what magnitude force is required to give a helicopter of mass m an acceleration of 0.10g upward? express your answer in terms of the variable m and appropriate constants.

The field strength on the loop axis at 10.0 cm from the loop center is 0.01 microtesla.

The field strength on the loop axis at 10.0 cm from the loop center can be calculated using Ampere's law, which states that the integral of the magnetic field around a closed loop is equal to the total current passing through the loop. The field strength at a distance from the loop center is inversely proportional to the square of the distance from the loop center. Thus, the field strength on the loop axis at 10.0 cm from the loop center is inversely proportional to 10.0 cm^2 or 100 cm^2, which is equal to 0.01 microtesla.
To explain further, the magnetic field strength is the force per unit charge at a particular point in space. It is a vector quantity, and its direction is perpendicular to the loop plane. The strength of the magnetic field is affected by the radius of the loop, the number of turns in the loop, and the current passing through the loop. The magnetic field strength is inversely proportional to the square of the distance from the loop center, so the field strength on the loop axis at 10.0 cm from the loop center is 0.01 microtesla.

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The star might be quite large in size, with a much larger surface area than the sun. This would increase its luminosity despite its cooler temperature.

The star has a high luminosity (100,000 x the sun's) and a cool temperature (3500 K) because of its size.

A star's luminosity is proportional to its size, so if a star is very large, it can have a high luminosity even if it is relatively cool.

Another possibility is that the star is in a phase of its life cycle where it has expanded and cooled, such as a red giant or supergiant, but still retains a high luminosity due to its large size.

These stars have relatively low surface temperatures, but their large sizes give them very high luminosities.

Therefore, this star is likely very large and thus has a very high luminosity despite its low temperature.

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The strobe light's flashes occur at a 70 Hz frequency.

The frequency of a sound pressure wave, also known as pitch, is the quantity of times every second that it repeats. A bullfrog cry is far downward communication than a whistle, while a cricket is much downward communication than a drum beat.

T is the amount of time between flashes in seconds, and f is the frequency expressed in Hertz (Hz).We obtain the following value by inserting the given value: f = 1 / (1/70) f = 70 Hz.

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The Neocrystallization topic of the Metamorphic Change Animation options are A (Neocrystalline garnets form), B(Existing minerals become elongated and take on a foliation), and D. (Existing minerals undergo plastic deformation. E. Neocrystalline garnets are compressed.)

Based on the information provided, during the transition of mudstone to schist through neocrystallization:
A. Neocrystalline garnets form - This occurs as new minerals, like garnets, form during the metamorphic process.
B. Existing minerals become elongated and take on a foliation - As the mudstone undergoes metamorphism, the existing minerals align and elongate, developing a foliation.
D. Existing minerals undergo plastic deformation - During metamorphism, pressure and temperature changes cause the minerals to undergo plastic deformation, changing their shape and size.
Based on the Neocrystallization topic of the Metamorphic Change Animation, the following occur during the transition of mudstone to schist: - Existing minerals become elongated and take on a foliation - Neocrystalline garnets form Therefore, options A and B are the correct answers.
So, the correct options are A, B, and D.

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When a ball is shot straight up into the air from the ground with initial velocity of 49ft/sec. assuming that the air resistance can be ignored, the maximum height that the ball goes up will be 73.96 ft.

This can be determined by using the kinematic equations for constant acceleration. The kinematic equation that relates the displacement, initial velocity, acceleration, and time is given by:

S = ut + 1/2 at²

where, S is the maximum height the ball goes up, u is the initial velocity of the ball, a is the acceleration of the ball, t is the time taken by the ball to reach maximum height.

Now, the initial velocity of the ball is u = 49 ft/s (given). Since the ball is thrown upwards, the acceleration of the ball will be downwards, i.e., a = -32.2 ft/s² (taken as negative since it is in the opposite direction to the motion)

At maximum height, the final velocity of the ball will be zero. Hence, using the equation, v = u + at, at maximum height, v = 0 and u = 49 ft/s, a = -32.2 ft/s²

Substituting these values in the equation,

v = u + at0

= 49 - 32.2*t

t = 1.52 s.

