The correct number of significant figures is 56.829079 (8).
What are significant figures?Significant figures, also known as significant digits, are the digits in a number that carry meaning contributing to its precision. They are used to express the level of confidence in a measurement. The number of significant figures in a measurement or calculation represents the number of digits that are known with some level of certainty, plus one final digit that is estimated. For example, the number 12.34 has four significant figures, while the number 0.001234 has only two significant figures.
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A uniform rod of mass M is in the shape of a semicircle of radius R (Fig. P14.45). Calculate the force on a point mass m placed at the center of the semicircle.
To calculate the force on the point mass m placed at the center of the semicircle, we need to consider the gravitational force acting on the mass m due to the uniform rod.
The gravitational force acting on the point mass m can be calculated using the equation:
F = G * (m * M) / R^2
where G is the gravitational constant, m is the mass of the point mass, M is the mass of the uniform rod, and R is the radius of the semicircle.
The uniform rod can be considered as a point mass located at the center of the semicircle, so the force on the point mass m can be simplified as:
F = G * (m * M) / R^2 = G * m * M / R^2
In conclusion, the force on the point mass m placed at the center of the semicircle is equal to the gravitational force between the point mass and the uniform rod, which is given by the equation F = G * m * M / R^2.
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can the magnitude of the displacement vector be more than the distance traveled?a. yesb. no
No The distance travelled by the body can never be greater than the magnitude of the displacement.
Is it possible for displacement to be larger than distance? Why?The displacement cannot be more than the distance because the distance is defined as the total amount of path covered by a moving body in a given time period, whereas the displacement is defined as the linear amount of path covered by a moving body in a given time period.
The shortest path and the entire path traversed on a straight road without turning are the same. As a result, if the automobile is traveling in a straight line without changing direction, the distance traveled and amount of displacement are equal. The resulting shaking has a wide range of values that vary depending on distance, surface material, and other factors.
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The current sensitivity of a moving coil galvanometer increase with decrease in _________?
The current sensitivity of a moving coil galvanometer increases with a decrease in its resistance.
What is Current Sensitivity?
Current sensitivity is a measure of the responsiveness of an instrument to the current flowing through it. In particular, it is the deflection produced by a given amount of current passing through a device. The higher the current sensitivity, the smaller the amount of current required to produce a given deflection, and thus the more sensitive the instrument is to changes in current.
This is because the current sensitivity of a galvanometer is defined as the deflection produced per unit of current passed through it. Therefore, a higher current sensitivity means that a smaller current can produce a larger deflection, which can be achieved by decreasing the resistance of the galvanometer. This is because a lower resistance will allow a larger current to flow through the coil, which will result in a larger deflection of the coil.
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Answer:
Resistance
Explanation:
Sensitivity of a moving coil galvanometer can be increased by increasing the number of turns in the coil, the area of coil and magnetic field whereas by decreasing the couple per unit twist of the suspension.
A runner whose initial speed is 29 km/h increases her speed to 31 km/h in
order to win a race. If the runner takes 5.0 seconds to complete this
increase in her speed, what is her acceleration?
The rate of change in velocity is known as acceleration.She thereby accelerated 0.027 m/s2 throughout her strong effort.
What is her acceleration?The rate of change in velocity is known as acceleration.Acceleration typically signals a change in speed, though this is not always the case.
Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating. The change in velocity divided by the time interval during which that change happened is the definition of acceleration (in its simplest form).
The formula is: a= v2 - v1 /t
Where:
Initial velocity is v1.
v2: final speed
t: the amount of time required for that acceleration
introducing the specified values into the equation
a=0.027 m/s2
where
a = 3.5 m/s - 31 m/s /15 m/s
She thereby accelerated 0.027 m/s2 throughout her strong effort.
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A marble with a mass of .4 kg is rolling down a ramp at a speed of 5 m/s and collides with a .25 kg marble sitting at rest. What is the final velocity of the first marble?
Students monitor the progress of a marble by measuring its speed and distance travelled. They calculate the speed using the formula Speed = Distance / Time.
How do you find the velocity of a marble?
Look for a space on the table or counter that is larger than a metre.Two books should be placed on one end of the desk.Then, lean the grooved ruler against the books.Place a different book at each end of the desk. The marble will come to a halt as a result of this book.Measure the distance between the book's one end and the end of the grooved ruler on the desk. The projected rolling distance of the marble is. Pay attention to the length here.Install the stopwatch.Roll the marble down the grooved ruler and begin timing.The stopwatch should start timing the moment the stone touches the table. Look up time tracking that is easily accessible.Keep track of the distance travelled.Using the equation Speed = Distance / Time, calculate the speed in metres per second. It will be necessary to convert from centimeters to metres.2 more times through #6-#10.The results of the three speed computations should be averaged.To learn more about marble's progress refer to:
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You ride your bike along a straight line from your house to a store 1704 m away. On your way back, you stop at a friend's house which is halfway between your house and the store.a. What is your displacement?b. What is the total distance traveled?c. After talking to your friend, you continue to your house. When you arrive back at your house, what is your displacement?d. What is the total distance you have traveled since first leaving your house?
