the magnetic field perpendicular to a circular wire loop 7.2 cm in diameter is changed from 0.30 t to -0.47 t in 140 ms , where means the field points away from an observer and - toward the observer. Calculate the induced emf. Express your answer using two significant figures. In what direction does the induced current flow?

Answers

Answer 1

The induced emf is equal to 1.56v. If the outward magnetic flux rises, the current must go counterclockwise. When the flux coupling with a conductor or coil changes, an electromotive force, or EMF.

EMF also called electromotive force  is the amount of energy delivered per unit of electric charge by a power source such as a generator or battery.

There are two ways to achieve this flow change: by statically inducing an emf in a certain area OR by dynamically inducing an emf in a certain area.

For example, the magnetic flux density is lower if fewer magnetic lines cover a larger cross-sectional area.

Knowing the magnetic flux also allows us to make a qualified estimate of the magnitude of the magnetic field in a certain area.

The surface integral of the normal component of the magnetic field is used to define the magnetic flux through the surface.

emf = \(\pi\)*r²(B2 - B1)/t

emf =  \(\pi\)*(51.84/4)*(0.32/130)*7

emf = 1.56v

The induced emf will be 1.56v and the direction of current must be clock wise.

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Related Questions

A locust jumps at an angle of 55.0° and lands 0.750 m from where it jumped.

Answers

Aproximately 1.09 m/s was the locust's first speed.

What role do vectors have in mechanics?

In engineering mechanics, vectors are used to express values with both a magnitude and a direction. For analysis, vector representations of a variety of engineering quantities—including forces, displacements, velocities, and accelerations—are required.

Δy = vsin(θ)t - 0.5gt²

0 = v*sin(55°)t - 0.5(-9.81 m/s²)*t²

t = 2vsin(55°)/g

Now, we can use the horizontal motion of the locust to find the initial velocity v. The horizontal distance traveled by the locust is given by:

Δx = v*cos(55°)*t

Substituting the expression for t that we just found:

0.750 m = vcos(55°)2vsin(55°)/g

Solving for v:

v = √(0.750 mg/(2sin(55°)*cos(55°)))

v ≈ 1.09 m/s

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In the nitrogen cycle, plants take in nitrates and convert them into

Answers

It is then converted into a ammonia.

A 180kg motorcycle has an acceleration of 20.5m/s^2. what was the net force applied to the motorcycle?

Answers

Answer:

3690 Newton

Explanation:

By using the F=ma formula we can find the Force if we know the mass and acceleration, so:

F= 180kg*20.5m/s^2

F=3690 kg*m/s^2 or 3690N

Protons and ____ have electric charge?

Answers

Electronssssssssssssssssssssssssssss
i believe it’s electrons

Twelve identical point charges q are equally spaced around the circumference of a circle of radius R. The circle is centered at the origin. One of the twelve charges, which happens to be on the positive x axis, is now moved to the center of the circle.

A) Determine the magnitude of the total electric force exerted on this charge.
Express your answer in terms of Coulomb's constant k and the variables q and R .
F total = ?

B)Determine the direction of the total electric force exerted on this charge.
Express your answer as an integer.
θ = ? degrees

Answers

Answer:

For B it is 0

Explanation:

I think

Hey does anyone know the answer?

Hey does anyone know the answer?

Answers

Answer:

C

Explanation:

The law of conservation of energy determines that energy cannot be created or destroyed.

The answer is c hope this helps

When converted to a household measurement, 9 kilograms is approximately equal to a

Answers

Answer:

900 Grams

Explanation:

1. How long would the car in Sample Problem C take to come to a stop from its initial velocity of 20.0 m/s to the west? How far would the car move before stopping? Assume a constant acceleration. Aron1​

Answers

The time taken, and the distance travelled by the car before stop, will be 5.3 second and -53.3 m west.

What is the distance?

The length of the path traveled by the body is known as the distance covered by the body.

Distance is a 1-dimensional phenomenon. its unit is a meter(m). The distance can be found by the product of velocity and time.

The given data in the problem will be

u is the initial velocity =20m/sec

t is the time =?

d is the distance =?

