The inner and outer surfaces of a cell membrane carry a negative and a positive charge, respectively. Because of these charges, a potential difference of about 0.076 V exists across the membrane. The thickness of the cell membrane is 7.30 10-9 m.
What is the magnitude of the electric field in the membrane?

Answer:

Lemon Juice

Explanation:

Acidic levels rise as pH levels decrease. The solution with the lowest pH level will always be more acidic. In this case, lemon juice is the solution with a lower pH level, therefore lemon juice is more acidic than coffee.

Hope this helps!

Final answer:

Lemon juice is the stronger acid compared to coffee, with a pH of 2 versus a pH of 5, meaning it is 1000 times more acidic.

Explanation:

The acidity of a solution is determined by its pH level, which measures the concentration of hydrogen ions (H+) in the solution. The pH scale ranges from 0 to 14, with lower numbers indicating more acidic solutions. In comparing lemon juice with a pH of 2 and coffee with a pH of 5, lemon juice is the stronger acid. Since pH is measured on a logarithmic scale, each pH unit represents a tenfold difference in hydrogen ion concentration. Thus, the difference between pH 2 and pH 5 is 103 or 1000 times. Therefore, lemon juice is 1000 times more acidic than coffee.

Answer

given,

frequency = 523 Hz

piano tuner hears = 2.00 beats/s

a) possible frequency = 523 ± 2

            525 Hz and 521 Hz

b) On tightening piano wire, tension will be increased which will cause an increase of frequency of piano wire. Since no. of beats heard is also increased, the frequency of piano wire must be greater than the frequency of oscillator.

     f p'   =   5+ f₀

     f p'   =  3 + 523 Hz   =   526 Hz.

c)  f   =   k x √T

  Let the tension at 523 Hz be T₀ and at 526 Hz it be T₁

  523  =   k x √T₀  

  T₀    =   523²/ k²

  T₁  =     526²/ k²

  % change in tension

        = [tex]\dfrac{T_0- T_1}{T_1}[/tex]

        = [tex]\dfrac{523^2- 526^2}{526^2}[/tex]

        = 1.13 %

Answer:

2000

Explanation:

Exposure indicator can be obtained using Carestream's formula for imagine pate.

Exposure indicator number = 2000 + [1000 x (log of exposure in mR)].

Given; log of exposure in mR = 1 mR

Exposure indicator number = 2000 + [1000 x (log 1)]

Exposure indicator number = 2000 + [1000 x (0)]

Exposure indicator number = 2000 + [0]

Exposure indicator number = 2000

Answer: the correct option is D (17m).

Explanation: The farthest distance at which a typical "nearsighted" frog can see clearly in air is 17m.

Answer:

b.

Explanation:

BMI is body mass index, it is calculated by dividing the weight of a person in kilogram by square of height in meters.

A high BMI is an indicator of obesity. Obese people are prone to death causing diseases like High Blood pressure, cardiac arrest and diabatese.  So, a high value of BMI values has the highest increased risk for premature mortality.

So the correct answer is 35 kg/m^2.

Answer:

C

Explanation:

Newton third law states that to every action force there is an equal and opposite reaction force. In the case of the car, the person pushes against the ground in other to get the car to move and consequently the ground exert a normal force opposite to the push on the person.

Answer:

2.the mass of the car is independent of gravity.

Explanation:

When mass and acceleration is multiplied we get the force.

[tex]F=ma\\\Rightarrow a=\dfrac{F}{m}[/tex]

Mass of an object is always constant anywhere in the universe. Acceleration of the car would be the ratio of the force and mass. As the mass is constant force the same force applied the acceleration is the same on Earth or Moon.

Hence, the mass of the car is independent of gravity.

The term saturated solution is used in chemistry to define a solution in which no more solute can be dissolved in the solvent. It is understood that saturation of the solution has been achieved when any additional substance that is added results in a solid precipitate or is let off as a gas.

Answer:Resultant force

Explanation:

The net given force is known as the resultant force. The resultant force is the single force that acts in place of other forces combined together.

