(12 points) Analysis from the point where the block is released to the point where it reaches the maximum height i) Calculate the highest height reached by the block (or the largest distance travelled along the ramp.) ii) Calculate the work done by the gravitational force. iii) Calculate the work done by the normal force. iv) Calculate the work done by the friction force.

Answers

Answer 1

Answer:

i) a₁ = -g (sin θ + μ cos θ), x = v₀² / 2a₁

ii) W = mg L sin  θ ,  iii)     Wₙ = 0

iv)  W = - μ m g  L cos  θ x

Explanation:

With a drawing this exercise would be clearer, I understand that you have a block on a ramp and it is subjected to some force that makes it rise, for example the tension created by a descending block.

The movement is that when the system is released, the tension forces are greater than the friction and the component of the weight and therefore the block rises up the ramp

At some point the tension must become zero, when the hanging block reaches the ground, as the block has a velocity it rises with a negative acceleration to a point and stops where the friction force and the weight component would be in equilibrium along the way. along the plane

i) Let's use Newton's second law

the reference system is with the x axis parallel to the ramp

Axis y

      N - W cos θ = 0

X axis

      T - W sin θ - fr = ma

the friction force is

      fr = μ N

      fr = μ mg cos θ

we substitute

      T - m g sin sin θ - μ mg cos θ = m a

      a = T / m - g (sin θ + μ cos θ)

With this acceleration we can find the height that the block reaches, this implies that at some point the tension becomes zero, possibly when a hanging block reaches the floor.

      T = 0

       a₁ = -g (sin θ + μ cos θ)

       v² = v₀² - 2a1 x

       v = 0       at the highest point

       x = v₀² / 2a₁

ii) the work of the gravitational force is

       W = F .d

       W = mg sin  θ   L

iii) the work of the normal force

the force has 90º with respect to the displacement so cos 90 = 0

         Wₙ = 0

iv) friction force work

friction force always opposes displacement

         W = - fr d

         W = - μ m g cos  θ L


Related Questions

Which of the following best distinguishes the relationship between applied research and basic research?

A Applied research commercializes the discoveries of basic research and brings them to the general public.
B Basic research takes place in academia, and complex research takes place in industry.
C Basic research provides fundamental knowledge that can be used to conduct applied research.
D Applied research is not published for peer review, but basic research must be.

Answers

Answer:

C. Basic research provides fundamental knowledge that can be used to conduct applied research.

Explanation:

Applied research is used to solve practical and specific problems. Basic research is used to advance theories and scientific knowledge; it might not result in an invention or a solution, but can be used to gain knowledge about a specific subject.

A uniform metre ruler scale balanced at 40 cm mark, when weight 25 gf and 10gf are suspended at 10cm mark and 75 cm mark respectively.Calculate the weight of the metre scale.​

Answers

Answer:

40 gf.

Explanation:

Please see attached photo for diagram.

In the attached photo, W is the weight of metre rule.

The weight of the metre rule can be obtained as follow:

Clockwise moment = (W×10) + (10×35)

Clockwise moment = 10W + 350

Anticlock wise moment = 25 × 30

Anticlock wise moment = 750

Clockwise moment = Anticlock wise moment

10W + 350 = 750

Collect like terms

10W = 750 – 370

10W = 400

Divide both side by 10

W = 400/ 10

W = 40 gf

Thus, the weight of the metre rule is 40 gf

Answer:

40 gf

Explanation:

The balance point of the uniform meter rule with the suspended weights = 40 cm = The pivot point

The location where the 25 gf weight is suspended = 10 cm

The location where the 10 gf weight is suspended = 75 cm

Let W represent the weight of the meter rule.