From the Newtons second law;

\(\rm F \triangle t = \triangle P \\\\ \triangle t = \frac{\triangle P }{F} \\\\ \triangle t = \frac{m(v_f-v_i)}{F} \\\\ \ \triangle t = \frac{2240 (0-20))}{8410} \\\\ \triangle t = 5.3 \ sec \\\\)

The distance travelled before the car stop is,

\(\rm \triangle t = \frac{1}{2} (v_f+v_i)\traingle t \\\\ \traingle x = \frac{1}{2} (-20+0)5.3 \\\\\ \triangle x= -53.3 m \ west\)

Hence,the time taken, and the distance travelled by the car before stop, will be 5.3 second and -53.3 m west.

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7. It has been suggested that rotating cylinders about 20 km in length and 8 km in diameter be placed in space and used as colonies. The purpose of the rotation is to simulate gravity for the inhabitants. Explain this concept for producing an effective imitation of gravity.

Answers

The concept of the centrifugal force is used for producing an effective imitation of gravity. It is an important concept in the mechanics.

What is centrifugal force?

when any body is executing circular motion about a fixed axis, an outward force act on that object to balance the body and to execute the circular motion. The outward force is known as the centrifugal force.

It is the pseudo force act in order to balance the centripetal force acting inward during the circular motion.

The centrifugal force is comes into the picture when any body executes circular motion about a fixed axis.

To simulate gravity for the inhabitants, the concept of the centrifugal force is used.

Hence, the concept of the centrifugal force is used for producing an effective imitation of gravity.

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Which of the following describes wavelength?
A.
the height of a wave
B.
the distance between crests of adjacent waves
C.
the distance a wave travels in a given amount of time
D.
the number of waves that pass a point in a given amount of time

Answers

D. The number of wave that pass a point in a given amount of time

You are a passenger in a car, holding a cup of water in one hand. The driver is
forced to stop suddenly, causing the water in your cup to spill out in front of
you. The water likely spilled because:
A. every force is balanced by an opposing force.
B. an object in motion tends to stay in motion.
C. rapid changes in direction cause deceleration,
D. a force is exerted by a change in acceleration.

Answers

Answer:

the answer is b because an object in motion stays in motion

The water likely spilled because of inertia of motion such that an object in motion tends to stay in motion. So, option B is correct.

What is meant by inertia ?

Inertia is defined as the property of matter by which it tends to continue its state of rest or uniform motion.

Here,

When you are travelling in a car, holding a cup of water in one hand and the driver of the car is forced to stop suddenly so that the water in the cup gets spilled out.

When the car was moving, the water in the cup was actually at the same speed relative to the car and cup. When the car is tend to stop suddenly, this causes a sudden change in acceleration of the car and thus the cup. As a result, the water in the cup spills out. This is due to the property of inertia that the water got spilled out.

According to the law of inertia, a body will preserve its state of rest or uniform motion unless an external force acts on it.

Here, the spilling out of water is the application of inertia of motion. That means the the water inside the cup which was moving forward and when the change in acceleration occurred, it got spilled in front of you thus tending to continue its state of motion.

Hence,

The water likely spilled because of inertia of motion such that an object in motion tends to stay in motion.

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Answer #49 please and thank you

Answer #49 please and thank you

Answers

when Force (N) is 10.0 Length (m) is 0.60

when Force (N) is 8.0 Length (m) is 0.40

when Force (N) is 4.0 Length (m) is 0.20

when Force (N) is 4.0 Length (m) is 0.20

when Force (N) is 2.0 Length (m) is 0.10

chatgpt

49. To find the length of a pendulum that has a period of 2.3 seconds on the Moon, where the gravitational acceleration (g) is 1.6 N/kg, we can use the formula:

Period (T) = 2π√(Length (L) / g)

Substituting the given values:

2.3 = 2π√(L / 1.6)

To solve for L, we can rearrange the formula:

L = (2.3 / (2π))^2 * 1.6

L ≈ 0.781 meters (or 78.1 centimeters)

So, the pendulum must be approximately 0.781 meters (or 78.1 centimeters) long to have a period of 2.3 seconds on the Moon.

