The amount of kinetic energy an object has depends on which feature of the object?

its motion
its position
its gravity
its height

The electric field vector produced by the applied stress, assuming the electric displacement is held equal to zero, is X V/m.

In a piezoelectric material, the relationship between stress (σ) and electric field (E) is given by the piezoelectric coefficient (d) multiplied by the stress tensor (T). The electric field vector can be calculated using the equation E = d * T.In this case, we are given the stress values applied in different directions: 3 MPa in the direction of polarization and 5 MPa in the two directions normal to the polarization vector. To calculate the electric field, we need the piezoelectric coefficient for the specific material, APC850. Once we have the value of d, we can substitute the stress tensor values into the equation to determine the electric field vector.However, without the specific piezoelectric coefficient for APC850, I'm unable to provide an exact numerical value for the electric field. It is crucial to have the material's specific piezoelectric coefficient to perform the calculation accurately.

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The kinetic energy (KE) of the emitted photoelectrons in the Sodium surface will be: lower compared to the KE of the photoelectrons in the Potassium surface.

The work function of a material is the minimum amount of energy required to remove an electron from its surface. If the work function of Sodium is greater than that of Potassium, it means that Sodium requires more energy to remove electrons compared to Potassium.

When photons of the same wavelength are incident on both surfaces, the energy of the photons is given by E = hf, where h is Planck's constant and f is the frequency of the photons (related to the wavelength).

For the photoelectric effect to occur, the energy of the incident photons must exceed the work function of the material. Since Sodium has a higher work function than Potassium, it will require photons with higher energy to exceed its work function and emit photoelectrons.

Therefore, the photons incident on the Sodium surface, despite having the same wavelength as those incident on the Potassium surface, will have lower energy. As a result, the kinetic energy of the emitted photoelectrons in the Sodium surface will be lower compared to the kinetic energy of the photoelectrons in the Potassium surface.

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The electric field is equal to zero at a point on the line through the ends of the meter stick located between the two charges, specifically between 0 cm and 50 cm.

To determine the point on the line where the electric field is zero, we can use the principle of superposition. The electric field produced by a point charge is given by Coulomb's law:

[tex]\[ E = \frac{{k \cdot |q|}}{{r^2}} \][/tex]

where E is the electric field, k is Coulomb's constant [tex](\(8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2\)), \(q\)[/tex] is the charge, and r is the distance from the charge.

Considering the positive charge at the 0.0 cm mark, the electric field it produces points away from it. Similarly, the negative charge at the 50.0 cm mark produces an electric field that points towards it.

Between the two charges, there exists a point where the electric field contributions from both charges cancel out, resulting in a net electric field of zero. This point can be determined by setting the electric field equations for the two charges equal to each other and solving for the position:

[tex]\[ \frac{{k \cdot |q_1|}}{{r_1^2}} = \frac{{k \cdot |q_2|}}{{r_2^2}} \][/tex]

Substituting the values [tex]\(q_1 = 5.00 \, \mu\text{C}\), \(r_1 = 0.00 \, \text{cm}\), \(q_2 = -4.00 \, \mu\text{C}\), and \(r_2 = 50.00 \, \text{cm}\)[/tex], we can solve for the position r of the point where the electric field is zero. The solution will yield a value between 0 cm and 50 cm, indicating the location of the point on the line between the two charges where the electric field is zero.

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The uncertainty in the position of a proton in an atomic nucleus is approximately equal to the diameter of the nucleus.

According to the principles of quantum mechanics, the Heisenberg uncertainty principle states that it is impossible to simultaneously determine the precise position and momentum of a particle. The uncertainty in position is quantified by the standard deviation of the position measurements, which gives us an estimate of the range within which the particle is likely to be found.

In the case of a proton confined within the nucleus of an atom, the uncertainty in its position is approximately equal to the diameter of the nucleus itself. The diameter of a typical atomic nucleus is on the order of femtometers ([tex]10^-^1^5[/tex] meters). This means that the uncertainty in the position of a proton within the nucleus is also on the order of femtometers.