Answer:

Explanation:

Heat flow in a circular rod is given by

[tex]Q=\frac{kAdT}{dx}[/tex]

where Q= heat flow

k=thermal conductivity

A=area of cross-section

dT=Change in temperature

dx=change in length

Also A can be written as

[tex]A=\pi r^2[/tex]

thus Q is Proportional to

[tex]Q\propto \frac{r^2}{l}[/tex]

For option (a)

[tex]Q\propto \frac{(2r_0)^2}{2l_0}[/tex]

[tex]Q\propto \frac{2r_0^2}{l_0^2}[/tex]

(b)[tex]Q\propto \frac{(2r_0)^2}{l_0}[/tex]

[tex]Q\propto \frac{4r_0^2}{l_0}[/tex]

(c)[tex]Q\propto \frac{r_0^2}{2l_0}[/tex]

(d)[tex]Q\propto \frac{r_0^2}{l_0}[/tex]

So Rod b will conduct the most Heat

Answer:

0.00000011 m

Explanation:

n = 0 for minimum thickness

t = Thickness

[tex]n_2[/tex] = Refractive index of the film = 1.25

[tex]\lambda[/tex] = Wavelength = [tex]550\times 10^{-9}\ m[/tex]

We have the formula

[tex]2n_2t=(2n+1)\dfrac{\lambda}{2}[/tex]

[tex]\\\Rightarrow t=(2n+1)\dfrac{\lambda}{4n_2}\\\Rightarrow t=(2\times 0+1)\dfrac{550\times 10^{-9}}{4\times 1.25}\\\Rightarrow t=0.00000011\ m[/tex]

The minimum thickness of the film is 0.00000011 m

While certain parts of your question cannot be answered without specific data such as the spring constant, we can deduce from the half frequency that the mass of the initial object must also be 300g. More mass on the spring would pull the equilibrium further down but we can't quantify without more details.

This question involves simple harmonic motion and Hooke's Law. Hooke's Law is F = -kx where F is the force, k is the spring constant, and x is the displacement. Simple Harmonic Motion deals with oscillations like that of a spring. However, without values for the spring constant (k) or initial speed of the object, we cannot calculate the frequency of the oscillation or speed of the object at any given point.

As for part (c), the frequency of the oscillation halves when a second mass is introduced. This implies that the system's mass has doubled as frequency is inversely proportional to the square root of the mass. Therefore, the initial object's mass would be 300g as well.

For part (d), without any specific figures such as the spring constant, the new equilibrium position below yi cannot be determined. Commonly, the force produced by the weight of the objects will be counteracted by the spring force when the system is in equilibrium. More mass would pull the spring further down until this equilibrium is achieved.

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The frequency of oscillation can be determined using the formula f = 1 / T. The speed of the object when it is 8 cm below the initial position can be calculated using the formula v = A * ω. The mass of the first object can be found by setting up two equations and solving for M. The new equilibrium position is slightly lower than the initial position yi.

(a) The frequency of an oscillation can be determined using the formula:

frequency (f) = 1 / period (T)

Since the object oscillates up and down, it completes one full cycle (2π radians) every time it goes from the highest point to the lowest point and back. The period (T) is therefore the time it takes for one complete cycle. The object reaches its lowest position when it is 10 cm below yi, so the total distance traveled is 10 cm. Since the object moves up and down symmetrically, we can calculate the period by dividing the total distance traveled by 2 times the amplitude (A):

T = 2π * sqrt(m / k)

where m is the mass of the object and k is the spring constant. Given that the spring is massless, the mass of the object does not affect the period. Therefore, we can calculate the period as:

T = 2π * sqrt(k)

From the period, we can compute the frequency using the formula provided above.

(b) The speed of the object when it is 8.0 cm below the initial position can be determined using the formula for the speed of an object in simple harmonic motion:

speed (v) = amplitude (A) * angular frequency (ω)

The angular frequency is related to the period by the formula:

angular frequency(ω) = 2π / period (T)

Using the given values, we can calculate the angular frequency and then substitute it into the equation for speed.

(c) When an object of mass 300 g is attached to the first object, the system oscillates with half the original frequency. Let's denote the mass of the first object as M and the spring constant as K. We can set up two equations to solve for the mass of the first object:

Equation 1: f = (1 / (2π)) * sqrt(K / M) (original frequency)

Equation 2: (f/2) = (1 / (2π)) * sqrt(K / (M + 0.3)) (new frequency)

By solving these equations simultaneously, we can find the mass of the first object.

(d) The new equilibrium position, with both objects attached to the spring, is determined by the combined mass of the two objects. Since the first object is now heavier due to the addition of the second object, the equilibrium position will be slightly lower than the initial position yi. The exact displacement can be calculated using the formulas for equilibrium position in simple harmonic motion.