Now, substituting u, a, and t in the equation,

S = ut + 1/2 at²

S = 49(1.52) + 1/2 (-32.2)(1.52)²

S = 73.96 ft

Therefore, the maximum height that the ball goes up is 73.96 ft.

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246.5ft.

The ball shot straight up into the air with an initial velocity of 49ft/sec will reach a maximum height, before it begins to fall back to the ground. Assuming no air resistance, the ball will reach a maximum height of 246.5ft.

To calculate this, use the formula h = (vi2) / (2g), where vi is the initial velocity and g is the acceleration due to gravity (g = 9.8m/s2).

Plugging in the values given, we get: h = (49ft/sec)2 / (2 * 9.8m/s2) = 246.5ft.

Therefore, the ball will reach a maximum height of 246.5ft.

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Answer:

i got 6

Explanation:lmk if i’m wrong

In the following question, among the conditions given, The peak vertical ground reaction force (not resultant force) from the beginning of the measurement through leaving the ground in your spreadsheet is the highest vertical force.

Hence The peak vertical ground reaction force (not resultant force) from the beginning of the measurement through leaving the ground in your spreadsheet is the highest vertical force that the ground exerts on your body during the time period in question. so then, in order To calculate this, you need to examine your spreadsheet and look for the highest vertical force value present in the data.

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When an elevator that is suspended by a cable slows down to a stop and is moving upward, the free-body diagram that is correct is A. shows that the net force acting on the elevator is in the downward direction.

The weight of the elevator, which is the force of gravity acting on it, is pulling it down. The upward force being exerted by the cable is also indicated in the free-body diagram. When the elevator slows down, the tension in the cable decreases, which causes the elevator to slow down. Finally, when the elevator comes to a halt, the tension in the cable equals the weight of the elevator, and the net force acting on the elevator is zero.

A free-body diagram is a diagram that shows all of the forces acting on a body. It can also be referred to as a force diagram. Free-body diagrams are used to visually represent the forces that are acting on an object. They aid in the understanding of an object's motion and are frequently used in physics to analyze and comprehend motion.

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In the inner solar system the largest surface fratures such as volacanos or valleys are found on the largest planets is a False  statement.

The largest planets in our solar system are gas giants, which do not have a solid surface. Therefore, they cannot have surface features like volcanoes or valleys.

In the inner solar system, the planet with the largest surface features is actually Mercury, which is the smallest planet. Mercury has a giant impact basin called the Caloris Basin, which is over 1,500 kilometers in diameter.

Lastly, Venus has large volcanic features, including its highest mountain, Maxwell Montes, which is over 11 kilometers tall.

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The apparent weight of a person with a mass of 78 kg in an elevator accelerating upward at 1.80 m/s2 is 91.2 kg.

This is calculated using the equation: apparent weight = mass x acceleration due to gravity + acceleration of elevator, which equals 78 kg x 9.81 m/s2 + 1.80 m/s2 = 91.2 kg.

Steps:

Therefore, the apparent weight of the person is 767.78 N + 140.4 N = 908.18 N.

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The immersion heater would take approximately 0.0465 minutes to heat 250g of water from 20°C to 100°C.

The number of minutes required for a 300W immersion heater to heat 250g of water from 20°C to 100°C can be calculated by applying the specific heat capacity formula.

According to the formula,

The amount of heat needed to increase the temperature of a substance is equal to the product of the mass of the substance, the specific heat capacity of the substance, and the change in temperature.

