A small object carrying a charge of -2.50 nc is acted upon by a downward force of 18.0 nn when placed at a certain point in an electric field

Answers

Answer 1
Missing question in the text:
"A.What are the magnitude and direction of the electric field at the point in question?

B.What would be the magnitude and direction of the force acting on a proton placed at this same point in the electric field?"

Solution:

A) A charge q under an electric field of intensity E will experience a force F  equal to:

[tex]F=qE[/tex]

In our problem we have [tex]q=-2.5 nC=-2.5\cdot 10^{-9} C[/tex] and [tex]F=18 nN = 18 \cdot 10^{-9} N[/tex], so we can find the magnitude of the electric field:

[tex]E= \frac{F}{q}= \frac{18\cdot 10^{-9}N}{2.5\cdot 10^{-9}C}=7.2 V/m [/tex]

The charge is negative, therefore it moves against the direction of the field lines. If the force is pushing down the charge, then the electric field lines go upward.

B) The proton charge is equal to

[tex]e=1.6\cdot 10^{-19} C[/tex]

Therefore, the magnitude of the force acting on the proton will be

[tex]F=eE=1.6\cdot 10^{-19} C \cdot 7.2 V/m=1.15 \cdot 10^{-18} N[/tex]

And since the proton has positive charge, the verse of the force is the same as the verse of the field, so upward.


Related Questions

Manuel is holding a 5kg box. How much force is the box exerting on him?In what direction

Answers

The force the box is exerting on Manuel is the weight of the box, downward:
[tex]W=mg=(5 kg)(9.81 m/s^2)=49.05 N[/tex]
and this force is perfectly balanced by the constraint reaction applied by Manuel's hand, pushing upward.
Final answer:

The box that Manuel is holding would exert a force of 49 N, directed downwards due to gravity. This calculation is done using the mass of the box and the acceleration due to gravity. According to Newton's third law, the force exerted by the box on Manuel would be in the opposite direction to which he lifts it.

Explanation:

The box that Manuel is holding exerts a force equal to its weight due to gravity. The weight can be calculated using the formula F = mg, where F is the force, m is the mass of the object, and g is the acceleration due to gravity. In this case, the mass of the box is 5 kg and assuming the acceleration due to gravity to be approximately 9.8 m/s², we can calculate the force as F = (5 kg) * (9.8 m/s²) = 49 N.

As for the direction, the direction of the force is always directed downwards or towards the center of the Earth because gravity is the force involved in this situation. To be more specific, the force that the box exerts on Manuel is in the opposite direction to which he lifts it, according to Newton's third law of motion which states that for every action, there is an equal and opposite reaction. Therefore, the box exerts a downward force of 49 Newtons on Manuel.

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After watching an advertisement for hand sanitizer on television, Ben decided to see just how effective the advertised hand sanitizer really was. Ben used warm water as his control. He compared the advertised sanitizer with two brands of hand soap. In all four trials he rubbed his hands together for two minutes. After using the three products and the control, he cultured the bacteria on his hands. He recorded the number of bacterial cultures that appeared on each culture plate. Ben's results can be seen in the data table. Ben concluded that both brands of soap were more effective in killing bacteria than the advertised hand sanitizer. What term BEST describes Ben's results for all four trials? A) biased B) inconclusive C) qualitative D) quantitative ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Here Ben checked the quality of three sanitizer

He took all three and checked how much effective each soap is to kill the bacteria

He analyzed and find out that both brands of soap were more effective in killing bacteria than the advertised hand sanitizer

He took his decision on the basis of quality so this is qualitative analysis

option C is correct

Answer:

It is C

Explanation:

The gravitational force between Earth and the Sun is a two-way force. Both the planet and the Sun attract each other. However, Earth revolves around the Sun rather than the Sun revolving around Earth. Which statement BEST explains the orbit of the Earth around the Sun? A) The Sun is at the center of the Solar System. B) The Sun’s mass is much greater than Earth’s. C) Earth rotates about its axis, but the Sun does not. D) Other planets also try to move the Sun around them.