Therefore, we can say that the uncertainty in the position of a proton confined to the nucleus of an atom is roughly the diameter of the nucleus.

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Answer:

180N

Explanation:

the gravity on Earth is six times the one on the moon

Answer:

I think 180N

Explanation:

the gravity of the surface of the earth is 6Times

more than the moon

The energy used for the 30-day period is 1,355,000 kJ, the average energy used is 45,166.67 kJ/day, and the electric bill for this month would be approximately $101.41.

To find the energy used for the 30-day period in kJ: a) Energy Used (kJ) = 1355 kWh * 1000 Wh/kWh = 1,355,000 Wh = 1,355,000 kJ

To find the average energy used in J/day: b) Average Energy Used (J/day) = Energy Used (kJ) / 30 days

Average Energy Used (J/day) = 1,355,000 kJ / 30 days = 45,166.67 kJ/day

To calculate the electric bill for this month: c) Electric Bill = Energy Used (kWh) * Cost per kWh Electric Bill = 1355 kWh * $0.0749/kWh = $101.4145. Therefore, your electric bill for this month would be approximately $101.41.

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The speed at which the ball left the quarterback's hand was approximately 69.93 mph.

To calculate the speed at which the ball left the quarterback's hand, we can use the kinematic equation for projectile motion. Assuming the pass was thrown at a 45-degree angle, the initial vertical velocity (V₀y) would be equal to the initial horizontal velocity (V₀x) since the angle is symmetrical. We can break down the motion into horizontal and vertical components.

Given that the pass traveled 83 yards (249 feet) in the air, we can use the equation for horizontal distance to find the initial horizontal velocity:

Distance = V₀x * time,

249 ft = V₀x * time.

Since the time of flight is the same for the horizontal and vertical components, we can express time as:

time = distance / V₀x,

time = 249 ft / V₀x.

For the vertical motion, the equation for vertical displacement is:

Displacement = V₀y * time + 0.5 * g * time²,

0 ft = V₀y * time - 16 ft/s² * time².

Since the vertical displacement is zero (the ball returns to the same height), we can solve for time:

0 = V₀y - 16 ft/s² * time,

V₀y = 16 ft/s² * time.

Now we can substitute the expression for time from the horizontal motion into the vertical motion equation:

V₀y = 16 ft/s² * (249 ft / V₀x),

V₀y = 3984 ft/s² / V₀x.

Since V₀y = V₀x, we can equate the two expressions for V₀y:

V₀x = 3984 ft/s² / V₀x,

V₀x² = 3984 ft/s²,

V₀x = √(3984 ft/s²).

To convert the velocity to mph, we multiply by the conversion factor:

V₀x = √(3984 ft/s²) * (3600 s/h) / (5280 ft/mi),

V₀x = √(3984 * 3600) / 5280 mph,

V₀x ≈ 69.93 mph.

Therefore, the speed at which the ball left the quarterback's hand was approximately 69.93 mph.

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We learn about objects of interest to intelligence through matter/energy interactions such as emission, reflection, refraction, and absorption.

Emission: Objects can emit energy in the form of light, heat, or other types of radiation. By detecting and analyzing the emitted radiation, we can gather information about the object's properties and composition.
Reflection: When light or other forms of energy bounce off an object's surface, we can observe and analyze the reflected radiation. The characteristics of the reflected radiation can provide insights into the object's shape, color, and surface properties.
Refraction: When energy passes through a medium and changes direction, such as when light bends while passing through a transparent object, it undergoes refraction. By studying the changes in the direction and intensity of the refracted energy, we can gain knowledge about the object's composition and structure.
Absorption: Objects can absorb certain types of energy, causing a decrease in its intensity. By examining the absorbed energy and the wavelengths that are absorbed, we can acquire information about the object's chemical composition and properties.
Through these interactions, scientists and researchers employ various instruments and techniques to gather data and learn about objects of interest, enabling us to deepen our understanding and make informed interpretations and analyses.