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Over-driving your headlights implies a situation where you are driving so fast that you won't be able to stop within the area illuminated by your headlights. Therefore, if you see an object in your path under such circumstances, you are likely not going to be able to stop in time to avoid hitting it. Headlights' range is usually 350 feet, and driving at a speed that requires a stopping distance greater than 350 feet is considered over-driving your headlights.

The phrase 'over-driving your headlights' refers to a situation where a driver is traveling at such a speed that their stopping distance is further than the distance illuminated by their headlights. Thus, if an object is within your path, you won't have enough time to stop your vehicle before hitting it, especially if you're speeding.

On most roads, the farthest your headlights can help you see ahead is around 350 feet. If you're driving faster than a speed that permits you to stop within these 350 feet, you're said to be 'over-driving' your headlights. If you're over-driving your headlights, and you see an object ahead then you will most likely not be able to stop in time to miss the object. This is because your vehicle's stopping distance will be greater than your visual distance, which is dependent on the capabilities of your headlights.

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Answer:

True

Explanation:

Entropy is a thermodynamic variable that always increases or remains constant, but does not decrease.

This indicates that energy is always transferred from a higher temperature system to a lower temperature system and not the other way around.

Entropy can also be thought of as what drives a system into equilibrium, and systems reach equilibrium through heat transmission.

The fact that the entropy of a closed system never decreases is a statement of the second law of thermodynamics.

Answer:

900 J

Explanation:

[tex]\Delta U[/tex] = Change in entropy = -300 J (Decrease)

[tex]W[/tex] = Work done = 600 J

[tex]Q[/tex] = Heat transferred

Change in internal energy is given by

[tex]\Delta U=W+Q\\\Rightarrow Q=\Delta U-W\\\Rightarrow Q=-300-600\\\Rightarrow Q=-900\ J[/tex]

The heat transferred to or from the system as heat is -900 J.

900 J is transferred. As heat is transferred from the system the sign is negative.

When 600 J of work is done on a system and the thermal energy of the system decreases by 300 J, the heat energy transferred to or from the system can be calculated using the First Law of Thermodynamics. In this case, -900 J of heat is transferred from the system.

When 600 J of work is done on a system and the thermal energy of the system decreases by 300 J, the change in internal energy of the system can be calculated using the First Law of Thermodynamics.

The First Law of Thermodynamics states that the change in internal energy of a system is equal to the heat added to or removed from the system plus the work done on or by the system. Mathematically, it can be expressed as:

ΔU = Q + W

Where ΔU represents the change in internal energy, Q represents the heat added to or removed from the system, and W represents the work done on or by the system.

ΔU = Q + 600 J

-300 J = Q + 600 J

Q = -300 J - 600 J

Q = -900 J

The negative sign indicates that the heat is transferred from the system.

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Answer:

The lack of jobs and lack of transportation to jobs

Explanation:

As it is seen, the establishment of the camping and hiking areas will dispatch buildings which were hospitals, shops and schools.

These buildings and facilities previously employed a number of workers and their removal hence, will reduce the number of available jobs.

Also, the new constructions will prove difficult in switching from one job to another.

Final answer:

The speed at which the water leaves the hole is 17.7 m/s, and the diameter of the hole is approximately 4.8 mm using Torricelli's theorem and the flow rate equation.

Explanation:

The scenario described involves principles of fluid dynamics within the field of physics, specifically Bernoulli's equation and the equation of continuity. To calculate the speed at which the water leaves the hole (a) and the diameter of the hole (b), we employ the Torricelli's theorem and the flow rate equation.

Using Torricelli's theorem, the speed (v) of water exiting the hole can be determined by the formula v = √(2gh), where g is the acceleration due to gravity (9.8 m/s²) and h is the height of the water column above the hole (16.0 m).

v = √(2 * 9.8 m/s² * 16.0 m) = √(313.6 m²/s²) = 17.7 m/s

To find the diameter of the hole, we use the flow rate Q = A * v, where Q is the flow rate (2.50 × 10³ m³/min), A is the area of the hole, and v is the speed of water leaving the hole. First, we convert the flow rate to m³/s by dividing by 60 (since there are 60 seconds in a minute):

Q (in m³/s) = (2.50 × 10³ m³/min) / 60 = 4.17 × 10µ m³/s

To find the area: A = Q / v, then to find the diameter (d), we use the area of a circle A = π * (d/2)². Rearranging and solving for d gives us:

d = 2 * √(Q / (π * v))
d = 2 * √((4.17 × 10µ m³/s) / (π * 17.7 m/s)) = 4.8 mm

(a) The speed at which the water leaves the hole is approximately 17.7m/s.