Specific heat capacity formula:

q = mcΔT

Where:
q = heat energy (Joules)
m = mass of substance (kg)

c = specific heat capacity of substance (Joules/kg°C)
ΔT = change in temperature (°C)

In this case, we have:
m = 0.25 kg (since 250g is equal to 0.25kg

c = 4.184 J/g°C (specific heat capacity of water)
ΔT = (100°C - 20°C) = 80°C

We need to convert the power of the immersion heater from Watts to Joules per second since the specific heat capacity formula requires the units of power to be in Joules per second (J/s).

1 Watt = 1 Joule/second (J/s)

So, the power of the immersion heater can be converted as follows:

300 Watts = 300 Joules/second (J/s)


q = mcΔT

to find the heat energy required to heat the water:

q = (0.25 kg) x (4.184 J/g°C) x (80°C)
q = 836.8 Joules

The time taken to heat the water can be calculated using the formula:

Power = Energy / Time

where Power is in Watts (J/s), Energy is in Joules, and Time is in seconds.

Time = Energy / Power

Time = 836.8 J / 300 J/s

Time = 2.79 seconds

So, the number of minutes required for the immersion heater to heat 250g of water from 20°C to 100°C is:

2.79 seconds ÷ 60 = 0.0465 minutes

Therefore, the immersion heater would take approximately 0.0465 minutes to heat 250g of water from 20°C to 100°C.

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The boat will bob up and down on ocean waves that have a wavelength of 36.0 m and a propagation speed of 4.80 m/s once every 7.50 seconds.

To solve the given question, we must use the formula:

n= v/f

Where: v is the velocity of the wave (in m/s)f is the frequency of the wave (in Hz)n is the number of cycles per second

Therefore, the frequency of the wave (in Hz) can be calculated by using the formula:

f= v/λ

where: v is the velocity of the wave (in m/s)λ is the wavelength of the wave (in m)

The frequency of the wave is 0.1333 Hz (approx).

Now, the number of cycles per second (n) is: n = v/λ

We can solve for n by dividing the velocity of the wave by the wavelength of the wave.

Therefore,

n= v/λ= (4.80 m/s) / (36.0 m)= 0.1333 Hz

So, the boat bob up and down 0.1333 times a minute on ocean waves that have a wavelength of 36.0 m and a propagation speed of 4.80 m/s.

1 Hz = 60 seconds,

0.1333 Hz = 7.50 seconds.

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The angular momentum of the Earth spinning on its axis is 7.1 × 10³⁰ kilogram meters squared per second.

Angular momentum is the quantity of rotation of a body that takes into account its mass and its rotational speed. Angular momentum = Moment of inertia × Angular velocity

where the moment of inertia is a measure of how an object's mass is distributed around its centre of rotation.

The moment of inertia of the Earth:

moment of inertia = 2/5 × mass × radius²

where the mass of the Earth is 5.97 × 10²⁴ kg and its radius is 6.38 × 10⁶ m.

Therefore, moment of inertia = 2/5 × 5.97 × 10²⁴ kg × (6.38 × 10⁶ m)²

                                                = 9.83 × 10³⁷ kg m²

Using the fact that the Earth completes one rotation every 24 hours, or 86400 seconds,

the angular velocity of the Earth:

angular velocity = 2π / time taken for one rotation

                           = 2π / 86400 seconds

                           = 7.27 × 10⁻⁵ radians per second

Finally, the angular momentum of the Earth spinning on its axis:

angular momentum = Moment of inertia × Angular velocity

                                 =9.83 × 10³⁷ kg m² × 7.27 × 10⁻⁵ radians per second

                                 = 7.1 × 10³⁰ kg m²/s

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The magnitude of the impulse on a 7.2-kg ball rolling at 2.4 m/s when it bumps into a pillow and stops can be calculated using the impulse-momentum theorem.

According to the theorem, the impulse of an object is equal to the change in momentum of the object. Since the ball has a mass of 7.2 kg and an initial velocity of 2.4 m/s, its initial momentum is 17.28 kg·m/s. As the ball stops when it hits the pillow, its final momentum is 0. The change in momentum is therefore -17.28 kg·m/s.

