Consider the two-slit experiment. Light strikes two slits that are a distance 0. 0236 mm apart. The path to the third-order bright fringe on the screen forms an angle of 2. 09° with the horizontal. What is the wavelength of the light?

Answer:

vii. c

ix. a

x. d

Explanation:

trust

The distance from the central maximum to the first-order minimum along a wall 6.50 m from the window is approximately 0.764 m.

To solve this problem, we can use the equation for the distance between adjacent maxima or minima in a single-slit diffraction pattern:

d*sin(theta) = m*lambda

where d is the width of the slit (in this case, the width of the window), theta is the angle between the direction of the diffracted wave and the direction of the incident wave, m is the order of the maximum or minimum (0 for the central maximum, 1 for the first-order minimum, 2 for the second-order maximum, etc.), and lambda is the wavelength of the microwaves.

We can rearrange this equation to solve for the distance between the central maximum and the first-order minimum:

sin(theta) = m*lambda/d

For the first-order minimum, m = 1. Plugging in the given values, we get:

sin(theta) = (1)*(5.00 cm)/(45.0 cm) = 0.111

To find the angle theta, we can use the small-angle approximation:

theta = sin(theta) = 0.111

Now we can use basic trigonometry to find the distance from the window to the first-order minimum on the wall:

tan(theta) = opposite/adjacent

opposite = tan(theta)*adjacent = tan(0.111)*(6.50 m) = 0.764 m

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The statements about limiting frictional force between two surfaces are given below(3) A and C is correct option.

The nature of surfaces in contact affects the limiting frictional force because the coefficient of friction depends on the properties of the surfaces in contact.

The area of surfaces in contact also affects the limiting frictional force because a larger surface area in contact results in a larger normal force, which increases the maximum frictional force that can be generated.

The normal reaction between the surfaces in contact is not directly related to the limiting frictional force, as it only affects the magnitude of the frictional force and not its limit. Therefore, statement B is not correct.

Thus the correct option is (3).

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Because the total voltage supplied by the battery is distributed among all the components in a series circuit, if a switch is closed, the potential difference across the resistor and bulb will remain unchanged.

The light cannot be turned on when the switch is open because the circuit is incomplete. The circuit lacks a closed-loop channel for the current to follow.

The potential difference between the two extremes of the arrangement in a series connection of resistors is equal to the total of the potential differences across individual resistors.

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When using statistics from news articles or information from other sources, people should exercise caution because they might not always reflect the whole picture or might be presented in a biased or misleading way.

Statistics are not always based on accurate or reliable data, and they can be readily manipulated or misunderstood to support an agenda or stance.

Before making any decisions or acting on the data, it is essential to confirm the information's source and take into account the context in which it is presented. Furthermore, outdated or based on a small sample size statistical data may have an impact on their reliability and accuracy.

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The maintenance of military defense and the national parks system that must be renewed every year falls under the category of government current spending, also known as government consumption.

Government current spending refers to the expenses incurred by the government on the day-to-day activities of providing public goods and services, such as education, healthcare, defense, and infrastructure maintenance.

This spending is financed through taxes and other forms of revenue collected by the government.

Government current spending is different from government capital spending, which involves investment in infrastructure, such as roads, bridges, and buildings.

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The correct answer is B. In nuclear reactions, some mass is converted to energy.

A nuclear reaction is the collision of two nuclei, or a nucleus and an external subatomic particle, to form one or more new nuclides. As a result, a nuclear reaction must result in the transformation of at least one nuclide.

The particle that is bombarding may be an alpha particle, a gamma-ray photon, a neutron, a proton, or a heavy ion.

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At 250 degrees Celsius, water is in the gaseous state, specifically as steam or water vapor.

Under normal atmospheric pressure, water boils and undergoes a phase transition from liquid to gas at 100 degrees Celsius. As the temperature increases beyond the boiling point, the water molecules gain enough energy to overcome intermolecular forces and transition into the gaseous state.

Therefore, at 250 degrees Celsius, water exists as a gas or steam rather than as a liquid.