We have that the location of the application of the weight of the meter rule is at the center, 50 cm mark, point

Given that the meter rule is balanced, and taking moment about the pivot point, we have;

The moment om the left hand side, LHS, of the pivot point = The moment on the right hand side, RHS, of the pivot point

The moment on the LHS = 25 gf × (40 cm - 10 cm) = 750 gf·cm

The moment on the RHS = W × (50 cm - 40 cm) + 10 gf × (75 cm - 40 cm)

The moment on the RHS = W·(10 cm)  + 350 gf·cm

∴ 750 gf·cm = W·(10 cm) + 350 gf·cm

W·(10 cm) = 750 gf·cm - 350 gf·cm = 400 gf·cm

W = (400 gf·cm)/(10 cm) = 40 gf

The weight of the meter scale (rule), W = 40 gf.

What happen to the frequency of transverse vibration of a stretched string if its tension is halved and the area of cross section of the string is doubled?

Answers

Answer:

The fundamental frequency of the stretched string is:

[tex]f=[/tex] [tex]\frac{1}{2} \sqrt{\frac{T}{L} }[/tex] [ T = Tension and μ = mass per unit length]

Here,

 μ = [tex]\frac{m}{L} = \frac{Vp}{L} = Ap[/tex]

[tex]f= \frac{1}{2} \sqrt{\frac{T}{Ap} }[/tex]

If T is halved and A is doubled,

[tex]f= \frac{1}{2} \sqrt{\frac{T'}{A'p} } = \sqrt{\frac{1}{2* 2* A* p} } = \frac{1}{2} (\frac{1}{2} \sqrt{\frac{T}{Ap} } = \frac{1}{2} f[/tex]

Thus, the frequency is reduced to half if its tension is halved and the area of cross-section of the string is doubled.

When the tension is halved and the area of cross section is doubled, the frequency increases by a factor of 1.414.

The frequency of transverse vibration of a stretched string is calculated as follows;

[tex]f = \frac{1}{2l} \sqrt{\frac{T}{\mu} }[/tex]

where;

T is the tension on the stringμ is the mass per unit length

[tex]f = \frac{1}{2l} \sqrt{\frac{T}{\mu} }\\\\f = \frac{1}{2l} \sqrt{\frac{Tl}{m} } \\\\f = \frac{l^2}{2l} \sqrt{\frac{T}{m} } \\\\f = \frac{A}{2l} \sqrt{\frac{T}{m}}[/tex]

when the tension is halved and the area of cross section is doubled, the frequency is calculated as;

[tex]\frac{f_1}{A_1 \sqrt{T_1} } = \frac{f_2}{A_2\sqrt{T_2} } \\\\f_2 = \frac{f_1 A_2\sqrt{T_2}}{A_1 \sqrt{T_1} }\\\\f_2 = \frac{f_1 \times 2A_1\sqrt{0.5T_1} }{\sqrt{T_1} }\\\\f_2 = \frac{f_1 \times 2A_1 \times 0.7071\sqrt{T_1} }{\sqrt{T_1} }\\\\f_2 = 1.414 f_1[/tex]

Thus, when the tension is halved and the area of cross section is doubled, the frequency increases by a factor of 1.414.

Learn more about tension in a string here: https://brainly.com/question/25743940

Satellite technology has allowed us to monitor areas that were once so remote that we had no way of monitoring them. Review the statements and choose the one that best describes how we can use this technology to benefit the environment.

Large ocean liners use satellites to aid in navigation. This type of navigation aid is also used on cruise ships. Using satellites can help these large ships navigate waters during bad storms.

Satellite surveillance can be used to aid in port security. Satellite data can be monitored and evaluated by complex computer systems. These systems can alert officials when something unusual occurs.

Satellite technology allows us to monitor and track the changes in the polar ice sheets. This can help us plan and direct conservation efforts for the animals that depend on polar ice in order to survive.

Satellite surveillance has allowed us to map areas that were previously too remote to observe. This helps developers to locate and choose sites for large resorts.

Answers

Don't worry I will help you pal...

"Satellite technology allows us to monitor and track the changes in the polar ice sheets. This can help us plan and direct conservation efforts for the animals that depend on polar ice in order to survive."