According to the question, the answer of distance will be:
a. Your displacement is 0 m.
b. The total distance traveled is 3408 m.
c. Your displacement is 0 m.
d. The total distance you have traveled since first leaving your house is 3408 m.
What is distance?
Distance is the amount of space between two objects or points. It is usually measured in units of length such as kilometers, miles, meters, or feet.
a)Displacement is defined as the total distance in a specific direction, and since you did not move in any direction, your displacement is 0 m.
b) You traveled 1704 m to the store and 1704 m back to your friend's house, so the total distance traveled is 3408 m.
c) Displacement is defined as the total distance in a specific direction, and since you did not move in any direction, your displacement is 0 m.
d) You traveled 1704 m to the store and 1704 m back to your house, so the total distance you have traveled since first leaving your house is 3408 m.
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identify and explain three factors that contribute to the high use of oil despite the limited supplies.
Factors that contribute to the high use of oil despite the limited supplies are levels of oil consumption, oil reserves, global exchange rates.
Levels of oil consumption, oil reserves, global exchange rates, environmental issues, politics, and oil speculation on the financial markets are the factors that contribute to the high use of oil despite the limited supplies.
As the population is increasing day by day the demand of oil is also increasing along with increasing population which is leading to the high use of oil despite of the fact that the supply of the oil is limited as any thing on this earth cannot be unlimited.
The price of oil depend on the three main factors: current supply, future supply, and expected global demand.
The world has proven reserves equivalent to 46.6 times its annual consumption levels. This means it has about 47 years of oil left (at current consumption levels and excluding unproven reserves).Generally, if the oil supply increases, prices respond by going down and rising if supply decreases, it basically depend upon the demand . if demand decreases, prices should decrease and rise if demand increases.
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find the magnitude of the electric field due to a charged ring of radius a and total charge q , at a point on the ring axis a distance a from the ring's center. express your answer in terms of the variables a , q , and coulomb constant k .
[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ R^{2} + x^{2} } }[/tex]The magnitude of electic field at a distance 'a' from the center of the ring is
[tex]E = \frac{K Q q }{ 2\sqrt{2} a^{2} }[/tex] where K = [tex]\frac{1 }{4 \pi }[/tex]∈
a = radius of ring
Q = uniform charge distribution over ring
q = another point charge located at a distance a from centre of ring
We know that the electric field at distance x from the center of ring of radius R is given by
[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ R^{2} + x^{2} } }[/tex]
according tho the question the radius of ring is equal to distance of q from centre of the ring
substituting R= a , x = a
we get
[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ a^{2} + a^{2} } }[/tex]
[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ 2 a^{2} } } }[/tex]
[tex]E = \frac{K Q q }{ 2\sqrt{2} a^{2} }[/tex]
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a good diffraction grating has 2060 lines/cm what is the distance between two lines in the grating? answer in units of cm. answer in units of cm.
Distance between two lines of grating is 4.85*10^-4 cm.
The act of bending light around corners where it spreads out and illuminates regions is known as the diffraction of light.
A optical element known as a diffraction grating splits light into numerous beams that move in various directions. The directions, as well as diffraction angles of these beams, depending on the wavelength of the incident light, the angle at which the wave strikes, and the distance or spacing between consecutive diffracting elements.
The distance between the two grating lines is calculated by taking the reciprocal of the grating value which is provided.
Distance between two lines of grating is, 1/2060 = 4.85*10^-4 cm.
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These ethical theories could endorse something like genocide under the right conditions: (Choose as many as you think are correct) Utilitarianism Cultural Relativism Egoism Natural Rights Theory Kantian Deontology
According to the utilitarian ethical theory, morality is decided by emphasising results.
This kind of consequentialism exists here. According to utilitarianism, a decision should be made if it would result in the greatest amount of benefit for the largest number of people. The utilitarian perspective holds that you should select the ice cream flavour that would make you feel the happiest if you are making a decision for yourself.
A variation of consequentialism known as utilitarianism holds that actions' results are the only criteria for what is right and bad. Utilitarianism takes into account the interests of every sentient being equally, unlike other consequentialist ideologies like egoism and altruism.
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Exercise 19: Earth has a mass of 5.98 x 1024 kg and a radius of 6.38 x 106 m. What is the moment of inertia of Earth as it turns on its axis?
The moment of inertia is represented by the following equations if we consider the earth to be a solid sphere spinning about its center: I ≈ 9.736 × (10)37 kgm2.
What is the moment of inertia of the earth?Taking into account that the earth's radius is 6.38 *1 0 6 m and its mass is 5.98 * 10 24 kg
The moment of inertia is represented by the following equations if we consider the earth to be a solid sphere spinning about its center:
I = 2 / 5 M R²
When the earth's radius is R and its mass, M,
This information is provided to us:
↦ M = 5.98 × (10 )24 kg
↦ R = 6.38 × (10) 6 m
With the aforementioned equation updated to include these values:
I = 2 / 5 ( 5.98 × (10 )24 kg ) ( 6.38 × (10)6 m )²
⇒ = 2 / 5 ( 5.98 × (10)24 kg ) ( 4.07044 × (10) 13 m ²)
⇒ 2 / 5 ( 2.4341 × (10 )38 kg m 2 )
⇒ = 9.736 × (10 )37 kg m 2.
