A uniform plane wave with parallel polarization is propagating in a lossless dielectric medium (l is € 1), and is incident obliquely onto a plane boundary with another lossless dielectric medium (u 2, E 2). (30%) (a) Derive the Snell's laws of reflection and refraction in terms of the refractive indices and angles. (b) Derive the general expressions for the reflection and the transmission coefficients of the EM field. Find such expressions in terms of the refractive indices if both media are nonmagnetic, i.e., M F M 240. (c) Derive the general expression for the Brewster angle. Find such an expression in terms of the refractive indices if both media are nonmagnetic. (d) Prove that, under the condition of no reflection, the sum of the Brewster angle and the angle of refraction is 90° if both media are nonmagnetic. (e) For total reflection to occur, find the condition for the medium property and the critical angle.

Answer:

Approximately \(39.6\; {\rm m\cdot s^{-1}}\) (assuming that \(g = 9.81\; {\rm m\cdot s^{-2}}\).)

Explanation:

Under the assumptions, vertical acceleration of the vehicle during the ride would be equal to the gravitational field strength: \(a = g = 9.81\; {\rm m\cdot s^{-2}}\).

Apply the following SUVAT equation to find the velocity of the vehicle at the bottom of the drop:

\(v^{2} - u^{2} = 2\, a\, x\),

Where:

Rearrange this equation to find \(v\):

\(\begin{aligned}v &= \sqrt{u^{2} + 2\, a\, x} \\ &\approx \sqrt{0^{2} + 2\, (9.81)\, (79.8)} \; {\rm m\cdot s^{-1}} \\ &\approx 39.6\; {\rm m\cdot s^{-1}}\end{aligned}\).

Hence, the speed of this vehicle at the bottom of the drop would be approximately \(39.6\; {\rm m\cdot s^{-1}}\).

Answer:

A....It is a crime sene

Explanation:

Electric field lines are a powerful tool to understand and visualize electric fields. They help to represent the direction and magnitude of the electric field at various points around a charged object.

The following statements are true about electric field lines:

A. Electric field lines cannot cross: This is because at the point where two field lines cross, there would be two directions for the electric field, which is impossible. Hence, the lines do not cross, and this is one of the fundamental characteristics of electric field lines.

B. Lines of electric field only originate from positive charges: Electric field lines originate from positive charges and terminate at negative charges. This is because positive charges repel positive charges and attract negative charges. Therefore, the electric field lines originating from a positive charge terminate at a negative charge.

C. Field lines point in the direction of the force the electric field creates on an electron: Electric field lines point in the direction of the force that would be experienced by a positive charge placed at any point in the field. Electrons, being negatively charged, would experience a force in the opposite direction to the electric field.

D. The strength of the electric field is greater in regions where the field lines are closer together: The density of field lines indicates the strength of the electric field. The closer the lines are, the stronger the field at that point.

E. In an electric-field-line drawing with many point charges, the number of field lines originating or terminating on each charge is proportional to the charge. That is, bigger charges have proportionally more field lines: The number of field lines originating or terminating on each charge is directly proportional to the magnitude of the charge.

F. The true strength of an electric field at any point can be determined from an electric field representation: The strength of the electric field at a point can be determined by the density of electric field lines at that point. However, the actual strength of the field would require quantitative measurements using instruments such as a voltmeter or an electrometer.

In conclusion, electric field lines are an essential tool in understanding the behavior of electric fields. They provide a visual representation of the electric field, its direction, and its strength at various points in space.

To know more about electric field visit :-

https://brainly.com/question/14372859

#SPJ1

Answer:

Force = Mass × Acceleration

\({ \tt{force = 2250 \times 4.3}} \\ = { \tt{9675 \: newtons}}\)

Answer:

D. X-rays have more energy than ultraviolet waves.

The top surface moves relative to the bottom surface by 1.167 x 10⁻⁶ m.

The distance the top surface move relative to the bottom surface is calculated as follows;

shear strain = F/(αx)

where;

shear strain = (14 )/(1.2 x 10⁷ x 0.00117 m)

shear strain = 0.000997

The movement of the top surface;

top surface movement = shear strain x thickness

= 0.000997  x 0.00117 m

= 1.167 x 10⁻⁶ m

Learn more about shear stress here: https://brainly.com/question/20630976

#SPJ1

The term that best describes the type of force Carmen is using is "contact force" . Contact force refers to the force that occurs when two objects physically touch or interact with each other.

