Answer:
λ = a
Explanation:
This is a diffraction exercise that is described by the expression
a sin θ = m λ
sin θ = m λ/ a
the first zero of the diffraction occurs for m = 1
sin θ = λ / a
angles are generally very small and are measured in radians
sin θ = θ = y / x
we substitute
[tex]\frac{y}{x} = \frac{\lambda}{a}[/tex]
the width of the central maximum is twice the distance to zero
w = 2y
in the exercise indicate that this width is equal to twice the distance to the screen (2x)
W = 2x
2y = 2x
we substitute
1 = λ/ a
λ = a
we see that the width of the slit is equal to the wavelength used.
Describe reflection and refraction. How do these processes enable astronomers to build telescopes? Do these principles work equally well for ALL types of non-optical telescopes; i.e. those built to view the non-visible regions of the electromagnetic spectrum (radio, infrared, ultraviolet, x-ray, gamma)? Explain carefully by using at least two specific examples from the list of the five.
Answer:
θ₁ = θ₂, n₁ sin θ₁ = n₂ sin θ₂
instruments can be built that concentrate light on a small surface
Explanation:
The two laws of optical geometry have been known for quite some time.
The law of reflection states that when a ray of light reaches a surface, the reflected ray comes out at the same angle as the incident ray.
θ₁ = θ₂
The law of refraction establishes how the direction of a light ray changes when it stops from one transparent medium to another.
n₁ sin θ₁ = n₂ sin θ₂
With any of these laws, instruments can be built that concentrate light on a small surface, which allows the weak light from the flares to be concentrated and objects to be measured and seen.
Electromagnetic radiation in its entire spectrum has the same properties, which is why telescopes of visible, infrared, and microwave light. Radio telescope, gamma rays use the same principles of the law of reflection and refraction. The main change between each instrument is the materials and which they are built,
a reflecting telescope must be built with a reflective surface, for example for microwaves metal surfaces are used
For gamma ray telescope it is preferred to constrict refracting telescope, therefore the material must be transparent to gamma rays
The radio telescope uses reflection and the surface is metallic, sometimes to reduce the weight the surface has holes smaller than the length of the donut that you want to measure.
The circuit has a 3 volt EMF and two ohm resistors. How much power in watts does this circuit draw? A) 4.5 , B) 24, C) 1.13 D) 2.67 E) 0.375 F) 1.5
Answer:
P = 4.5 watts
Explanation:
Given that,
EMF of the circuit, E = 3 volt
The resistance of the resistors, R = 2 ohms
We need to find the power of this circuit. The relation between power, emf and resistance is given by the formula as follows :
[tex]P=\dfrac{V^2}{R}[/tex]
Substitute all the values,
[tex]P=\dfrac{3^2}{2}\\\\P=4.5\ W[/tex]
So, the power of this circuit is equal to 4.5 watts.
Which is true?
a) A changing magnetic field produces a constant perpendicular magnetic field.
b) A changing magnetic field produces a changing perpendicular magnetic field.
c) A changing magnetic field produces a constant parallel magnetic field.
d) A changing magnetic field produces a changing parallel magnetic field.
e) A changing magnetic field produces an electric field.
Answer:
e) A changing magnetic field produces an electric field.
Explanation:
Ok, we start with a magnetic field and let's study how it affects the motion of a single electron. As the magnetic field changes, it will cause an electromotive force, that moves the electron, and because now we have a moving electron, now we will have an electric field. (Such that the direction of the electromotive force opposes the direction in which the magnetic field changes). This also can be deduced if we look at the third Maxwell's equation:
dE/dx = -dB/dt
This says that the spatial change in an electric field depends on how the magnetic field changes as time pass.
Then the correct option is e) A changing magnetic field produces an electric field.
Please answer the one you know!
A researcher would like to perform an experiment in a zero magnetic field, which means that the field of the earth must be canceled. Suppose the experiment is done inside a solenoid of diameter 1.0 m, length 4.6 m , with a total of 5000 turns of wire. The solenoid is oriented to produce a field that opposes and exactly cancels the 52 μT local value of the earth's field.
What current is needed in the solenoid's wires?
Express your answer to two significant figures and include the appropriate units.
