You are comparing the beam waste for two different situations with the goal of using the smallest beam waste possible. A Nd-YAG laser system emits light at 532 nm and the beam is 8 mm in diameter. You also have a Ti-sapphire laser that emits at 855 nm and has a beam diameter of 6 mm. Compare the beam waist for both laser systems using a focusing lens with a focal length of 10 mm. Assume the light fills the lenses in each case
Answer:
comparing the beam waist for both lasers ( ratio of the beam waists )
4.536 μm / 2.117 μm = 2.14
Explanation:
Nd-YAG laser system : emits at 532 nm , beam diameter = 8 mm
Ti-sapphire laser system : emits at 855 nm , Beam diameter = 6mm
Comparing the beam waist for both lase systems using a focusing lens
Focal length = 10 mm
assumption : light fills lenses in each laser system
Beam waist radius ( W ) = [tex](\frac{2\beta }{\pi } )(\frac{F}{D} )[/tex]
β = wavelength , D = diameter illuminated , F = focal length
For
Nd-YAG laser system
β = 532 mm , D = 8 mm
hence ( Wn ) = [tex](\frac{2\beta }{\pi } )(\frac{F}{D} )[/tex] = ( 2*532 / π ) ( 10 / 8 ) = 2.117 μm
For
Ti-sapphire laser
β = 855 nm , D = 6 mm
hence ( Wt ) [tex](\frac{2\beta }{\pi } )(\frac{F}{D} )[/tex] = ( 2* 855 ) / π ) ( 50 / 6 ) = 4.536 μm
comparing the beam waist for both lasers ( ratio of the beam waists )
4.536 μm / 2.117 μm = 2.14
In medieval warfare, one of the greatest technological advancement was the trebuchet. The trebuchet was used to sling rocks into castles. You are asked to study the motion of such a projectile for a group of local enthusiast planning a medieval war reenactment. Unfortunately an actual trebuchet had not been built yet, so you decide to first look at the motion of a thrown ball as a model of rocks thrown by a trebuchet. Specifically, you are interested in how the horizontal and the vertical components of the velocity for a thrown object change with time. 1. Make a large rough sketch of the trajectory of the ball after it has been thrown. Draw the ball in at least five different positions; two when the ball is going up, two when it is going down, and one at its maximum height. Label the horizontal and vertical axes of your coordinate system.
2. On the sketch, draw and label the expected acceleration vectors of the ball (relative sizes and directions) for the five different positions. Decompose each acceleration vector into its vertical and horizontal components.
3. On the sketch, draw and label the velocity vectors of the object at the same positions you chose to draw your acceleration vectors. Decomposes each velocity vector into its vertical and horizontal components. Check to see that the changes in the velocity vector are consistent with the acceleration vectors.
4. Looking at the sketch, how does someone expect the ball's horizontal acceleration to change with time? Could you give a possible equation giving the ball's horizontal acceleration as a function of time? Graph this equation. If there are constants in your equation, what kinematic quantities do they represent? How would someone determine these constants from the graph?
5. Looking at the sketch, how does someone expect the ball's horizontal velocity to change with time? Is it consistent with the statements about the ball's acceleration from the previous question? Could you give a possible equation for the ball's horizontal velocity as a function of time? Graph this equation. If there are constants in the equation, what kinematic quantities do they represent? How would someone determine these constants from the graph?
6. Could you give a possible equation for the ball's horizontal position as a function of time? Graph this equation. If there are constants in the equation, what kinematic quantities do they represent? How would someone determine these constants from the graph? Are any of these constants related to the equations for horizontal velocity or acceleration?
7. Repeat questions 4-6 for the vertical component of the acceleration, velocity, and position. How are the constants for the acceleration, velocity and position equations related?
Answer:
2) a_y= -g 3) vₓ=constant v_y = v_{oy} - g t, 4) vₓ = v₀ₓ - ax t
5) changes the horizontal speed, should change range
7) changes the vertical speed change the maximum height
Explanation:
1) After reading your long writing, we are going to solve the exercise, in the attachment you can see the different vectors.
