the amount of work (in j) an external agent must do to stretch the spring 7.40 cm from its unstretched position (in joule)

The total work done on a particle is given by the formula:

W = (1/2)mvf^2 - (1/2)mvi^2

where m is the mass of the particle, vi is the initial velocity, and vf is the final velocity.

For vi = 5 m/s and vf = 2 m/s, the final velocity is less than the initial velocity, so the total work is positive.

For vi = -2 m/s and vf = -5 m/s, the final velocity is less than the initial velocity, so the total work is positive.

For vi = -5 m/s and vf = 2 m/s, the final velocity is greater than the initial velocity, so the total work is negative.

For vi = 5 m/s and vf = -2 m/s, the final velocity is greater than the initial velocity, so the total work is negative.

For vi = -5 m/s and vf = -2 m/s, the final velocity is less than the initial velocity, so the total work is positive.

Therefore, the total work done on the particle is positive for vi = 5 m/s and vf = 2 m/s, and for vi = -2 m/s and vf = -5 m/s.

In order for work to be done, there must be a displacement of the object in the direction of the force applied. If the force and displacement are perpendicular, then no work is done.

Work can be positive, negative, or zero, depending on the direction of the force and the displacement. Positive work is done when the force and the displacement are in the same direction, negative work is done when they are in opposite directions, and zero work is done when there is no displacement or when the force and displacement are perpendicular.

Work is a transfer of energy, and as such it can change the kinetic energy, potential energy, or both of an object.

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Answer:

in image

Explanation:

I don't think so it helped but through this you can do the question exactly like this ( in this way) ...

The speed of sound is found out to be 349.4 ms⁻¹ from the frequency of the seventh resonance heard when the water level is 217.75 cm below the top of the tube.

Frequency of wave:

v = nλ

where, v = speed of sound, n = frequency, λ = wavelength

Speed of sound:

v = frequency n × wavelength λ

Frequency, n = v/λ

Wavelength, λ = v/n

The 7th resonance frequency of the tuning fork is given by:

n = 7 × f

where, f is the frequency of the tuning fork

Speed of sound, v = nλ

Speed of sound, v = 7fλ

Speed of sound, v = 7 × 256 Hz × λ

λ = 1.3671 m

Distance travelled by the sound wave in the water column is L = h + l

where, h = length of the air column and l = length of water column where the resonance was heard.

L = h + l

L = 217.75 cm + 50 cm

L = 267.75 cm = 2.6775 m

Length of the air column, h = L - l

where, l = length of water column where the resonance was heard.

h = 2.6775 m - 0.5 m

h = 2.1775 m

Wavelength of sound wave in air column, λ₁ = 4h

λ₁ = 4 × 2.1775 m

λ₁ = 8.71 m

Frequency of the sound wave in air column is given by:

n = v/λ₁

n = 349.4 ms⁻¹ / 8.71 m

n = 40.112 Hz

The 7th resonance frequency of the tuning fork is given by:

n = 7 × f

40.112 Hz = 7 × f

Frequency of the tuning fork, f = 5.73 Hz.

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ans= train Q

Sol= 4.5×60= 270

6×60= 360

270÷180=1.5

360÷270=1.3...

1.3... <1.5

The velocity of wreckage immediately after impact = 9.68 m/s and the compass heading is 45 deg (for the second answer).

Mass of 1950 kg Oldsmobile = 1950 kg

Velocity of Oldsmobile = 15.4 m/s

Mass of a truck hauling animal feed = 3992 kg

Velocity of a truck hauling animal feed = 9.9 m/s

Conservation of Momentum Formula Used,

Momentum before collision = Momentum after collision(m1 × v1) + (m2 × v2) = (m1 + m2) × V'

Calculation for Momentum before Collision = (m1 × v1) + (m2 × v2)

Momentum before Collision = (1950 kg × 15.4 m/s) + (3992 kg × 9.9 m/s)

Momentum before Collision = 30129 + 39560.8

Momentum before Collision = 69689.8 kg-m/s

Let V' be the velocity of the wreckage immediately after the impact.