50. Ranking Task:

To rank the pendulums according to their periods, we need to consider both the length and mass of each pendulum.

Ranking from least to greatest period:

1. A: 10 cm long, mass = 0.25 kg

2. C: 20 cm long, mass = 0.25 kg

3. B: 10 cm long, mass = 0.35 kg

There is a tie between pendulums A and C, as they have the same length but different masses.

the pilot of a new stealth helicopter which has a mass of 15000 kg and was traveling 180 m / s accelerated to 250 m / s in six seconds to make sure he could rescue those in need how much force was used to accelerate the helicopter and what was the helicopters final momentum ​

Answers

Answer:

pf = 3750000 kg.m/s

F = 175000 N

Explanation:

Constant Acceleration

An object moves with constant acceleration if its velocity changes uniformly in time.

If we call vo to the initial speed, vf the final speed, and t the time, then the acceleration is calculated as:

\(\displaystyle a=\frac{v_f-v_o}{t}\)

The new stealth helicopter was traveling at vo=180m/s and changed to vf=250 m/s in t=6 seconds, thus the acceleration was:

\(\displaystyle a=\frac{250-180}{6}\)

\(a=11.67~m/s^2\)

Please note this number is shown rounded to the nearest hundredth, but it was stored in the calculator's memory with full precision. This fact affects the next calculation as will be noted below.

The acceleration must be produced for some net force that can be calculated by:

F = m.a

Where m=15000 Kg is the mass of the helicopter. Thus:

F = 15000 * 11.67

F = 175000 N

The above product would lead to the inaccurate result of 175050 if the acceleration would have not used with its full representation in the calculator's memory.

The momentum of an object of mass m and velocity v is:

p = m. v

The final momentum of the helicopter is:

pf = m.vf = 15000*250 m/s

pf = 3750000 kg.m/s

Note: When performing calculations over intermediate results, it's important to keep them as accurate as possible to preserve the accuracy of the final result.

A pendulum of mass 12 kg is released from rest at some height, as shown by
point A in the image below. At the bottom of its arc at point B, it is traveling at
a speed of 19 m/s. What is the approximate amount of energy that has been
lost due to friction and air resistance? (Recall that: g = 9.8 m/s²)

20 m

A35
B186
C78
D112

A pendulum of mass 12 kg is released from rest at some height, as shown bypoint A in the image below.

Answers

The energy lost to friction and air resistance is 186 J.

option B.

What is the energy lost to friction and air resistance?

The energy lost to friction and air resistance is calculated from the change in the mechanical energy of the pendulum.

The initial potential energy of the pendulum at the initial position is calculated as;

PEi = mghi

where;

m is the massg is gravityh is the initial height

P.Ei = 12 kg x 9.8 m/s² x 20 m

P.Ei = 2,352 J

The final kinetic energy of the pendulum is calculated as follows;

K.Ef = 0.5 x 12 kg x (19 m/s)²

K.Ef = 2,166 J

ΔE = 2,166 J - 2,352 J

ΔE = -186 J

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This graph shows how the concentration of a reactant changed during a
chemical reaction. Which sentence best describes how the concentration of
the reactant changed?

This graph shows how the concentration of a reactant changed during achemical reaction. Which sentence

Answers

Answer: B

Explanation: A P E X

The sentence best describes how the concentration of the reactant changed is it decreased gradually as the reaction progressed.

The correct option is B.

What is chemical reaction?

The chemical reaction is the reaction between two reactants which led to the formation of products.

The products are substances which forms after reaction. The reactants are the substances which are original materials.

This graph shows how the concentration of a reactant changed during a chemical reaction.

The sentence best describes how the concentration of the reactant changed is it decreased gradually  as the reaction progressed.

Thus, the correct option is B.

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Select the diagrams that show the absorption of energy by electrons to produce an atom with an electron in the excited state Check all that apply.

Answers

These are the absorption of energy by electrons.

What is electron?