The boiling point of water, where it transitions from liquid to gas, occurs at 100 degrees Celsius at standard atmospheric pressure (1 atmosphere or 101.3 kilopascals). At temperatures below the boiling point, water exists as a liquid.

Therefore, at 250 degrees Celsius, water is well above its boiling point. It would be in the form of a hot liquid rather than a gas. The high temperature causes the water molecules to have greater kinetic energy, resulting in increased movement and a higher average temperature of the liquid.

It's important to note that the state of water can change depending on the pressure. At higher pressures, the boiling point of water increases, and at lower pressures, it decreases.

However, under standard atmospheric pressure, water at 250 degrees Celsius would still remain in the liquid state.

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The mass of the object can be found using the formula: m = 37.1 kg and a = 9.13 m/s, and force F = 1.92 N.

1. Mass Finding: Let F = ma =[tex]mv^2/r[/tex]

F is the centripetal force, m is the mass of the object, v is the velocity and r is the radius of the circular path.

Plugging in the given values, we get:

1345 N = m x 36.2 m/s

m = 37.1 kg

a = [tex](2.4 m/s)^2/1.5 m[/tex]

a = 3.84 m/s

2. The centripetal force can be found using the formula:

F = [tex]mv^2/r,[/tex] where m is the mass of the tetherball, v is its tangential velocity and r is the length of the tetherball rope.

Plugging in the given values, we get:

F = [tex]0.4 kg * (2.4 m/s)^2/1.5 m[/tex]

F = 1.92 N

The centripetal force experienced by Melissa and Cody together can be found using the formula:

3. F = (m1 + m2) x a x r, where m1 and m2 are the masses of Melissa and Cody respectively, a is the centripetal acceleration and r is the radius of the circular path.

Plugging in the given values, we get:

F = (55 kg + 65 kg) x 2.2 m/s x 6 m

F = 2376 N

68 N = m x (2.7 m/s)/0.8 m

m = 7.24 kg

a = (2.7 m/s)/0.8 m

a = 9.13 m/s

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To estimate the maximum number of cars that can safely travel on a road at a given speed, the traffic fanatic should consider the free-flow speed, headway between cars at different speeds, and other factors affecting traffic flow.

The traffic fanatic's assumption is based on the concept of traffic flow theory, which aims to understand and predict the behavior of traffic on a road network. The safe distance between cars is known as the "headway" and it is dependent on the speed of the cars.

The traffic flow theory proposes that the maximum traffic flow occurs at a certain speed called the "optimal speed" or "free-flow speed". At this speed, the headway between cars is minimized, and the maximum number of cars can safely travel on the road.

The function N(s) represents the number of cars that can pass a given spot per minute at a given speed s. In this case, the function is modeled as N(s) = 150, which means that the maximum number of cars that can pass the given spot per minute is 150, regardless of the speed.

However, in reality, the number of cars that can pass a given spot per minute varies with speed. At speeds lower than the free-flow speed, the headway between cars increases, and the number of cars that can pass the given spot decreases. At speeds higher than the free-flow speed, the headway between cars decreases, and the number of cars that can pass the given spot also decreases due to increased congestion and potential accidents.

Therefore, to estimate the maximum number of cars that can safely travel on a particular road at a given speed, the traffic fanatic should consider the free-flow speed and the headway between cars at different speeds. She can use traffic flow models such as the Greenshields model or the Underwood model to estimate the traffic flow at different speeds and densities.

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An electrolytic cell is defined as a cell in which an electric current drives a nonspontaneous reaction. The correct answer is B)

An electrolytic cell is a type of electrochemical cell that uses electrical energy to drive a nonspontaneous chemical reaction. In contrast to a galvanic cell, where a spontaneous chemical reaction produces an electric current, an electrolytic cell uses an external power source to drive an otherwise nonspontaneous reaction.

In an electrolytic cell, a voltage is applied to the electrodes, causing electrons to flow from the anode to the cathode. The anode is the electrode where oxidation occurs, and the cathode is the electrode where reduction occurs.

The electrical energy is used to force the nonspontaneous reaction to occur, with the electrode reactions being driven in the opposite direction to their natural direction.

