1) For the diagram below, you are looking down from above at a puck sliding on a frictionless
tabletop. The puck is sliding at a constant speed along a circular fence and just leaves
contact with the fence at position B. The fence and puck are also frictionless.
B
B
a) On the top drawing draw vectors and label them
for
any forces acting parallel to the table top on
the puck at positions A and B.
b) On the side views below, draw vectors and label
them for any forces acting perpendicular to the
tabletop.
side view at A
side view at B
c) Which of the forces above are inward forces?
d) Which of the forces above are outward forces?
e) What would be the equation for the net force on
the puck?
f) On the top drawing at position B draw a line at least
an inch long showing the path the puck will travel
after point B. How do you know?
g) On the bottom drawing, draw and label a velocity
and an acceleration vector on the puck at positions
A and B.
h) At position A is the net force on the puck zero?
How do you know?
i) At position B is the net force on the puck zero?
How do you know?

In a radio telescope, the role that the mirror plays in visible-light telescopes is played by a large metal dish (antenna).

A radio telescope works by collecting and analyzing radio waves emitted by celestial objects. To collect these radio waves, the radio telescope has a large metal dish, also known as an antenna.

This metal dish gathers radio waves from space and reflects them into the radio telescope's receiver.Spectrometer is a scientific instrument used to measure the intensity of different wavelengths of light in a spectrum.

It is an essential tool for astronomers as it helps to understand the nature of celestial objects by analyzing the light that they emit.Interferometer is a device used in radio telescopes to improve the resolution of images.

It is used to combine the signals from multiple telescopes, allowing astronomers to study more distant objects with greater accuracy.

Special lenses are used in visible-light telescopes to focus light onto the detector or camera. They help to produce clear images by reducing distortions caused by aberrations and other optical imperfections.

Computer software is used in all types of telescopes to process and analyze the data collected by the telescope.

It allows astronomers to create images, measure the intensity of different wavelengths of light, and make other calculations.

The role that the mirror plays in visible-light telescopes is replaced by a large metal dish in radio telescopes, which collects and reflects radio waves into the telescope's receiver.

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The orbital radius at which a satellite would maintain a constant position with the Jupiter is equal to 7.14 x 10^6 meters.

Jupiter is the largest planet in our solar system. To determine the radius at which a satellite would maintain a constant position, we first need to determine the time it takes for a satellite to complete one orbit around Jupiter and then relate it to the radius using the Kepler's law of planetary motions.

According to Kepler's third law, the period of a planet's orbit squared is equal to the size semi-major axis of the orbit cubed when it is expressed in astronomical units. The relation between different parameters can be given as follows:

T^2 = (4π^2 / GM) x R^3

where: T = the time it takes for the satellite to complete one orbit

M = the mass of Jupiter

R = the radius of orbit

G = the gravitational constant

To maintain a constant position, the orbital radius of the satellite must be same as that of Jupiter which is equal to 0.41 days. Substituting the values in the above equation and solving for R, we get:

R^3 = T^2 x (GM/4π^2)

⇒ R^3 = [tex]R^3 = \frac{(6.6743 * 10^-11)(1.898*10^27)}{4(3.14)^2} *(0.41)^2[/tex]

∴ R ≅ 7.14 x 10^6 meters

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Free fall is the motion of an object in a gravitational field, where gravity is the only force acting upon it. It is different from movement in the y-direction because in free fall, the object's speed and direction of motion is constantly changing, whereas in the y-direction the object moves at a constant speed. It is also different from movement in the x-direction because the object experiences no acceleration in the x-direction. Examples of free fall include an apple falling from a tree, or a person skydiving from an airplane.

Free fall refers to the motion of an object that is falling due to gravity with no other forces acting on it except for the force of gravity. The movement in the y-direction refers to the vertical movement of an object. Movement in the x-direction refers to the horizontal movement of an object. The following are the differences between free fall and movement in the y and x directions.