This is the answer because the other answers don't really tackle helping the environment head-on instead it sorta helps society instead. Since we are looking for the ways satellite tech can help the environment and the polar ice caps is a wonderful example of that...we can conclude that the third answer will most likely be the correct answer for this question

Hope this helped you!!!! :)

It was found that ice cream sales decrease significantly as the temperature outside decreases; a very strong relationship was found. What is the most likely correlation coefficient from this hypothetical study

Answers

Answer:

Value closest to 1

Explanation:

It is described from the scenario above that ice cream sales decreases as the outside temperature increases, hence showing a strong relationship between both variables (icream sales and temperature). The correlation Coefficient is a metric used in regression modeling to depict the strength of relationship between two variables, (The dependent and independent variables). Correlation Coefficient ranges from (-1 to +1). With values close to 1 or - 1. Also the positive and negative signs are used to show the type of relationship between the variables. If an increase in variable A leads to a decrease in variable B, then we have negative correlation (-) ; while an increase or decrease in both variables depicts a positive correlation. The most likely correlation Coefficient for the study above will be a positive value which is close to 1 since the relationship is described as strong.

Q011) The Doppler effect a. occurs when the frequency of sound waves received is lower if the wave source is moving toward you than if it's moving away. b. occurs when the pitch of a sound gets lower if the source is receding. c. is the basic explanation for the blue shift of light in our Universe. d. can be applied only to sound waves.

Answers

Answer:

Option (c) is correct.

Explanation:

The apparent change in the frequency of light due to the relative motion between the source and the observer is called Doppler's effect.

When the source is moving towards the observer which is at rest, the apparent frequency increases and if the observer is moving away the frequency of sound decreases.

It occurs for both light and sound.  

So, to explain the blue shift of light in the universe is due to the Doppler's effect of light.

Find the sum. Express the answer in scientific notation. (1.54 x 10^6)+(6.15 x 10^6)​

Answers

Answer:

[tex] { \tt{(1.54 \times {10}^{6}) + (6.15 \times {10}^{6}) }} \\ = { \tt{(1.54 + 6.15) \times {10}^{6} }} \\ = { \tt{7.69 \times {10}^{6} }}[/tex]

Which statement is correct about how the temperature of an object changes?
Group of answer choices

The molecules making up object collide with the molecules of the other and some of the potential energy from a cooler object is transferred to the warmer one.

The molecules making up object collide with the molecules of the other and some of the kinetic energy from a warmer object is transferred to the cooler one.

The molecules making up object collide with the molecules of the other and some of the kinetic energy from a cooler object is transferred to the warmer one.

The molecules making up object collide with the molecules of the other and some of the potential energy from a warmer object is transferred to the cooler one.

Answers

The molecules making up object collide with the molecules of the other and some of the kinetic energy from a warmer object is transferred to the cooler one.

Two blocks, one of mass 5 kg and the other of mass 2 kg, are attached to opposite ends of a light string and hung vertically from a massless, frictionless pulley. Initially the heavier block is held in place a distance 2.5 m above the floor, the lighter block is just touching the floor, and the cord is taut. Then the heavier block is released and comes crashing to the floor while the cord slackens and the lighter block continues to rise. What is the maximum height reached by the lighter block

Answers

Answer:

[tex]H_{max}=3.4m[/tex]

Explanation:

From the question we are told that:

Mass 1 [tex]m_1=5kg[/tex]

Mass  [tex]m_2=2kg[/tex]

Distance above floor [tex]d=2.5m[/tex]

Generally the equation for Conservation of energy is mathematically given by

[tex]0.5m_1v^2+0.5m_2v^2=2mg[/tex]

[tex]0.5m_1v^2+0.5m_2v^2=2g(m_1-m_2)[/tex]

[tex]v^2(0.5*m_1+0.5*m_2)=2*g(m_1-m_2)[/tex]

[tex]v^2(0.5*5+0.5*2) = 2 * 9.8 * (5 - 2)[/tex]

[tex]v^2=\frac{58.8}{3.5}[/tex]

[tex]v=4.1m/s[/tex]

Generally the equation for The maximum height of lighter block  is mathematically given by

[tex]H_{max}=d+\frac{v^2}{2g}[/tex]

[tex]H_{max}=2.5+\frac{16.2}{2*9.81}[/tex]

[tex]H_{max}=3.4m[/tex]

Potential Energy (kJ)
Reaction Progress →
A) Does this graph represent an endothermic or exothermic reaction? Explain your answer. (2 points) HELP PLEASE ITS URGENT !!