The process of electrolysis is used in a wide range of industrial applications, such as the production of aluminum, chlorine, and sodium hydroxide. It is also used in electroplating and in the purification of metals.

The correct answer is B)

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The statement "The image is always to the right of the lens" is false.

However, the statement "The image can be upright or inverted" is true.

When an object is placed to the left of a converging lens, the image can be formed in different positions depending on the distance of the object from the lens and the focal length of the lens.

If the object is located at a distance greater than twice the focal length of the lens, the image will be real, inverted and located to the right of the lens.

If the object is located between the focal length and twice the focal length of the lens, the image will still be real and inverted but located on the same side of the lens as the object.

If the object is located at a distance less than the focal length of the lens, the image will be virtual, upright and located on the same side of the lens as the object.

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The total distance traveled by the van is 75 meters and the total distance traveled by the police officer is 37.5 meters at the point of catching up with the van.

What is Velocity?

Velocity is a physical quantity that describes the rate at which an object changes its position with respect to time. It is a vector quantity, which means it has both magnitude and direction. The magnitude of velocity is the speed of the object, while the direction of velocity is the direction in which the object is moving.

The van's speed is greater than the speed limit, so it will maintain a constant speed of 15 m/s. The police officer starts from rest and has a constant acceleration of 3.0 m/[tex]s^{2}[/tex]. Let's denote the time it takes for the police officer to catch up to the van as t. Using the equation of motion for the police officer's velocity, we have:

[tex]v_{police[/tex] = [tex]a_{police * t[/tex]

Using the equation of motion for the van's displacement, we have:

[tex]d_van[/tex]= [tex]v_van * t[/tex]

At the point when the police officer catches up with the van, their displacements will be equal, so we can set these two equations equal to each other and solve for t:

v_[tex]v_{police * t[/tex] = [tex]d_{van[/tex]

[tex]a_{police[/tex] *[tex]t^{2}[/tex] = [tex]v_{van[/tex] * t

3.0 * t^2 = 15 * t

t = 5 seconds

Therefore, it will take the police officer 5 seconds to catch up with the van.

(b) To find the officer's speed at that point, we can use the equation of motion for the police officer's displacement:

[tex]d_{police[/tex] = (1/2) *[tex]a_{police[/tex] *

[tex]d_{police[/tex] = (1/2) * 3.0 * [tex]5^{2}[/tex]

[tex]d_{police[/tex] = 37.5 m

Using the time t = 5 seconds, we can now find the officer's speed at that point using the equation:

[tex]v_{police[/tex]= [tex]a_{police[/tex] * t

[tex]v_{police[/tex] = 3.0 * 5

[tex]v_{police[/tex] = 15 m/s

Therefore, the officer's speed at the point of catching up with the van is 15 m/s.

(c) To find the total distance each vehicle has traveled at that point, we can use the equations of motion for each vehicle:

[tex]d_{van[/tex] = [tex]v_{van[/tex] * t

[tex]d_{police[/tex] = (1/2) * [tex]a_{police[/tex] * [tex]t^{2}[/tex]

Using the time t = 5 seconds, we can substitute the values of [tex]v_{van[/tex] and [tex]a_{police[/tex]:

[tex]d_{van[/tex] = 15 * 5

[tex]d_{van[/tex]= 75 m

[tex]d_{police[/tex]= (1/2) * 3.0 *[tex]5^{2}[/tex]

[tex]d_{police[/tex]= 37.5 m

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Answer:

Explanation:

are a great explanation for this. You could also actually learn something instead of searching sutff up. U will be a fialure i tell you.

The force acting on the 12 kg mass would be 11 N.

To solve this problem, we need to use the work-energy principle, which states that the work done by a force on an object is equal to the change in the object's kinetic energy.

First, we need to calculate the initial and final kinetic energy of the 12 kg mass.

The initial kinetic energy is given by:

K₁ = (1/2) * m * v₁²

= (1/2) * 12 kg * (11 m/s)²

= 726 J

The final kinetic energy is given by:

K₂ = (1/2) * m * v₂²

= (1/2) * 12 kg * (26 m/s)²

= 936 J

The change in kinetic energy is:

ΔK = K₂ - K₁

= 936 J - 726 J

= 210 J

Next, we need to calculate the work done by the unknown force. We can do this by using the formula:

W = F * d * cosθ

where W is the work done, F is the force, d is the displacement, and θ is the angle between the force and displacement vectors.