Answer:
I = 3.81 x 10⁴ A
Explanation:
The magnetic field of a solenoid must be equal to the field of earth:
[tex]Field\ of\ Earth = Field\ of\ Solenoid\\52\ T = \mu n I\\I = \frac{52}{\mu n}[/tex]
where,
I = current passing through solenoid = ?
μ = permeability of free space = 4π x 10⁻⁷ N/A²
n = no. of turns per unit length = [tex]\frac{5000\ turns}{4.6\ m}[/tex] = 1086.96 /m
Therefore,
[tex]I = \frac{52\ T}{(4\pi\ x\ 10^{-7}\ N/A^2)(1086.96\ /m)}[/tex]
I = 3.81 x 10⁴ A
A uniform electric field is present in the region between infinite parallel plane plates A and B and a uniform electric field is present in the region between infinite parallel plane plates B and C. When the plates are vertical, is directed to the right and to the left. The signs of the charges on plates A, B and C may be:_______.
A. -- ,--, --
B. + , -- , --
C. + , --, +
Answer:
the correct answer is C +, - , +
Explanation:
The electric field for positive charges is outgoing and for negative charges it is directed towards the charge.
Let's apply this to our case:
On plates A and B the field goes to the right, therefore plate A must be positive
In plates B and C the way it goes to the left, so the field is selected from it, this implies that plate C is positive
therefore plate B must be negative for both cases
when checking the correct answer is C +, - , +
What is the power generated by a motor boat that applies a 1500 N force over 1000 m in 60 seconds?
What is a gravitational force?
Answer:
It is the force that pulls down an object on the air
Answer: a downward pull on any object
Explanation:
Two resistors are connected in parallel. If R1 and R2 represent the resistance in Ohms (Ω) of each resistor, then the total resistance R is given by 1R=1R1+1R2. Suppose that in fact, these two resistors are actually potentiometers (resistors with variable resistance) and R1 is increasing at a rate of 0.4Ω/min and R2 is increasing at a rate of 0.6Ω/min. At what rate is R changing when R1=117Ω and R2=112Ω?
Answer:
1/Re= 1/R1 + 1/R2
Explanation:
Two resistors are connected in parallel. If R1 and R2 represent the resistance in Ohms (Ω) of each resistor, then the total resistance R is given by [tex]\mathbf{\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}[/tex]. Thus, the rate of R changes when R₁ = 117 Ω and
R₂ = 112 Ω is 0.25 Ω/min
For a given resistor connected in parallel;
[tex]\mathbf{\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}[/tex]
Making R from the left-hand side the subject of the formula, then:
[tex]\mathbf{R = \dfrac{R_1R_2}{R_1+R_2}}[/tex]
Given that:
[tex]\mathbf{R_1 = 117,}[/tex] [tex]\mathbf{R_2 = 112 }[/tex]Now, replacing the values in the above previous equation, we have:
[tex]\mathbf{R = \dfrac{13104}{229}}[/tex]
However, the differentiation of R with respect to time t will give us the rate at which R is changing when R1=117Ω and R2=112Ω.
So, by differentiating the given equation of the resistor in parallel with respect to time t;
[tex]\mathbf{\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}[/tex], we have:
[tex]\mathbf{\dfrac{1}{R^2}(\dfrac{dR}{dt})=\dfrac{1}{R_1^2}(\dfrac{dR_1}{dt})+\dfrac{1}{R_2^2}(\dfrac{dR_2}{dt})}[/tex]
[tex]\mathbf{(\dfrac{dR}{dt})=R^2 \Bigg[ \dfrac{1}{R_1^2}(\dfrac{dR_1}{dt})+\dfrac{1}{R_2^2}(\dfrac{dR_2}{dt})\Bigg]}[/tex]
[tex]\mathbf{\dfrac{dR}{dt}=(\dfrac{13104}{229})^2 \Bigg[ \dfrac{0.4}{117^2}+\dfrac{0.6}{112^2}\Bigg]}[/tex]
[tex]\mathbf{\dfrac{dR}{dt}=3274.44 \Bigg[ (7.7052 \times 10^{-5} )\Bigg]}[/tex]
[tex]\mathbf{\dfrac{dR}{dt}=0.25\ \Omega /min}[/tex]
Therefore, we can conclude that the rate at which R is changing R1=117Ω and R2=112Ω is 0.25 Ω/min
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A rifle fires a pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by from its unstrained length. The pellet rises to a maximum height of 6.10 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.