The correct answer is option A.

In this scenario, Carmen is physically picking up boxes and pushing the cart, which involves direct contact between her body, the boxes, and the cart.

Contact forces are classified as a type of mechanical force, which includes various interactions such as pushing, pulling, lifting, and carrying objects. These forces arise due to the electromagnetic interactions between the atoms and molecules of the objects involved.

Friction (option B) is a specific type of contact force that resists the relative motion or tendency of motion between two surfaces in contact. While friction may be present when Carmen pushes the cart, it is not the primary force being described in this situation.

Gravity (option C) is a non-contact force that attracts objects towards each other due to their masses. While gravity is always present, it is not directly involved in Carmen's action of picking up the boxes and pushing the cart.

Non-contact forces (option D) refer to forces that act on objects without any physical contact. Examples include magnetic forces, electrical forces, and gravitational forces. However, in this scenario, Carmen's actions involve direct physical contact, so non-contact forces do not apply.

For more such information on: force

https://brainly.com/question/12785175

#SPJ8

the Curies discovered the existence of the elements radium and polonium in their research of pitchblende.

Answer:

radium and polonium

Explanation:

Because I googled it.

Answer:

3 meters

Explanation:

Answer:

Explanation:

The charge must be negative so that force in a downward electric field will be upward so that its weight is balanced .

Let the charge be - q .

force on charge

= q x E where E is electric field

= q x 680

weight = 1.6 x 10⁻³ x 9.8

so

q x 680 = 1.6 x 10⁻³ x 9.8

q = 1.6 x 10⁻³ x 9.8 / 680

= 23 x 10⁻⁶ C

- 23 μ C .

The centripetal force in Newtons provided by the friction between the blade of the skate and the ice is 490 N

The following data were obtained from the question:

The centripetal force can be obtained as illustrated below:

F = mv²/r

= (50 × 7²) / 5

= (50 × 49) / 5

= 2450 / 5

= 490 N

Thus, we can concluded that the centripetal force is 490 N

Learn more about centripetal force:

https://brainly.com/question/14021112

#SPJ1

The amount the needle on the meter is deflected A. increases

This phenomenon can be explained by Faraday's law of electromagnetic induction. According to this law, when a magnetic field (created by the bar magnet) passes through a coil of wire, it induces an electric current in the wire. This induced current generates its own magnetic field, which interacts with the magnetic field of the bar magnet.

The deflection of the meter needle is a result of this induced current. When the number of coils of wire is increased, there is a greater number of wire loops for the magnetic field to pass through. This leads to a stronger induction of electric current, resulting in a larger deflection of the meter needle.

By increasing the number of coils, more magnetic flux is linked with the wire, resulting in a higher induced electromotive force (emf) and a greater current. This increased current produces a stronger magnetic field around the wire, leading to a larger deflection on the meter. Therefore, increasing the number of coils of wire enhances the magnetic field interaction, resulting in an increased deflection of the meter needle. Therefore, Option A is correct.

Know more about Faraday's law here:

https://brainly.com/question/1640558

#SPJ8

Answer: 1.348 meters

Explanation: Although the sign is missing from the location of the 4.00 kg object, it is assumed to be positive. The net moment of all the objects about the center of mass must be zero. Let the center of mass be on the y axis at a point  c . Adding the four moments together, we get:

(2.00)(3.00−c)+(3.00)(2.50−c)+(2.50)(0−c)+(4.00)(0.500−c)=0

6.00−2.00c+7.50−3.00c+0−2.50c+2.00−4.00c=0

11.5c=15.50

c=  1.348 metres

The center of mass is on the y axis at  y  = 1.348 metres.