Free fall vs movement in y-direction

In free fall, the object falls freely with no other force acting on it except gravity. However, in the movement in y-direction, the object can either be rising, falling, or staying still due to the presence of other forces like air resistance or thrust. For instance, when a ball is thrown into the air, it moves in the y-direction, but eventually, it stops rising and starts falling due to the force of gravity.

Free fall vs movement in x-direction

In free fall, the object falls vertically with no horizontal movement. However, in movement in the x-direction, the object moves horizontally with no vertical movement. For example, when a ball is thrown horizontally, it moves in the x-direction but does not experience any vertical movement.  

Examples

A few examples of free fall are an apple falling from a tree, a skydiver falling from a plane, and a stone falling from a cliff.

A few examples of movement in the y-direction are an airplane taking off, a rocket launching into space, and a ball thrown into the air.

A few examples of movement in the x-direction are a car moving along a straight road, a roller coaster moving along a straight track, and a person walking in a straight line.

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The resistance of the given aluminum bar is approximately [tex]1.62 \times 10^{-4} \ \Omega m[/tex].

To calculate the resistance of the aluminum bar, we need to use the formula:

[tex]R = (\rho \times L) / A[/tex]

Where R is the resistance, ρ is the resistivity of aluminum, L is the length of the bar, and A is the cross-sectional area of the bar.

The resistivity of aluminum is approximately [tex]2.65 \times 10^{-8}[/tex] ohm-meters (Ωm).

First, we need to convert the dimensions of the cross-sectional area from centimeters to meters:

1.18 cm = 0.0118 m

5.23 cm = 0.0523 m

Then, we can calculate the cross-sectional area of the bar:

[tex]A = (0.0118\ m) \times (0.0523\ m) = 6.16654 \times 10^{-4} \ m^2[/tex]

Now we can substitute the values into the formula for resistance:

[tex]R = (2.65 \times 10^{-8} \Omega m \times 3.78 m) / (6.16654 \times 10^{-4} \ m^2)[/tex]

[tex]R = 1.62 \times 10^{-4}[/tex]

Hence the resistance is [tex]1.62 \times 10^{-4} \ \Omega m[/tex].

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Answer:

The Ability to do work

Explanation:

energy is needed to do work because without energy no work can be done due to the fact that there is no energy

The time it takes for the electrons to get from the car battery to the starting motor is 353 ms.

To calculate the time it takes for electrons to get from a car battery to the starting motor, we can use Ohm's law. According to Ohm's law, the current (I) through a wire is equal to the voltage (V) divided by the resistance (R). In this case, the current is 300A and the resistance is equal to the resistance of the copper wire (R = ρL/A), where ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area. Using this information, the resistance of the copper wire is 0.85Ω. Therefore, the time it takes for the electrons to get from the car battery to the starting motor is equal to the voltage divided by the resistance, or 300V/0.85Ω = 353 ms.
To explain further, current is a measure of the amount of electrons passing through a conductor, in this case the copper wire, in a certain amount of time. Voltage is a measure of the energy per unit of charge, meaning it is how much energy each electron will have when it passes through the wire. Resistance is a measure of the opposition that a material has to the flow of electric current. In this case, the resistance of the copper wire is equal to the resistivity of the copper, multiplied by the length of the wire, divided by the cross-sectional area of the wire. Using this information, the time it takes for the electrons to get from the car battery to the starting motor can be calculated as 300V/0.85Ω = 353 ms.

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The rotational kinetic energy of a flywheel increases by 80% when its rotational speed increases by 40%. This is because the rotational kinetic energy of a flywheel is directly proportional to the square of its angular velocity.

The rotational speed of a flywheel increases by 40%. The percentage increase in its rotational kinetic energy is approximately 96.8%. Suppose the initial rotational speed of the flywheel is n1 and the initial rotational kinetic energy is K.E.1. After the speed of the flywheel is increased by 40 percent, the new speed is n2 = n1 + 0.4n1 = 1.4n1.

