A 4.00–kg block is set into motion up an inclined plane with an initial speed of vi = 8.60 m/s (see figure below). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of theta = 30.0° to the horizontal.An inclined plane makes an angle of theta with the horizontal. A block is shown on the plane at two different positions, a distance d apart. An arrow labeled vi is above the lower position of the block, and points up and to the right, parallel to the plane.
(a) For this motion, determine the change in the block's kinetic energy.
(b) For this motion, determine the change in potential energy of the block–Earth system.
(c) Determine the friction force exerted on the block (assumed to be constant).
(d) What is the coefficient of kinetic friction?

Answers

Answer 1

A 4.00–kg block is set into motion up an inclined plane with an initial speed of vi = 8.60 m/s . The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of θ(theta) = 30.0° to the horizontal. The principles of energy conservation state that energy cannot be created or destroyed, only transferred or transformed. The total energy of a system remains constant if no external forces act upon it. (a) For this motion, the change in the block's kinetic energy is : ΔK = Kf - Ki = 0 - Ki = -Ki.  (b) For this motion, the change in potential energy of the block–Earth system is zero.  (c)  The friction force exerted on the block is m * g * sin(θ) . (d) 0.5 is the coefficient of kinetic friction.

(a) To determine the change in the block's kinetic energy, we need to calculate the initial and final kinetic energies. The initial kinetic energy (Ki) can be calculated using the formula Ki = (1/2) * m * vi^2, where m is the mass and vi is the initial velocity. Plugging in the values, we have Ki = (1/2) * 4.00 kg * (8.60 m/s)^2. The final kinetic energy (Kf) is zero since the block comes to rest. The change in kinetic energy (ΔK) is then given by ΔK = Kf - Ki = 0 - Ki = -Ki.

(b) The change in potential energy (ΔPE) of the block-Earth system can be determined using the formula ΔPE = m * g * h, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical distance traveled along the inclined plane. Since the block moves horizontally, there is no change in height (h) and therefore, no change in potential energy (ΔPE = 0).

(c) The friction force exerted on the block can be determined using the equation f_friction = m * g * μ, where m is the mass, g is the acceleration due to gravity, and μ is the coefficient of kinetic friction. Since the block comes to rest, the friction force must be equal in magnitude and opposite in direction to the force component pulling it down the incline, which is m * g * sin(θ).

(d) To find the coefficient of kinetic friction (μ), we can set up an equation using the friction force calculated in part (c) and the force component pulling the block down the incline. We have m * g * sin(theta) = m * g * μ. The mass cancels out, and we are left with μ = sin(theta). Plugging in the value of theta = 30.0°, we find μ = sin(30.0°) ≈ 0.5.

Therefore, the coefficient of kinetic friction for this motion is approximately 0.5.

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Related Questions

Explain the function and the difference between figure 1 and 2

Explain the function and the difference between figure 1 and 2

Answers

Answer:

figure one (step up transformer) helps in increasing the output voltage

figure two (step down transformer) helps in decreasing the output voltage

Start
Finish
8 min
Time
0 min
1 min
2 min
3 min
4 min
5 min
6 min
7 min
Temperature
90°C
83°C
78°C
73°C
68°C
64°C
60°C
57°C
54°C
O 45 degrees celsius/min
O 450 degrees celsius/min
O 4.5 degrees celsius/ min
O 0.45 celsius/min
hos

Answers

What is the actuall question?

this is a type of protein that helps to speed up metabolic reactions while remaining unchanged.

Answers

Answer:

A fundamental task of proteins is to act as enzymes—catalysts that increase the rate of virtually all the chemical reactions within cells.

climate change serves to intensify the _______________ because as the temperature of the air increases, more water evaporates into the air.

Answers

Climate change serves to intensify the water cycle by increasing the air temperature and causing more water to evaporate into the air.

This intensification of the water cycle is leading to more frequent and intense precipitation events, such as heavy rainfall and storms, as well as more prolonged droughts in some regions.

The resulting changes in water availability and quality can have significant impacts on ecosystems, agriculture, and human societies.

Mitigating climate change and adapting to its consequences is thus crucial, and requires concerted efforts from all sectors of society.

The intensification of the water cycle highlights the urgent need for effective policies, technologies, and practices to manage water resources sustainably in a changing climate.

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Give a description of of lower mantle

Answers

Answer:

The lower mantle is the liquid inner layer of the earth from 400 to 1,800 miles below the surface.

Explanation:

The cockroach originated on Earth more than 250 million years ago and is thriving today all over the world. A giant deer (more than 2m tall!) evolved less than 1 million years ago and become extinct around 11,00 years ago.