(b) The diameter of the hole is approximately 1.74mm.

Given:

- The depth of the hole below the water level, [tex]\( h = 16.0 \)[/tex] m

- The rate of flow, [tex]\( Q = 2.50 \times 10^{-3} \) m\(^3\)/[/tex]min

Part (a): Speed of Water Leaving the Hole

We can use Torricelli's Law to determine the speed at which the water leaves the hole:

[tex]\[ v = \sqrt{2gh} \][/tex]

where:

- [tex]\( g \)[/tex] is the acceleration due to gravity[tex](\( 9.8 \) m/s\(^2\))[/tex]

- [tex]\( h \)[/tex] is the height of the water above the hole

Plugging in the values:

[tex]\[ v = \sqrt{2 \times 9.8 \times 16.0} \][/tex]

[tex]\[ v = \sqrt{2 \times 9.8 \times 16.0} \][/tex]

[tex]\[ v = \sqrt{313.6} \][/tex]

[tex]\[ v \approx 17.7 \text{ m/s} \][/tex]

Part (b): Diameter of the Hole

First, convert the flow rate to cubic meters per second:

[tex]\[ Q = 2.50 \times 10^{-3} \text{ m}^3/\text{min} \][/tex]

[tex]\[ Q = \frac{2.50 \times 10^{-3}}{60} \text{ m}^3/\text{s} \][/tex]

[tex]\[ Q = 4.17 \times 10^{-5} \text{ m}^3/\text{s} \][/tex]

The flow rate ( Q ) can also be expressed as:

[tex]\[ Q = A \cdot v \][/tex]

where:

- ( A ) is the cross-sectional area of the hole

- ( v ) is the speed of the water leaving the hole

Rearranging to solve for ( A ):

[tex]\[ A = \frac{Q}{v} \][/tex]

[tex]\[ A = \frac{4.17 \times 10^{-5}}{17.7} \][/tex]

[tex]\[ A \approx 2.36 \times 10^{-6} \text{ m}^2 \][/tex]

The area ( A) of a circular hole is given by:

[tex]\[ A = \pi \left( \frac{d}{2} \right)^2 \][/tex]

Solving for the diameter[tex]\( d \)[/tex]:

[tex]\[ d = 2 \sqrt{\frac{A}{\pi}} \][/tex]

[tex]\[ d = 2 \sqrt{\frac{2.36 \times 10^{-6}}{\pi}} \][/tex]

[tex]\[ d = 2 \sqrt{7.51 \times 10^{-7}} \][/tex]

[tex]\[ d \approx 1.74 \times 10^{-3} \text{ m} \][/tex]

[tex]\[ d \approx 1.74 \text{ mm} \][/tex]

Answer:

The magnitude on the resultant force on the object = 18.03 N

Explanation:

Resultant Force: The resultant force of two or more forces acting on a body in a given direction is the single force obtained when the two forces are combined, which produces the same effect as the two forces acting together.

Since both forces makes an angle of 90° with each other,

Fr = √(F₁² + F₂²)......................... Equation 1

Where Fr = resultant force on the object F₁ = The force pulling the body northward, F₂ = The force pulling the body southward.

Given: F₁ = 10 N,  F₂ = 15 N

Substituting these values into equation 1

Fr = √(10² + 15²)

Fr = √(100 + 225)

Fr = √325

Fr = 18.03 N

Therefore the magnitude on the resultant force on the object = 18.03 N

The resultant force when an object is pulled by 10 N northward and 15 N southward is 5 N towards the south, found by subtracting the smaller force from the larger one.

In physics, when multiple forces act on an object, they combine to create a resultant force. If two forces of equal magnitude are pulling in opposite directions, they cancel out and the resultant force is zero. However, in this case, the forces acting on the object are different: 10 N northward and 15 N southward.

To find the resultant force, we simply subtract the smaller force from the larger one, considering the opposing directions. So, here 15 N (south) - 10 N (north) gives us 5 N towards the south.

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Final answer:

Tech A is correct in stating that the drop center is used for tire installation, while Tech B is incorrect; the drop center's primary purpose isn't to prevent the tire from detaching at low pressure.