Velocity after Collision is V'

Calculation for Velocity after Collision = (m1 × v1) + (m2 × v2) / (m1 + m2)V'

= (1950 × 15.4) + (3992 × 9.9) / (1950 + 3992)V'

= 57606.8 / 5942V'

= 9.68 m/s

Given, the 1950 kg car was traveling East on Saginaw Street which means the wreckage was moving North-East (45 degrees)

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A P-N-P transistor is turned on when the base is negative with respect to the emitter.

The operation of a P-N-P transistor is based on the principle of a semiconductor diode. When a small current is applied to the base, it causes a larger current to flow through the emitter and collector. This is because the base-emitter junction is forward-biased, allowing electrons to flow from the emitter to the base. At the same time, the collector-base junction is reverse-biased, allowing holes to flow from the base to the collector.

This flow of electrons and holes produces a current gain. The amount of current gain depends on the type of transistor and the amount of current applied to the base.

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The energy needed to heat the water and the copper tank to 55°C is 25,083,080 J.

Q = mCΔT

m = 150 kg (mass of water)

C = 4.18 J/g°C (specific heat capacity of water)

ΔT = 55°C - 15°C = 40°C (change in temperature)

Using the formula, we get:

[tex]Q_{water}[/tex] = mCΔT

[tex]Q_{water}[/tex] = (150 kg) x (4.18 J/g°C) x (40°C)

[tex]Q_{water}[/tex] = 25,080,000 J

m = 20 kg (mass of tank)

C = 0.385 J/g°C (specific heat capacity of copper)

ΔT = 55°C - 15°C = 40°C (change in temperature)

Using the formula, we get:

[tex]Q_{tank}[/tex] = mCΔT

[tex]Q_{tank}[/tex] = (20 kg) x (0.385 J/g°C) x (40°C)

[tex]Q_{tank}[/tex]= 3080 J

Finally, we can add the two energies together to get the total energy needed:

[tex]Q_{total}[/tex] = [tex]Q_{water}[/tex] [tex]+[/tex] [tex]Q_{tank}[/tex]

[tex]Q_{total}[/tex] [tex]= 25,080,000 J + 3080 J[/tex]

[tex]Q_{total}[/tex] [tex]= 25,083,080 J[/tex]

Energy is a fundamental concept that refers to the ability of a physical system to do work or cause a change. It is a scalar quantity that is measured in units of joules (J) in the International System of Units (SI). According to the law of conservation of energy, energy cannot be created or destroyed, but it can be transformed from one form to another. This means that the total amount of energy in a closed system remains constant.

Energy is a crucial concept in many areas of physics, including mechanics, thermodynamics, and electromagnetism. Understanding energy is essential for understanding how the physical world works, and it has numerous applications in technology and everyday life, from powering our homes and vehicles to the production of food and the functioning of our bodies.

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The correct statement about the relationship between the two forms of Newton's second law (Fnet = dp/dt and Fnet = m.a) is option D "Fnet = m.a reduces to Fnet = dp/dt if the momentum of the object does not change with time.

Newton's second law of motion states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. In other words, Fnet = m.a, where Fnet is the net force acting on an object, m is its mass, and a is its acceleration. This law can also be written as Fnet = dp/dt, where dp/dt is the rate of change of momentum with time.

Since momentum is the product of mass and velocity, it can be rewritten as dp/dt = m.dv/dt + v.dm/dt, where v is the velocity of the object. If the mass of the object remains constant over time, then v.dm/dt is zero and dp/dt reduces to m.dv/dt, which is equal to Fnet.

Therefore, Fnet = dp/dt reduces to Fnet = m.a if the object's acceleration does not change with time. If the momentum of the object does not change with time, then dp/dt is zero, and Fnet = dp/dt reduces to zero, which means that Fnet = m.a is also zero. Therefore, Fnet = m.a reduces to Fnet = dp/dt if the momentum of the object does not change with time.

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The Planck constant is 1.41 x 10-34 Js, the work function Φ for sodium is 2.39 eV, and the cutoff wavelength λ₀​ for sodium is 590 nm.

Using the data, we can calculate the Planck constant, work function, and cutoff wavelength for sodium.

To start, we use the formula E = hc/λ, where E is the stopping potential, h is the Planck constant, c is the speed of light, and λ is the wavelength.

To find the Planck constant, we rearrange the equation to get h = Eλ/c.

Plugging in the values from the data, we get

h = (1.85 V)(300 nm)/(3 x 108 m/s)

= 1.41 x 10-34 Js.