Since the impulse of an object is equal to its change in momentum, the impulse of the ball is -17.28 kg·m/s. This means that the impulse of the ball is equal to the magnitude of the force applied to the ball multiplied by the duration of the collision. Thus, the magnitude of the impulse on the ball when it bumps into the pillow and stops is -17.28 kg·m/s.

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The given statement a constructor which has thrown an exception will also return a reference to its constructed object is false  because when an exception is thrown during the construction of an object, the constructor does not complete its initialization process.

As a result, the constructed object may be in an invalid or partially constructed state, which can lead to unexpected behavior if the object is used later in the program. A constructor cannot return a value, not even a reference to its constructed object. Instead, the constructor initializes the object's data members and sets up the object's state. If a constructor throws an exception, the object is not fully constructed and is therefore not valid. The exception can be caught and handled by the caller of the constructor.

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The damping ratio of the system can be calculated as 0.13.

What is displacement?

Displacement at resonance, Xn = 0.6 inches

Displacement at very high RPM, Xv = 0.15 inches

Natural frequency of a system is:

f = (1/2π) * √(k/m)

where k is the stiffness of the system and m is its mass.

Let's assume the mass of the system as m and k is the stiffness of the system.

When the motor is at resonance, the frequency of the system is: n = f

where n is the frequency of the system.

When the motor is running at very high rpm, the frequency of the system is given as:v = f

where v is the frequency of the system.

Now, let's assume the damping coefficient of the system as c.

The displacement of the system:

X = [Xn * exp(-ζωnt)] * sin(ωdt)

where X is the displacement of the system, ζ is the damping ratio of the system, ωn is the natural frequency of the system and ωd is the frequency of the applied force.

The maximum value of the displacement is:

Xmax = Xn / (2ζ * √(1 - ζ²))

Here, Xmax = 0.6 inches when the motor is at resonance Xmax = 0.15 inches

when the motor is running at very high RPM, putting the given values of Xmax in the above equation, we can find the value of the damping ratio, ζ.

For resonance:0.6 = Xn / (2ζ * √(1 - ζ²))

=> 2ζ * √(1 - ζ²)

= Xn / 0.6=> 4ζ² * (1 - ζ²)

= Xn² / 0.36=> 4ζ⁴ - 4ζ² + 0.26244

= 0

Solving this quadratic equation gives us the value of ζ as 0.32.

For high RPM:

0.15 = Xn / (2ζ * √(1 - ζ²))

=> 2ζ * √(1 - ζ²)

= Xn / 0.15=> 4ζ² * (1 - ζ²)

= Xn² / 0.0225

=> 4ζ⁴ - 4ζ² + 1.728 = 0

Solving this quadratic equation gives us the value of ζ as 0.13.

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A force of 245 N must be applied vertically to lift the bag off the baggage cart.

The force that must be applied vertically to lift a bag off a baggage cart, given that the bag has a mass of 25 kg, can be determined using the formula F = m*g

where F is force, m is mass, and g is acceleration due to gravity. The value of g is 9.8 m/s².So, F = 25 kg x 9.8 m/s² = 245 N. Therefore, a force of 245 N must be applied vertically to lift the bag off the baggage cart.

The mass of the bag = 25 kg.The formula used is, F = m*gwhereF = Force required to lift the bagm = Mass of the bagg = Acceleration due to gravityF = 25 kg x 9.8 m/s² = 245 N.

Therefore, a force of 245 N must be applied vertically to lift the bag off the baggage cart.