Answers

Answer:

Endothermic reaction

Explanation:

(a) Endothermic reaction: These are reactions that absorb heat from the surrounding during a chemical reaction. The enthalpy change for endothermic reaction is always positive,  and the energy level of the product is higher than that of the reactant

(b) Exothermic reaction: These are reactions that release heat to the surrounding during chemical reaction. The enthalpy change for exothermic reaction is always positive, and the energy level of the product is lower than that of the reactant.

From the diagram in the question,

Since the energy level of the product is higher than that of the reactant then the reaction is an endothermic reaction and as such, ΔH is positive

Compare the vertical and horizontal components of velocity for a ball launched at an angle on a level surface. How do the vertical and horizontal components of the ball's velocities change as it travels through the air?

Answers

Answer:

horizontal velocity remaing constan thorough out the motion but the vertical motion's velocity changes due to the gravity acting on it.

for everl 1 second the velocity decreases by 9.8 that is the gravity

Using diagram 1.1 and diagram 1.2, compare the number of turn of the coils, the pattern of the iron fillings and the angle of deflection of the ammeter pointer

Answers

Answer:

The number of turns in the second coil is more than the coil 1.

Explanation:

The magnetic field lines are the imaginary path on which an isolated north pole moves if it is free to do so.

The tangent at any point to the magnetic field line, gives the direction of magnetic field at that point.

More be the crowd ness of magnetic field lines more is the strength of magnetic field.

Here the crowd ness of magnetic field lines is more in figure 2 , so the magnetic filed in figure 2 is more than 1. It shows that the number of turns in the second coil is more than the 1 and also the current in the coil 2 is more than 1 .

A ball tied on a string rotates in a circular path as shown above. The only forces acting on the ball at any point are the weight and of the string. What is the equation for the net centripetal force at point C?

Answers

Answer:

the third one T-W

Explanation:

the direction of the Tension and weight are opposite

En la figura, la tensión desarrollada en cada
cuerda está dada por los dinamómetros:
T1=8 N y T2=6 N, y el ángulo de inclinación
de la primera cuerda es de 45°. Determine la
masa de la caja que debe sostener y el
ángulo con respecto a la horizontal.

Answers

Answer:

Parte A

El ángulo con respecto al horizonte, de la segunda cuerda es de aproximadamente 19,47°

Parte B

La masa de la caja que se va a sostener es de aproximadamente 0,7808 kg.

Explanation:

Parte A

Los parámetros dados son;

La tensión en la cuerda, T₁ = 8 N

La tensión en la cuerda, T₂ = 6 N

El ángulo de inclinación de la primera cuerda con la horizontal, θ₁ = 45°

Sea θ₂ el ángulo de inclinación de la segunda cuerda, obtenemos;

T₁·cos (θ₁) = T₂·cos (θ₂)

∴ 8 N × cos (45°) = 6 N × cos (θ₂)

cos (θ₂) = 8 N × cos (45°) / (6 N) = (√2)/2 × (4/3) = (2·√2)/3

θ₂ = arcos ((2·√2) / 3) ≈ 19,47°

El ángulo con respecto al horizonte, de la segunda cuerda, θ₂ ≈ 19,47°

Parte B

El peso de la caja, W = T₁·sin (θ₁) + T₂·sin (θ₂)

∴ W = 8 N × sen (45 °) + 6 N × sen (19,47 °) ≈ 7,66 N

El peso de la caja que se va a sostener, W ≈ 7,66 N

La masa de la caja que se va a sostener, m ≈ 7,66 N / (9,81 m/s²) ≈ 0,7808 kg

A gas is enclosed in a confainer fitted with a piston of cross sectional area 0.10 the pressureof the gas is maintained in 8000 when hat is slowlh transferred the piston is pushed up through a distance of 4.0cm If 42j of heat is transferred to the system during expansion wht is the change im internal energy of th system

Answers

Answer:

10 Joule

Explanation:

The solution and answer are well written in the Pic above.