Answer:

Explanation:

If a particle to move from point A, where the electric potential is 14.7 V, to point B, where the electric potential is −24.5 V, the change in electric potential is expressed as:

∆V = VB-VA

Given VB = -24.5V

VA = 14.7V

∆V = -24.5-14.7

∆V = -39.2V

To calculate the change that occurs in the particle's electrostatic potential energy, when the particle is an electron, we will use the formula:

∆U = q∆V where q is the charge on the electron

Charge on an electron = -1.6×10^-19C

∆U = -1.6×10^-19C×-39.2

∆U = 62.72×10^-19 Joules

For a proton:

q = 1.6×10^-19C

∆U = 1.6×10^-19C×-39.2

∆U = -62.72×10^-19 J (calculation is similar as above, the only difference is the sign)

For a neutral hydrogen atom:

Charge on a neutral hydrogen atom is +1

∆U = 1×-39.2

∆U = -39.2Joules

For a singly ionized helium atom

Charge on the atom q = +1

∆U = 1×-39.2

∆U = -39.2Joules

Answer:

The speed of the knife after passing through the target is 9.33 m/s.

Explanation:

We can find the speed of the knife after the impact by conservation of linear momentum:

\( p_{i} = p_{f} \)

\( m_{k}v_{i_{k}} + m_{t}v_{i_{t}} = m_{k}v_{f_{k}} + m_{t}v_{f_{t}} \)

Where:

\( m_{k}\): is the mass of the knife = 22.5 g = 0.0225 kg

\( m_{t}\): is the mass of the target = 300 g = 0.300 kg

\( v_{i_{k}}\): is the initial speed of the knife = 40.0 m/s

\( v_{i_{t}} \): is the initial speed of the target = 2.30 m/s

\(v_{f_{k}}\): is the final speed of the knife =?

\( v_{f_{t}} \): is the final speed of the target = 0 (it is stopped)

Taking as a positive direction the direction of the knife movement, we have:

\( m_{k}v_{i_{k}} - m_{t}v_{i_{t}} = m_{k}v_{f_{k}} \)  

\( v_{f_{k}} = \frac{m_{k}v_{i_{k}} - m_{t}v_{i_{t}}}{m_{k}} = \frac{0.0225 kg*40.0 m/s - 0.300 kg*2.30 m/s}{0.0225 kg} = 9.33 m/s \)

Therefore, the speed of the knife after passing through the target is 9.33 m/s.

I hope it helps you!              

Answer:

3.35

Explanation:

Got it on Acellus

The light of wavelength 485 nm passes through a single slit. The single between the first (m=1) and second (m=2) interference minima is 3.36°.

Diffraction is the phenomenon of bending of waves through obstacles.  

Given is the wavelength λ= 485 nm, silt width d =  8.32 *10⁻⁶ m, then the angle θ will be

d sinθ =mλ

for m=1, sin θ₁ = λ/d

for m=2, sin θ₂ = 2λ/d

Substitute the values into both expressions to find the angles,

sin θ₁ = 485 x 10⁻⁹ /  8.32 *10⁻⁶

θ₁ = 3.34°

and sin θ₂ = (2 x  485 x 10⁻⁹ )/  8.32 *10⁻⁶

θ₂ = 6.7°

The angle between m =1 and m=2 will be

θ₂ -θ₁ = 6.7° - 3.34° =3.36°

Thus, angle between the first (m=1) and second (m=2) interference minima is 3.36°.

Learn more about diffraction.

https://brainly.com/question/12290582

#SPJ2

Answer:

a) The potential energy of the system is 1/9 of the total mechanical energy, when \(x= \frac{1}{3}\cdot A\).

b) The fraction of the total mechanical energy that is kinetic if the displacement is 1/2 the amplitude is 1/2.

c) The maximum kinetic energy is increased by a factor of 9.

Explanation:

a) From Mechanical Physics, we remember that the mechanical energy of mass-spring system (\(E\)), measured in joules, is the sum of the translational kinetic energy (\(K\)), measured in joules, and elastic potential energy (\(U\)), measured in joules. That is:

\(E = K + U\) (1)

By definitions of translational kinetic energy and elastic potential energy, we have the following expressions:

\(K = \frac{1}{2}\cdot m \cdot v^{2}\) (2)

\(U = \frac{1}{2}\cdot k\cdot x^{2}\) (3)

Where:

\(m\) - Mass, measured in kilograms.