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The example of functional fixedness is: B) Natasha doesn't think of using her CD case as an ice scraper to clear her windshield.

The example of functional fixedness is: B) Natasha doesn't think of using her CD case as an ice scraper to clear her windshield. Functional fixedness refers to a cognitive bias where an individual is unable to see alternative uses or functions for an object beyond its typical or intended purpose. In this case, Natasha is unable to think of using her CD case as an ice scraper, indicating functional fixedness.

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Answer:

7.35..kg

Explanation:

Hope this will help you

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Answer:

v₂ = 16 m/s

Explanation:

We can use the continuity equation, which is as follows:

[tex]A_1v_1 = A_2v_2\\[/tex]

where,

A₁ = Area of inlet = πd²/4

A₂ = Area of outlet = π(d/2)²/4 = πd²/16

v₁ = velocity at inlet = 4 m/s

v₂ = velocity at outlet = ?

Therefore,

[tex](\frac{\pi d^2}{4})(4\ m/s)=(\frac{\pi d^2}{16})v_2\\\\[/tex]

v₂ = 16 m/s

The angular magnification produced by the reflecting telescope when a 3.05 m focal length eyepiece is used is approximately -1.97.

To calculate the angular magnification produced by a telescope, we can use the formula

Angular Magnification = - (fobjective / feyepiece)

Where:

fobjective is the focal length of the objective mirror

feyepiece is the focal length of the eyepiece

In this case, the objective mirror has a radius of curvature of 12.0 m, so its focal length (fobjective) is half of the radius of curvature:

fobjective = 12.0 m / 2 = 6.0 m

The focal length of the eyepiece is given as 3.05 m (feyepiece).

Substituting the values into the formula:

Angular Magnification = -(6.0 m / 3.05 m)

Angular Magnification = -1.97

Since the angular magnification is negative, it indicates that the image produced by the telescope is inverted.

Therefore, the angular magnification produced by the reflecting telescope when a 3.05 m focal length eyepiece is used is approximately -1.97.

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The radii r₁, r₂, and r₃ of the nuclei 4,2He, 236,92U, and 56,26Fe are  1.9044 x 10⁻¹⁵ meters, 4.3944 x 10⁻⁵ meters, 4.3944 x 10⁻¹⁵ meters.

The radii of atomic nuclei can be estimated using the empirical formula known as the "constant density model." According to this model, the radius (r) of a nucleus can be approximated using the equation:

r = r0 A¹/³

where r0 is a constant and A is the mass number of the nucleus.

The value of r0 is typically taken to be around 1.2 fm (femtometers) or 1.2 x 10⁻¹⁵ meters.

For the nucleus 4,2He (helium-4):

A = 4

r0 = 1.2 fm

r1 = 1.2 fm × 4¹/³

≈ 1.2 fm × 1.587

≈ 1.9044 fm

≈ 1.9044 x 10⁻¹⁵ meters

Therefore, r1 = 1.9044 x 10⁻¹⁵ meters.

For the nucleus 236,92U (uranium-236):

A = 236

r0 = 1.2 fm

r2 = 1.2 fm × 236¹/³

≈ 1.2 fm × 6.118

≈ 7.3416 fm

≈ 7.3416 x 10⁻¹⁵ meters

Therefore, r2 = 7.3416 x 10⁻¹⁵ meters.

For the nucleus 56,26Fe (iron-56):

A = 56

r0 = 1.2 fm

r3 = 1.2 fm × 56¹/³

≈ 1.2 fm × 3.662

≈ 4.3944 fm

≈ 4.3944 x 10⁻¹⁵ meters

Therefore, r3 = 4.3944 x 10⁻¹⁵ meters.

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18.22 kg/mol is the molar mass of the gene fragment if a bacterial gene fragment of 10.0 mg is dissolved in enough water to make 30.0 ml of solution.

What is a solution?

In a homogenous mixture of two or more components, a solution is defined as having particles less than one nanometer in size. Solutions come in many forms, such as sugar and salt solutions, soda water, etc. In a solution, each element appears as a separate phase.

