Suppose a point charge is located at the center of a spherical surface. The electric field at the surface of the sphere and the total flux through the sphere are determined. Now the radius of the sphere is halved. What happens to the flux through the sphere and the magnitude of the electric field at the surface of the sphere? (a) The flux and field both increase.(b) The flux and field both decrease.(c) The flux increases, and the field decreases. (d) The flux decreases, and the field increases.(e) The flux remains the same, and the field increases. (f) The flux decreases, and the field remains the same.

The answers for question numbers 3 and 4 is correct. For question number 9, the average speed is 2.5 mi /hr and for question number 10 the speed is 5 yards / s.

We know that,

v = d / t

where,

v = Speed

d = Distance

t = Time

1 ) v = 360 / 6 = 60 km / h

2 ) v = 120 / 3 = 40 mi / h

3 ) v = 18 / 6 = 3 m / s

4 ) v = 1000 / 20 = 50 m / min

5 ) t = 6pm - 5 pm = 1 hr

    v = 2.5 / 1 = 2.5 mi / hr

6 ) v = 1.5 / 0.33 = 4.5 mi / hr ( Since 20 min = 20 / 60 = 0.33 hr )

   d = 4.5 * 1 = 4.5 mi

7 ) d = 20 * 1 = 20 mi ( Since 60 min = 1 hr )

8 ) d = 60 * 2 = 120 mi

9 ) Distance per lap = 0.5 mi

     Total laps = 10

     Total distance = 10 * 0.5 = 5 mi

     v = 5 / 2 = 2.5 mi / hr

10 ) v = 100 / 20 = 5 yards / s

Therefore, the answer for:

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Option(c) is Kilometer is correct. Kilometer unit for length is greater than a meter.

Worldwide adoption of the International System of Units (SI) as a system of measurement units is widespread. For convenience, this updated version of the metric system is based on the number 10. The metric prefixes or the SI prefixes are a collection of prefixes that have been established. According on the prefixes, the unit is either a multiple or a fraction of base ten. It enables the zeros of very small or very high numbers to be reduced, for example, from 7,500,000 Joules to 1 nanometer and from 0.000000001 meter to 7.5 Megajoules, respectively. Additionally, some SI prefixes have a group of symbols before the unit symbol.

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The relativistic time it takes the proton to travel the milky way is 9.877 × 10⁻⁷ s

Since the question has to do with relativistic motion, we need to find the relativistic time it takes the proton to travel the milky way. First, we use the equation for relativistic kinetic energy, we have

K = mc(γ - 1) where

So, making γ subject of the formula, we have

γ  = K/mc + 1

Substituting the values of the variables into the equation, we have

γ  = K/mc + 1

γ  = 1.602J/(1.6726 × 10⁻²⁷ kg × 3 × 10⁸ m/s) + 1

γ  = 1.602J/(5.0178 × 10⁻¹⁹ J) + 1

γ  = 0.3193 × 10¹⁹ + 1

γ  = 3.193 × 10¹⁸

Now since the proper diameter of the milky way d = 10⁵ ly, since the length moved by the proton is going to be contracted, the actual distance moved by the proton is

d' = d/γ

= 10⁵ ly/3.193 × 10¹⁸

= 0.3132 × 10⁻⁻¹³ ly

= 0.3132 × 10⁻⁻¹³ × 9.46 × 10¹⁵ m

= 2.963 × 10² m

Next we need to find the velocity of the proton from

γ = 1/[√(1 - (v/c)²]

3.193 × 10¹⁸ = 1/[√(1 - (v/c)²]

√(1 - (v/c)² = 1/3.193 × 10¹⁸

√(1 - (v/c)² = 0.3132 × 10¹⁸

1 - (v/c)² = (0.3132 × 10⁻¹⁸)²

1 - (v/c)² = 0.0981 × 10⁻³⁶

(v/c)² = 1 - 0.0981 × 10⁻³⁶

(v/c)² = 1 - 0.0000000000000000000000000000000000981

(v/c)² = 0.9999999999999999999999999999999999019

(v/c)² ≅ 0.99999

(v/c) = √0.99999

v/c = 0.999994999987

v = 0.999994999987c

So, the time it takes the proton to travel the milky way is t = d/v

= 2.963 × 10² m/0.999994999987c

= 2.963 × 10² m/2.99998499996 × 10⁸ m/s

= 0.9877 × 10⁻⁶ s

= 9.877 × 10⁻⁷ s

So, the time it takes the proton to travel the milky way is 9.877 × 10⁻⁷ s

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Answer:

The farmer is moving at 10 m / 40 s = .4 m/s

2 min 20 sec = 140 sec

The farmer will have moved 140 * .4 = 56 m

To cover the x-axis twice he will have moved x = 10

56 - 50 = 6 m   and he will have moved a distance of 6 on the y-axis

S = (10^2 + 6^2)^1/2 = 11.7 m from the origin

The acceleration of Mr. Henderson Porsche is 54545.45 mi/hr².