The electrons are an atom's negatively charged building blocks. An atom's entire population of electrons comes together to create a negative charge that balances out the positive charge of the protons in the atomic nucleus. Electrons are incredibly little compared to all the other atom's parts.

What is atom ?

A negatively charged electron or electrons surround the core nucleus of an atom, which is made up of one or more of them. Protons and neutrons, which are comparatively heavy particles, are present in the positively charged nucleus in one or more quantities.

We call the shell is complete if they have 2 electrons ( in the first shell only) called duplet or 8 electrons ( in any shell except the first ) called octate.

1) In the first figure, the duplet is complete. ( 2 electrons in the first shell). But the second one has only 4 and octate is incomplete, still the third shell has one electron. So this is the excited state.

2) In second picture, first shell has only one electron and duplet is not complete. Still the second shell has two electrons. This is the excited state.

3) In third picture, first shell has completed duplet and second shell has completed the octate. But third shell is not completed. Still the forth shell has three electrons. So, this is also the excited state.

4) Forth picture has complete duplet and complete octate. Higher shells have no electrons. So, this is not excited state.

5) In fifth picture also, atom has completed duplet and octate. Higher orbit ( third ) has two electrons. Though, the octate is complete, higher shells have no electrons. So this is not a excited state.

Therefore, these are the absorption of energy by electrons.

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A flat sheet of paper of area 0.450 m2 is oriented so that the normal to the sheet is at an angle of 600 to a uniform electric field of magnitude 18 N C-1. What is the magnitude of the electric flux through the sheet? A. 3.22 N m2 C-1 B. 21.42 N m2 C-1 C. 5.04 N m2 C-1 D. 11.72 N m2 C-1 E. 4.05 N m2 C​

Answers

The magnitude of the electric flux through the sheet is 4.05 N m² C⁻¹ (Option E).

The electric flux through a surface is given by the product of the electric field strength and the area of the surface projected perpendicular to the electric field.

In this case, the electric field strength is 18 N C⁻¹, and the area of the sheet projected perpendicular to the electric field is 0.450 m²

(since the normal to the sheet makes an angle of 60° with the electric field). Multiplying these values gives the electric flux:

Electric flux = Electric field strength × Area

Electric flux = 18 N C⁻¹ × 0.450 m²

Electric flux = 8.1 N m² C⁻¹

In summary, the magnitude of the electric flux through the sheet is 4.05 N m² C⁻¹. This value is obtained by multiplying the given electric field strength by the projected area of the sheet perpendicular to the electric field.

The angle of 60° is taken into account to determine the effective area for calculating the flux.(Option E).

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Final Exam
This course has focused on narrative, informative, and argumentative writing. Your final exam is
designed for you to demonstrate your mastery in distinguishing the differences between these
three modes of academic writing and writing in each of these modes.
Topic:
Life as a high school senior
Task 1 Narrative
Write a short constructed response as a narrative. In other words, write at least one paragraph
as a narrative that tells your story as a high school senior. Use narrative techniques.
Task 2 Informative
Write a short constructed response as an informative text. In other words, write at least one
paragraph that informs/explains the life of a high senior.
Task 3 Argumentative
Write a short constructed response as an argument. In other words, write at least one paragraph
that argues to your parents what you need as a high school senior, why a college should accept
you, why an employer should hire you, OR why a branch of the military should accept you.

Final ExamThis course has focused on narrative, informative, and argumentative writing. Your final exam

Answers

This final exam is about your life and what you’ve been through. I wouldn’t recommend using the things I’ll show you in this “answer” I recommend you to think far back about what happened and what got you here and stuff like that like I said I wouldn’t recommend using this but if you can’t think of anything then you can use it but i strongly recommend you write it then use this but here it is:

Task 1 Narrative:
As a high school senior, I found myself constantly juggling multiple responsibilities and trying to navigate the complexities of teenage life. Between classes, extracurricular activities, and preparing for college, I often felt overwhelmed and stressed. However, I also experienced some of the most thrilling and memorable moments of my life during this time. From prom to graduation, I cherished every opportunity to make lasting memories with my friends and family. Looking back, I realize that my senior year taught me valuable lessons about hard work, perseverance, and the importance of enjoying the moment.