The ratio between the mass and the amount of a chemical compound's constituents is known as the compound's molar mass. A substance's molar mass is a bulk attribute rather than a molecular one.

π = cRT

c = n/V

n = w/m = 10*10^-3 /[m*30*10^-3]M

m = RT/383.14 = 18.22 kg/mol

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The turbine generates entropy at a rate of about 2.4944 kW/K. The option that comes closest to the provided values is (c) 3.34 kW/K.

To find the rate of entropy generation in the turbine, we need to apply the concept of entropy balance. The rate of entropy generation can be determined by calculating the difference between the entropy flow into and out of the system.

Given:

Inlet conditions:

Pressure at inlet (P₁) = 0.18 MPa

Mass flow rate (m) = 1.6 kg/s

Exit conditions:

Pressure at exit (P₂) = 1 MPa

Temperature at exit (T₂) = 60 degrees C = 333.15 K

First, we need to determine the specific entropy at the inlet and outlet states. We can use the properties of Refrigerant-134a to find these values.

From the saturation table for Refrigerant-134a at 0.18 MPa (inlet pressure), we can find the corresponding saturation temperature T1.

At P₁ = 0.18 MPa:

Saturation temperature T1 = 20.83 degrees C = 293.98 K

From the superheated table for Refrigerant-134a at 1 MPa (exit pressure) and 60 degrees C (exit temperature), we can find the specific entropy value S2.

At P₂ = 1 MPa, T₂ = 60 degrees C:

Specific entropy S₂ = 1.559 kJ/(kg·K)

The rate of entropy generation in the turbine can be calculated as:

Rate of entropy generation = m * (S₂ - S₁)

Where:

m = mass flow rate

S₂ = Specific entropy at the exit

S₁ = Specific entropy at the inlet

Substituting the values:

Rate of entropy generation = 1.6 kg/s * (1.559 kJ/(kg·K) - 0)

Rate of entropy generation = 1.6 kg/s * 1.559 kJ/(kg·K)

Rate of entropy generation ≈ 2.4944 kW/K

Therefore, the rate of entropy generation in the turbine is approximately 2.4944 kW/K.

Among the given options, the closest one is (c) 3.34 kW/K.

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To determine the angular radius of the rings observed in a Michelson interferometer, we can use the formula: Angular radius = λ / (2πd)

where λ is the wavelength of light and d is the path difference. a) For the first (smallest diameter) ring: λ = 632.8 nm = 632.8 × 10^(-9) m. d = 20 μm = 20 × 10^(-6) m. Angular radius = (632.8 × 10^(-9)) / (2π × 20 × 10^(-6)). b) For the tenth ring, the path difference would be 10 times larger than for the first ring, so the new path difference would be: d' = 10 × d = 10 × 20 × 10^(-6) m. Angular radius = (632.8 × 10^(-9)) / (2π × 10 × 20 × 10^(-6)) By calculating these expressions, you can find the values for the angular radii of the first and tenth rings observed in the Michelson interferometer using the given wavelength and path difference.

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You should aim below the observed fish to make a direct hit.  It's essential to practice and gain experience to develop a better understanding of how refraction affects your aim in different situations.

When light passes from one medium (air) to another (water), it undergoes refraction, which causes the light rays to change direction.

This phenomenon is the reason why objects submerged in water appear to be at a different position than they actually are.

To understand how refraction affects spearfishing, we need to consider the path of light rays.

When you look at a fish in the water, the light rays coming from the fish travel through the water and then enter your eyes.

However, when you aim the spear at the fish, the light rays from the fish will follow a different path due to refraction.

The key point is that light rays bend towards the perpendicular when they pass from a less dense medium (air) to a more dense medium (water).

This means that the fish will appear higher in the water than it actually is. To compensate for this apparent displacement, you need to aim below the observed fish.

The exact amount you need to aim below the fish depends on factors such as the angle at which you are viewing the fish and the depth of the water. To calculate the correct aiming point, you can use the concept of the apparent shift caused by refraction.