Now to find the work function Φ for sodium, we use the equation Φ = hc/λ - E.

Plugging in the values from the data, we get

Φ = (1.41 x 10-34 Js)(3 x 108 m/s)/(400 nm) - 0.82 V = 2.39 eV.

Finally, to find the cutoff wavelength λ₀ for sodium, we use the equation λ₀​ = hc/Φ.

Plugging in the values from the data, we get

λ₀​ = (1.41 x 10-34 Js)(3 x 108 m/s)/2.39 eV = 590 nm.

Therefore, the Planck constant is 1.41 x 10-34 Js, the work function Φ for sodium is 2.39 eV, and the cutoff wavelength λ₀ for sodium is 590 nm.

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The proton accelerates from rest in a uniform electric field of 600 n/c. In order to find the time interval it takes for the proton to reach a speed of 1.50 mm/s.

We need to use the equation v = v₀ + at, where v is the final velocity, v₀ is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time interval. The acceleration of the proton in the electric field is a = E/m, where E is the electric field and m is the mass of the proton. Substituting these values into the equation gives us:

1.50 mm/s = 0 + (600 n/c/1.67 x 10⁻²⁷ kg) x t

Rearranging the equation and solving for t gives us the time interval:
t = 1.50 mm/s/(600 n/c/1.67 x 10⁻²⁷ kg)

t = 8.33 x 10⁻¹³ s

t = 8.33 ms

Therefore, it takes the proton 8.33 ms to accelerate from rest to a speed of 1.50 mm/s in the uniform electric field of 600 n/c.

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The tension in the right-hand side wire is 6525 N.

Given:

To find: Tension in the right-hand side wireWe know that the sum of forces acting in a vertical direction should be equal to 0 as there is no acceleration in the vertical direction. ∑Fv = 0In the horizontal direction, there are no forces acting on the system.

∑Fh = 0Now considering forces in the vertical direction: T1 + T2 = (Weight of scaffold + Weight of the box) gT1 + T2 = (180 + 580) x 9.8T1 + T2 = 7644 N1. From the diagram, we can see that the box is nearer to the left side. Hence, the tension force in the left wire is greater than the tension force in the right wire.

T1 > T22. Let's take moments about the right end of the scaffold as shown in the figure below.

Now, we can substitute the value of T2 in equation (1):

To find T2, we can substitute the value of T1 in equation (2):

Therefore, the tension in the right-hand side wire is 6525 N.

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The Kuiper belt is a disk-like region between the outer planets and the Oort cloud. Thus, option A is correct

The Kuiper belt, also known as the trans-Neptunian region, is a doughnut-shaped region of space beyond Neptune that is home to an estimated 100,000 tiny, icy objects.

It is named after Dutch-American astronomer Gerard Kuiper, who first proposed its existence in 1951.

The belt ranges in distance from 30 to 50 astronomical units (AU) from the Sun, which is about 2.8 to 4.7 billion miles away.

The Kuiper belt objects are believed to be remnants from the formation of the solar system. They are small and mostly made up of ice and dust, similar to comets.

Some Kuiper belt objects, such as Pluto and Eris, are classified as dwarf planets.

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If the object in motion has some magnetic properties or contains a magnet, we can use another magnet to change its direction of motion by exerting a force on it through magnetic interaction. This principle is known as the Lorentz force.

Here's how we can set up the experiment:

Take a magnet and place it on a flat surface.

Take another magnet or the object with magnetic properties that is in motion.

Hold the magnet or the object in your hand and bring it close to the stationary magnet without touching it.

Move the magnet or the object towards the stationary magnet and observe its behavior.

If the magnet or the object has the same polarity as the stationary magnet, they will repel each other, and the motion of the object will be deflected in a direction away from the stationary magnet. If the magnet or the object has opposite polarity to the stationary magnet, they will attract each other, and the motion of the object will be deflected in a direction towards the stationary magnet.

Here's a diagram to help you visualize the setup:

                 N   S          N   S

       __________    __________

      |                       |  |                     |

      |   M1               |  |           M2     |

      |__________|  |__________|

              ( )                             ( )

               |                               |

        Motion              Stationary

        Object                 Magnet

In this diagram, M1 represents the motion object or magnet, and M2 represents the stationary magnet. The N and S represent the North and South poles of the magnets. The arrows indicate the direction of motion and the direction of the magnetic field.