Answers

The correct choice would be

B) The Sun’s mass is much greater than Earth’s

The sun as we know has greatest mass in our solar system and lighter objects tends to orbit around the heavier objects. the mass of earth is very much smaller as compared to that of the sun. hence the earth orbits around the sun due to the force of gravitational attraction between the two objects.

Answer:

B. The sun's mass is much greater than Earth's.

Explanation:

I got it right on UsaTestPrep

Hope this helps!

From: Aug1e

If the kinetic energy of an electron is 4.1e-18 j, what is the speed of the electron? (you can use the approximate (nonrelativistic) formula here.)

Answers

The kinetic energy of the electron is
[tex]K= \frac{1}{2}mv^2 [/tex]
where [tex]m=9.1 \cdot 10^{-31} kg[/tex] is the mass of the electron and v its speed. Since we know the value of the kinetic energy, [tex]K=4.1 \cdot 10^{-18} J[/tex], we can find the value of the speed v:
[tex]v= \sqrt{ \frac{2K}{m} }= \sqrt{ \frac{2\cdot 4.1 \cdot 10^{-18}J}{9.1 \cdot 10^{-31}kg} } = 3\cdot 10^6 m/s[/tex]

Final answer:

To find the speed of an electron with a given kinetic energy of 4.1e-18 J, use the non-relativistic kinetic energy formula. The calculation reveals the speed is approximately 2.7 x 10⁶ m/s, validating the use of the classical formula.

Explanation:

If the kinetic energy of an electron is 4.1e-18 J, calculating the speed of the electron involves using the non-relativistic kinetic energy formula, KE = ½mv², where KE is the kinetic energy, m is the mass of the electron (9.11 x [tex]10^-^3^1[/tex] kg), and v is the speed of the electron.

First, rearrange the formula to solve for v, resulting in v = √(2KE/m). Substituting the given kinetic energy and the mass of an electron, we get v = √([tex]2*4.1e^-^1^8[/tex] J / (9.11 x [tex]10^-^3^1[/tex] kg)). Calculating this provides a numerical value for the electron's speed.

After calculating, you'll find that the electron's speed is approximately 2.7 x 10⁶ m/s, which is fast but still less than the speed of light, indicating that using the non-relativistic formula is justified in this scenario.

A bag of sports equipment has a mass of 10.0 kilograms and a weight of

Answers

A bag of sports equipment that has a mass of 10.0 kilograms and a weight of: 98 N 

The weight of the bag of sports equipment is 98N

From the question,

We are to determine the weight of a bag of sports equipment that has a mass of 10.0 kg

The weight of an object with a given mass can be determined by using the formula

W = mg

Where

W is the weight

m is the mass

and g is the acceleration due to gravity (g = 9.8 m/s²)

From the given information,

m = 10.0 kg

∴ Weight of the bag of sports equipment,

W = 10.0 × 9.8

W = 98 N

Hence, the weight of the bag of sports equipment is 98N

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It takes Harry 34 s to walk from x1 = -11 m to x2 = -54 m .

Answers

Missing question:
"What is his velocity? Please answer using two sig figs in m/s."

Solution
The relationship between velocity (v), space (S) and time (t) is
[tex]v= \frac{S}{t} [/tex]
The space covered by Harry is
[tex]S=x_1 - x_2 = -11 m-(-54 m)=43 m[/tex]
and so the velocity is 
[tex]v= \frac{43 m}{34 s} =1.26 m/s[/tex]

In the equation for centripetal force, which expression represents the centripetal acceleration of the object?

Answers

Second  Newton's law states acceleration of an object is proportional to the force that acts on the object and inversely proportional to the mass of the object.
We can write it down like this:
[tex]F=ma[/tex]
Now, let us take a look at the equation of a centripetal force:
[tex]F_{cp}=\frac{mv^2}{r}[/tex]
Now we simply apply Newton's second law:
[tex]ma=\frac{mv^2}{r}\\ a=\frac{v^2}{r}[/tex]
Basically, whenever you have a force and you want to find the acceleration you just divide the force with mass.