Why do YOU think one animal thrived and the other perished?

Answers

Answer:

I believe one lived and the other became extinct is because of hunters. No one really cares about cockroaches because they serve no purpose whatsoever other than just being a burden to society. But the deer, can be killed for meat, as a coat, as a rug, etc. So no wonder its gone now. I'm not justifying killing animals for meat and its fur is okay, I'm just explaining what it can go to use for, and what other people would use it for.

That's what I think. :)

Hope this helps!

Brainliest please?

Answer:

The cockroach thrived because of its number and survivability they can survive nukes and still walk just fine. They are not on the hit list for humans to hunt because they gain no benefit. The dear was a huge target with lots of meat and fur for humans to hunt and the male giant dear had antlers so big that if one broke they would fall and break their neck from the weight. Also being big means they could not hide in the forest to hide from predators at the time Cave Bears, saber tooths, Cave lions, and humans because they would get stuck in the tree and shrubs cus of their antlers, that's why they perished.

Explanation:

Typically, astronomers express the right ascension of a star on the sky in what units?.

Answers

Typically, astronomers express the right ascension of a star on the sky in hours, minutes, and seconds.

The positions of the stars in relation to one another are largely constant. Orion and Taurus are constantly converging. Draco is always near Ursa Minor. When we look at the sky, the stars are a never-ending backdrop painting that barely move in relation to one another.

There are some minute movements as we orbit the sun throughout the year. Stars closer to us move more left and right than stars farther away. It makes sense, even if it only has a small impact. If you keep your eyes fixed out into the distance as you walk down the street, you'll notice that objects farther away move less in relation to you than ones closer to you.

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how long would it take to get to the moon going around 75 miles an hour

Answers

The moon is our only known natural satellite, which means it's the only natural object that orbits Earth. At its closest, it is 223,700 miles away from Earth. So if you were riding in a car going 70 miles per hour, it would take you 135 days to get there.

) when starting from rest, how long, in seconds, does it take the child to reach the bottom of the slide?

Answers

The child's acceleration is 4/9 m/s^2. To find the acceleration, we can use the equation: acceleration = change in velocity/time.

In this case, the child starts from rest, so their initial velocity is 0 m/s. We can use the final velocity and the time to find the acceleration.

First, we can find the final velocity of the child using the equation: final velocity = initial velocity + acceleration x time. Substituting 0 for initial velocity and 3 seconds for time, we get:

final velocity = 0 + acceleration x 3

Next, we can use the distance formula to find the final velocity, which is: final velocity = √(2 * acceleration * distance).

Setting these two equations equal to each other and solving for acceleration, we get:

acceleration = final velocity^2 / (2 * distance) = (2 * 2 / 3^2) = 4/9 m/s^2

So, the child's acceleration is 4/9 m/s^2.

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The correct question for the answer is

A child goes down a slide, starting from rest. If the length of the slide is 2 m and it takes the child 3 seconds to go down the slide, what is the child’s acceleration?

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A block hangs in equilibrium from a vertical spring The equilibrium position sags by 9.00 cm when a second identical block is added. Part A What is the oscillation frequency of the two-block system?

Answers

When a second identical block is added, a block hangs in equilibrium from a vertical spring. The oscillation frequency of the two-block system is 1.17 Hz.

To determine the oscillation frequency of the two-block system, we need to use the formula:

\(f = (1/2\pi)\sqrt{(k/m)}\)

where f is the frequency, k is the spring constant, and m is the mass of the two-block system.

Since the two-block system is in equilibrium, we know that the weight of the two blocks is equal to the spring force. Let's assume that each block has a mass of m. Then, the weight of the two-block system is 2mg, where g is the acceleration due to gravity.

The spring force is given by Hooke's Law:

F = -kx

where F is the spring force, k is the spring constant, and x is the displacement from equilibrium.

When one block is added to the system, the equilibrium position sags by 9.00 cm, or 0.0900 m. Therefore, the spring force when one block is added is:

\(F_1 = -kx_1 = -k(0.0900)\)

When two blocks are added, the equilibrium position sags by 2(0.0900) = 0.1800 m. Therefore, the spring force when two blocks are added is:

\(F_2 = -kx_2 = -k(0.1800)\)

Since \(F_2 = 2F_1\) and\(F_1 = mg\) therefore k can be calculated as,

\(3F_1 = k (0.09 + 0.18)\)

\(k = (3mg)/0.27\)

\(k = 109m N/m\)

Substituting the mass of the two-block system, 2m, and the spring constant, 109m N/m, into the formula for the oscillation frequency, we get:

\(f = (1/2\pi ) \sqrt{(k/m)} = (1/2\pi ) \sqrt{(109m) / (2m)} = 1.17 Hz.\)

Therefore, the oscillation frequency of the two-block system is approximately 1.17 Hz.