\(v\) - Velocity of the mass, measured in meters per second.

\(k\) - Spring constant, measured in newtons per meter.

\(x\) - Elongation of the spring, measured in meters.

If we know that \(U = \frac{1}{9}\cdot E\), \(k = k\) and \(E = \frac{1}{2}\cdot k \cdot A^{2}\), then:

\(\frac{1}{18}\cdot k\cdot A^{2} = \frac{1}{2}\cdot k\cdot x^{2}\)

\(\frac{1}{9}\cdot A^{2} = x^{2}\)

\(x= \frac{1}{3}\cdot A\)

The potential energy of the system is 1/9 of the total mechanical energy, when \(x= \frac{1}{3}\cdot A\).

b) If we know that \(k = k\), \(x = \frac{1}{2}\cdot A\) and \(E = \frac{1}{2}\cdot k \cdot A^{2}\), then the equation of energy conservation associated with the system is:

\(\frac{1}{2}\cdot k\cdot A^{2} = \frac{1}{4}\cdot k\cdot A^{2}+K\)

\(K = \frac{1}{4}\cdot k\cdot A^{2}\)

The fraction of the total mechanical energy that is kinetic if the displacement is 1/2 the amplitude is 1/2.

c) From the Energy Conservation equation associated with the system, we know that increasing the amplitude by a factor of 3 represents an increase in the elastic potential energy by a factor of 9. Then, the maximum kinetic energy is increased by a factor of 9.

The gauge pressure at B is 11.5 kPa.

From continuity equation,

Velocity of water B = (2* π* 3²)/ (2* π* 1²) = 9 m/s

Then from Bernoulli's equation,

v²/2 + Ф + p/ρ = constant

ρ = 1000 kg/m³

3²/2 + Ф + 50000/1000 = 9²/2 + Ф + P/1000

Pressure at B = 11.5 kPa

Pressure measured in relation to atmospheric pressure is known as gauge pressure. The gauge pressure is positive when the atmospheric pressure is above that level and negative when it is below it.

In actuality, air pressure raises the pressure in any fluid that isn't contained by a hard container. Pascal's principle. is the reason. why this occurs. In relation to atmospheric or barometric pressure, gauge pressure is referred to. In a perfect vacuum of space, there is no matter, hence the pressure is known as absolute pressure.

The most popular measures for measuring vacuum are torr (milli-meter of mercury), micron (micrometer of mercury), and inch of mercury (inHg). While the units of torr, micron, and in Hg often denote absolute pressure, inHg typically denotes gauge pressure.

To know more about gauge pressure:

https://brainly.com/question/14809055

#SPJ4

When the direction of a current changes 60 times in a second, the current is said to be 60 Hz.

While the passing current does not affect the wavelength, the operating frequency does.A sine wave's period, which is defined as the interval between two identical spots on the wave, will be roughly 16.6 milliseconds at a rate of 60Hz (60 oscillations per second), as depicted in the diagram.

A frequent word for 60 cycles per second, or more commonly 60 Hertz, is the frequency of dc power (Hz).In honor of German physicist Heinrich Hertz, who established the transmission and presence of electric oscillations, the latter unit is used.

To know more about current changes visit:

https://brainly.com/question/28574212

#SPJ1

Answer: 4R

Explanation:R=pL/A

R second wire=p2L/1/2A

=4R

In a scenario where an egg is free-falling from a nest in a tree and neglecting air resistance, there is one force acting on the egg and the force is unbalanced which is denoted as option B.

This is referred to as an external agent which is capable of influencing the motion of an object or body. It is also capable of changing the state of rest of a body and the unit in Newton.

When an object is falling from a height and there is no air resistance then the only force acting on it is gravitational force which is unbalanced as there is no equal and opposite force to make it stable.

Read more about Force here https://brainly.com/question/388851

#SPJ1

The minimum stopping distance of the car is determined as 8 m.