Velocity is the directional speed of an object, body, or particle in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.

We know that acceleration of a body is Change in Velocity per unit time.

[tex]a=\frac{v-u}{t}[/tex]

Here ,

v is the Final Velocity,

u is the Initial Velocity and;

t is the time taken.

In the given question ,

The Porsche accelerated from 0 to 60 miles per hour in four seconds.

u = 0 mi/hr

v = 60 mi/hr

t = 4 sec

[tex]t=\frac{4}{3600}{~}hr\\[/tex]

[tex]t=\frac{1}{900} {~}hr[/tex]

t  = 0.0011 hr

Then,

[tex]a=\frac{v-u}{t}[/tex]

[tex]a=\frac{60-0}{0.0011}[/tex]

[tex]a=54545.45 {~}mi/hr^{2}[/tex]

Hence, the acceleration of the Porsche is 54545.45 mi/hr².

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Answer:

[tex]{ \rm{power, \: p = current \times p.d}} \\ { \rm{50 = 4.5 \times (current \times resistance)}} \\ { \rm{50 = 4.5 \times (4.5 \times r)}} \\ { \rm{resistance = \frac{50}{ {4.5}^{2} } }} \\ \\ { \rm{resistance = 2.5 \: ohms}}[/tex]

The block's third dimension is 2.77 cm.

The mass of the osmium block is 1 kg.

The dimensions of the rectangular osmium block are 4 cm × 4 cm.

Density is defined as the mass of the object by the volume of the object.

density = mass / volume

Now, the volume of a rectangle is:

Volume = length × breadth × height

And now let's assume that the block's height is y.

Then,

Volume = length × breadth × height

Volume = 4 cm × 4 cm × y cm

Osmium now has a density of ρ = 22.57 g/cm³.

Therefore, the density of the rectangular osmium will be:

density = mass / volume

[tex]\rho = \frac{1{~}kg}{4{~}cm {~}\times {~}4{~}cm {~}\times {~} y}[/tex]

[tex]22.57 {~}g/cm^{3}=\frac{1000{~}g}{4{~}cm \times 4{~}cm \times y}[/tex]

[tex]16{{~}cm^{2} \times y{~} =\frac{1000{~}g}{22.57{~} g/cm^{3}}[/tex]

16y cm² = 44.31 cm³

Dividing each side of the equation by 16 cm²,

( 16y cm² ÷ 16 cm²) = ( 44.31 cm³ ÷ 16 cm² )

y = 2.77 cm

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The complete question is mentioned below:

The density of osmium is 22.57 g/cm³. If a 1.00kg rectangular block of osmium has two dimensions of 4.00 cm x 4.00 cm, calculate the third dimension of the block.

Answer:

8.33 m/s^2

Explanation:

The equation for force is Force = mass * acceleration. The force is 500 N, and the mass is 60 kg, so substituting those into the equation you get that 500 = 60 * acceleration. Divide 500 by 60 to get the acceleration, which is 8.33 m/s^2.

Hope this helps! Let me know if you have any confusion!

The angle θ is 36.3° and the angle ϕ is 26.4°.

A vector quantity is a quantity having both magnitude and direction.

To add vector quantities and get their resultants, we need to apply the parallelogram law of vector addition

Let A and B are two vectors and C is their resultant, then according to the parallelogram law

C^2 = A^2 + B^2 + 2ABcosθ, where  θ is the angle between the two vectors

On applying the parallelogram law in the given diagram,

(40)^2 = 30^2 + 60^2 - 2(30)(60)cosθ

Θ = 36.3°

And

30^2 = 40^2 + 60^2 - 2(40)(60)cosϕ

Φ = 26.4°

Thus, the angle θ is 36.3° and the angle ϕ is 26.4°.

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The work done by the spring force while it is compressed to the length of 6m is 0.58 J.

The definition of work done includes both the forces applied to the body and the total displacement of the body. When we apply force "F" to a block, the body moves with some acceleration, or, additionally, its speed increases or decreases depending on the direction of the force. The system's kinetic energy changes as speed increases or decreases. Since we are aware that energy cannot be created or destroyed, it must be changed into another form. This perspective refers to it as completed work. When negative energy is finished, the energy declines, and when positive energy is finished, the energy rises.