Then the new kinetic energy K.E.2 of the flywheel is given by K.E.2 = (1/2)I(n2^2)where I is the moment of inertia of the flywheel.Since n2 = 1.4n1, we have [tex]K.E.2 = (1/2)I(1.96n1^2) = 0.98I(n1^2).[/tex].

Therefore, the percentage increase in the rotational kinetic energy of the flywheel is approximately 96.8%.

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Yes, a charge can move on a curved (non-linear) path if it is placed in the middle of the plates.

This is because the electric field is non-uniform in this region, and the force acting on the charge will be non-uniform. As a result, the charge will experience a net force that is not in the same direction as the electric field, and its path will be curved.

The direction of the force acting on the charge is determined by the direction of the electric field at the location of the charge, and the sign of the charge itself.

If the charge is positive, it will experience a force in the direction of the electric field. If it is negative, it will experience a force in the opposite direction to the electric field.

In order to determine the exact path that the charge will follow, you need to know the magnitude and direction of the electric field at each point in space.

This can be calculated using the principles of electrostatics, which relate the electric field to the charge density and the geometry of the system.

Once you know the electric field, you can use Newton's laws of motion to determine the path of the charge, taking into account any other forces that may be acting on it.

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The bike and rider must halt at a breaking distance of 5.17 meters.

d=2.2v+fracv220 gives the braking distance, in feet, of a car moving at v miles per hour. Most motorcycle riders have a maximum braking force (what an experienced rider can do) of about 1 G, which, at 45 mph, results in a complete stop of the motorcycle in 67 feet (20 meters).

To resolve this issue, we can apply the equation of motion for uniformly accelerated motion:

v² = u² + 2as

To solve for s, we can rewrite the equation as follows:

s = (v² - u²) / (2a)

We are aware that the acceleration is determined by dividing the net force by the mass:

a = F_net / m

where m is the mass and F net is the net force.

a = F_net / m = -140 N / 82.0 kg

= -1.71 m/s²

We may now change the values for s in the equation:

s = (0² - 4.2²) / (2*(-1.71))

= 5.17 m

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A metal object is suspended from a spring scale are: the three forces acting on the submerged object are buoyant force, gravitational force, and tension force. The gravitational force is responsible for pulling the object downwards. The buoyant force is responsible for pushing the object upwards due to the density of the liquid. The tension force is responsible for maintaining the equilibrium of the object.

To find the volume of the object, we need to use the formula: Volume of the object = Mass of the object / Density of the object .The mass of the object can be calculated using the gravitational force: Mass of the object = Gravitational force / Acceleration due to gravity (g)Mass of the object = 920 N / 9.8 m/s²Mass of the object = 93.87 kg.

The density of the object can be calculated using the formula: Density of the object = Mass of the object / Volume of the object. The volume of the object can be calculated using the equation: Volume of the object = (Gravitational force - Buoyant force) / Density of the fluid Volume of the object = (920 N - 750 N) / (1000 kg/m³)Volume of the object = 0.17 m³c. Now we have the mass and volume of the object.

Using these values, we can calculate the density of the metal using the formula: Density of the object = Mass of the object / Volume of the object Density of the object = 93.87 kg / 0.17 m³Density of the object = 552.76 kg/m³The density of the metal is 552.76 kg/m³.

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The speed of waves on the slinky is 2.42 m/s.

The speed of a wave is the distance it travels in a given amount of time.

The speed of waves on the slinky can be calculated using the equation:

v=fλ

where v is the wave speed, f is the frequency, and λ is the wavelength).

Using the given values of f=4.4 Hz and λ=0.55 m, we can calculate the speed of the wave to be 2.42 m/s.

So, the wave is traveling at a speed of 2.42 m/s, which means that it will travel 2.42 meters in one second.

The frequency of the wave is 4.4 Hz, which means that the wave completes one cycle in 0.23 seconds. Since the wave is traveling at a speed of 2.42 m/s, this means that it will take 0.23 seconds for the wave to complete one cycle.