Task 2 Informative:
As a high school senior, life is both exciting and challenging. Seniors are focused on preparing for college, deciding on their career path, and making lasting memories with their friends. The senior year is a time to reflect on the past and make plans for the future. Students are encouraged to participate in extracurricular activities, such as sports, clubs, and volunteer work, as these activities can enhance their college applications and provide valuable life experience. Seniors are also expected to maintain good grades and take challenging courses to demonstrate their academic abilities. Overall, the senior year is a critical time for students as they transition from high school to college and beyond.

Task 3 Argumentative:
As a high school senior, I need my parents' support in preparing for college and pursuing my career goals. I believe that I have demonstrated my academic abilities by maintaining a high GPA and taking challenging courses. I have also participated in extracurricular activities, such as volunteering and sports, which have helped me develop important skills such as leadership, teamwork, and time management. I am confident that I have the qualities and abilities that colleges and employers are looking for, and I am eager to pursue my dreams. Therefore, I urge my parents to support me in my efforts to apply to colleges, seek internships, and explore different career paths.

What kind of waves can travel through empty space or a vacuum?
A.Sound
B.Light
C.Frequency
D.Wavelength

Answers

Answer:

the answer is B.

Answer:

light

Explanation:

you can see stuff in space but cant hear it

Work out the velocity v at the end of a rollercoaster ride (0). (rearrange the equation for KE to make velocity v the subject)
KE=1/2mv^2

Answers

Explanation:

If the kinetic energy of an object is given and we need to find its velocity of motion, then we can find it by using the formula of kinetic energy as :

\(K=\dfrac{1}{2}mv^2\)

m is mass of the object

We can rearrange the above equation such that,

\(v=\sqrt{\dfrac{2K}{m}}\)

Hence, this is the velocity at the end of a rollercoaster ride.

Write 8.0090 x 10^2 in standard form . (Example of standard form: 4550)Blank 1:

Answers

We are given the following number in scientific notation:

\(8.0090\times10^2\)

To convert this number into standard form we will move the decimal point a number of times equal to the exponent of the ten. Since the exponent is positive we will move the point to the right, like this:

\(8.0090\times10^2=800.90\)

Therefore, the standard form of the number is 800.90

-Help Please-
What is recycling? (Write 4 Sentences)

1.
2.
3.
4.

Answers

Answer:

Recycling is the action or process of converting waste into reusable material. Recycling can be done in many different ways such as using Coca-Cola tin cans and cutting them in half to design a pencil holder. Or it may be also cutting a flat waste wood-building piece to design a chair. Or may be recycling plastic water bottles to use them again.

Explanation:

The

is located 12 to 50 kilometers from Earth’s surface.

Both the

get colder as altitude increases.

The ozone in the

protects people from ultraviolet (UV) radiation.

The
has the highest temperature of any layer in Earth’s atmosphere.

Answers

The thermosphere has the highest temperature of any layer in Earth’s atmosphere.

What is the atmosphere?

The term troposphere is the region that is found  12 to 50 kilometers from Earth’s surface. This region is found to be the region where you can find a lot of gases.

Both the Troposphere and the stratosphere  get colder as altitude increases. However, the ozone in the stratosphere  protects people from ultraviolet (UV) radiation.

The thermosphere has the highest temperature of any layer in Earth’s atmosphere.

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Particles q₁ +8.0 μC, q2 +3.5 μC, and
93-2.5 μC are in a line. Particles q₁ and q2 are
separated by 0.10 m and particles q2 and q3 are
separated by 0.15 m. What is the net force on
particle q₂?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
+8.0μ.C
+91
0.10 m
+3.5 C
+92
0.15 m
-2.5μ C
93

Particles q +8.0 C, q2 +3.5 C, and93-2.5 C are in a line. Particles q and q2 areseparated by 0.10 m and

Answers

The net force on particle q₂, located between particles q₁ and q₃, is approximately 189000 N. The force exerted by particle q₁ on q₂ is positive and equals 252000 N, while the force exerted by particle q₃ on q₂ is negative and equals -63000 N.