This question is incomplete, the complete question is;
A rifle fires a 2.10 × 10⁻² kg pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by 9.10 × 10⁻² m from its unstrained length. The pellet rises to a maximum height of 6.10 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.
Answer:
the spring constant is 303.5 N/m
Explanation:
Given the data in the question;
There is a potential energy associated with the spring;
we know that potential energy = kinetic energy
mgh = [tex]\frac{1}{2}[/tex]kx²
where k is the spring constant and x is the compression
as the pallet is fired, the spring gives kinetic energy which is converted into gravitational potential energy
so
m = 2.10 × 10⁻²
g = 9.81 m/s²
h = 6.10 m
x = 9.10 × 10⁻² m
we substitute
mgh = [tex]\frac{1}{2}[/tex]kx²
2.10 × 10⁻² × 9.81 × 6.10 = [tex]\frac{1}{2}[/tex] × K × ( 9.10 × 10⁻² )²
1.256661 = 0.0041405 × K
K = 1.256661 / 0.0041405
K = 303.5 N/m
Therefore, the spring constant is 303.5 N/m
A copper wire has a mass of 29.33 mg/cm and has a length of 2.5 cm.
Find the weight of the copper wire.
a wave travels one complete cycle in20sec and has wavelength of 1000mm.what is the speed
Answer:
20000
Explanation:
Speed = Wavelength x Wave Frequency. In this equation, wavelength is measured in meters and frequency is measured in hertz (Hz), or number of waves per second. Therefore, wave speed is given in meters per second, which is the SI unit for speed.
Which of the following is true of the deep
water layer of the ocean?
A. warmest and least dense of the ocean layers
B. experiences a rapid decrease in temperature
C. is warm in the summer and cold in the winter
D. cold all year round
the pencil has a shadow. is the pencil opaque or transparent?
Explanation:
Pencil is clearly an opaque object because, we cannot see through it. For example, take a pencil in your front. You will observe that, you are not able to see the objects behind it. And that is why you can say that pencil is an opaque object.
Answer:
A pencil is opaque
Explanation:
A pencil is opaque, because light cannot pass through it and shadow is created.
Vector A is 3 units length and points along the positive x-axis vector B is 4 units in length and points along negative y-axis .find magnitude and direction of the vector (a) A+B (b)A-B
Answer:
a) < 3 , -4 >
b) < 3 , -4 >
Explanation:
a) If you can imagine this, adding vectors is like putting them "tip to tail", where you put the beginning point of vector B to the end point of vector A (or vice versa). Your new vector (A+B) would be from the "tip" of vector A to the "tail" of vector B.
Mathematically, this is the same as adding the x-components of each vector together as well as the y-components.
Vector A: 3 units along the positive x-axis: < 3 , 0 >
Vector B: 4 units along the negative y-axis: < 0 , -4 >
A+B = < 3 , 0 > + < 0 , -4 > = < (3+0) , (0+(-4)) > = < 3 , -4 >
b) Subtracting is like adding a negative, so you could use the same "tip to tail" visual by adding the negative of vector B instead (which is B in the opposite direction).
Vector A: < 3 , 0 >
Vector B: < 0 , -4 >
Vector -B: < 0 , 4 >
A-B = A+(-B) = < 3 , 0 > + < 0 , 4 > = < (3+0) , (0+4) > = < 3 , 4 >
A golf ball strikes a hard, smooth floor at an angle of 27.0 ° and, as the drawing shows, rebounds at the same angle. The mass of the ball is 0.0200 kg, and its speed is 33.0 m/s just before and after striking the floor. What is the magnitude of the impulse applied to the golf ball by the floor? (Hint: Note that only the vertical component of the ball's momentum changes during impact with the floor, and ignore the weight of the ball.)
Answer:
J = 3.564 N.s
Explanation:
From the given information:
angle θ = 27°
mass = 0.0200 kg
speed = 33.0 m/s
To determine the impulse applied using the equation:
J = m(2V cos θ)
J = 0.0200 (2 × cos (27.0))
J = 0.0200 (2 × 0.8910)
J = 0.03564
J = 3.564 N.s
3. Provide two examples of static electric charge.
Answer: 1. walking across a carpet and touching a metal door handle 2. pulling your hat off and having your hair stand on end.