Please help me with this!!!​

Answers

Answer:

Its all about figuring out what numbers you times by

Explanation:

soooooooooo just x the numbers until you get it right, and i'm guessing your in a school soooo ask your teacher aswell :)

. What is a normal force? It acts against an object slowing it down. It acts perpendicular to an object. It acts with an object adding to its speed. It acts parallel to an object.

Answers

Answer:

Explanation:

This is basically asking you what the definition of Normal force is. Normal force is the force that pushes back against the weight of something that is sitting (or standing or lying) perpendicular to it. That's why, when you stand on a floor you don't crash through the floor OR go shooting up into space. The Normal force is equal but opposite to your weight. The floor exerts the normal force (pushing up and is positive) while your weight is opposing it (pushing down and is negative.)  Perpendicular is the key word here, I believe.

A normal force acts perpendicular to an object. It is the force exerted by a surface to support the weight of an object resting on it.

The normal force acting against an object slowing it down or acting with an object adding to its speed, are not accurate descriptions of the normal force. The normal force primarily deals with the support of an object on a surface and is directed perpendicular to that surface.

Normal force is the force that pushes back against the weight of something that is sitting (or standing or lying) perpendicular to it. That's why, when you stand on a floor you don't crash through the floor OR go shooting up into space. The Normal force is equal but opposite to your weight. The floor exerts the normal force (pushing up and is positive) while your weight is opposing it (pushing down and is negative.)

Therefore, A normal force acts perpendicular to an object. It is the force exerted by a surface to support the weight of an object resting on it.

To know more about the normal force:

https://brainly.com/question/13622356

#SPJ3

Which forms of energy determine temperature: translational kinetic energy, rotational kinetic energy, vibrational kinetic energy, or all of these

Answers

oh this question seems to be difficult I don't think I can answer this

A plane is flying a circular path at a speed of 55.0 m/ s, with a radius of 18.3 m. The centripetal force needed to maintain this motion is 3000 N. What is the plane's mass?

Answers

The plane has a centripetal acceleration a of

a = v ²/r

where v is the plane's tangential speed and r is the radius of the circle. By Newton's second law,

F = mv ²/r

Solve for the mass m :

m = Fr/v ² = (3000 N) (18.3 m) / (55.0 m/s)² ≈ 18.1 kg

In which region is there most likely to be a volcano
A
B
C
D

Answers

Most volcanoes are found along a belt, called the “Ring of Fire” that encircles the Pacific Ocean. Some volcanoes, like those that form the Hawaiian Islands, occur in the interior of plates at areas called “hot spots.”
So D is your answer

Please help it's for a test.

A car of mass 1000kg is traveling 30m/s

a) What is the kinetic energy?

b) How high will it have to travel up a hill to have the same potential as kinetic energy as this speed? Remember Ep-Ek

Answers

Answer:

Explanation:

[tex]KE=\frac{1}{2}mv^2[/tex] so filling in:

[tex]KE=\frac{1}{2}(1000)(30)^2[/tex] so to 2 sig figs (which is actually not accurate, but oh well...)

KE = 450000 J

If we want to find out how high it will have to travel up a hill so that its PE is the same as the KE at this speed, we set the value for KE = to PE:

450000 = (1000)(9.8)h so

[tex]h=\frac{450000}{(1000)(9.8)}=45.9m[/tex]

1.how would you calculate the atomic mass of an atom of silver (at)?
2.the element chlorine (CI) has 17 protons and 17 electrons. What happens to an atom of chlorine (CI) if it gains an electron?
3. How does an atom differ from a molecule?
4. How do protons, neutrons, and electrons differ?
5. The element lithium (Li) has 3 protons and 3 electrons. The element fluorine (F) has 9 protons and 9 electrons. An atom of the element lithium (Li) transfers an electron to an atom of the element fluorine (F). Which type of bond results between The atoms, and what happens to the charges in each of the atoms?
6. Why do the minerals graphite and diamond look different even though they’re made from the same element, carbon (c)?