To find the net force on particle q₂, we need to calculate the individual forces exerted on q₂ by particles q₁ and q₃ and then determine their sum.

The force between two charged particles can be calculated using Coulomb's law:

F = k * |q₁ * q₂| / r²

Where F is the force between the particles, k is the electrostatic constant (k ≈ 9.0 x \(10^9\) Nm²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them.

First, let's calculate the force exerted on q₂ by q₁:

F₁₂ = k * |q₁ * q₂| / r₁₂²

F₁₂ = (9.0 x \(10^9\) Nm²/C²) * |(8.0 μC) * (3.5 μC)| / (0.10 m)²

F₁₂ ≈ 252000 N

The force is positive because q₁ and q₂ have opposite charges.

Next, let's calculate the force exerted on q₂ by q₃:

F₂₃ = k * |q₂ * q₃| / r₂₃²

F₂₃ = (9.0 x \(10^9\)Nm²/C²) * |(3.5 μC) * (-2.5 μC)| / (0.15 m)²

F₂₃ ≈ -63000 N

The force is negative because q₂ and q₃ have the same charge.

Finally, we can find the net force on q₂ by summing the individual forces:

Net force = F₁₂ + F₂₃

Net force = 252000 N + (-63000 N)

Net force ≈ 189000 N

The net force on particle q₂ is approximately 189000 N.

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based on these insights, you create your primary message. which of the following reflect the expectations of a primary message? A
Although electric vehicle sales demand is on the rise, low availability of charging stations and short battery range are significant hurdles that Gaea must overcome
B
Electric vehicle sales demand is expected to grow by more than 400% by 2025. However, the number of publicly available vehicle charging stations is a significant factor in consumer buying decisions. Currently, there are many locations with so few charging stations that electric car owners would run out of power when traveling between stations. Vehicle battery range is also a significant factor for consumers. In 2020, the average battery range was 210 miles. However, the vast majority of people say they will not buy an electric car until the battery range is at least 300 miles per charge
C
Electric vehicle demand is skyrocketing
D
The number of publicly available vehicle charging stations is a significant factor in consumer buying decisions. Therefore, Gaea must begin building vehicle charging stations

Answers

The insights to be used in creating a primary message is that; Electric vehicle demand is skyrocketing. Option C

What are electric vehicles?

We can see that the demand for electric vehicles has increased in the recent times. Why has the demand for electric vehicles increased? We know that in the recent times there has been a push for the use of cleaner energy.

This has made a strong impressions upon governments around the would and has led to an increase in the rate at which any kind of research that tries to fund the use of devices that use alternative energy to fossil fuels is concerned.

As a result of this, there has been an increase in the demand and the use of the electric vehicles especially in the developed countries where more people can be able to afford the vehicles.

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A box of mass 3.0 kg
slides down a rough vertical wall. The gravitational force on the box is 29.4 N. When the box reaches a speed of 2.5 m/s, you start pushing on one edge of the box at a 45∘
angle (use degrees in your calculations throughout this problem) with a constant force of magnitude Fp= 23.0 N, as shown in (Figure 1). There is now a frictional force between the box and the wall of magnitude 13.0 N. How fast is the box sliding 2.8 s
after you started pushing on it?

Answers

The speed of the box 2.8 s after you started pushing on it is 9.1 m/s.

What is gravitational force?

The gravitational force is a force of attraction that attracts all the physical forms having mass.

Given, gravitational force on the box is 29.4 N.

At the instant you start pushing the box, normal force is equal in magnitude to the gravitational force, which is 29.4 N. Given, frictional force 13.0 N, so : Fnet = 23.0 sin 45 - 13.0 - 29.4 = -9.7 N

d = (1/2)at² = (1/2)(-9.7/3.0)(2.8)^2 = -27.1 m.

Negative sign indicates that the box has moved in opposite direction to the force you applied.

As, v² = u² + 2as,

v = sqrt(2as) = sqrt(2(9.7/3.0)(27.1)) = 9.1 m/s.