Therefore, the speed of waves on the slinky traveling with a frequency of 4.4 Hz and having a wavelength of 0.55m  is 2.42 m/s.

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To determine g, you must graph distance vs. time squared. When you draw a straight line that passes through the origin of this graph, you can use the slope of the line to determine the acceleration due to gravity g.

To yield a straight line whose slope could be used to calculate a numerical value for the acceleration due to gravity g, the quantity that should be graphed on the vertical axis is the distance (d) and the quantity that should be graphed on the horizontal axis is the time (t). Gravity acceleration, denoted by the letter "g," is the rate at which a falling object increases its speed. A constant acceleration is generated by gravity acceleration, and it is used to describe falling bodies. In any experiment to determine the acceleration due to gravity g, the distance an object travels over a period of time must be measured, recorded, and plotted.

The equation to use for measuring the distance d is: d = 1/2gt^2. The above equation shows that distance d depends on the time t and gravity acceleration g. We can rewrite the equation to give the acceleration due to gravity g by dividing both sides by t^2:g = 2d/t^2. Therefore, to determine g, you must graph distance vs. time squared.

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Answer:

The energy stored in the field decreases because the magnet moves in the direction of the field.

Explanation:

Answer:

To find the average speed after 2 minutes, we need to calculate the total distance covered in 2 minutes and divide it by 2.

Total Distance after 2 minutes = 75m

Total Time after 2 minutes = 2 minutes

Average Speed after 2 minutes = Total Distance / Total Time

Average Speed after 2 minutes = 75m / 2 min = 37.5 m/min

Therefore, the average speed after 2 minutes is 37.5 m/min.

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The relationship between force and potential energy can be found using: calculus and examining the graph of the equation PE = Fd

Potential energy is a form of stored energy that results from the force of gravity or from a conservative force. The relationship between force and potential energy is described by the equation PE = Fd, where PE is potential energy, F is force, and d is displacement.

To calculate potential energy using calculus, start by taking the integral of force with respect to displacement. This will give you the work done by the force, which is equal to the potential energy. Mathematically, this is represented as PE = ∫Fd. This equation can be used to find the potential energy of an object if you know the force and the displacement.

The relationship between force and potential energy can also be determined by examining the graph of the equation PE = Fd. This graph is a straight line with a slope of d and a y-intercept of zero. The slope of the line represents the displacement, while the y-intercept represents the potential energy.

As the force increases, the potential energy increases by the same amount as the force multiplied by the displacement. In summary, the relationship between force and potential energy can be found using calculus. The equation PE = Fd can be used to calculate potential energy from force and displacement.

The graph of this equation is a straight line with a slope of d and a y-intercept of zero, and it shows that as the force increases, the potential energy increases by the same amount as the force multiplied by the displacement.

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Answer:

Explanation:

Durante as aulas, os estudantes da 3ª série deveriam escolher uma entre as três atividades físicas possíveis, sendo elas: natação, futsal e dança. Na turma, 25% escolheram dança, 15% escolheram natação, e os outros 24 estudantes escolheram futsal. Podemos afirmar que, nessa turma, existe um total de:

A) 64 alunos

B) 55 alunos

C) 48 alunos

D) 45 alunos

E) 40 alunos

If the coefficient of kinetic friction between the road and car tires is 0.694, the car will travel approximately 57.4 meters before it comes to a complete stop.

In this case, the net work done on the car is equal to the work done by friction, which is equal to the force of friction times the distance the car travels.

Therefore:

W_net = W_friction = f_friction x d

where f_friction is the force of friction and d is the distance the car travels.

The force of friction is given by:

f_friction = μ_k x N

where μ_k is the coefficient of kinetic friction and N is the normal force.

Since the car is on a flat road, the normal force is equal to the weight of the car, which is given by:

N = m x g

where m is the mass of the car and g is the acceleration due to gravity.