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The work done by the force (in one-hundredth of Joule) on the distance AB is -15300×J/100. The total work done by the forces acting on the body over the distance AB is -153 J. The magnitude of the acceleration of the body is 1.53 m/s².

a) To find the work done by the force on the distance AB, we first need to find the displacement vector from point A to point B:

Displacement vector, AB = B - A

= (28-2, 75-8, 68-0) = (26, 67, 68)

Now, we calculate the dot product of the force vector and the displacement vector:

F • AB = (2,1,-4) • (26,67,68)

= 2(26) + 1(67) - 4(68)

= 52 + 67 - 272

= -153
The work done by the force on the distance AB in one-hundredth of Joule is given by:
Work = F • AB

=-15300×J/100.

b) Since there is only one force acting on the body, the total work done by the forces acting on the body over the distance AB is the same as the work done by the force F:
Total work = -153 J

c) The acceleration of the body is given by Newton's Second Law of Motion:

F = ma

=> a = F/m

where F is the force and m is the mass of the body.

a = F/m

= (2, 1, -4)/3

= (0.67, 0.33, -1.33) m/s²

Therefore, the magnitude of the acceleration of the body is

|a| = √(0.67² + 0.33² + (-1.33)²) ≈ 1.53 m/s² (corrected to the nearest hundredth of m/s²).

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As a percentage of their total volumes, the cores of Uranus and Neptune are smaller than the cores of Saturn and Jupiter.

Uranus, Neptune, Saturn, and Jupiter are all gas giant planets with a layered structure consisting of a core, mantle, and atmosphere. The size of the core relative to the rest of the planet is determined by the planet's formation and evolution history.

Jupiter and Saturn are known to have relatively large cores compared to their overall size, while Uranus and Neptune are believed to have smaller cores.

However, the exact sizes and compositions of the cores of these planets are still a subject of research and debate. As a result, it is difficult to provide a precise comparison of the sizes of the cores of these planets as a percentage of their total volumes.

Based on current knowledge, it is generally accepted that the cores of Uranus and Neptune are smaller than the cores of Saturn and Jupiter as a percentage of their total volumes.

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The distance at which the music is just barely audible to a person with a normal threshold of hearing depends on the intensity level of the sound and the threshold of hearing.

The threshold of hearing is the lowest level of sound that can be heard by the human ear. It is typically measured in decibels (dB) and varies depending on the frequency of the sound.

The most common method for measuring the threshold of hearing is through audiometry, which involves presenting sounds of varying intensities and frequencies to the subject and determining the lowest level at which they can hear the sound.

Sound intensity level decreases with distance from the source according to the inverse square law, which states that the intensity of a sound wave decreases as the square of the distance from the source.

This means that if the distance from the source is doubled, the sound intensity level will decrease by a factor of four.

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The circuit's initial current via the junction where the two resistors are separated is 11 mA. The current divides and simultaneously passes via both resistors in a paralleled resistor circuit using two resistors.

A battery and many capacitors are linked in series. The capacitors have a comparable amount of charge.

A battery and many capacitors are linked in series. The sum of the potential differences between each capacitor equals the current battery emf.

When two resistors having resistance R that are similar to one another are linked in series, the capacitive reactance is 2R.

Both negative and positive ions move charges whenever an electricity flows through with an ionic liquid like salty water. Energy is measured in electron-volts.

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The direction the automobile should move to generate the maximum motional emf in the antenna, with the top of the antenna positive relative to the bottom towards the east.

A magnetic field is an area surrounding a magnet or an electric current, characterized by the presence of a force that can attract or repel other magnetic materials. The concept of magnetic fields is significant in a variety of contexts, including electromagnetism, particle physics, and ferromagnetism.

According to Faraday's Law of Electromagnetic Induction, the emf generated in a conducting wire moving in a magnetic field is proportional to the strength of the magnetic field and the velocity of the conductor.

The magnitude of the emf is given by ε = Blv sinθ, where

- ε is the magnitude of the induced emf,

- B is the magnetic field strength,

- l is the length of the wire in the magnetic field,

- v is the speed of the conductor relative to the magnetic field, and

- θ is the angle between the velocity vector and the magnetic field vector.