In this case, the displacement is 22 meters, and the angle θ is 30 degrees. So we have:

W = F * d * cosθ

= F * 22 m * cos(30°)

= 19.1 F

Finally, we can use the work-energy principle to solve for the unknown force:

W = ΔK

19.1 F = 210 J

F = 11 N

Therefore, the force acting on the 12 kg mass is 11 N.

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The spring constant for this particular spring is 60,000 N/m.

To calculate the spring constant (k) for a spring, you can use Hooke's Law, which states that the force (F) required to stretch or compress a spring by a certain distance (x) is proportional to that distance. The formula for Hooke's Law is:

F = k * x

In your question, the spring is stretched 0.50 m (x) and the force applied is 30,000 N (F). We need to find the spring constant (k). To do this, we can rearrange the formula:

k = F / x

Now, we can plug in the given values:

k = 30,000 N / 0.50 m

k = 60,000 N/m

So, the spring constant for this particular spring is 60,000 N/m. This value represents the stiffness of the spring, meaning that it takes 60,000 Newtons of force to stretch the spring by one meter. A higher spring constant indicates a stiffer spring, whereas a lower spring constant means the spring is more easily stretched or compressed. In this case, the spring is relatively stiff, requiring a substantial amount of force to change its length.

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A force that exists between any two objects that have mass: gravity. The correct option is C.

Gravity is a natural force that attracts two objects with mass towards each other. It is the reason why objects fall to the ground when dropped, and it is also responsible for keeping planets and other celestial bodies in their orbits.

The other terms, motion (A), velocity (B), and friction (D), are related to the movement and interaction of objects, but they are not the specific force that exists between objects with mass. Remember, gravity is the force that exists between any two objects that have mass. The correct option is C.

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Complete question:

A force that exists between any two objects that have mass:

A. motion

B. velocity

C. gravity

D. friction

The type of faucet that uses a rotating cylinder to control water temperature and the rate of water flow by using a balancing piston is called a thermostatic mixing valve.

A thermostatic mixing valve is a mechanical device designed to provide precise control over the temperature of the water coming out of the faucet. It is commonly used in showers, baths, and other plumbing fixtures where maintaining a consistent and comfortable water temperature is important.

The valve consists of a central rotating cylinder that contains both hot and cold water inlets. As you turn the handle or lever of the faucet, the cylinder rotates, allowing you to adjust the proportion of hot and cold water that mixes together.

Inside the cylinder, there is a balancing piston that is sensitive to changes in water temperature and pressure. This piston helps to maintain a consistent temperature by adjusting the flow rates of hot and cold water.

When you set the desired temperature, the piston moves to balance the flow of hot and cold water, ensuring that the mixed water remains at a constant temperature regardless of any fluctuations in the supply temperature or pressure.

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According to the question the rod is stretched by 0.0009 mm when the ride is at rest.

Length is the measurement of the size of an object or the distance between two points. It is typically measured in units of length such as centimeters, meters, or feet. Length is also used to describe a physical dimension or an abstract concept such as time or distance. In mathematics, length is a fundamental concept that is used in various areas of study, including geometry, calculus, and trigonometry.

The total weight of the two riders is 1900 N, and the rod is vertical when the ride is at rest. To calculate the change in length of the rod (ΔL), we must use the equation:
ΔL = W/AE
Where W is the weight, A is the area of the cross-sectional rod, and E is the Young's Modulus of the material.
For a steel rod with a circular cross section, the area A is equal to πr2, where r is the radius of the rod. Assuming that the rod is 10 mm in diameter, the radius is 5 mm, and the area is approximately 78.5 mm2.
The Young's Modulus of steel is approximately 200 GPa.
Plugging these values into the equation, we get:
ΔL = (1900 N) / (200 GPa)(78.5 mm²)
ΔL = 0.0009 mm
Therefore, the rod is stretched by 0.0009 mm when the ride is at rest.