Substituting the given values, we get:

N = m x g = 1000 kg x 9.81 m/s² = 9810 N

f_friction = μ_k x N = 0.694 x 9810 N ≈ 6808.14 N

Now we can use the work-energy theorem to find the distance the car travels:

W_net = ΔK = 0 - 1/2 x m x v²

where ΔK is the change in kinetic energy, which is equal to the initial kinetic energy of the car (1/2 x m x v²) since the car comes to a complete stop.

Substituting the values, we get:

W_net = f_friction x d = -1/2 x m x v²

6808.14 N x d = -1/2 x 1000 kg x (19.6 m/s)²

d = -1/2 x 1000 kg x (19.6 m/s)² / 6808.14 N

d ≈ 57.4 m

Therefore, the car distance before it stops = 57.4 meters.

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The minimum elevation angle necessary to hit the target 4050 feet away with a muzzle velocity of 1000 feet per second is 45 degrees.

Let α be the angle of elevation at which the gun is aimed.

Then, tan α = Opposite Side / Adjacent Side

tan α = 4050 / (1000 * time of flight)

Let h be the target's height above the gun's level.

Since the target's altitude is unknown, we'll assume it to be h = 0.

Since the gun is fired horizontally, its initial velocity has no vertical component. In the vertical direction, the projectile is influenced solely by gravity.

Since the horizontal distance traveled by the projectile is 4050 feet and the initial velocity is 1000 feet per second,

t = (4050 / 1000) seconds

On substituting the value of t,

we get, tan α = 4050 / (1000 * 4.05)

tan α = 1

Therefore, the angle of elevation of the gun is 45°.

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The impulse given to the nail is -101.527616 J (Joules).

The impulse given to the nail if a 13-kg hammer strikes a nail at a velocity of 7.8 m/s and comes to rest in a time interval of 8.4 ms is calculated using the formula J = FΔt.

Here, F is the force, Δt is the time interval, and J is the impulse. Use the given information to solve the question. Here, m/s stands for meters per second, and ms stands for milliseconds.

F = maF = m (Δv / Δt)

where, m is the mass of the hammer, and Δv is the change in velocity of the hammer.

Δv = -7.8 m/s (negative because the hammer is coming to rest)

Δt = 8.4 ms = 0.0084 s

F = 13 kg x (-7.8 m/s) / 0.0084 sF = -12095.24 N

The force exerted on the nail is -12095.24 N.

The impulse given to the nail is J = FΔt.

J = -12095.24 N x 0.0084 sJ = -101.527616 J (Joules)

Therefore, the impulse given to the nail is -101.527616 J (Joules).

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The sound level produced by a chorus of 45 singers would be approximately 88.3 dB.

Assuming that the sound level of each singer is independent and the same, the sound level produced by a chorus of 45 singers can be calculated using the following formula:

L2 = L1 + 10 log (N2/N1)

where:

L1 = the sound level of one singer = 71.8 dB

N1 = the number of singers in the original group = 1

N2 = the number of singers in the new group = 45

L2 = the sound level of the new group

Substituting the values in the formula, we get:

L2 = 71.8 + 10 log (45/1)

L2 = 71.8 + 10 log (45)

L2 = 71.8 + 16.5

L2 = 88.3 dB

Therefore, the sound level produced by a chorus of 45 singers would be approximately 88.3 dB, assuming all the singers are singing at the same intensity at approximately the same distance as the original singer.

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The camera should be now focused at a distance of 16 meters.

The camera, in this case, should focus on the distance from the mirror to the object reflected by the mirror. The distance should be twice the distance of the object to the mirror.

The mirror image and the object should be equidistant from the mirror. This implies that the distance of the object from the mirror is equal to the distance of the mirror image from the mirror.

The distance that the camera should focus on is equal to the distance from the object to the mirror, multiplied by 2. Therefore, Distance from the object to the mirror = 8 meters

Distance from the camera to the object = distance from the mirror to the object, which is twice the distance from the mirror to the object

Distance from the camera to the object = 2 × 8 meters = 16 meters

Therefore, the camera should be focused at a distance of 16 meters.