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Explain why there is a voltage between the two terminals of the secondary coil

Answers

Answer:

The coils are not electrically connected. ... the primary coil current produces a magnetic field, which changes as the current changes. the iron core increases the strength of the magnetic field. the changing magnetic field induces a changing potential difference (voltage) in the secondary coil.

There is a voltage between the two terminals of the secondary coil because the magnetic field/magnetic flux is strengthened by the iron core. The secondary coil's potential difference (voltage) changes as the magnetic field changes. Energy is transferred by law of conversation .

What is magnetic flux?

Magnetic flux is the number of magnetic field lines passing through a closed surface.

What is electromagnetic induction?

There is a change in magnetic flux associated with a coil it gives rise to an induced current and hence an induced EMF in the coil. This phenomenon is called electromagnetic induction.

What is law of conservation of energy?

Law of conservation of energy states that energy can neither be created nor be destroyed . It can only be converted from one form to another form.

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Write a boolean expression that tests if b is outside the set of integers from 6 to 16 inclusive. your expression should use one of the logical operators (and, or, or not).

Answers

The boolean expression that tests if b is outside the set of integers from 6 to 16 inclusive can be written as: \(not (b > = 6 and b < = 16)\)

This expression utilizes the logical operators "not," "and," and ">=, <=," to perform the desired test.

Let's break it down:

- \("b > = 6"\) checks if b is greater than or equal to 6.

- \("b < = 16"\) checks if b is less than or equal to 16.

-\("b > = 6 and b < = 16"\) checks if b satisfies both conditions, i.e., if it falls within the range from 6 to 16 inclusive.

- Finally, "\(not (b > = 6 and b < = 16)"\) negates the result of the previous expression, effectively checking if b is outside the specified range.

If the expression evaluates to True, it means b is outside the range from 6 to 16 inclusive. If it evaluates to False, it means b is within the specified range.

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a red shirt appears red because?

a. the shirt reflects red light

b. the shirt absorbs red light

c. the shirt emits green and blue light

d. the shirt reflects magenta and blue light

Answers

Red shirt appears red because:

a. The shirt reflects red light

A red shirt appears red because the shirt reflects red light.

Thus, An important topic for astronomers is "red shift." The phrase can be taken literally; when the light's wavelength is extended, the light is perceived as having "shifted" toward the red portion of the spectrum.

When a source of sound moves in relation to an observer, sound waves experience a similar phenomenon.

The frequency of sound waves varies if the source of the sound and the observer are moving relative to one another, according to Austrian mathematician Christian Andreas Doppler, who made this discovery.

The observer hears a frequency that is higher when the two are moving closer together and lower when they are moving farther apart and red shift.

Thus, A red shirt appears red because the shirt reflects red light.

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Approximately 1. 000 g each of four gasses h2, ne, ar, and kr are placed in a sealed container all under1. 5 atm of pressure. Assuming ideal behavior, determine the partial pressure of the h2 and ne?.

Answers

Answer:2.25atm , because doubling the number of moles of Ar doubles its partial pressure.

Explanation:

Slope should always be written as a fraction, not a decimal. True or false?

Answers

False. Slope can be expressed as either a fraction or a decimal. Both forms are valid and commonly used in mathematics. The choice of representation depends on the context and personal preference.

When slope is expressed as a fraction, it is in the form of rise over run. For example, a slope of 2/3 means that for every 2 units of vertical change (rise), there is 3 units of horizontal change (run). This fraction form can provide a clear visual understanding of the slope. On the other hand, slope can also be expressed as a decimal, which is the result of dividing the rise by the run. Decimal slope values are commonly used in calculations and equations. They can be more precise and convenient for certain mathematical operations. In summary, whether to express slope as a fraction or a decimal is a matter of choice and can vary based on the specific mathematical context or personal preference. Both forms are valid and serve different purposes in different situations.

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If a person is picking up a book with the force of 50 N and the gravity is pushing down with 15 N, what is the net force?

Answers

Answer:

\(the \: net \: force = \: 50 - 15 = 35.\)

Answer:

Net force is going to be GREATER FORCE - LESS FORCE if they are working in opposite direction

so,

         50N - 15N = 35N

Consider an incandescent lightbulb. If you wanted to turn a 10-w lightbulb into a 100-w lightbulb, how would you change the temperature of the filament inside the bulb?.