Answers

Answer:

1. atomic mass of silver 108

2. 18 electrons

3.an atom is the smallest particle of a substance that can exist by itself.

molecules are groups of atom

Explanation:

1. periodics table

2. gains electron, becomes negative

Answer:

To determine the atomic mass of silver, or any other element, add the number of protons and the number of neutrons together.

If a chlorine atom gains an electron, it will have an unequal number of protons and electrons, which makes it an ion. Because electrons are negatively charged, the ion will be negatively charged, also called an anion.

An atom is the smallest component of an element that retains all of the chemical properties of that element. A molecule is two or more atoms that have bonded together.

Protons and neutrons are found in the nucleus of an atom, while electrons are found in the area surrounding the nucleus of an atom. Protons have a positive charge, electrons have a negative charge, and neutrons have no charge.

Because the lithium atom loses a negatively charged electron, it becomes a positively charged ion, or cation. Because the fluorine gains a negatively charged electron, it becomes a negatively charged ion, or anion. A bond between an anion and a cation is an ionic bond.

Graphite and diamond look different because the carbon atoms bond to one another in different ways in the two minerals. This gives each mineral a unique lattice structure and, as a result, a different physical appearance.

Based on what you have read provide two positives and two negatives the Suarez family would face if they switch to organic farming

Answers

Hi, you did not enter the text about the Suarez family, which makes it impossible for this question to be answered accurately. However, from the context of your question, it is possible to see that you want to know two positive and negative points that the Suarez family would observe when starting a planting of organic agriculture.

Among the negative points, we can say that organic agriculture has a high cost, as the techniques used in it require a greater number of resources, which can make not only the service more expensive, but also the product. A second negative point is that the techniques used in organic agriculture are more difficult than the techniques used in conventional agriculture, since all management of organic crops must be carried out without the application of chemical products.

Among the positive points, we can say that the growing number of consumers of organic products can increase the profit that the family will have from the sale of these products. In addition, the family will have healthier, less polluted and more productive land.

Answer:

Sample response: Organic farming would have higher costs, and would be more complex than conventional farming. However, the Suarez family could charge a higher price for organic produce. This type of farming also would be better for the land.

Explanation:

what is the least count of screw gauge and vernier calliper (9th grade) please help! ​

Answers

The least count is the smallest unit of measurement which an instrument can take accurately

Help me and I'll make u Brainliest and follow u

Answers

26. D. crushing the sugar cube and dissolving it in water.

27. A. atom

28. B. molecule

29. B. plum pudding model of Joseph John Thomson

30. B. He used cathode ray tubes which showed that all atoms contain tiny negatively charged subatomic particles or electrons

31. D. protons and neutrons are relatively heavier than electrons.

¿Qué diferencia una magnitud fundamental de una derivada?

Answers

Answer:

Explanation:

Una magnitud fundamental es aquella que se define por si misma y es independiente de las demás (masa, tiempo, longitud, etc.). magnitud derivada. Una magnitud derivada es aquella que se obtiene mediante expresiones matemáticas a partir de las magnitudes fundamentales (densidad, superficie, velocidad).

Una magnitud fundamental es aquella que se define por si misma y es independiente de las demás (masa, tiempo, longitud, etc.). magnitud derivada. Una magnitud derivada es aquella que se obtiene mediante expresiones matemáticas a partir de las magnitudes fundamentales (densidad, superficie, velocidad).


A car is moving at 30km/h. What is its speed in m/s? Give your answer to 2 significant figures.

Answers

Explanation is in the attachment

hope it is helpful to you

What is Unit and standard unit?​

Answers

Answer:

The standard quantity with which we carry out the measurement of any physical quantity of the same kind is called a unit.