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Because the gasoline expands more quickly than the steel can,4.44 L is the amount that will overflow

Define  thermal expansion.

The propensity of matter to vary in volume in response to temperature changes is known as thermal expansion. A substance's particles move more when it is heated, maintaining a greater average separation. Thermosets experience linear thermal expansion since they are employed in solid form.

The phenomena known as thermal expansion can be seen in solids, liquids, and gases. An object or body expands during this process when heat (temperature) is applied. The term "thermal expansion" refers to an object's propensity to change its dimensions as a result of heat, including length, density, area, and volume.

volume 216 L

Temperature  T1 is 13. 5°C, T2 is 36. 0°C

T will be 22.5 K

Amount of gasoline that overflows:

9.14 x 10(-6)/K *V*T^2

9.14 x 10(-6)/K x 216 L x 22.5 K x 22.5 K = 4.44 L

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When two bumper cars collide into each other and each car jolts backwards, this is an example of: Newton's Third Law of Motion also known as the law of action and reaction.

Newton's Third Law states that for every action, there is an equal and opposite reaction. In the case of the bumper cars, when they collide, the force exerted by Car A on Car B (the action) is equal in magnitude and opposite in direction to the force exerted by Car B on Car A (the reaction).

This is why both cars experience a jolt in opposite directions after the collision.

To recap, the situation you described with the two bumper cars colliding and jolting backwards is an example of Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.

This law helps us understand the behavior of objects during collisions and interactions, and it plays a crucial role in understanding the principles of physics.

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Two charged metal spheres are separated by 0.1m and have a force of [tex]8.1 \times 10^{-8}N[/tex] between them. If the size of the charges is tripled, the force between them will increase to [tex]7.29 \times 10^{-7}N[/tex].

The force between two charged spheres is given by Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Therefore, if the size of each charge is tripled, the force between the spheres will increase by a factor of 9, since the product of the charges is now three times greater.

To calculate the force, we can use the formula [tex]F = kQ1Q2/d^2[/tex], where k is the Coulomb constant, Q1 and Q2 are the charges on the spheres, and d is the distance between them. Since the spheres are identical and equally charged, we can represent their charges as Q and Q, respectively.

Substituting the given values, we get:

[tex]8.1 \times 10^{-8} = kQ^2/0.1^2[/tex]

Solving for Q, we get:

Q = [tex]\sqrt{(8.1 \times 10^{-8} \times 0.1^2 / k)}[/tex]

Q = [tex]3 x 10^{-8} C[/tex]

Now, if we triple the size of each charge, the force between the spheres will be:

F' = [tex]k(3Q)^2/0.1^2[/tex]

F' = [tex]9kQ^2/d^2[/tex]

F' = [tex]9(8.1 \times 10^{-8})[/tex]

F' = [tex]7.29 \times 10^{-7} N[/tex]

Therefore, the force between the spheres will increase from [tex]8.1 \times 10^{-8}N[/tex] to [tex]7.29 \times 10^{-7}N[/tex] if the size of each charge is tripled.

In summary, the force between two charged spheres is proportional to the product of their charges and inversely proportional to the square of the distance between them. If the size of each charge is tripled, the force between the spheres will increase by a factor of 9.

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The net force acting on the airplane is the centripetal force required to keep the airplane moving in a circular path. The angular acceleration of the airplane is 12.25 [tex]rad/s^2.[/tex]

The centripetal force is given by:

[tex]F = m * a_c[/tex]

where

F is the net force,

m is the mass of the airplane, and

[tex]a_c[/tex] is the centripetal acceleration.

The centripetal acceleration is given by:

[tex]a_c = v^2 / r[/tex]

where

v is the speed of the airplane and

r is the radius of the circle.

Since the airplane is in level flight, the net thrust of the engine is perpendicular to the tethering wire.

Therefore, it does not contribute to the centripetal force. The centripetal force is provided by the tension in the wire.

The tension in the wire is given by:

[tex]T = F_c = m * a_c[/tex]

where [tex]F_c[/tex] is the centripetal force.