2) The acceleration vectors are vertical and directed downwards due to the attraction of the Earth (gravity force) this force is constant, on the x axis there is no acceleration
3) the velocity vectors on the x-axis are constant because there are no relationships and the y-axis changes value according to the expression
v_y = v_{oy} - gt
at the point of maximum height, vy = 0 is equal to the maximum height
4) For someone to change the horizontal acceleration we must assume a friction with the air, in this case they relate it would be in the opposite direction to the horizontal speed
In the graph it would be directed to the left, therefore the velocity would be
vₓ = v₀ₓ - ax t
5 and 6) If someone changes the horizontal speed, they should change the range of the shot for greater horizontal speed, the rock goes further.
the equations of motion are
x = v₀ₓ t
y = v_{oy} t - ½ g t²
7) If someone changes the vertical speed change the maximum height, but not the scope of the shot, for higher speed higher maximum height,
the equations of motion are the same.
If the bar magnet on the left were broken in half, what statement correctly predicts how the two halves of the magnet would react
to the magnet on the right?
Answer:
According to the law of magnetism, "Like poles repel, unlike poles attract" If the bar magnet on the left is broken, both halves will consequently have two poles, the north and south poles. If the right sides of both halves are of the south pole, the bar magnet on the right is of the north pole
What causes coastal erosion
La erosión costera es la pérdida o desplazamiento de tierra, o la remoción a largo plazo de sedimentos y rocas a lo largo de la costa debido a la acción de olas, corrientes, mareas, agua impulsada por el viento, hielo transportado por el agua u otros impactos de marejadas ciclónicas.
When a skydiver is 1200 meters in the air they open the parachute. They are moving
cown for 400 seconds before landing. What is the skydiver's average velocity?
48 m/s down
48 m/s up
3 m/s up
3 m/s down
Answer:
3m/s up
Explanation:
An important problem that all electric circuits have is the fact that since current is flowing through the traces connected the components, the circuit is generating a complex magnetic field during operation. You can shield electric fields pretty easily using a Faraday cage, but how do you shield your device from the magnetic field it is generating itself
Answer:
grid or metal sheets or metal foams
Explanation:
Electric and magnetic fields are generated in electrical circuits that often cause interference in the measurements made.
To avoid these interferences, shields are generally used for the electric fields, Farday boxes are used, which are metal grids connected to earth.
For the magnetic field there is also a grid or metal sheets or metal foams,
It should be noted that the gaps in the screening must be smaller than the wavelength of the radiation to be screened.
Are the orbits of the planets on the same plane?
Yes, more or less
No, they're all over the place
Answer: yes
Explanation:
Two identical R = 6.77 ohm light bulbs are is series circuit
with a 17.8 volt battery. What is the power (watt) of both
glowing bulbs?
Answer:
the power of the two light bulbs is 23.4 W
Explanation:
Given;
the resistance of the two identical light bulbs in series, R₁ and R₂ = 6.77 ohms and 6.77 ohms respectively
battery voltage , V = 17.8 V
The equivalent resistance of the two light bulbs, R = R₁ + R₂
R = 6.77 + 6.77
R = 13.54 ohms
The power of the two light bulbs is calculated as follows;
[tex]P = IV = (\frac{V}{R} )V = \frac{V^2}{R} = \frac{17.8^2}{13.54} = 23.4 \ W[/tex]
Therefore, the power of the two light bulbs is 23.4 W
A car traveling at 10 m/s slams into a trash can on the side of the road. The trash can
sticks to the front of the car and they move as one object. If the momentum is
conserved, what would happen to the velocity of the car after the collision?
The velocity would decrease
It would remain the same
The velocity would increase
The car comes to rest
Answer:
The velocity would decrease
Explanation:
Let
[tex]m_1[/tex] = Mass of car
[tex]m_2[/tex] = Mass of trash can
[tex]u_1[/tex] = Initial velocity of car = 10 m/s
[tex]u_2[/tex] = Initial velocity of trash can = 0
v = Velocity of combined mass
From the question the momentum balance of the system will be
[tex]m_1u_1+m_2u_2=(m_1+m_2)v\\\Rightarrow v=\dfrac{m_1u_1+m_2u_2}{m_1+m_2}\\\Rightarrow v=\dfrac{10m_1}{m_1+m_2}[/tex]
The velocity would decrease as now the mass of the car and trash will both be moving as one. The mass would increase resulting in a lower velocity of the combined mass.