Therefore, the speed of the box 2.8 s after you started pushing on it is 9.1 m/s.

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B. Exercises
Exercise 1
Direction: identfy the plumbing symbols in each item Write your answer on the space
provided before each number​

B. ExercisesExercise 1Direction: identfy the plumbing symbols in each item Write your answer on the spaceprovided

Answers

Answer:

please I do not understand that question

g if the distance between the Earth and the Sun were increased by a factor of 2.87, by what factor would the strength of the force between them change

Answers

We have that the  the strength of the force between the Sun and the moon  is mathematically given as

F2=0.12140F1N

Strength of the Force

Question Parameters:

Distance between the Earth and the Sun were increased by a factor of 2.87,

Generally the equation for the  Gravitational Force   is mathematically given as

\(F=\frac{Gm1m2}{d^2}\\\\Where\\\\f1/f2=d1^2/d2^2\\\\Therefore\\\\F2=\frac{F1*d1}{3.23^2}\\\\F2=\frac{F1*1}{2.87^2}\\\\\)

F2=0.12140F1N

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A certain spring has a spring constant k1 = 660 N/m as the spring is stretched from x = 0 to x1 = 35 cm. The spring constant then changes to k2 = 250 N/m as the spring is stretched to x2 = 65 cm. From x2 = 65 cm to x3 = 89 cm the spring force is constant at F3 = 105 N.
Write an equation for the work done in stretching the spring from x1 to x2.
Calculate the work done, in joules, in stretching the spring from x1 to x2.
Calculate the work, in joules, necessary to stretch the spring from x = 0 to x3.

Answers

(a) The equation for the work done in stretching the spring from x1 to x2 is ¹/₂K₂Δx².

(b) The work done, in stretching the spring from x1 to x2 is 11.25 J.

(c) The work, necessary to stretch the spring from x = 0 to x3 is 64.28 J.

Work done in the spring

The work done in stretching the spring is calculated as follows;

W = ¹/₂kx²

W(1 to 2) = ¹/₂K₂Δx²

where;

k is spring constantΔx is compression of the spring

W(1 to 2)  =  ¹/₂(250)(0.65 - 0.35)²

W(1 to 2)  = 11.25 J

W(0  to 3) = ¹/₂k₁x₁² + ¹/₂k₂x₂² + ¹/₂F₃x₃

where;

k₁ is first spring constantk₂ is second spring constantF₃ is third force applied to the spring

W(0  to 3) = ¹/₂(660)(0.35)² + ¹/₂(250)(0.65 - 0.35)² + ¹/₂(105)(0.89 - 0.65)

W(0  to 3) = 64.28 J

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In a mass spectrometer, a specific velocity can be selected from a distribution by injecting charged particles between a set of plates with a constant electric field between them and a magnetic field across them (perpendicular to the direction of particle travel). If the fields are tuned exactly right, only particles of a specific velocity will pass through this region undeflected. Consider such a velocity selector in a mass spectrometer with a 0.105 T magnetic field.
Part (a) What electric field strength, in volts per meter, is needed to select a speed of 3.8 × 106 m/s?
Part (b) What is the voltage, in kilovolts, between the plates if they are separated by 0.75 cm?

Answers

Answer:

a).\($3.99 \times 10^5 \ v/m$\)

b). 2.9925 kV

Explanation:

Given :

For mass spectrometer

The magnetic field = B

B = 0.105 T

a).  Given speed, v = \($3.8 \times 10^6 \ m/s$\)

We known

\($\frac{E}{B}=v$\)

∴ \($E= 3.8 \times 10^6 \times 0.105$\)

      \($=3.99 \times 10^5 \ v/m$\)

b). Now spectrometer, d = 0.75 cm

                                      \($d=0.75 \times 10^{-2} \ m$\)

We known

\($E=\frac{V}{d}$\)

\($V = E\times d$\)

\($V = 3.99 \times 10^5 \times 0.75 \times 10^{-2}$\)

\($V = 2.9925 \times 10^3 \ V$\)

   = 2.9925 kV

 

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