Explanation
:)
Let's explore the assumptions we made. Look closely at Jessie's motion as she runs. In calculating her power output, we assumed that the work she did was equal to the work done by the force of gravity on her body. Do you think that is a good assumption
Answer:
No, it is not a good assumption
Explanation:
From the given information:
The work Jessie did was quite more than the work done by the force of gravity. This is because the gravity of the force on her body is perpendicular to its motion and the work done by Jessie is due to the muscular force of her body. Hence, the total power she produced is more than the calculated amount.
. Monochromatic light illuminates two slits that are 0.33 mm apart. The adjacent bright lines of the interference pattern on a screen 2.30 m away from the slits are 0.44 cm apart. What is the wavelength of the light
Answer:
the wavelength of the light is 6.313 × 10⁻⁷ m
Explanation:
Given the data in the question;
for a double slit interference;
θ = nλ/d
for adjacent lines
θ = λ/d
and d = 0.33 mm = 0.00033 m
and θ = 0.44 × 10⁻² m / 2.30 m
so
λ = θ × d
λ = ( 0.44 × 10⁻² m / 2.30 m ) × 0.00033 m
λ = 0.001913043478 × 0.00033 m
λ = 6.313 × 10⁻⁷ m
Therefore, the wavelength of the light is 6.313 × 10⁻⁷ m
Which are properties of a liquid? Check all that apply.
Answer:
the property of liquid are
1 they can flow from one place to another if surface is slanted
2 it cannot be compressed
A proton (with charge of 1.6 x 10^-19 C and mass of 1.7*10^-27 kg) traveling at a speed of 57,600,630 m/s in the + x-direction enters a region of space where there is a magnetic field of strength 0.5 T in the - z-direction. What would be the radius of the circular motion that the proton would go into if it is "trapped" in this magnetic field region?
Answer:
r = 1,224 10⁻² m
Explanation:
For this exercise let's use Newton's second law
F = m a
the force is magnetic
F = q v x B
The bold letters indicate vectors, the module of this expesion is
F = q v B
The direction of the force is found by the right hand rule
thumb points in the direction of the velicad + x
fingers extended in the direction of B -z
the palm is in the direction of the force + and
the acceleration of the proton is cenripetal
a = v² / r
we substitute
q v B = m v² / r
r = [tex]\frac{m \ v}{q \ B}[/tex]
let's calculate
r = [tex]\frac{1.7 \ 10^{-27} \ 5.760063 \ 10^7 }{1.6 \ 10^{-19} \ 0.5 }[/tex]
r = 1,224 10⁻² m
a student starts his lawnmower by applying a constant tangential force of 150 N to the 0.3 kg disk-shaped flywheel. the radius of the flywheel is 18 cm. what is the flywheels angular acceleration? b. what is the angular speed of the wheel after it has turned through one revolution,( neglect friction and motor compression.) c. what is the tangent speed of a point on the rim of the flywheel?
Answer:
okay
Explanation:
please I don't know
What must happen to a sound making object for it to make sound?
A: it must be made of metal
B: it must be in a vacuum
C: it must have force applied to it
D: it must be bent
Answer:
option b
Explanation:
........................
Which climate zone has hot summers, cold winters, and average amounts of precipitation throughout the year?
A. Equator
B. Polar
C. Temperate
D. Tropical
Answer:
i believe its temperate
Explanation:
The climate zone that has hot summers, cold winters, and average amounts of precipitation throughout the year is the temperate climate zone. So, option C is correct.
What is meant by climatic zone ?Climatic zones are defined as the areas that have different climatic conditions over the world.
Here,
The climate zone that hot summers, cold winters and average amounts of precipitation throughout the year is the temperate climate zone.
The temperate climate zones are the areas that have mild temperature condition that are located between the subtropical and the polar regions. These are zones with moderate rainfall that is throughout the year. The temperature in this zone will change greatly between the summer and winter seasons. These zones are hotter during the summer and very cold during the winter.
The temperate zone has an average precipitation of 800 mm.
Hence,
The climate zone that has hot summers, cold winters, and average amounts of precipitation throughout the year is the temperate climate zone.
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Someone please help me...
the distance from the Earth to the sun equals 1 AU. Neptune is 30 AU from the sun. How far is Neptune from the Earth?