What is the magnitude of the gravitational force of attraction be-
tween two asteroids in space, each with a mass of 50,000 kg,
separated by a distance of 3800 m?
Famed stunt pilot, Cleonvia Thread, pulls out rapidly from a dive. He is traveling at 222 mi/h at the bottom of his trajectory, and at that instant is traveling on a curve of radius 820 ft. r v What acceleration does he
Answer:
0.39 m/s²
Explanation:
From the question,
a = v²/r.................... Equation 1
Where v = velocity, r = radius.
Given: v = 222 mi/h = (222×0.44704) m/s = 9.83 m/s, r = 820 ft = (820×0.3048) m = 249.94 m.
Substitute thses values into equation 1
a = 9.83²/249.94
a = 96.63/249.94
a = 0.39 m/s²
Hence the acceleration is 0.39 m/s²
The value of the centripetal acceleration is equal to 4g.
Data Given;
v = 222mi/hdistance (r) = 820ftCentripetal AccelerationUsing formula of centripetal acceleration,
[tex]a_c = \frac{v^2}{r}\\ [/tex]
v = (222 * 1.467) ft/s
v = 325.6 ft/s
substitute the values into the formula
[tex]a_c = v^2/r\\ a_c = \frac{325.6^2}{820}\\ a_c = 129.28 ft/s^2\\ [/tex]
But the value of g = 32.174 ft/s62
This makes a = 4g.
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Two people pull on the wagon each with a constant 20N force. Both people pull to the left. What is the Net Force on the wagon?
Answer:
I dont understand what you are trying to ask
Explanation:
The work-energy theorem states that the work done on an object is equal to a change in which quantity?
kinetic energy
displacement
potential energy
mass
The work-energy theorem states that the net work done by the forces on an object equals the change in its kinetic energy.
Answer:
a kinetic energy
Explanation:
Why is the city of Hoboken, NJ (20 minutes from Newark) and other coastal cities in the United suing ExxonMobile?
Answer:
is that youuuuuuu? fine.
A man whose mass is 69 kg and a woman whose mass is 52 kg sit at opposite ends of a canoe 5 m long, whose mass is 20 kg. Suppose that the man moves quickly to the center of the canoe and sits down there. How far does the canoe move in the water
Answer:
the canoe moved 1.2234 m in the water
Explanation:
Given that;
A man whose mass = 69 kg
A woman whose mass = 52 kg
at opposite ends of a canoe 5 m long, whose mass is 20 kg
now let;
x1 = position of the man
x2 = position of canoe
x3 = position of the woman
Now,
Centre of mass = [m1x1 + m2x2 + m3x3] / m1 + m2 + m3
= ( 69×0 ) + ( 52×5) + ( 20× 5/2) / 69 + 52 + 20
= (0 + 260 + 50 ) / ( 141 )
= 310 / 141
= 2.19858 m
Centre of mass is 2.19858 m
Now, New center of mass will be;
52 × 2.5 / ( 69 + 52 + 20 )
= 130 / 141
= 0.9219858 m { away from the man }
To get how far, the canoe moved;
⇒ 2.5 + 0.9219858 - 2.19858
= 1.2234 m
Therefore, the canoe moved 1.2234 m in the water
The canoe move in the water will be 1.2234 m. The canoe move depending on the center of mass of the bodies.
What is the center of mass?The center of mass of an item or set of objects is a place specified relative to it. It's the average location of all the system's components, weighted by their mass.
The centroid is the location of the center of mass for simple rigid objects with homogeneous density. The center of mass of a uniform disc shape, for example, would be at its center.