As we move M1 towards M2, the magnetic interaction will exert a force on M1, causing it to change its direction of motion. The direction of deflection will depend on the polarity of the magnets.

Note: It's important to keep in mind that the magnetic force is only one of the many factors that can affect the motion of an object. Other factors such as friction, air resistance, and gravitational forces can also play a significant role.

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The point at which the warning will do no good is 7.50 m above the man's ears.

When a water-filled balloon is released from rest at a height of 10.0 m above the ears of a man, the warning will do no good if shouted after the balloon reaches a certain point. Assuming that the air temperature is 20°C and ignoring the effect of air resistance, this point is 7.50 m above the man's ears.

The vertical displacement (d) can be determined using the equation [tex]d = \frac{vf2}{2g}[/tex], where vf is the final velocity and g is the acceleration due to gravity (9.81 m/s2).

Since the balloon was released from rest, the initial velocity is 0 m/s. Therefore, [tex]d = \frac{02 }{ 2} (\frac{9.81 m}{s2} ) = 0[/tex]m. Since the initial height was 10.0 m, the final height is 10.0 m + 0 m = 10.0 m.

The point at which the warning will do no good is 7.50 m above the man's ears, so the final height of the balloon must be 10.0 m - 7.50 m = 2.50 m.

Therefore, the point at which the warning will do no good is 7.50 m above the man's ears.

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Explanation:

Planets closer to the sun will appear to transit from time to time

   = 2      Venus and Mercury     ( I suppose you could include the Moon..an eclipse ....haha)

All of the planets further from the sun than earth will not transit

Potentially ALL of the planets could transit the sun (earth included)  if observed outside solar system   HOWEVER if you are not observing from near the orbital plane of

the planets NONE of them would transit

For maximum transits, the planets should all be in the same orbital plane and the observer should be very close to this plane also.

The correct answer is option D.2 years

According to Kepler's Third Law of Planetary Motion, T² is proportional to r³, where T is the period of revolution of the planet and r is the distance between the planet and the star.

In order to solve for T,  

AU = 1

Astronomical Unit = the average distance between the Earth and the Sun = 149.6 million kilometres

Therefore, the planet is orbiting at a distance of 149.6 million kilometres from the star.

Substituting the values of r and solving for

T².T² ∝ r³T² ∝ (149.6)³T²

= (149.6)³T²

= 3.522 x 10¹²T

= √3.522 x 10^¹²T

= 1.87 x 10⁶ seconds

T = 31,100 minutes

T = 518 hours

T = 21.6 days

T = 2 years

Therefore, the orbital period of the planet with twice the mass of Earth orbiting at a distance of 1 AU from a star with the same mass as the Sun is 2 years.

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The change in the distance between the friends changing when the distance between them is 200 m is 7.85m.

Consider a right-angled triangle with the radius of the circular track as one side of the right angle. Then the other two sides are the distance covered by the runner (in a single lap) and the distance between the runner and his friend.

Since the radius is perpendicular to the line connecting the friend and the center of the track, we can call it the hypotenuse of the triangle.

Let x be the distance between the runner and his friend. We are given that x = 200 m.Using the Pythagorean theorem, we can find the distance covered by the runner in a single lap of the track.

e can now differentiate the above expression with respect to time to find the rate of change of the distance covered by the runner (this will also be the rate of change of the distance between the runner and his friend).Hence,

2x(dx/dt) = 2 (distance covered by runner)(d(distance covered by runner)/dt)

dx/dt = (distance covered by runner)

(d(distance covered by runner)/dt) / x

Substituting x = 200 m and d(distance covered by runner)/dt = 7 m/s, we get:

dx/dt = (223.6 m)(7 m/s) / 200 m = 7.85 m/s.

Rounding off to two decimal places, we get:

dx/dt = 7.85 m/s.

Therefore, the answer is 7.85.



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As a positively charged glass rod is brought near the knob of the electroscope, the separation of the leaves will increase.

What is Charge?

Charge is a fundamental property of matter that determines how objects interact with each other through the electromagnetic force. It is a physical property that can be positive or negative and can be measured in coulombs (C).