Answer:

v^2/r

Explanation:

Took the review

Latent heat of fusion refers to which changes of state?

Answers

The enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a solid to a liquid, (or resulting from the release of energy from a substance during transition ...

Answer:

Explanation:

The amount of energy required to change the state of matter at constant temperature is called latent heat.

There are two types of latent heat.

1. Latent heat of fusion: The amount of heat required to convert 1 kg of ice at 0 degree Celsius into 1 kg water at 0 degree Celsius is called latent heat of fusion.

2. Latent heat of vaporization: The amount of heat required to convert 1 kg of water at 100 degree Celsius into 1 kg steam at 100 degree Celsius is called latent heat of vaporization.

List at least 3 physical properties that the professor describes of his newly discovered flubber

Answers

Whales
Quails
Trails Its a physical property

Answer:

Flubber is a combination of two words Fluid+ Rubber. It means flubber has physical properties of both fluid and rubber(solid).

Physical properties of Flubber are as follows

1. It has elasticity like rubber

2. It can take the shape of the container in which it is filled. It does not have any particular shape like fluid.

3.It has viscoplastic nature

4. It is gelatinous

5. It flows under low pressure and can break when high pressure is applied on it.

Which of these best explains the ability of small insects to walk on the surface of still water?

Answers

they're not as dense/don't have much mass as the water so they can walk on water.

The ability of small insects to walk on water is due to surface tension, which results from cohesive forces among water molecules. This tension creates a thin 'skin' at the water's surface that can support the weight of light objects, such as insects.

The ability of small insects to walk on the surface of still water can be best explained by the phenomenon of surface tension. Surface tension is created due to the cohesive forces between water molecules at the liquid-air interface. This cohesion results in a thin 'skin' forming at the surface, which can support the weight of small insects like water striders. These insects distribute their weight over their long legs, ensuring that the force they exert is less than the surface tension holding the water molecules together, allowing them to effectively 'walk' on water.

An example of this can be seen when a paper clip or a thin razor blade is carefully placed on the surface of water without sinking, demonstrating the strength of surface tension.

Three people are pushing a 500 kg of box in the same direction. applied forces are 30 n, 20 n, and 10 n respectively. if the acceleration of the box is 0.02 m/s2, what is the magnitude of a force created by friction?

Answers

The total force applied by the three people is:
[tex]F=30 N+20 N+10 N=60 N[/tex]
This force is pushing toward the direction of the motion, while the  frictional force [tex]F_f[/tex] points in the opposite direction.
We can write Newton's second law applied to the block: the resultant of the two forces must be equal to the product between the block's mass and its acceleration
[tex]F-F_f = ma[/tex]
We know the mass of the block, m=500 kg, and the acceleration, [tex]a=0.02 m/s^2[/tex], so we can find the friction:
[tex]F_f = F-ma=60 N - (500 kg)(0.02 m/s^2)=50 N[/tex]

when you squeeze the rubber bulb of a perfume atomizer how do you change the air pressure at the top of the tube

Answers

You push air and perfume out of the tube, creating a small vaccum that pulls more perfume into the tube

Solid-state storage is quickly replacing forms of _____ on small devices like the ipod.

Answers

Solid-state storage is quickly replacing forms of microdrives on small devices like the ipod.

A bolt is dropped from a bridge under construction, falling 80 m to the valley below the bridge. (a) how much time does it take to pass through the last 17 % of its fall? what is its speed (b) when it begins that last 17 % of its fall and (c) just before it reaches the ground?

Answers

im sorry i looked at this for a good 3 minutes and cant figure it out

A wave travels through water at a speed of 3 m/s and has a frequency of 10 Hz. What is the wavelength of the wave?