Due to the given conditions in the question, we can use the above formula for calculating the maximum emf. To generate the maximum motional emf in the antenna, the automobile should move in a direction perpendicular to both the antenna and the Earth's magnetic field. The angle between the velocity vector and the magnetic field vector should be 90°.

1: Identify the direction of the magnetic field. In this case, the magnetic field is directed toward the north and downward at an angle of 65.0° below the horizontal.

2: Determine the direction perpendicular to both the antenna and the magnetic field. This can be done by using the right-hand rule. Point your right thumb in the direction of the magnetic field (north and downward at 65.0° below the horizontal) and your right index finger in the direction of the antenna (vertical). Your right middle finger will then point in the direction of the motion required to generate the maximum emf (perpendicular to both the magnetic field and the antenna).

The direction the automobile should move to generate the maximum motional emf in the antenna, with the top of the antenna positive relative to the bottom, is to the east.

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The force acting on a conductor 0.25 m long carrying a current of 0.5 A in a magnetic field with a flux density of 0.4 T is 1 N.

The force acting on a conductor carrying a current in a magnetic field is given by the equation F=BIL, where F is the force, B is the magnetic flux density, I is current, and L is the length of the conductor.

To calculate Force:
1. Substitute the given values into the equation: F = BIL
2. F = (0.4 T) (0.5 A) (0.25 m)
3. F = 1 N

Therefore, A conductor that is 0.25 meters long and has a current of 0.5A flowing through it experiences a force of 1N when placed in a magnetic field with a flux density of 0.4T.

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Wavelength of light = 5 x 10^-7 m = 500 nm.Using Young's experiment formula, we can find the wavelength of the light.

Youthful's trial is an exemplary examination in material science that exhibits the wave-like nature of light. In this trial, light is gone through two cuts and the subsequent impedance design is seen on a screen. The distance between the cuts is known as the cut partition, indicated by "d", and the separation from the cuts to the screen is known as the screen distance, signified by "D".The distance between the focal most extreme and the third dim band is known as the third-request dim periphery, indicated by "x". We are given that the cut partition, d, is 1.5 x 10^-4 m, the screen distance, D, is 1.0 m, and the third-request dim periphery, x, is 1 cm (or 0.01 m).To decide the frequency of the light, indicated by λ, we can utilize the accompanying recipe:

λ = (xd)/D

Subbing the given qualities, we get:

λ = (0.01 m)(1.5 x 10^-4 m)/(1.0 m) = 1.5 x 10^-7 m = 150 nm

Accordingly, the frequency of the light is 150 nanometers. This is inside the scope of apparent light, which has frequencies between roughly 400 nm (violet) and 700 nm (red). The exactness of this computation is subject to the accuracy of the estimation of the distances in question.

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The current that would pass through the body is 0.92 A.

Current is a measure of the rate of flow of electric charge in a circuit and is measured in amperes (A). Ohm's law describes the relationship between voltage, current, and resistance in an electrical circuit.

Using Ohm's Law, the current that would pass through the body can be calculated as:

I = V/R, where V is the voltage and R is the resistance.

In this scenario,

V = 120 V

R = 130,000 ohms

Substituting these values in the formula, we get:

I = 120 V / 130,000 ohms = 0.92 A.

Therefore, approximately 0.92 amperes (or 920 milliamperes) of current would pass through the body.

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"  deep currents circulate seawater around the globe due to differences in the density of water at different locations. two factors that can alter the density of water are salinity and temperature. " The correct Answers are option : A & D.

The density of seawater depends on various factors, including salinity and temperature. Salinity is the measure of  amount of dissolved salts in seawater, and affect the density of water because saltwater is denser than freshwater. Temperature plays a crucial role in density of seawater, as cold water is denser than warm water. These factors can lead to  formation of currents circulate seawater around  globe, transferring heat and nutrients across vast distances in the ocean. Hence option A & D are correct.