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The two stars separated by one degree on the celestial sphere imply that they are relatively close together.

This can be determined by the degree measurement, as one degree of arc is roughly equivalent to one-sixtieth of a degree of the Earth's circumference.

This implies that the two stars are relatively close together in terms of the celestial sphere, meaning they may even be located within the same constellation.

In addition to their proximity, the degree of separation between the two stars may also indicate that they are physically close together.

The further apart two stars appear in the night sky, the further away they actually are from one another. Therefore, a one-degree separation implies that the stars are quite close together in space.

The relative closeness of the stars may also have implications for their age and luminosity.

Stars that are relatively close together in space will have been formed from the same nebula, meaning they will likely be of the same age and share similar luminosities.

The degree of separation between the two stars may even provide an indication of how they were formed, potentially indicating that they were formed in the same event or were ejected from the same star system.

Two stars separated by one degree on the celestial sphere are likely to be quite close together in terms of the night sky, physical proximity, and age/luminosity.

Understanding the degree of separation between the two stars can provide valuable information regarding the formation and proximity of these two stars.

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If the conducting cube is changed or replaced with other one has a positive charge carriers then there will be no change in electric field.

The direction of the generated electric field remains the same, opposing the change in magnetic flux, if the conducting cube is switched out for a conducting cube with positive charge carriers.

This is caused by the electromagnetic induction law of Faraday, which states that a shifting magnetic field causes a shifting electric field. Lenz's law states that the generated electric field always operates in the opposite direction to the change in magnetic flux that caused it.

The right-hand rule for electromagnetic induction should be used to identify the direction of the generated electric field. The thumb of the right hand points towards the direction of the shifting magnetic field if the fingers are curled in this manner.

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More work was done on the box by the 5.4 n force when: it was supported and carried 1.9 m horizontally across the room.

The 5.4 N vertical force did more work on the box when it was supported and carried 1.9 m horizontally across the room. This is because work is the product of force and distance, meaning more work is done when the force is greater and the distance is longer. In this case, the force remained the same, but the distance traveled was greater, so more work was done.

When the box was pushed 1.9 m horizontally across the smooth table by a 5.4 N horizontal force, less work was done on the box. This is because although the force remained the same, the distance traveled was shorter. As a result, less work was done by the 5.4 N force.

To summarize, more work was done on the box by the 5.4 N force when it was supported and carried 1.9 m horizontally across the room. This is because work is the product of force and distance, and the distance was greater in this case.

Conversely, less work was done on the box when it was pushed 1.9 m horizontally across the smooth table by the 5.4 N force since the distance traveled was shorter.

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At the instant where the cart leaves the ramp, the velocities of the ramp and the cart are relative to the ground as [tex](mgh/m+M)^{1/2}[/tex] and [tex](2gh(m+M)/3m)^{1/2}[/tex] respectively.

The velocities of the ramp and cart relative to the ground at the instant the cart leaves the ramp can be calculated using conservation of energy and momentum. The velocity of the cart relative to the ground can be found using conservation of energy as follows:

mgh = 1/2mv² + 1/2Iw²

where m is mass of cart, g is acceleration due to gravity, h is height of ramp, v is velocity of cart relative to ground, I is moment of inertia of ramp about its center of mass and w is angular velocity of ramp about its center of mass.

The velocity of ramp relative to ground can be found using conservation of momentum as follows:

mv = (m+M)V

where M is mass of ramp and V is velocity of ramp relative to ground.

Solving these equations simultaneously gives:

[tex]V = mgh/(m+M)^{1/2}[/tex]

[tex]v = 2gh(m+M)/(3m)^{1/2}[/tex]

where h = height of ramp.

Therefore, at the instant when cart leaves the ramp, velocity of cart relative to ground will be [tex](2gh(m+M)/(3m))^{1/2}[/tex] and velocity of ramp relative to ground will be [tex](mgh/(m+M))^{1/2}[/tex].