The angular acceleration of the airplane is given by:

[tex]\alpha = a_c / r[/tex]

Substituting the values given:

[tex]F_c = m * a_c[/tex]

    = T = 0.6 N

[tex]a_c = v^2 / r[/tex]

[tex]0.6 N = m * v^2 / r[/tex]

[tex]v^2 = F_c * r / m[/tex]

[tex]v = \sqrt{ (F_c * r / m)[/tex]

  [tex]=\sqrt{(0.6 N * 0.2 m / 0.5 kg)[/tex]

 = 0.49 m/s

  [tex]a_c = v^2 / r[/tex]

      = 0.49 m/s / 0.2 m

      = 2.45 [tex]m/s^2[/tex]

      [tex]\alpha = a_c / r[/tex]

          [tex]= 2.45 m/s^2 / 0.2 m[/tex]

          = 12.25 [tex]rad/s^2[/tex]

Therefore, the angular acceleration of the airplane is 12.25 [tex]rad/s^2.[/tex]

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The intensity of an electromagnetic wave will therefore rise by a factor of four if both the electric and magnetic fields of the wave double in magnitude.

The square of the amplitude of the electric field, the square of the amplitude of the magnetic field, or the sum of the amplitudes of the two fields determines the intensity of an electromagnetic wave.

The wave change's intensity grows by a factor of four.

In physics, the transmitted power per unit area measured in the plane perpendicular to the direction of the energy's transmission is known as the intensity or flux of radiant energy. The base unit in the SI system is kg/s³ or watts per square meter (W/m²). With waves like sound waves or electromagnetic waves like light or radio waves, intensity most frequently refers to the average power transfer over the course of the wave. There are various circumstances where energy is transferred to which intensity can be applied.

The energy density (energy per unit volume) at a place in space and the speed at which the source is moving can both be used to determine intensity.

The complete questions is,

If both the electric and magnetic fields of an electromagnetic wave double in magnitude, how does the intensity of the wave change?

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The speeds of the six spaceships will be recorded differently by observers in different frames of reference, and their recorded speeds will depend on their relative positions and orientations to the observer.

According to Einstein's theory of relativity, the speed of an object is not an absolute quantity but is relative to the observer's frame of reference. In the case of the six spaceships, as they zoom past the intergalactic speed trap, their speeds will be recorded differently by an observer in different frames of reference.

Assuming the observer is at rest with respect to the speed trap, the speeds of the spaceships can be calculated using the formula [tex]$v = c \left(\sqrt{1-\left(\frac{L_0}{L}\right)^2}\right)$[/tex], where c is the speed of light, L0 is the rest length of the spaceship, and L is the length of the spaceship as measured by the observer.

Therefore, the recorded speeds will depend on the observer's position relative to the direction of the spaceship's motion. If the observer is directly in front of the spaceships, the lengths of the spaceships will be contracted, and their speeds will appear higher than if the observer was behind them.

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The net force on particle 92 is zero, which means it is in equilibrium and not accelerating.

The electric force between charged particles can be calculated using Coulomb's law, which states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

To find the net force on particle 92, we need to calculate the electric forces acting on it due to the other particles in the line. The force on particle 92 due to particle 91 can be calculated using Coulomb's law:

F_92,1 = kq_1q_2 / r²

            = (9x10⁹ Nm²/C²) * (-1.60x10⁻¹⁹ C) * (1.60x10⁻¹⁹ C) / (0.001 m)²

            = -2.30x10⁻¹⁴ N

The force on particle 92 due to particle 93 can also be calculated using Coulomb's law:

F_92,3 = kq_2q_3 / r²

            = (9x10⁹ Nm²/C²) * (-1.60x10⁻¹⁹ C) * (-1.60x10⁻¹⁹ C) / (0.001 m)²

            = 2.30x10⁻¹⁴ N

Since the forces due to particles 91 and 93 are equal in magnitude but opposite in direction, they cancel out each other. As a result, the net force acting on particle 92 is zero.

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The cable should have a diameter of approximately 0.092 cm or an order of magnitude of one centimeter.