Un alambre de plástico, aislante y recto mide 10 cm de longitud y tiene una densidad de carga de +150 nC/m, distribuidos de manera uniforme por toda su longitud. Se encuentra sobre una mesa horizontal. A) Encuentre la magnitud y la dirección del campo eléctrico que produce este alambre en un punto que está 8 cm directamente arriba de su punto medio. B) Si el alambre ahora se dobla para formar un círculo que se coloca aplanado sobre la mesa, calcule la magnitud y la dirección del campo eléctrico que produce en un punto que se encuentra 6 cm directamente arriba de su centro.

Answers

Answer:

English only

Explanation:

When solving problems related to Electric Fields, care must be taken about symmetries. In our particular case when we take a look to at the drawings of the attached file, we realize:

1.-By symmetry each dx associated at a, has an opposite dx with point b as reference. The respective dE ( the charge is uniform ) is the same, as the charge of the wire is positive the force and the Field on a test charge (+) located at h will be upward, therefore the components dEx will cancel each other and the Electric Field becomes E = Ey = ∫ 2×dE× cosθ

The solutions:

A) Ey = 4623 N/C

B) Ey = 19.34 N/C

E = Ey = ∫ 2×dE× cosθ

Here     cosθ   = h/ d   ⇒  cosθ = h/√h² + x²      dE = K× dQ / d²

d² = h² + x²

k = 8.9 ×10⁹ Nm²C⁻²  ;   dQ = λ×dx     λ = 150×10⁻⁹ C    h = 0.08 m

Then by substitution

Ey =  2 ∫[K× λ×dx/ (h² + x²) ] × h / √h² + x²

reordering that equation:

Ey = 2×K×λ×h ∫ dx / [√ ( h² + x² ) ]³          (2)

To solve the integral we make use of a change of variables

x = h × tanα     then   x² = h² ×tan²α   and  dx = h× sec²α dα

plugging that values in equation (2)

Ey  =  2×K×λ×h ∫  h× sec²α× dα / [√ ( h² + h²tan²α)]³

Ey  = 2×K×λ×h² ∫ sec²α× dα / [ h × √ (1 + tan²α)]³            1 + tan²α = sec²α

Ey = 2×K×λ×h²× ∫ (sec²α / h³× sec³α )×dα

Ey = 2×K×λ/h × ∫ ( 1 / secα dα

Ey = 2×K×λ/h × sinα             now we αneed to come back to our original variables:

as   x = h × tanα         tanα = x/h   then x is the opposite leg in a right triangle  and h the adjacent one then the hypothenuse is √ (h² + x²)         then    sin α = x/ √ (h² + x²)      

Ey = 2×K×λ/h × x/ √ (h² + x²) |₀⁰°⁰⁵

Ey  = 2×8.9×10⁹× 150×10⁻⁹× 5×10⁻²/8× 10⁻²× √ 10⁻² ( 8 + 5 )   N/C

Ey = 4623 N/C

To answer the second question again we will make use of symmetries if you look at drawing ( Figure 2 ) you see that again the components in direction of x-axis cancel each other and the components in y-axis direction will add. Then

Ey = ∫ dE× cosθ

following the same procedure  we will find:

Ey = ∫ [K×λ × dl/d²] × h/ d

The importan point here is that the radius of the circle is

2×π×r = 0.01      ( the length of the wire)  ⇒  r = 0.16×10⁻² m

And we need to take into account that the integration is over the circle and the length of the circle is 0.01 m or ××2×π×r. All other factors are constant. Then by substitution

Ey = [K×λ ×h×  / ( √ r² + h²)³ ] × 10⁻²    N/C

Ey = 8.9 × 10⁹ × 150× 10⁻⁹ × 6× 10⁻² × 10⁻² / √ 10⁻² ( 0.16 + 6)

Ey = 0.8 × 10² / 6

Ey = 19.34 N/C

An instrument rated pilot is planning a flight under IFR on July 10, this year. Before conducting the flight, the pilot must have

Answers

Answer: See explanation

Explanation:

From the information given, we are informed that an instrument rated pilot is planning a flight under IFR on July 10, this year.

It should be noted that before conducting the flight, the pilot must have performed and logged the prescribed tasks and repetitions that are required for instrument currency no earlier than January, 10 for the year.

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