Answers

V=wavelength*frequency

3 m/s=wavelength*10 Hz

3m/s=10 Hz

wavelength= .3

Answer:

Wavelength of the wave, λ = 0.3 m

Explanation:

It is given that,

The speed of the wave, v = 3 m/s

The frequency of the wave, f = 10 Hz

We know the relationship between the frequency, wavelength and the speed of the wave. Mathematically, it can be written as :

[tex]speed=frequency\times lambda[/tex]

or

[tex]v=f\times \lambda[/tex]

[tex]\lambda=\dfrac{v}{f}[/tex]

[tex]\lambda=\dfrac{3\ m/s}{10\ Hz}[/tex]

[tex]\lambda=0.3\ m[/tex]

Hence, the wavelength of the wave is 0.3 m

the record for a ski jump is 180 m set in 1989. Assume the jumper comes off the end of the ski jump horizontally and falls 90 m vertically before contacting the ground . what was the initial horizontal speed of the jumper?

Answers

Let's write the equations of motion on both x- (horizontal) and y- (vertical) axis. On the x-axis, it's a uniform motion with constant velocity vx. On the y-axis, it is a uniformly accelerated motion with initial height h=90 m and acceleration of [tex]g=9.81 m/s^2[/tex] pointing down (so with a negative sign):
[tex]S_x(t)=v_x t[/tex]
[tex]S_y(t)=h- \frac{1}{2} gt^2[/tex]

First, let's find the time at which the jumper reaches the ground. This happens when Sy(t)=0:
[tex]0=h- \frac{1}{2} g t^2[/tex]
and so 
[tex]t= \sqrt{ \frac{2h}{g} }= \sqrt{ \frac{2\cdot 90m}{9.81 m/s^2} }=4.28 s [/tex]

Then, we can find the horizontal speed. In fact, we know that at the time t=4.28 s, when the jumper reached the ground, he covered exactly 180 m, so Sx=180 m. Using this into the law of motion in x, we find
[tex]v_x= \frac{S_x}{t} = \frac{180 m}{4.28 s} =42 m/s[/tex]

On its own, a certain tow-truck has a maximum acceleration of 3.0 m/s2. what would be the maximum acceleration when this truck was towing a bus of twice its own mass?

Answers

Let's call [tex]a_1=3 m/s^2[/tex] the maximum acceleration of the truck alone. The force produced by the engine to accelerate the truck in this situation is
[tex]F= ma_1[/tex]
with m being the mass of the truck alone.

If we attach a bus of twice the mass of the truck, now the whole system (truck+bus) has a mass of (m+2m)=3m. And in this case, the force produced by the engine is
[tex]F=3m a_2[/tex]
with a2 being the new acceleration. 
The engine is always the same, so the force produced is still the same, so we can equalize F written in the first equation and in the second equation:
[tex]m a_1 = 3 m a_2[/tex]
and find a2, the new acceleration:
[tex]a_2 = \frac{m a_1}{3 m}= \frac{a_1}{3}= \frac{3 m/s^2}{3}=1 m/s^2 [/tex]

The maximum acceleration would be 1.0 m/s² when this truck was towing a bus of twice its own mass

[tex]\texttt{ }[/tex]

Further explanation

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

[tex]\boxed {F = ma }[/tex]

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

[tex]\texttt{ }[/tex]

Given:

initial acceleration = a₁ = 3.0 m/s²

mass of tow-truck = m₁ = m

mass of bus = m₂ = 2m

Asked:

final acceleration = a₂ = ?

Solution:

[tex]\texttt{Initial Force of Tow-Truck = Final Force of Tow-Truck }[/tex]

[tex]F_1 = F_2[/tex]

[tex]m_1 a_1 = m_2 a_2[/tex]

[tex]m (3.0) = (m + 2m) a_2[/tex]

[tex]3m = 3m (a_2)[/tex]

[tex]a_2 = 3m \div 3m[/tex]

[tex]\boxed{a_2 = 1.0 ~ \mathtt{ m/s^2}}[/tex]

[tex]\texttt{ }[/tex]

Conclusion :

The maximum acceleration would be 1.0 m/s²

[tex]\texttt{ }[/tex]

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[tex]\texttt{ }[/tex]

Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

On a beautiful night in Washington D.C., you see a mirror image of the Washington Monument and surrounding scenery. What causes this mirror image?