This is because the positively charged glass rod will induce a negative charge on the metal knob of the electroscope. The negative charges will repel the electrons in the metal leaves, causing them to move away from each other and increasing their separation. The greater the amount of charge on the glass rod, the greater the separation between the leaves will be.

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A set of beliefs can be said to be pseudoscientific if it lacks one or more of the three features of science and empirical evidence.

Pseudoscience is a set of claims, beliefs, or practices that are presented as scientific but lack empirical evidence, are inconsistent with scientific facts, or are based on incorrect assumptions. Pseudoscience can be seen in a variety of fields, including medicine, psychology, and the paranormal.

Science is defined by three characteristics: empiricism, theory construction, and parsimony or simplicity. Empiricism is the use of evidence to establish scientific facts, while theory construction is the development of a conceptual framework that explains and predicts these facts.

Parsimony is the principle that the simplest explanation is the best one, meaning that theories should not include unnecessary assumptions or complexity. However, pseudoscientific practices often lack one or more of these characteristics. They may fail to use empirical evidence or instead rely on anecdotal evidence or personal experience. Their theories may not be testable or may be inconsistent with established scientific facts. They may also be unnecessarily complex or based on assumptions that have no basis in reality.

Hence, a set of beliefs can be said to be pseudoscientific if it lacks one or more of the three features of science and empirical evidence.

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Answer:

✓ 1. radio 2. infrared 3. orange 4. green 5. ultraviolet

Explanation:

The magnitude of the magnetic force experienced by proton 2 will be less than the force experienced by proton 1. This is because the force experienced by a proton is related to the direction of its motion relative to the direction of the magnetic field.

As proton 1 is travelling from east to west, its motion is parallel to the magnetic field, which is aligned in a north-south direction in the continental United States. This means that proton 1 will experience a greater force due to the magnetic field than proton 2, which is travelling in a north-south direction and thus has a motion perpendicular to the magnetic field.
To understand this more clearly, we can consider the equation for the magnetic force:

F = qvB sin θ.

In this equation, the force experienced by a particle is related to the charge (q), velocity (v), and magnetic field strength (B). The sine of the angle between the velocity and magnetic field (θ) is also important as it determines how much of the force will be experienced by the particle. As proton 1's motion is parallel to the magnetic field, it will experience the full force due to the magnetic field, whereas proton 2's motion is perpendicular to the magnetic field and it will only experience a fraction of the force. The magnitude of the force experienced by proton 2 will be lower than the force experienced by proton 1.

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The acceleration of the cart at this instant is calculated to be 5.17 m/s² to the right.

Newton's second law explains that acceleration of any object is directly related to net force and inversely related to the mass.

To determine the acceleration of the cart, we need to calculate the net force acting on it.

The net force is the vector sum of the two forces:

Net force = Force a + Force b = 77 N to the right - 15 N to the left = 62 N to the right

Using Newton's second law, F = ma, where F is the net force and m is the mass of the cart, we can calculate the acceleration:

a = F/m = 62 N / 12 kg = 5.17 m/s

Therefore, the acceleration of the cart at this instant is 5.17 m/s² to the right.

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Star A's light will take longer to reach us.

The power dissipation in the ion channel is 4.9 mW given that the potential difference across the ion channel is 70 mv

The power dissipated by a resistor is given by the formula:P = V² / RwhereP = PowerV = VoltageR = Resistance

The power dissipated in the ion channel is unknown. However, we can consider the ion channel to have a resistance of 1 Ω. This is because the resistance of an ion channel is very small and close to zero. So, we can assume the resistance of the ion channel as 1 Ω.As we know the potential difference across the ion channel, we can use the above formula to find the power dissipated in the ion channel.P = (70 mV)² / 1 ΩP = 0.0049 W = 4.9 mW

Therefore, the power dissipation in the ion channel is 4.9 mW.

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The speed of the sports car at impact when kinetic friction between tires and road is 0.80 is 15.55 m/s.

It is given that Mass of sports car, ms = 910 kg, Mass of SUV, mSUV = 2100 kg, and Initial velocity of sports car, us = ?, Final velocity of sports car, v = 0, Initial velocity of SUV, uSUV = 0, Final velocity of SUV, vSUV = 0, and Coefficient of kinetic friction, μk = 0.80. Distance covered before stopping, s = 2.5 m.