To make a direct hit while spearfishing, you should aim below the observed fish.

However, keep in mind that this is a general guideline, and the specific aiming point may vary depending on the viewing angle and water conditions.

It's essential to practice and gain experience to develop a better understanding of how refraction affects your aim in different situations.

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A) Speed of the skier at the bottom of the slope is 30.1 m/sec. B) She is going to cross the patch with velocity  11.4 m/s. C) The average force  exerted on the snowdrift is  9,500 N.

a)

The total mechanical energy of the skier at the top of the slope is given by:

E = mgh

where m is the mass of the skier, g is the acceleration due to gravity, and h is the height of the slope.

Substituting the given values, we get:

E = (63.0 kg)(9.81 m/s²)(65.0 m) = 40,515 J

The work done by friction forces on the skier as she descends is given by:

W = 10.9 kJ = 10,900 J

By the work-energy principle, we know that:

W = ΔE

where ΔE is the change in mechanical energy of the skier.

Therefore:

ΔE =[tex]E_f - E_i = W[/tex]

where[tex]E_f[/tex] is the final mechanical energy of the skier at the bottom of the slope and [tex]E_i[/tex] is her initial mechanical energy at the top of the slope.

Solving for [tex]E_f[/tex] , we get:

[tex]E_f = E_i + W = 51,415 J[/tex]

At the bottom of the slope, all of the initial potential energy has been converted to kinetic energy. Therefore:

[tex]E_f[/tex] = (1/2)mv²

where v is the speed of the skier at the bottom of the slope.

Substituting the given values and solving for v, we get:

v = √(2[tex]E_f[/tex] /m) = 30.1 m/s

b)

The skier is moving horizontally across a patch of soft snow where the coefficient of kinetic friction is 0.21. The average force of air resistance on the skier is 180 N.

The net force acting on the skier is given by:

[tex]F_{net} = F_{air} + F_{friction}[/tex]

where[tex]F_{air}[/tex] is the force of air resistance and [tex]F_{friction}[/tex] is the force of friction.

The force of friction is given by:

[tex]F_{friction}[/tex]= μmg

where μ is the coefficient of kinetic friction, m is the mass of the skier, and g is the acceleration due to gravity.

Substituting the given values, we get:

[tex]F_{friction}[/tex]= (0.21)(63.0 kg)(9.81 m/s²) = 130.9 N

Therefore:

[tex]F_{net}[/tex]= 180 N - 130.9 N = 49.1 N

The acceleration of the skier is given by:

a = [tex]F_{net}[/tex]/m

Substituting the given values, we get:

a = 49.1 N / 63.0 kg = 0.78 m/s^2

The distance traveled by the skier across the patch of soft snow is given by:

d = 65.0 m

Using the kinematic equation:

[tex]v_f[/tex]² = [tex]v_i[/tex]² + 2ad

where[tex]v_i[/tex] is the initial velocity (which we assume to be zero),[tex]v_f[/tex] is the final velocity, a is the acceleration, and d is the distance traveled.

Substituting the given values and solving for [tex]v_f,[/tex]we get:

[tex]v_f[/tex]= √(2ad) = 11.4 m/s

c)

The skier hits a snowdrift and penetrates 3.0 m into it before coming to a stop. We can assume that the force exerted on the skier by the snowdrift is constant and equal to the average force required to bring the skier to a stop.

The work done by the snowdrift on the skier is given by:

W = Fd

where F is the average force exerted on the skier and d is the distance penetrated into the snowdrift.

The work done by the snowdrift is equal to the change in kinetic energy of the skier:

W = ΔK

where ΔK is the change in kinetic energy of the skier.

At the bottom of the slope, the kinetic energy of the skier was:

[tex]K_i[/tex] = (1/2)mv² = (1/2)(63.0 kg)(30.1 m/s)² = 28,500 J

At the point where the skier comes to a stop, her kinetic energy is zero. Therefore:

ΔK = -[tex]K_i[/tex]= -28,500 J

Substituting the given values and solving for F, we get:

F = W/d = ΔK/d = 9,500 N

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As you move from the positive plate to the negative plate in the gap of a parallel plate capacitor, the electric field is directed from the positive plate to the negative plate. The electric field lines are parallel and uniform between the plates.