Explanation:

Tech A says that most wheels have a drop center or deep well that is used in installing a tire on the wheel. Tech B says that the drop center or deep well is used to prevent the tire from coming off the wheel in the case of low tire pressure. The answer here is that Tech A is correct. The drop center or deep well feature on a wheel is indeed primarily designed to help in the installation and removal of the tire. It allows the bead of the tire to drop into a recessed area, giving enough slack to work the tire over the rim. On the other hand, Tech B’s statement is not accurate. While the drop center might incidentally help keep the tire on the rim in the case of low pressure, its primary purpose is not to prevent the tire from coming off the wheel.

Answer:

mass=2326kg

Explanation:

Archimedes' principle states that when an object is submerged into a liquid, it appears lighter in weight due to the buoyant force applied by the liquid in upward direction. Buoyant force is equal to the weight of the liquid displaced by the object. An object floats on the surface of liquid or floats partially submerged when weight of the displaced liquid is greater than weight of the object.

the mass f he box=74kg

densty=mass /vlme

1000=mass/2.4

mass =2400kg

apparent mass wen completely submerged will be

2400-74kg

mass=2326kg

Answer:

B

Explanation:

Newton’s Second Law of Motion

Newton’s Second Law of Motion states that ‘when an object is acted on by an outside force, the mass of the object equals the strength of the force times the resulting acceleration’.

This can be demonstrated dropping a rock or and tissue at the same time from a ladder. They fall at an equal rate—their acceleration is constant due to the force of gravity acting on them.

The rock's impact will be a much greater force when it hits the ground, because of its greater mass. If you drop the two objects into a dish of water, you can see how different the force of impact for each object was, based on the splash made in the water by each one.

Answer: B

Explanation:

Answer:

When an electrical current passes through a wire, a magnetic field is generated around it. Likewise, if the magnetic field around a wire is changed ( for example by rotating a coil inside a stationary manger), electricity will move through the wire.

Answer:

t = 1.07 seg

Explanation:

First we are going to solve the differential equation for the velocity:

[tex]\frac{dv}{dt} = -2v-32[/tex]

This is a differential equation of separable variables

[tex]\frac{dv}{-2v-32} = dt[/tex]

Multiplying by -1 to both sides of the equation

[tex]\frac{dv}{2v+32} = -dt[/tex]

We integrate the left side with respect to the velocity and the right side with respect to time

[tex]\frac{ln(2v+32)}{2} = -t +k[/tex]

          where k is a integration constant

ln(2v+32) = -2t + k

   [tex]2v +32 = e^{-2t+k}[/tex]

   [tex]2v + 32 = ce^{-2t}[/tex]

   [tex]v = ce^{-2t} -16[/tex]

We determine the constant c with the initial condition v(0) = -50

  [tex]-50 = ce^{-2(0)} -16[/tex]

           -50 + 16 = c

               c = -34

Then

[tex]v(t) = -34e^{-27}-16[/tex]

When the velocity is -20 ft/s the time is:

[tex]-20 = -34e^{-2t}-16[/tex]

[tex]\frac{-4}{-34} = e^{-2t}[/tex]

[tex]ln(\frac{4}{34} ) = -2t[/tex]

t = 1.07 seg

To determine the time at which the skydiver's velocity reaches 20 feet per second, we integrate the given differential equation dv/dt = -2v - 32 with initial conditions and solve for the time t when the velocity function v(t) equals -20.

The student's question involves solving a first-order linear differential equation to find the time at which a skydiver's velocity reaches a certain value after her parachute opens. The differential equation dv/dt = -2v - 32 represents the velocity of the skydiver, and we must use initial conditions to solve it. Given that the skydiver's initial velocity is -50 feet per second and the safe landing speed is 20 feet per second, we need to integrate the differential equation to find the function v(t) and then solve for t when v(t) equals -20 feet per second (since velocity is negative when descending).

Answer:

Shorter path

Explanation:

For all turning vehicles, the rear wheels follow Shorter path than the front wheels.

Any turning vehicle, the rear(the back part of something, especially a vehicle.) wheels follow a shorter path than the front wheels. The longer the vehicle is, the greater the difference will be in path. Trucks initially swing out before making a turn

Answer:

The answer is C "think about the problem first, systematically consider all factors, and form a hypothesis"

Explanation:

In physics there is some basic fomula that sir Isacc Newton proposed under the topic of motion. The three formulas are below;

1) v=u+at

2)v^2=u^2+2as

3)s=ut+(1/2)(at^2)

the variables are explained below;

u= initial velocity of the body

a=acceleration/Speed of the body

t= time taken by the body while travelling

s= displacement of the body.