The minimum stopping distance of the car is calculated as follows;

d = (u²)/(2a)

where;

when the minimum stopping distance = 2 m, initial velocity = 40 km/hr = 11.11 m/s

2 = (11.11²)/(2a)

a = (11.11²)/(2 x 2)

a = 30.86 m/s²

when the speed becomes 80 km/h, the minimum stopping distance is calculated as;

u = 80 km/h = 22.22 m/s

d = (22.22² )/ (2 x 30.86)

d = 8 m

Learn more about minimum stopping distance here: https://brainly.com/question/13030196

#SPJ1

parameters given are:

time= 8.2 seconds

g(acceleration due to gravity)= \(9.8 m/s{2}\)

(a) skydivers downward velocity is given as

Vf = Vo + g(t)

Vf= 0 + 9.8 + (8.2)

Vf= \(80.36 m/s^{2}\)

(b) distance of the skydiver below the helicopter

h= Vo + 1/2 gt^2

h= 0 + (0.5) *(9.8) * (8.2)^2

h= 0.5* 9.8 * 67.24

h= 329.48m

What is Velocity?

Velocity is the rate at which an object changes its direction.

The skydivers downward velocity is 80.36m/s^2

The distance form the skydiver to the helicopter is 329.48 meters

In conclusion, initial velocity in the given question is equal to zero.

Learn more about velocity at: https://brainly.com/question/23803673

#SPJ1

A program that could do an instantaneous analysis of video motion will be useful it in a sportscast to analyze events as they occur.

A motion video is defined as the display of video images at a rate (such as thirty frames per second) that causes objects to appear to move smoothly and continuously.

Sports inherently involve fast and accurate motion, which can be difficult for competitors to master but also for coaches and trainers to analyze and audiences to follow. Because of the nature of most sports, monitoring with sensors or other devices attached to players or equipment is generally not possible. This opens up a plethora of opportunities for the use of computer vision techniques to assist competitors, coaches, and the audience

Learn more about motion on:

https://brainly.com/question/27802581

#SPJ1

The maximum speed of a 2.0 g particle that oscilates between x= 2.00 mm to x = 8.00 mm is 70.71 m/s.

Speed is the ratio of distance to time of a body.

To calculate the maximum speed of the particle, we use the formula below.

Formula:

Where:

From the Graph in the question,

Given:

Substitute these values into equation 1

Hence, the maximum speed is 70.71 m/s.

Learn more about speed here: https://brainly.com/question/4931057

#SPJ1

Answer:

Explanation:

We can use Hooke's law to solve this problem. Hooke's law states that the force required to extend or compress a spring by some distance x is proportional to that distance. Mathematically, this can be written as:

F = kx

where F is the force applied to the spring, x is the distance the spring is stretched or compressed, and k is the spring constant, a measure of the stiffness of the spring.

To find the spring constant, we can use the given information that a 20g weight causes an extension of 0.72cm in the spring. We can convert the weight to force using the acceleration due to gravity, g:

F = mg = (0.02 kg)(9.8 m/s^2) = 0.196 N

Now we can solve for the spring constant:

k = F/x = 0.196 N / 0.0072 m = 27.2 N/m

Finally, we can use this spring constant to find the extension caused by an 80g weight:

F = mg = (0.08 kg)(9.8 m/s^2) = 0.784 N

x = F/k = 0.784 N / 27.2 N/m = 0.0288 m

So the extension caused by an 80g weight is 0.0288 m or 2.88 cm.

Answer:

free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s/s. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s/s in The Physics Classroom Tutorial in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy.

g = 9.8 m/s/s, downward

( ~ 10 m/s/s, downward)

Explanation:

Look It Up!

Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Use the Gravitational Fields widget below to investigate how location affects the value of g.

C. 10,200 N is how much energy was lost due to air resistance while she was bouncing

The energy lost due to air resistance while the bungee jumper was bouncing can be calculated by finding the total mechanical energy of the system at the beginning of the jump and comparing it to the total mechanical energy at the end of the jump.

At the beginning of the jump, the total mechanical energy is given by:

Ei = mgh

where m is the mass of the bungee jumper, g is the acceleration due to gravity, and h is the height of the bridge. Therefore, at the beginning of the jump:

50 x 30 x 10 - 1/2 x 30^2 x 10

= 15000 - 4500

= 10,200 N

Read more on energy here:https://brainly.com/question/13881533

#SPJ1