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If Jordan escapes, he will be 61 m behind the lion, , the lion will be 6m away from the land rover when it catches Jordan.

Jordan takes 1 second to react and turn around, and then he runs at a velocity of 5 m/s. This means that he will reach the land rover in (6m / 5m/s) = 1.2 seconds. At the same time, the lion is running at a velocity of 50 km/h, which is (50 km/h * (1000m/1 km)) / (60s/1min) = 833.33 m/s. This means that the lion will reach Jordan in (26m / 833.33m/s) = 0.031 seconds.

Jordan will reach the land rover before the lion reaches him, so he escapes. Since the lion started 26m away, and has a velocity of 833.33 m/s, it will take (26m / 833.33m/s) = 0.031 seconds for the lion to cover the 26m and reach Jordan. In this same amount of time, Jordan will have covered (0.031s * 5m/s) = 0.155 m. Therefore, Jordan will be 61m behind the lion.

If Jordan is caught, he will be 6m away from the land rover. This is because the land rover is 6m away from him and the lion started 26m away from him, but will reach Jordan after 0.031s. This means that the lion will cover a distance of (0.031s * 833.33m/s) = 25.94m in that time, and Jordan will only cover (0.031s * 5m/s) = 0.155m. Therefore, the lion will be 6m away from the land rover when it catches Jordan.

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Approximately [tex]1.31 \times 10^{20}[/tex] electrons are transferred in a strong lightning bolt carrying an electric charge of 21 C.

The electric charge of one electron is equal to [tex]-1.602 \times 10^{-19}[/tex] Coulombs (C). Therefore, we can calculate the number of electrons transferred by dividing the total charge transferred by the charge of a single electron:

Number of electrons = Total charge transferred / Charge of a single electron

Number of electrons = [tex]\frac{21 C }{-1.602 \times 10^{-19} C}[/tex]

The number of electrons ≈ [tex]1.31 \times 10^{20} electrons[/tex]

Hence the number of electrons transferred during the lightning bolt is [tex]1.31 \times 10^{20}[/tex].

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To determine the temperature increase if a specific amount of heat energy is transferred to the gas at a constant volume, we will use the equation:

Q = nCvΔT,

where Q is the amount of heat energy transferred, n is the number of moles of gas, Cv is the heat capacity at a constant volume, and ΔT is the temperature change.

The expression to determine the temperature change is:

ΔT = Q / (nCv)

where ΔT is the change in temperature, Q is the amount of heat energy transferred, n is the number of moles of gas, Cv is the specific heat capacity at constant volume.

For this case, the formula to calculate the change in temperature if a certain amount of heat energy is transferred to the gas at constant volume is given by:

ΔT = Q / (nCv)

Where; ΔT = temperature change, n = number of moles of gas, Cv = specific heat capacity at constant volume, Q = amount of heat energy transferred.


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The natural length of the spring is 5 cm.

Given dataThe amount of work done to stretch a spring from 7 cm to 9 cm is 6 J.The amount of work done to stretch a spring from 9 cm to 11 cm is 10 J.

The formula for potential energy stored in a spring is

    U=12kx2

Here,

U is potential energy stored in a spring

k is a spring constantx is the displacement of the spring from its natural length

U = 12kx2

Thus, U is proportional to x2

For the first stretching, we have

U1 = 12k(0.02)2

For the second stretching, we have

U2 = 12k(0.02)2

The difference in the amount of work done to stretch a spring is proportional to the difference in the potential energy stored in the spring.

So,U2 - U1 = 10 J - 6 J= 4 J= 12k(0.02)2 - 12k(0.02)2= 12k(0.04)k = 4/3

The natural length of the spring is given by x0 = U/k

Here, U is the potential energy stored in a spring when stretched by x So, the natural length of the spring is

x0 = 12kx02x0 = 12(4/3)(0.05)2x0 = 5 cm

Therefore, the natural length of the spring is 5 cm.

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