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If both elements of the water heater in this residence are energized at the same time, they will draw 37.5 amperes of current. Each element of the water heater is rated at 240 volts at 4500 watts.

To calculate the current drawn by each element, we can use Ohm's law: V = IR, where V is the voltage, I is the current, and R is the resistance.
The resistance of each element can be calculated using the formula: [tex]R = V^2/P[/tex], where R is the resistance, V is the voltage, and P is the power.
So, the resistance of each element is:
[tex]R = V^2/P[/tex]
[tex]R = 240^2/4500[/tex]
R = 12.8 ohms
When both elements are energized at the same time, they are connected in parallel. The total resistance of two resistors in parallel can be calculated using the formula:
1/R_total = 1/R1 + 1/R2
So, the total resistance of the two elements is:
1/R_total = 1/12.8 + 1/12.8
1/R_total = 0.15625
R_total = 6.4 ohms
Now, we can use Ohm's law to calculate the current drawn by both elements:
I = V/R_total
I = 240/6.4
I = 37.5 amperes

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The surface charge density on the belt is 2 A/cm.

The surface charge density on the belt can be computed by dividing the charge flow rate (100 A) by the width of the belt (50 cm). This yields a surface charge density of 2 A/cm.

Charge is the basic physical property of matter that allows it to produce and experience electrical and magnetic effects. Charge carriers are particles which are free to move, and in this case, they are moving along the belt.

The belt acts as a conductor and carries the charge with it. As the belt moves, it carries the charge into the sphere, where the charge accumulates and produces a surface charge density.

The surface charge density is a measure of the electric charge per unit area on the surface of a conductor, and in this case, it is 2 A/cm.

Charge carriers move in response to electric and magnetic fields. In this case, the charge is moving from the source to the sphere due to the electric field created by the source.

As the charge moves, the electric field changes, resulting in the charge carriers picking up speed.

This explains why the belt is travelling at 30 m/s - the electric field is strong enough to propel the charge carriers at this speed.

The surface charge density on the belt is 2 A/cm, and this is the result of the charge carriers travelling along the belt due to the electric field created by the source of charge.

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The normal-mode wavelengths decrease when the air in an organ pipe is replaced by helium, at the same temperature. This is because helium has a lower molar mass than air, and therefore a lower speed of sound, which causes the normal-mode wavelengths to decrease.

The normal-mode wavelengths are determined by the length of the pipe L and the speed of sound in the pipe

V.λn = 2L/nVn is the index of the mode, which can be any integer.

When helium is used instead of air, the speed of sound in the pipe rises because the mass of the helium molecules is smaller than that of the air molecules, so the gas molecules must travel quicker to achieve the same speed. Because the wavelength of a standing wave must fit into the pipe precisely, the increase in velocity causes the wavelength to decrease. The normal-mode wavelengths will be lowered as a result of this.

Thus, the answer is the normal-mode wavelengths decrease.

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The value of  uncharged capacitor in series with a 10.0-microfarad capacitor, given that each capacitor has a voltage of 3.00 volts, can be calculated using the formula for equivalent capacitance in series and  formula for charge on a capacitor. The value of c is approximately 4.00 microfarads.

To determine the value of c, which is [tex]1/Ceq = 1/C1 + 1/C2[/tex] . Initially, the 10.0-microfarad capacitor has a charge of [tex]Q = CV = (10.0 * 10^{-6 }F) * 12.0 V = 1.20 * 10^{-4} C[/tex].

When it is connected in series with uncharged capacitor with capacitance c,  charge is shared between the two capacitors. The charge on  10.0-microfarad capacitor is also equal to the charge on  uncharged capacitor, which is given by [tex]Q = (3.00 V) * C[/tex] .

Equating the two expressions for Q and solving for c, we get [tex]C = Q/3.00[/tex] [tex]V = (1.20 * 10^{-4 C}) / (3.00 V) = 4.00 * 10^{-5 F}[/tex]. Therefore,  value of c is approximately 4.00 microfarads.

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