We know that the total momentum of the system remains conserved, we can write:

ms * us + mSUV * uSUV = (ms + mSUV) * v

Thus,

ms * us = (ms + mSUV) * v

The speed of the sports car at impact when kinetic friction between tires and road is 0.80 is 15.55 m/s.

It is given that Mass of sports car, ms = 910 kg, Mass of SUV, mSUV = 2100 kg, and Initial velocity of sports car, us = ?, Final velocity of sports car, v = 0, Initial velocity of SUV, uSUV = 0, Final velocity of SUV, vSUV = 0, and Coefficient of kinetic friction, μk = 0.80. Distance covered before stopping, s = 2.5 m.

We know that the total momentum of the system remains conserved, we can write:

ms * us + mSUV * uSUV = (ms + mSUV) * v

Thus,

ms * us = (ms + mSUV) * v

Since the two cars skid together, the frictional force provides the reduction to the motion of the cars. The reduction force F = μk * N where N is the normal force acting on the cars, N = (ms + mSUV) * g where g is the acceleration due to gravity, g = 9.8 m/s².

We have to find the speed of the sports car at impact i.e. us. So, using the equations of motion with constant acceleration, we can write:

us² - 2 * μk * (ms + mSUV) * g * s / (ms + mSUV) = v²

us² = 2 * μk * (ms + mSUV) * g * s / ms

us = sqrt [2 * 0.80 * (910 + 2100) * 9.8 * 2.5 / 910]

us = 15.55 m/s

Therefore, the speed of the sports car at impact is 15.55 m/s.

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Answer:

7500Joules

Explanation:

workdone= force × Distance

The correct option is D; The cart moved at a constant velocity of 0.5m/s for the entire 7 seconds.

Constant acceleration is represented as a horizontal line on the acceleration graph. The slope of the velocity graph represents the acceleration. On the velocity graph, constant acceleration Equals constant slope = straight line.

Acceleration is represented in a velocity-time graph by the slope, or steepness, of the graph line. If the line slopes upward, as seen in the figure between 0 and 4 seconds, velocity increases, and acceleration is positive. The velocity-time graph will be a curve when the acceleration increases with time, as anticipated by the equation: v = u + at.

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"The required angle Ф between the filter's polarizing axis and the direction of polarization of light necessary to increase the ratio of the clouds' intensity to that of the blue sky so that it is three times the normal value is 65.9°."

A photographer wants to click a picture of a cloud formation, the ratio of clouds intensity to that of the blue sky photographer uses polarizing filter from Malus law,

I = I₀ cos²Ф

So, I f = I i cos²Ф

As the light from cloud is polarized, its intensity reduces to half.

I c = I₀/2

The intensity of light from sky is polarized light.

I s = I₀ cos²Ф

Hence, the ratio of intensities is,

I c/I s = (I₀/2)/(I₀ cos²Ф)

3 = (I₀/2)/(I₀ cos²Ф)

cos²Ф = 1/6

Thus, the required angle is Ф = cos⁻¹(1/√6) = 65.9°

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A 1 kg box falls two metres from a shelf and lands on the ground after 0.021 seconds. The box impacted the ground with a force of around 524.7 N.

The box impacted the ground with a force of around 524.7 N.

Explanation: We can determine the force using the equation F = m * (v/t), where m is the box's mass, v is the velocity change (which is the ultimate velocity because the box starts at rest and comes to a halt), and t is the time it takes for the box to stop.

Given that the box falls 2 metres and its terminal velocity is 0 m/s, v = 2 m/s.

524.7 N is equal to F = 1.1 kg * (2 m/s / 0.021 s).

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. Additionally, Star 1 has prominent hydrogen lines, indicating a lower temperature than Star 2. Therefore, the statements can be sorted into the true and false bins as indicated above.

True: Star 1 has a longer lifetime than Star 2; Star 2 is bluer than Star 1; Star 2 has a lower mass than Star 1; Star 1 has prominent hydrogen lines.

False: Star 2 has a higher luminosity than Star 1; Star 2 is cooler than Star 1.

The spectra of the two main sequence stars illustrate some differences between the two stars. Star 1 is on the left and has a longer lifetime than Star 2, which is on the right. This is evident from the intensity axes that are not on the same scale. Star 2 has a lower mass than Star 1, is bluer than Star 1, and has a lower luminosity

for such more questions on hydrogen lines

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