This is because the positive plate creates a positive electric field pointing away from it, while the negative plate creates a negative electric field pointing towards it. The net result is a uniform electric field directed from positive to negative.

The magnitude of the electric field remains constant throughout the gap between the plates, assuming there are no external influences or variations. This uniform electric field distribution is a characteristic of a parallel plate capacitor and is essential for its functioning in storing electric charge.

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Answer:

it goes up until we help it to but the moment we stop support it gets affected by gravity and goes back

Explanation:

Alpha Centauri, the star closest to the sun, is located 4.3 light years away. Alpha Centauri and Earth are separated by around 4.1 × 10¹⁶ meters.

To convert the distance of 4.3 light-years (ly) to meters, we can use the conversion factor of 1 light-year equal to 9.461 × 10¹⁵ meters. Multiplying 4.3 by this conversion factor gives us the distance in meters:

4.3 ly * 9.461 × 10¹⁵ meters/ly = 4.0853 × 10¹⁶ meters

Rounding to two significant figures, the distance to Alpha Centauri is approximately 4.1 × 10¹⁶ meters. This distance represents the vast scale of interstellar distances.

Alpha Centauri is the closest star system to our solar system, yet its distance is still incredibly immense. Understanding these astronomical distances helps us appreciate the vastness of the universe and the challenges involved in space exploration and interstellar travel.

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Answer:

T=502.5N

Ax=171.8N

Explanation:

The computation of the tension T in the rope and the forces exerted by the pin at A is shown below:

vertical forces sum = Ay + Tsin20 + T - 245 - 883 = 0

Now  

horizontal forces sum = Ax - Tcos70

Now Moment about B

-Ay × 4.8 + 245 × 2.4 + 883 × 1.8=0

Ay=453.6N

Now substitute in sum of vertical forces T=502.5N

Ax=171.8N

a. The tension (T) in the rope is equal to 502.51 Newton.

b. The forces exerted by the pin at A is equal to 171.86 Newton.

Given the following data:

To calculate the tension (T) in the rope and the forces exerted by the pin at A:

First of all, we would determine the vertical force by taking moment about point B as shown in the diagram.

[tex]-A_y \times 4.8 + 883 \times 1.8 + 245 \times 2.4 =0\\\\-4.8A_y + 1589.4 + 588 =0\\\\4.8A_y= 3237\\\\A_y=\frac{2177.4}{4.8} \\\\A_y= 453.63 \;Netwon[/tex]

The tension (T) in the rope would be calculated by the sum of the vertical component of forces, which is given by:

[tex]\sum F_x = A_y + Tsin20 + T - 245 - 883 = 0\\\\453.63 + 0.3420T + T -1128=0\\\\1.3420T = 1128-453.63\\\\1.3420T =674.37\\\\T =\frac{674.37}{1.3420}[/tex]

Tension, T = 502.51 Newton.

To find the forces exerted by the pin at A, we sum the vertical component of forces, which is given by:

[tex]\sum F_y = A_x - Tcos70 =0\\\\A_x =Tcos70\\\\A_x = 502.51 \times cos70\\\\A_x = 502.51 \times 0.3420\\\\A_x = 171.86\;Newton[/tex]

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Int he abve image relating to rock cycle, A = Igneous Rock

B = Metamorphic Rock

C = Sedimentary Rock.

The rock cycle is a continuous process that describes the transformation of rocks through various geological processes. It involves the formation, breakdown, and reformation of three main types of rocks

The cycle starts with the formation of igneous rocks through the solidification of molten magma or lava. These rocks can then be weathered and eroded into sediments,which are compacted and cemented to form   sedimentary rocks.

Under intense heat and pressure,these rocks can undergo metamorphism, resulting in   the formation of metamorphic rocks.