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The magnitude of the electric field along the positive z axis due to the ring is equal to Ez = kqz/√(z² + a²)^{3/2}.

Given the following data:

Radius of ring = a.

Charge of ring = q.

Coulomb's constant, k = = 1/4πε₀.

An electric field can be defined as a region in which charged particles are placed with force being applied on the particle as a result of the field.

In order to determine the magnitude of the electric field along the positive z axis, we would apply Coulomb's law in order to find the electric field due to a point charge:

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

Where:

Note: The value of r is equal to √(z² + a²) and cosθ is equal to z/√(z² + a²).

Substituting the value of r into Coulomb's law, we have;

[tex]E = k\frac{q}{(\sqrt{z^2 + a^2}) ^2}[/tex]

Along the z-direction, the electric field is given by:

dz = dEcosθ

Integrating, we have:

∫dz = ∫dEcosθ

Ez = Ecosθ

[tex]E_z = (\frac{kq}{(\sqrt{z^2 + a^2}) ^2})\frac{z}{\sqrt{z^2 + a^2}} \\\\E_z = \frac{kqz}{(\sqrt{z^2 + a^2}) ^\frac{3}{2} }[/tex]

Ez = kqz/√(z² + a²)^{3/2}.

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Complete Question:

Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference. What is the magnitude of the electric field along the positive z axis due to the ring? Use k in your answer, where k = 1/4πε₀

A balloon clings to a wall after it is negatively charged by rubbing because the wall is positively charged.

Yes, opposite charges attract each other. When a positive charge and a negative charge interact with each other, their forces act from the direction of positive to the direction of negative charge. As a result opposite charges attract each other while on the other hand, similar charges repel each other because their forces move in the opposite direction so they repel each other.

So we can conclude that a balloon clings to a wall after it is negatively charged by rubbing because the wall is positively charged.

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The best advice Marta’s supervisor could give her regarding the long answers she is giving is to adapt her communication style (option D).

Communication is the concept or state of exchanging data or information between entities.

A communication is said to be effective when the information passed across is perfectly understood by the recipient.

According to this question, Marta gives long and involved answers to every question, even simple ones. She also uses technical vocabulary even if the people she is talking to do not understand it.

This means that the best advice Marta’s supervisor could give her regarding the long answers she is giving, so as to communicate effectively, is to adapt her communication style.

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The horizontal component of the magnetic field is 12.6 μT.

The magnetic influence on moving electric currents, electric charges, and magnetic materials is described by a magnetic field, which is a vector field. When a charge moves through a magnetic field, a force that is perpendicular to both its own velocity and the magnetic field operates on it.

The horizontal component of the Earth's magnetic field is perpendicular to the axis of a circular coil with five turns and a diameter of D = 30.0 cm that is vertically orientated.

A coil current of I = 0.600 A causes a horizontal compass to deflect 45.0° from magnetic north when it is positioned in the coil's center.

Let B be the magnetic field and R be the radius of the circular coil.

Then the horizontal component of the Earth's magnetic field is given as:

[tex]B(h) = B(coil) = \frac{\mu_{0} NI}{2R}[/tex]

[tex]B(h) =\frac{4 \pi \times 10^{-7}\times(5)\times(0.6)}{0.3}[/tex]

B(h) = 12.6 μT

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The resultant force is 10.77 pounds.

We need to know about vector to solve this problem. Force is included to vector because it has magnitude and also direction. The resultant force can be determined using cosine law. It can be written as

F² = F1² + F2² - 2F1 . F2 cos(θ⁰)

From the question above, we know that:

F1 = 10 pounds

F2 = 14 pounds

θ = 50°

By substituting the parameter, we get

F² = F1² + F2² - 2F1 . F2 cos(θ⁰)

F² = 10² + 14² - 2. 10 . 14 cos(50⁰)

F² = 100 + 196 - 280 . 0.64

F² = 100 + 196 - 280 . 0.64

F² = 116.02

F = 10.77 pounds

Hence, the resultant force is 10.77 pounds.

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No, the speed does not depend on position, it depends on the change of position.

An item can start at x = -3 and be moving by the time it reaches x = 0 since we know that the displacement is independent of the coordinate system's origin.

Speed is characterized as the rate at which an object's position changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity. Speed is defined as s = distance/time.

There are four different forms of speed.

constant speed

varying speed

typical speed

Instantaneous speed

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An astronaut could 6 times higher on the moon than on earth if his takeoff speed is the same in both locations.