Answer:
1 astronomical unit, or AU, is the average distance from the Earth to the Sun; that's about 150 million km. So, Neptune's average distance from the Sun is 30.1 AU. Its perihelion is 29.8 AU, and it's aphelion is 30.4 AU.
Short Answer: it is 29
Explanation:
sorry if its wrong
Answer:
29
Explanation:
I just took a test! not only that but the other person who answered this question had the corrected answer.
Lightning produces a maximum air temperature on the order of 104K, whereas a nuclear explosion produces a temperature on the order of 107K. Find the order of magnitude of the wavelength radiated with greatest intensity by each of these sources. Name the part of the EM spectrum where you would expect to radiate most strongly.
Answer:
tex]2.898\times 10^{-7}\ \text{m}[/tex] ultraviolet region
[tex]2.898\times 10^{-10}\ \text{m}[/tex] x-ray region
Explanation:
T = Temperature
b = Constant of proportionality = [tex]2.898\times 10^{-3}\ \text{m K}[/tex]
[tex]\lambda[/tex] = Wavelength
[tex]T=10^4\ \text{K}[/tex]
From Wein's law we have
[tex]\lambda=\dfrac{b}{T}\\\Rightarrow \lambda=\dfrac{2.898\times 10^{-3}}{10^4}\\\Rightarrow \lambda=2.898\times 10^{-7}\ \text{m}[/tex]
The wavelength of the radiation will be [tex]2.898\times 10^{-7}\ \text{m}[/tex] and it is in the ultraviolet region.
[tex]T=10^7\ \text{K}[/tex]
[tex]\lambda=\dfrac{2.898\times 10^{-3}}{10^7}\\\Rightarrow \lambda=2.898\times 10^{-10}\ \text{m}[/tex]
The wavelength of the radiation will be [tex]2.898\times 10^{-10}\ \text{m}[/tex] and it is in the x-ray region.
An amusement park ride swings back and forth once every 60.0 s. What is the ride's frequency?
The Answer choices are in the image above
Answer:
Option B. 0.016 Hz
Explanation:
From the question given above, the following data were obtained.
Period (T) = 60 s
Frequency (f) =?
Frequency and period are related according to the following equation:
Frequency = 1 / period
f = 1/T
With the above formula, we can obtain the frequency of the ride as follow:
Period (T) = 60 s
Frequency (f) =?
f = 1/T
f = 1/60
f = 0.016 Hz
Thus, the rider's frequency is 0.016 Hz
PLEASE HELP! I'LL GIVE BRAINLEST
A drone accelerates from rest to a speed of 300 m/s in 3 s. What is the acceleration of the drone? How far will the drone go?
Answer:
(i) 100 m/s²
(ii) 450 m
Explanation:
From the question,
Using,
(i) a = (v-u)/t................. Equation 1
Where a = acceleration of the drone, v = final velocity of the drone, u = Initial velocity of the drone, t = time.
Given: v = 300 m/s, u = 0 m/s (from rest), t = 3 s
Substitute these values into equation 1
a = (300-0)/3
a = 300/3
a = 100 m/s²
Hence the acceleration of the drone is 100 m/s²
(ii) using,
s = ut+at²/2.................... Equation 2
Where s = distance traveled by the drone.
also substitute the values above into equation 2
s = 0(3)+100(3²)/2
s = 50×9
s = 450 m
A pulley in the shape of a solid cylinder of mass 1.50 kg and radius 0.240 m is free to rotate around a horizontal shaft along the axis of the pulley. There is friction between the pulley and this shaft. A light, nonstretching cable is wrapped around the pulley, and the free end is tied to a 2.00 kg textbook. You release the textbook from rest a distance 0.900 m above the floor. Just before the textbook hits the floor, the angular speed of the pulley is 10.0 rad/s. What is the speed of the textbook just before it hits the floor
Answer:
the speed of the textbook just before it hits the floor is 2.4 m/s
Explanation:
Given the data in the question;
mass of pulley = 1.50 kg
radius of pulley = 0.240 m
mass of text book = 2.0 kg
height from which text book was released = 0.9 m
angular speed of the pulley = 10.0 rad/s
the speed of the textbook just before it hits the floor = ?
the speed of the textbook v = angular speed of the pulley × radius of pulley
we substitute
v = 10.0 rad/s × 0.240 m
v = 2.4 m/s
Therefore, the speed of the textbook just before it hits the floor is 2.4 m/s