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a copper wire has a radius of 1 [mm]. the wire is carrying a current of 1 [a] in the positive z direction. determine the velocity vector of the electrons inside the copper wire (hint: see the similar example in notes 3, as use the same parameters for the copper as in this example.)
The velocity vector of the electrons can be represented as:
v = v_d * z = v_d * (0, 0, 1)
where z is the unit vector in the positive z direction.
To determine the velocity vector of the electrons inside the copper wire,
we can use the drift velocity formula, which relates the drift velocity of electrons to the electric current and the density of electrons in a conductor.
The drift velocity can be calculated as:
v_d = I / (neA)
where I is the current,
n is the number of electrons per unit volume, e is the charge of an electron, and
A is the cross-sectional area of the wire.
For copper, n can be calculated as:
n = (8.5 x 10^28 electrons/m^3) * (density of copper / 63.54 g/cm^3)
With a wire radius of 1 mm, the cross-sectional area can be calculated as:
A = πr^2
= π * (1 x 10^-3 m)^2
So, plugging in the values, we have:
v_d = 1 A / (n * A)
= 1 A / (8.5 x 10^28 electrons/m^3 * π * (1 x 10^-3 m)^2)
The velocity vector of the electrons is in the same direction as the current, which is the positive z direction,
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Suppose a 2.5um wide slit produces its first minimum for 405nm light. A) Calculate the angle at which this occurs for the 405nm light in degrees. B) where is the first minimum in degrees for 740nm light?
A) To calculate the angle at which the first minimum occurs for 405nm light, we need to use the equation θ = λ/d, where θ is the angle in degrees, λ is the wavelength of the light, and d is the slit width. Thus, for 405nm light, we have θ = 405nm/2.5um = 162°.
B) To calculate the angle for 740nm light, we can use the same equation, so θ = 740nm/2.5um = 296°. Thus, the first minimum for 740nm light occurs at an angle of 296°.
the rear window in a car is approximately a rectangle, 1.6 m m wide and 0.55 m m high. the inside rearview mirror is 0.60 m m from the driver's eyes, and 1.70 m m from the rear window.
By the use of law of reflection To get a complete view of the rear window of the car is enough for the rear-view mirror to have a height of 0.1137m or 11.37cm
According to the law of reflection, the angle of incidence and reflection is equal.
[tex]\theta_r=\theta_i[/tex]
Both the incident and reflected rays lay on the same plane.
Plane mirrors are reflective surfaces where each point of the mirror has the same normal direction to the surface. As a result, the size of the images produced by flat mirrors is equal to that of the object, and the image's distance is equal to that of the object.
Mathematically, the plane mirror equation yields,,
[tex]i=-o[/tex]
The virtual nature of the image is represented by the negative symbol. The plane mirror's lateral magnification is,
[tex]m=\frac{-i}{o}[/tex] = 1.
We are assuming that the top of the mirror, with unknown height
h, matches the driver's eyes. The height of the window is
H= 0.55m, while the distances from the mirror to the eyes and from the window to the mirror are d=0.60m and D=1.70m, respectively.
The following is how the reflection process works: An angle is created when a light beam from the window hits the mirror, reflected on the road, reaches the driver's sight. The worst case scenario occurs at the window's angle's lowest point. [tex]\theta_r[/tex], . The mirror's height must be adjusted to guarantee that the reflected light hits the driver's eyes.
. Using the trigonometric relations,[tex]Tan \theta=\frac{H-h}{D+d}[/tex]
for the large lower triangle, and,
[tex]Tan \theta=\frac{h}{d}[/tex] for the small upper one.
Equating the tangents results in the equation,
[tex]\frac{h}{d}=\frac{H-h}{D+d}[/tex]
solving for h
h=[tex]\frac{Hd}{D+2d}[/tex]
Substituting the numeric values,
[tex]h=\frac{0.55m\times0.60m}{1.70m +2\times0.60m}[/tex]
h=0.1137m
To get a complete view of the rear window of the car is enough for the rear-view mirror to have a height of 0.1137m or 11.37cm
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The energy given off as heat by 500 g of an alloy as it cools by 25°C raises the
temperature of 250 g of water from 20°C to 28°C. Calculate the specific heat
of the alloy (in J/kg K). Remember that the specific heat of water is 4180 J/kg-K.
Upload a copy of your calculations and your answer.
Answer:
Below
Explanation:
The heat the water gains is the heat lost by the metal ...
Hw = .25 kg * (28- 20 C) * 4180 J/(kg K) = 8360 J
So the metal gains 8360 J and cools by 25 °C
500g = .5 kg
8360 /(.5kg* 25 C) = 668.8 J /(kg K)
Note: Remember that a degree C = one K)