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The balloon has a radius of 7.00 m. Given the density of air ([tex]1.29 kg/m^3[/tex]) and the density of helium ([tex].179 kg/m^3[/tex]), the question asks for the additional mass (payload) the balloon can lift, considering its structure mass of 900 kg.

To calculate the additional mass the balloon can lift, we need to determine the buoyant force acting on the balloon. The buoyant force is equal to the weight of the displaced air, which can be calculated using Archimedes' principle.

First, we find the volume of the balloon by using the formula for the volume of a sphere: [tex]V = (4/3)\pi r^3[/tex], where r is the radius of the balloon. Plugging in the given radius of 7.00 m, we get [tex]V = (4/3)\pi (7.00)^3 = 1436.76 m^3[/tex].

Next, we calculate the weight of the displaced air by multiplying the volume by the density of air: [tex]weight = volume *density = 1436.76 m^3 *1.29 kg/m^3 = 1851.08 kg[/tex].

Since the balloon's structure mass is already given as 900 kg, we subtract this value from the weight of the displaced air to find the additional mass the balloon can lift: additional mass = weight of displaced air - structure mass = 1851.08 kg - 900 kg = 951.08 kg.

Therefore, the balloon can lift an additional mass of 951.08 kg.

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Electrical Energy is defined as the amount of work done by an electric current, or by the electrical charges that pass through a given area, as they move between two points that differ in electric potential.

Its unit is Joules (J).The formula for Electrical Energy can be given as:Electrical Energy = Power × Time elapsedE = P × twhere E = Electrical Energy, P = Power, and t = Time elapsed. The resistance of the hairdryer is 9.6 ohms and operates at 120 volts for 2.5 minutes.Power is given by the formula:P = (V²/R)P = (120)² / 9.6P = 1500 Watts = 1500 J/sNow, to calculate the total electrical energy used by the dryer during this time interval, we need to substitute the values of Power and Time elapsed in the formula:

E = P × tE = 1500 × 2.5E = 3750 J

Hence, the correct option is (1) 2.9 × 10³J.Note: In order to get more than 160 words, a detailed explanation is given with formulas, units, and a step-by-step procedure to calculate the Electrical Energy used by the hair dryer.

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The value of resistance R must be 7.77 x 10⁴ Ω to give a percent decrease in angular frequency of 5.0% compared to the value calculated in part A.

In part A,

the angular frequency is ω = 3.3 x 10⁵ rad/s.

To find the value of resistance R to give a 5.0% decrease in angular frequency, the following formula is used,

ω' = ω (1 - δ)

where

ω is the original angular frequency,

ω' is the new angular frequency,

δ is the percentage decrease.

Substituting the given values,

ω' = 3.3 x 10⁵ rad/s (1 - 5.0/100)

ω' = 3.135 x 10⁵ rad/s

Now we can use the formula for angular frequency to calculate the value of resistance R as follows:

ω = 1/√(LC - R²)

R = √(LC - ω'²)

R = √((0.420 H)(2.50 x 10⁻⁵ F) - (3.135 x 10⁵ rad/s)²)

R = 7.77 x 10⁴ Ω

Therefore, the value of resistance R must be 7.77 x 10⁴ Ω to give a percent decrease in angular frequency of 5.0% compared to the value calculated in part A.

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Kinetic energy is the energy possessed by a body as a result of its motion. Therefore, the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s is 104,640.625 J which is closest to option A, i.e., 127,575 J.

It is calculated by multiplying half of the mass of a body with the square of its velocity. The kinetic energy formula can be written as, KE = (1/2)mv2Where,KE is the kinetic energy of the body, m is the mass of the body, v is the velocity of the body. Now, let us apply the above formula to find the kinetic energy of the given roller coaster car whose mass is 625 kg and speed is 18.3 m/s.KE = (1/2)mv2KE = (1/2) x 625 x (18.3)2KE = (1/2) x 625 x 334.89KE = 104,640.625 J.

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