From lunar circle, space explorers guided cameras through the window of their space apparatus toward catch photographs of the moon's surface. The nearest look we've had at the moon came from the sendoff of NASA's Apollo program during the 1960s. Somewhere in the range of 1967 and 1972, a progression of missions handled the primary men on the moon. At the point when the following space explorer to arrive at the moon strolls on the lunar surface in 2024, she'll confront radiation levels multiple times higher than on Earth. While Apollo mission space travelers. The prompt surface was extremely fine, as best we could see peering down from 15 feet. Off somewhere out there was an exceptionally clear skyline, perhaps with a rock.

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The possible hypothesis "different masses of objects fall to the ground at different rates" is a tenable hypothesis.

Thus, A reasonable explanation for an observation is a hypothesis. Every experiment begins with the formulation of a hypothesis. The experiment would now either support or refute the theory that has been proposed.

Remember that an experiment requires both an independent and a dependent variable. The dependent variable is the one that changes when the independent variable changes, but the independent variable is the one that we must keep manipulating.

In this situation, "different masses of objects fall to the ground at different rates" is a tenable hypothesis.

Thus, The possible hypothesis "different masses of objects fall to the ground at different rates" is a tenable hypothesis.

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The thing that happens when you push or pull a water tube is that the force makes the tube to speed up, slow down, or be in one place.

It is very hard when pulling  water and if a person need to consistently pull air out of the tube before water makes it to the pump, it is very  difficult and some pumps may or cannot do it.

In regards to pushing, when a person is pushing above the Center of Gravity, one is pushing the said object into the ground and thus is increasing the rate of friction.

If a person is pulling you are said to be pulling above the Center of Gravity and lowering friction.

So, The thing that happens when you push or pull a water tube is that the force makes the tube to speed up, slow down, or be in one place.

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The speed of the wave in the rod is

[tex]The speed of the wave in the rod is $v = \sqrt{\frac{Y}{\rho}} = \sqrt{\frac{20\times 10^{10}\ \mathrm{N/m^2}}{7.86\times 10^3\ \mathrm{kg/m^3}}} = 5044\ \mathrm{m/s}$[/tex]

5044m/s

A sound wave is the pattern of disruption brought on by the movement of energy moving through a medium as it propagates away from the source of the sound (such as air, water, or any other liquid or solid substance). Pressure waves are produced when an item vibrates, such as a ringing phone, and these waves are known as sound waves. The surrounding medium's particles are disturbed by the pressure wave, and those particles disrupt the particles next to them, and so on. Like ocean waves, the disturbance's pattern causes outward movement in all directions. Usually in all directions and with decreased intensity as it gets further away from the source, the wave transmits the sound energy through the medium.

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Answer:

•So he stays healthy.

•He has energy and time to do it.

The clock in the kitchen downstairs is slower than the clock in the bedroom upstairs

A major idea that we could glean from relativity is that there are no absolutes in the universe. Everything in the universe depends on which frame of reference we are. Observations may differ depending on the frame of reference of the observer.

In the theory of Einstein, relativity comes in handy to clarify the distortion that is caused in time and space owing to matter in the universe as the basis for gravity.

We know that from the theory of relativity, the clock that is under the influence of a greater gravitational field would be slower. As such, the clock in the kitchen downstairs is slower than the clock in the bedroom upstairs because the clock in the kitchen downstairs is subjected to a greater gravitational field.

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When the syringe is compressed the pressure spike to a value more than twice its initial value because the temperature of the gas increases.

Pressure is the force applied perpendicularly to an object's surface in relation to the area across which it is applied (symbol: p or P). Gauge pressure is the pressure when compared to the ambient pressure.

Various units are used to express pressure. The pound-force per square inch (psi), which is equal to one newton per square metre (N/m2) in the SI, is the standard unit of pressure in the imperial and U.S. customary systems. Some of these results derive from dividing a unit of force by a unit of area. The atmosphere, which is equal to this pressure, and the torr, which is defined as 1760 of this, are two other ways to describe pressure.

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The charge-to-mass ratio in the second case is 4 times less because of e/M = 0.96x10⁸ N.

The electron beam that travels from the negatively charged cathode to the positively charged anode at the opposite end of the vacuum tube is known as a cathode ray.

As the electron, J. J. Thomson showed that the same beam deflections resulted in tubes having cathodes made of different materials and containing various gases before evacuation.