A. Absorbed light


B. Reflected light


C. White light


D. Refracted light

Answers

your answer would be B, Reflected light! hope this helps
Its B, (20 chars plz don't report)

Andy has two strong magnetic marbles of equal size. What will happen when he puts the two marbles about 2 centimeters apart?

Answers

Answer: Both marbles will experience an electrostatic force. If they have like charges the force will be repulsive. If they have opposite charges the force will be attractive.

Explanation.

The electrostatic force is the repulsive or attractive force between charged objects.

This are the basic characteristic of electrostatic force:

1) Charged objects will experience electrostatic force..

2) The electrostatic force is proportional to the product of the charges, so both objects will experience the same electrostatic force: the product of their charges.

3) The electrostatic force is inversely related to the square of the distance that separates their center. So, the more separated they are, the weaker the force.

4) If the two objects have the same kind of charge (both positive or both negative) the force will be of repulsion.

5) If the two objects have opposite charge (one positive and the other negative) the electrostatic force will be atttractive.

Referring to the map of the temperature field in the room, where was the warmest field found?

Answers

Final answer:

The warmest field on a temperature map is indicated by warmer colors such as red or orange. On maps like those from the WMAP spacecraft, red represents higher temperatures. In thermographic maps of buildings, warmer areas show where heat transfer is most severe.

Explanation:

The warmest field on a map showing temperature variations can typically be found in regions marked with a warmer color, such as red or orange, indicating higher temperatures. In the context of the map used by the WMAP spacecraft to show fluctuations in the cosmic microwave background, red represents areas of higher temperature and higher density. Similarly, thermographic maps of buildings, like Figure 1.32, use color to indicate variations in temperature, with warmer areas potentially signifying regions where heat transfer is most severe, such as through windows.

It's important to carefully analyze the colors and legends provided on the map to determine the precise locations of the warmest fields. When maps show global temperature changes, such as Figure 24.9.5, the land areas and the Arctic are noted for having experienced the greatest increases in temperature relative to mid-20th-century baseline values.

The pilot of an airplane traveling 180km/h wants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is directly overhead?

Answers

Final answer:

To calculate the time the supplies should be dropped before the plane is directly overhead, use the equation for free-fall motion and plug in the values given. The supplies should be dropped approximately 5.06 seconds before the plane is directly overhead.

Explanation:

To determine how many seconds before the plane is directly overhead the supplies should be dropped, we need to calculate the time it takes for the supplies to fall 160 m. We can use the equation for free-fall motion:

Time = sqrt((2 * distance) / g)

where distance is the height the supplies need to fall and g is the acceleration due to gravity. Plugging in the values, we get:

Time = sqrt((2 * 160 m) / 9.8 m/s²) ≈ 5.06 seconds

Therefore, the supplies should be dropped approximately 5.06 seconds before the plane is directly overhead.

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Find the momentum p, in the laboratory frame of reference, of a proton moving with a speed of 0.805
c. use 938mev/c2 for the mass of a proton.

Answers

Explanation of how to calculate the momentum of a proton moving at 0.805c using the relativistic momentum formula.

The momentum (p) of a proton moving at 0.805c can be calculated using the relativistic momentum formula:

[tex]p = (m * v) / \sqrt{(1 - v^2 / c^2)[/tex]

Substitute the mass of a proton (938 MeV/c^2), the velocity (0.805c), and the speed of light (3 x 10^8 m/s) into the formula to find the momentum value.

If you were creating an electrical circuit and ran out of wire what materials would you use
A:yarn
B:licorice strings
C:plastic knitting needle
D:tin foil

Answers

For wires, you need to use material with as little resistance as possible.