The given data in the problem is;
m₁ is the mass of man = 69 kg
m₂ is the mass of woman whose= 52 kg
m₃ is the mass of canoe = 20 kg
L is the length of canoe = 5 m
x₁ is the position of the man
x₂ is the position of the canoe
x₃ is the position of the woman
The center of mass will be;
[tex]\rm COM= \frac{[m_1x_1 + m_2x_2 + m_3x_3]}{ m1 + m2 + m3} \\\\ \rm COM= \frac{[69 \times 0 +52 \times 5 + 20 \times 2.5]}{ 69+ 52 + 20} \\\\ \rm COM= (0 + 260 + 50 ) / ( 141 )\\\\ \rm COM = 310 / 141 \\\\ \rm COM = 2.19858 m[/tex]
The new center of mass is;
[tex]\rm COM= \frac{52 \times 2.5 }{69+52+20} \\\\ \rm COM=\frac{130}{141} \\\\ \rm COM= 0.9219 m[/tex]
The distance to find how the canoe moved will be found by;
[tex]\rm x= 2.5+0.9219-2.1985 = 1.2234[/tex]
Hence the canoe move in the water will be 1.2234 m.
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In the figure, a 32 cm length of conducting
wire that is free to move is held in place
between two thin conducting wires. All of the
wires are in a magnetic field. When a 6.0 A
current is in the wire, as shown in the figure,
the wire segment moves upward at a constant
velocity.
The acceleration of gravity is 9.81 m/s?.
a) Assuming the wire slides without friction
on the two vertical conductors and has a mass
of 0.13 kg, find the magnitude of the minimum
magnetic field that is required to move the
wire.
Answer in units of T. b) What is the direction?
Answer:
.66354 T
Explanation:
Use F=ILB
B = [tex]\frac{F}{IL}[/tex]
B = Magnetic field
F= force due to magnetic
I= current
L= length in meters
F = mg
Final formula:
B=[tex]\frac{mg}{IL}[/tex]
B=[tex]\frac{(.13)(9.8)}{(6)(.32)}[/tex]
B= .66354
ayo btw ion know how to find direction, my b G
The minimum magnetic field required to move the wire is 66354 T.
The direction of magnetic field is normal to the page outwards.
What is magnetic field?The region surrounding a magnet that experiences the effects of magnetism is known as the magnetic field. When describing the distribution of the magnetic force within and around a magnetic object in nature, the magnetic field is a useful tool.
Given parameter:
Current passing through the wire, I = 6.0 A.
Length of the wire ,L = 32 cm = 0.32 m.
Mass of the wire, m = 0.13 Kg.
Acceleration due to the gravity, g = 9.8 m/s².
We know that, force acting on a current caring wire due to magnetic field is, F=ILB
Where,
B = Required magnetic field.
To find the minimum magnetic field that is required to move the
wire, force acting on a current caring wire due to magnetic field is equal to weight the wire, that is, mg.
Hence, we can write,
mg = ILB
⇒ B = mg/IL
= (0.13 * 9.8)/(6.0 * 0.32)
=0.66354 Tesla
Hence, the minimum magnetic field is 0.66354 Tesla.
b) By using Maxwell's right hand thumb Rule along current flow, the direction of magnetic field is determined as normal to the page pointing outwards.
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Suppose a rocket in space is accelerating at 1.5 m/s2. If, at a later time, the rocket quadruples its thrust (i.e., net propelling force), what is the new acceleration?
identify the types of motion in each activity.1.walking a long a hallway. 2.motion of the blades of the fan. 3.earths rotation 4.ball moving on the ground. 5.soldiers marching.