The elect's load = 1.6x10⁻¹⁹ C

The mass = 9.1x10⁻³¹ kg

e/m = 1.6x10⁻¹⁹/ 9.1x10⁻³¹ = 0.1 758 10 10¹² N

The homogenize has an electron of charge of 1.6x10⁻¹⁹ C

The mass M = 1.673x10⁻²⁷ ka

e/M = 1.6x10⁻¹⁹/1.67x10⁻²⁷ = 0.96x10⁸ N

In the second case, it is 4 times less

Thus, the charge-to-mass ratio in the second case is 4 times less because of e/M = 0.96x10⁸ N.

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The car’s velocity when it passed the checkpoint was of: 60 m/s

The formula and procedure we will use to solve this exercise is:

vi = [(2 *x)/ t] - vf

Where:

Information about the problem:

Applying the initial velocity formula we have:

vi = [(2 *x)/ t] - vf

vi = [(2 * 225m)/5 s ] - 30 m/s

vi = [(450 m)/5 s ] - 30 m/s

vi = 90 m/s - 30 m/s

vi = 60 m/s

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

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The car's acceleration would be for a mass of 4 kg is 3 m/s²

Given the information below:

12 Newtons of force.

Increasing speed Equals

By using Newton's Second Law of Motion, we can determine the mass of the car:

According to Newton's second law of motion, force is equal to the rate at which momentum changes. Force is defined as mass times acceleration for a constant mass.

force= mass* acceleration

This formula provides Newton's Second Law of Motion mathematically;

12= mass*3

mass=12/ 3

mass=4 kilogram

By changing the parameters in the formula, we obtain;

= 4 kilos of mass.

As a result, the vehicle with a mass of 4 kg would accelerate at 3 m/s².

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The average velocity or displacement of a particle for the first time interval is Δs / Δt = 6 cm/s.

Solution:

As we know that displacement is calculated in centimeters and the unit of time is second.

The average velocity for the first interval [1,2] is given

Δs / Δt = s (t2) - s (t) / t2 - t1

Δs / Δt = 2sin2  π  + 3cos 2 π -  ( 2sin π + 3cos π ) / 2 - 1

Δs / Δt = 2(0) + 3(1) - 2(0) - 3 (-1) / 1

Δs / Δt = 6 cm/s

Thus the average velocity or displacement of a particle for the first time interval is Δs / Δt = 6 cm/s

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The complete question is:

The displacement of a particle moving back and forth along a line is given by the following equation s(t) = 2sin π t + 3cos π t. Estimate the instantaneous velocity of the particle when t = 1

35 kilometers per hour is equivalent to 9.73 metres per seconds.

Speed is the rate of distance that is traversed in a given time. It can be calculated by dividing the distance moved by the time taken as follows:

Speed = distance/time

Speed can be measured in the following units;

The conversion factor of kilometers per hour to metres per seconds is as follows:

1 kilometre per hour = 0.278 metre per second

35 kilometers per hour = 9.73 metres per seconds

Therefore, 35 kilometers per hour is equivalent to 9.73 metres per seconds.

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The dot product of velocity vector and acceleration vector at maximum height is equal to zero.

[tex]$\overrightarrow{v}.\overrightarrow{a}= 0[/tex]

We have a football player who kicked a football in order to do a goal.

We have to determine the relationship between the direction of the velocity and acceleration vectors when the football reaches its maximum height.

Projectile motion is the two - dimensional motion of an object thrown or projected into the air such that it moves under the influence of acceleration of gravity.

According to the question -

Assume that the velocity with which the projectile was fired is u m/s.

Therefore, it can be resolved into two components as -

[tex]\overrightarrow{u} =[/tex] u(x) + u(y) = u cosθ [tex]a_{x}[/tex] + u sinθ [tex]a_{y}[/tex].

Now, when the projectile reaches the maximum height, it will no longer cover any vertical height but it will keep moving in the horizontal direction. Therefore - the vertical component of the velocity will become zero. Therefore -

[tex]\overrightarrow{u} =[/tex] u(x) + u(y) = u cosθ [tex]a_{x}[/tex] + 0 = u cosθ [tex]a_{x}[/tex]

Now, refer to the figure attached for reference -

At the maximum height, the velocity vector is in the horizontal direction and the vector for the acceleration due to gravity is vertically downwards.

Therefore - the acceleration vector and velocity vector will have an angle of 90° between them. Assume -

Velocity at maximum height = v = u cosθ [tex]a_{x}[/tex]

and acceleration = a = g = 9.8 m/[tex]s^{2}[/tex]

Therefore -

The dot product of velocity vector and acceleration vector is equal to zero.

[tex]\overrightarrow{v}.\overrightarrow{a}= 0[/tex]

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