It would be messy and possibly dangerous, but the only item on this
list that could possibly substitute for wire is the tin foil. 

Why is it important to know the direction of the force applied to a moving object and the direction in which the object is moving when determining the work done on the object?

A. Only the component of the force perpendicular to the motion is used to calculate the work.

B. If the force acts in the same direction as the motion, then no work is done.

C. When there is an angle between the two directions, the cosine of the angle must be considered.

D. A force at a right angle to the motion requires the use of the sine of the angle.

Answers

C is correct.  The work-force relation is given by W=F·d, where F is force vector, and d is the displacement vector.  The dot is the dot product, which is a measure of how parallel the two vectors are.  It can be restated as the product of two vector magnitudes times the cosine of the angle between them.  Therefore work is a scalar, not a vector, since the dot product returns a scalar.  
[tex]W=Fdcos(\theta)[/tex]

Answer:

C. When there is an angle between the two directions, the cosine of the angle must be considered.

Explanation:

I can confirm answer is C.

While parachuting, a 66.0-kg person experiences a downward acceleration of 2.60 m/s2. 1) what is the downward force on the parachute from the person? (express your answer to three significant figures?

Answers

Final answer:

The downward force on the parachute from the 66.0 kg person experiencing a downward acceleration of 2.60 m/s2 is 171.6 newtons, calculated using Newton's second law of motion (F = ma).

Explanation:

The question asks for the downward force on the parachute from a person with a mass of 66.0 kg experiencing a downward acceleration of 2.60 m/s2. To find this force, we use Newton's second law of motion, which states that force (F) equals mass (m) times acceleration (a), or F = ma.

To calculate the force, we multiply the person's mass (66.0 kg) by the given acceleration (2.60 m/s2):

F = 66.0 kg × 2.60 m/s2
 = 171.6 N

The downward force exerted on the parachute by the person is therefore 171.6 newtons, expressed to three significant figures.

The cone cells of the human eye are sensitive to three wavelength ranges, which the eye interprets as blue (419nm), green (531 nm), and red(558nm). if the optic nerve in the eye requires 2.0x10^-17j of energy to initiate the sight impulses to the brain, how many photons of blue light, green light, and red

Answers

Sorry, This is one of the questions i wouldn't know, Hope you find it though

The number of photons of blue light required is 42 photons of blue light

The number of photons of green light required is 53 photons of green light

The number of photons of red light required is 56 photons of red light

The energy of one photon of light is calculated using the formula:

E = h * c / λ

where h, Planck's constant  = 6.63 * 10⁻³⁴ Js

speed of light c = 3 * 10⁸ m/s

λ = wavelength of light

wavelength of blue light = 419 nm = 4.19 * 10⁻⁷ m

wavelength of green light = 531 nm = 5.31 * 10⁻⁷ m

wavelength of red light = 558 nm = 5.58 * 10⁻⁷ m

Number of photons of light = Energy of light / Energy of one photon of light

Energy of light required by optic nerve = 2.0 * 10⁻¹⁷ J

Energy of one photon of blue light,

E = (6.63 * 10⁻³⁴ Js * 3 * 10⁸ m/s) / 4.19 * 10⁻⁷ m = 4.74 * 10⁻¹⁹ J

Number of photons of blue light = 2.0 * 10⁻¹⁷ J / 4.74 * 10⁻¹⁹ J

Number of photons of blue light = 42 photons of blue light

Energy of one photon of green light,

E = (6.63 * 10⁻³⁴ Js * 3 * 10⁸ m/s) / 5.31 * 10⁻⁷ m = 3.74 * 10⁻¹⁹ J

Number of photons of green light = 2.0 * 10⁻¹⁷ J / 3.74 * 10⁻¹⁹ J

Number of photons of green light = 53 photons of green light

Energy of one photon of red light,

E = (6.63 * 10⁻³⁴ Js * 3 * 10⁸ m/s) / 5.58 * 10⁻⁷ m = 3.56 * 10⁻¹⁹ J

Number of photons of red light = 2.0 * 10⁻¹⁷ J / 3.56 * 10⁻¹⁹ J

Number of photons of red light = 56 photons of red light

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If you mix equal amounts of cyan pigments and magenta pigments on a sheet of white paper, what color will you see on the paper?
A. Red
B. Blue
C. Black
D. Yellow
E. Cyan
F. Magenta

Answers

Cyan and magenta mixed together will give you B) BLUE.