To determine the diameter of the cable needed to support a tension of 20.0 kN, we can use the principle of cross-sectional area. The maximum tension that a wire can withstand is proportional to its cross-sectional area. Therefore, to support a tension that is 83.33 times greater than the maximum tension of a single wire, the cross-sectional area of the cable must also be 83.33 times greater.

The cross-sectional area of a wire is given by the formula A = πr², where A is the cross-sectional area, and r is the radius of the wire. Since the diameter of the wire is given as 1.00 mm, the radius is 0.50 mm or 0.005 cm. Therefore, the cross-sectional area of a single wire is:

A₁ = π(0.005 cm)² = 0.00007854 cm²

To find the diameter of the cable, we can use the formula for the cross-sectional area of a circle:

A₂ = πr₂²

where A₂ is the cross-sectional area of the cable and r₂ is the radius of the cable.

We know that the cross-sectional area of the cable needs to be 83.33 times greater than the cross-sectional area of a single wire:

A₂ = 83.33 A₁ = 83.33 x 0.00007854 cm² = 0.00654 cm²

Substituting this value into the formula for the cross-sectional area of a circle:

πr₂² = 0.00654 cm²

r₂² = 0.00654/π

r₂ = √(0.00654/π) = 0.046 cm

Therefore, the radius of the cable is 0.046 cm, and the diameter is twice that:

d = 2r₂ = 0.092 cm or 0.92 mm (to two significant figures)

In conclusion, the cable should have a diameter of the order of magnitude of one centimeter (0.092 cm).

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k/m = (2 * g * Δh) / [((1 - 0.79) * original length)^2] - (2 * g * Δh) * 0.21 / E

To determine the ratio of the spring constant to the helicopter's mass, we need to consider the change in potential energy and the work done by the shock absorbers.

Change in Potential Energy:

The change in potential energy of the helicopter as it descends can be calculated using the formula: ΔPE = mgh, where m is the mass of the helicopter, g is the acceleration due to gravity, and h is the change in height.

In this case, the helicopter descends vertically, so the change in height is equal to the compression of the shock absorbers.

ΔPE = mgΔh

Work Done by the Shock Absorbers:

The work done by the shock absorbers can be calculated using the formula: W = (1/2)kΔx^2, where k is the spring constant and Δx is the change in length of the shock absorbers.

In this case, the shock absorbers compress to 79% of their original length, which means the change in length is Δx = (1 - 0.79) * original length.

W = (1/2)k[(1 - 0.79) * original length]^2

Energy Absorbed by the Air in the Tires:

The energy absorbed by the air in the tires can be calculated as a percentage of the initial energy. Let's denote the initial energy as E.

Energy absorbed = 0.21 * E

Since the energy absorbed by the air in the tires is heat energy, it does not contribute to the work done by the shock absorbers.

Equating the Energy:

The change in potential energy is equal to the sum of the work done by the shock absorbers and the energy absorbed by the air in the tires:

ΔPE = W + Energy absorbed

mgΔh = (1/2)k[(1 - 0.79) * original length]^2 + 0.21 * E

Now we can solve for the ratio of the spring constant (k) to the helicopter's mass (m):

k/m = (2 * g * Δh) / [((1 - 0.79) * original length)^2] - (2 * g * Δh) * 0.21 / E

Please note that to obtain a specific numerical value for the ratio, we would need to know the values of g, Δh, original length, and E.

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The density  of the petrol in the storage tank is approximately: 703 kg/m³.

To determine the density of the petrol in a storage tank with a height of 4.7m and a pressure at the base of 32.3 kPa, we can use the following formula:

Pressure = Density × Gravity × Height

Where Pressure is given as 32.3 kPa, Gravity is 9.81 m/s² (as provided), and Height is 4.7m. To find the density, we can rearrange the formula as follows:

Density = Pressure / (Gravity × Height)

Now, we can plug in the values:

Density = 32,300 Pa / (9.81 m/s² × 4.7m)

Density ≈ 703 kg/m³

Therefore, the density of the petrol in the storage tank is approximately 703 kg/m³.

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Complete question:

A storage tank contains petrol to a height of 4. 7m. If the pressure at the base of the tank is "32. 3" kPa, determine the density of the petrol. Take the acceleration due to gravity to be 9. 81ms⁻².