Answer:
Explanatation
1 is just walking
2 spinging
3 roatating
4 rolling
5 stomping there feet
Those should be right but if im wrong then just someone eles the brainly
What is the mechanical advantage of a lever that has an input arm of 6 meters and an output arm of 2 meters
Answer:A
Explanation:I TOOK THE Test
The certain forest moon travels in an approximately circular orbit of radius
14,441,566 m with a period of 6 days 10 hr, around its gas giant exoplanet host. Calculate the mass of the exoplanet from this
information. (Units: kilograms)
Answer:
Mass of Exoplanet = 0.58 kg
Explanation:
First, we will calculate the speed of the forest moon:
[tex]speed = v = \frac{Circumference}{time}\\[/tex]
circumference = 2πr = 2π(14441566 m) = 90739035.3 m
time = 6 days 10 hr = (6 days)(24 h/1 day)(3600 s/1 h) + (10 h)(3600 s/1 h)
time = 554400 s
Therefore,
[tex]v = \frac{90739035.3\ m}{554400\ s}\\\\v = 163.67\ m/s[/tex]
We know that the centripetal force on forest moon will be equal to the gravitational force given by Newton's Gravitational Law, as follows:
[tex]Centripetal\ Force = Gravitational\ Force\\\frac{m_{moon}v^2}{r} = \frac{Gm_{moon}m_{exoplanet}}{r^2}\\\\m_{exoplanet} = \frac{v^2r}{G}\\\\m_{exoplanet} = \frac{(163.67\ m/s)^2(14441566)}{6.67\ x\ 10^{-11}\ N.m^2/kg^2}[/tex]
Mass of Exoplanet = 0.58 kg
Help me please I have other ones like this too on my page please help!
Brainliest!!! Write: Forces are all around us. Imagine that your teacher has asked you to teach a lesson to your peers about forces. Explain, in detail, how you experience forces in your everyday life.
4. When scientists calculate the trajectory a satellite takes on its way to
study a planet, what do you think they use?
5 points
A Speed and velocity
B. Velocity and acceleration
O C. Speed, velocity, and acceleration
O D. Speed only
When scientists calculate the trajectory a satellite takes on its way to
study a planet, they use C. Speed, Velocity, and acceleration.
A trajectory, often known as a flight path, is the route taken by an object moving under the influence of gravity. Typically, the phrase is applied when referring to projectiles or satellites. A parabola curve is usually a decent approximation of the trajectory form when an object is propelled for in a short distance.
When scientists calculate the trajectory a satellite takes on its way to
study a planet they take the speed, velocity, and acceleration into consideration.
The formula for calculating the trajectory can be expressed as:
[tex]\mathbf{y = h + xtan (\alpha) - \dfrac{gx^2 }{2V_o^2cos^2 (\alpha)}}[/tex]
where;
h = height show the distanceV = velocityg = acceleration due to gravityLearn more about trajectory here:
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clarity the term fair discrimination
Answer:
The discrimination which is based on affirmative action, inherent requirement of a particular job, productivity and compulsory discrimination by law are termed as fair discrimination.
hope it helps :)
Explanation:
A. 10g
B.33g
C.40g
D.42g
Answer:
From the graph, it looks like 40 g
Explanation:
See where the NaCl line crosses the red vertical line = 40 gm
Which soil is best for growing most plants?
Answer:
sandy loam
Explanation:
The best soil for most plants to ensure optimum growth is a rich, sandy loam. This soil is an even mixture of all three main types of soil. In most cases, you'll need to amend the soil with compost. Depending on how compact the soil is, you may need to add peat moss and sand.
Which device or set of devices is contained in a mobile telephone?
Un teléfono móvil o teléfono celular es un dispositivo portátil que puede hacer o recibir llamadas a través de una portadora de radiofrecuencia, mientras el usuario se está moviendo dentro de un área de servicio telefónco. El enlace de radiofrecuencia establece una conexión con los sistemas de conmutación de un operador de telefonía móvil, que proporciona acceso a la red telefónica pública conmutada (PSTN). La mayoría de los servicios de telefonía móvil modernos utilizan una arquitectura de red celular, y por lo tanto los teléfonos móviles son, con frecuencia, llamados celulares, especialmente en Hispanoamérica. En España, se utiliza más el término móvil.
The total kinetic energy of an object depends on two (2) factors. Select those factors from the list below.
Mass
Density
Volume
Velocity
During an experiment, Ellie records a measurement of 0.0034 m. How would
she write her measurement in scientific notation?
A. 3.4 x 10-3 m
B. 3.4 x 10-4 m
O C. 3.4 x 10-5 m
D. 3.4 x 10-2 m
Answer:
(A) She needs to move the decimal point by 3 places
____ is based on the acceptance of rules and laws.
Multiple Choice
1. Rational-legal authority
2. Traditional authority
3. Legal power
4. Political power