Hope this helps! :)

how did the world form

Answers

Many people believe in the big bang theory but i believe God created the heavens and the earth with his own hands.
After the big bang 4.6 billion years ago, rocky materials came together. They were extremely hot. Over time they cooled down. soon after another Earth sized rock collided with the earth, Breaking off a large chunk. This chunk became what we know today as the moon.

Hope I helped!
~ Zoe

A box is initially sliding across a frictionless floor toward a spring which is attached to a wall. the box hits the end of the spring and compresses it, eventually coming to rest for an instant before bouncing back the way it came. the work done by the spring on the box as the spring compresses is:

Answers

The elastic potential energy of a spring is given by
[tex]U= \frac{1}{2}kx^2 [/tex]
where k is the spring's constant and x is the displacement with respect to the relaxed position of the spring.

The work done by the spring is the negative of the potential energy difference between the final and initial condition of the spring:
[tex]W=-\Delta U = \frac{1}{2}kx_i^2 - \frac{1}{2}kx_f^2 [/tex]

In our problem, initially the spring is uncompressed, so [tex]x_i=0[/tex]. Therefore, the work done by the spring when it is compressed until [tex]x_f[/tex] is
[tex]W=- \frac{1}{2}kx_f^2 [/tex]
And this value is actually negative, because the box is responsible for the spring's compression, so the work is done by the box.

A circular disk has surface charge density 24 nc/cm2 what will the surface charge density be if the radius of the disk is doubled?

Answers

Answer: 6 nC / cm^2

Justification:

1) Keeping the same charge (constant charge) the charge density is inversely realted to the surface.

=> charge density = A / surface

where A is a constant

2) Surface is prortional to square of the radius, so the charge density is inversely related to the square of the radius:

=> charge density = B / (radius)^2

where B is a constant

3) this shows that if the radius is doubled the density falls to 1/4:

charge density = B / (2* radius)^2 = B / [ 4*(radius)^2 ] = (1/4) B / (radius)^2

Conclusion: when the radius is doubled the density charge falls to one quarter.

=> [24 nC/cm^2 ] / 4 => 6nC / cm^2.
The surface charge density of a circular disk is given by the following relationship:

σ = [tex] \frac{Q}{\pi*R^{2}} [/tex] -- (A)

Where,

σ = Surface charge density.
Q = Charge on the surface
R = Radius of the circular disk.

Now according to the above equation, we can infer:
1) Surface charge density σ is directly proportional to the Charge Q on the surface of the disk.
2) Surface charge density σ is inversely proportional to the square of Radius R of the circular disk.

As the charge is 24nC on the circular disk, and there is no evidence of charge being changed in the question, I would assume that the charge is constant.

Let's apply the condition:
If R = 2R(if the radius of the disk is made doubled)

Plug in the value in (A):
A => σ(new) = [tex] \frac{Q}{\pi*(2R)^{2}} [/tex]

Therefore,
 σ(new) = [tex] \frac{Q}{\pi*4*R^{2}} [/tex]

Hence,
σ(new) = (1/4)σ

Conclusion:
If the Radius of the disk is doubled, the new surface charge density would become one-fourth of the old surface charge density. Hence,

σ(new) = [tex]( \frac{1}{4})( \frac{24nC}{cm^{2}} )[/tex]

Ans: σ(new) = 6nC/[tex]cm^{2}[/tex]

-i
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