Therefore to solve keatons problem, the factors(variables) in the formulas above need to be systematically considered. Since the ball was dropped from the top of the building, the initial velocity is 0 because the body was at rest. Also the acceleration will be acceleration due to gravity (9.8m/s^2)

The correct relationship between the bathroom scale readings at the top, middle, and bottom of a ferris wheel ride is that they are all the same.

When you and your friend are riding on a ferris wheel moving with constant velocity, the bathroom scale readings at the top, middle, and bottom of the ride can be compared. Since the ferris wheel is moving at a constant velocity, there is no acceleration and thus no net force acting on you. This means that your apparent weight will be the same at all three points on the ride. Therefore, the correct relationship is option 3: Rt = Rb = Rm.

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Answer:

Technicians A and B are both correct

Explanation:

A quick take-up valve in a quick take-up master cylinder assembly which reduces fluid flow noise and restriction caused by fluid flowing in one mode of operation through an incipiently or substantially closed valve spring coil stack. The check valve arrangement has a coil compression limiting device and also has the outlet orifice so positioned as not to require fluid flow through the check valve spring coils while the check valve is open.

If the brake warning light is NOT on and there are no visible brake fluid leaks, your master cylinder may be worn or leaking internally allowing the brake pedal to slowly sink when pressure is applied to it. This type of condition will be most noticeable when you are holding constant pressure against the brake pedal at a stop light. If the pedal sinks or requires pumping to keep your car from creeping ahead, the master cylinder needs to be replaced.

Answer:

Gravitational Force

Explanation:

Gravitational force also called gravity or gravitation is an attractive force that keeps two objects in space. Gravitational force is an attractive force that tends to pull matters together. Every objects in the universe experience gravitational pull.  Planets, stars, galaxies, are held together by gravity. It is a weak force. The weight of an object is the product of gravitational force acting on its mass.

Newton's Law of Universal Gravitation states the force of attraction between two masses m₁ and m₂ in the universe is directly proportional to the product of their masses and inversely proportional to the square of their distance apart.

                                 [tex]F = G\frac{m_{1}m_{2}}{r^2}[/tex]

Where;

F is the gravitational force,

G is the gravitational constant = 6.67 × 10¹¹ m³/kg/s,

m1 and m2 are the masses of the objects,

r is the distance between the centers of the masses

The tension in the left rope is expressed by [tex]T_{L} = W\cdot \left(1-\frac{x}{L} \right)[/tex]. For [tex]x = 0[/tex], [tex]T_{L} = W[/tex].

A representation of the system is presented in the image attached below. Let suppose that the entire system represents a rigid body, that is, a body whose geometry cannot be neglected and does not experiment deformation due to the application of external loads.

The tension in the left rope ([tex]T_{L}[/tex]) can be found by applying Newton's laws and D'Alembert's Principle applied on the rightmost point of the bar:

[tex]\Sigma F = W\cdot (L-x)-T_{L}\cdot L = 0[/tex]

[tex]T_{L} = \frac{W\cdot (L-x)}{L}[/tex]

[tex]T_{L} = W\cdot \left(1-\frac{x}{L} \right)[/tex]   (1)

The tension in the left rope is expressed by [tex]T_{L} = W\cdot \left(1-\frac{x}{L} \right)[/tex]. For [tex]x = 0[/tex], [tex]T_{L} = W[/tex]. [tex]\blacksquare[/tex]

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Considering a situation where there is no horizontal acceleration, the tension in the left rope (TL) equals the weight of the person when x equals zero (x=0). Since the only forces on the static system are weight (W) and the tensions in the two ropes, and they are in equilibrium, the tension in either rope will be the same as the weight.

The question requires us to find the tension in the left rope (TL), given that x equals zero. Using the equilibrium equation under the condition of no horizontal acceleration and no external forces except the weight (W) and the two tensions, TL and TR, we can conclude the magnitudes of the tensions TL and TR must be equal.

Given the scenario, the only forces acting on the system are the weight of the walker (W) and the tensions in the ropes. If the system is static, the net external force is zero, which means the sum of the forces should also equal zero according to Newton's second law. Hence, expressing the tension TL in terms of W becomes simple given that the system is in equilibrium. Under these conditions, the tension in the rope should equal the weight of the supported mass, making TL equal to W.

Therefore, since x is zero and we are neglecting other variables like rope weight and the angle of the ropes, the tension TL in the left rope becomes equivalent to the weight of the person. Hence the tension (TL) equals W.

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