Answers

By using the blackbody radiation formula, the temperature of the filament inside the bulb is changed by a factor of 10⁰'²⁵.

To tackle this issue, we need to understand black body radiation. A black body object's energy emission is inversely proportional to its area and the temperature to the fourth power. It may be established that

P = A . e . σ . T⁴

where P (power), A (surface area), e (emissivity), ( 5.67 x 10¯⁸ W/m²K⁴), and T (temperature) are all variables.

From the question above, we know that

P1 = 10 watt

P2 = 100 watt

T1 = T1

By using the black body radiation formula, the ratio of temperature is

T1⁴ / T2⁴ = P1 / P2

Hence,

T1⁴ / T2⁴ = P1 / P2

T1⁴ / T2⁴ = 10 / 100

T1⁴ / T2⁴ = 1 / 10

T2⁴ = 10T1⁴

T2 = ⁴√(10T1⁴)

T2 = T1 x 10⁰'²⁵

Thus, the temperature of the filament inside the bulb is changed by a factor of 10⁰'²⁵.

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GOOD MFRNING
PAGE NO.:
DATE:
cap a b
body have larger mess be holter than another of smaller
maws if they are same temperature why,
at the​

Answers

Answer:

umm im confused

Explanation:

Answer:

larger mass more the molecule more heat absorbed

and vice versa .Thats the reason ok?

Write the cautions which are taken to keep the magnetic properties of magnetsa) Don’t hammer it b) don’t drop it c) don’t heat it d) all of these


PLS HELP GUYS ITS URGENTTT!! I AM IN CLASS ...PLEASE!!

Answers

Answer:

D

Explanation:

These all can impact the magnetic properties

what is the weight of a 45kg box
____ N

Answers

The weight of a \(45 kg\) box is \(441.45 N\).

Weight refers to the measure of the force exerted on an object due to the gravitational pull of the Earth.

Given the mass of the box is \(m=45 kg\).

The weight of an object (\(W\)) can be found by multiplying the mass of the object (\(m\)) by the acceleration due to gravity (\(g\)).

So, \(W=mg\).

It is known that acceleration due to gravity, \(g=9.81 m/s^2\).

Hence, the weight of the box, \(W=(45kg)\times (9.81 m/s^2)\).

\(\Rightarrow W=441.45 (kg\cdot m/s^2)\\\Rightarrow W=441.45 N\)

Therefore, the weight of the box is \(441.45 N\).

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Using your knowledge of the wave nature of sound, EXPLAIN who heard the basketball hit the backboard first, the ESPN cameraman or photographer? Explain your answer.
A - The camera man
B - the photographer under Miami’s goal.

Answers

Answer:

I can not see the image, so i will answer in a general way.

As you know, the sound behaves like a wave, this means that the sound needs some time to cover a given distance. An example of this motion can be seen when you drop a little stone in water, and you can see how the waves expand.

This means that the one who will hear the sound first, will be always the one that is closer to the source of the sound, in this case, the sound comes from the ball hitting the backboard, then the one who is closer to the backboard will hear the sound first.

is the change in position of an object

Answers

Displacement is the change in position

Answer:

Explanation:

In my opinion motion is the correct answer

Gallium is a solid metal at room temperature, but it will melt to a liquid in your hand. the melting point of gallium is 85.6 f. what is this tempature on the celsius scale and the kelvin scale?

Answers

Fahrenheit  =  85.6°F

Celsius  =  (5/9) (Fahrenheit - 32)

Celsius  =  (5/9) (85.6 - 32)

Celsius  =  (5/9) (53.6)

Celsius  =  29.78°C

Kelvin  =  Celsius + 273.15

Kelvin  =  29.78 + 273.15

Kelvin  =  302.93K  

The melting point of a solid is the temperature at which it transforms into a liquid under atmospheric pressure. At this time, both the liquid and solid states coexist peacefully. The Celsius temperature is 29.78°C and that of Kelvin is 302.93K.

The typical definition of the melting point is the temperature at which a substance transforms from a solid to a liquid. The melting point of a liquid is the temperature at which the liquid transforms from a solid to a liquid under atmospheric pressure.

Melting is the process of a solid changing from a solid to a liquid when heated to a specific temperature.

Celsius  =  (5/9) (Fahrenheit - 32)

Celsius  =  (5/9) (85.6 - 32)

Celsius  =  (5/9) (53.6)

Celsius  =  29.78°C

Kelvin  =  Celsius + 273.15

Kelvin  =  29.78 + 273.15

Kelvin  =  302.93K  

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In which of the two situations described is more energy transferred?
Situation A - a cup of hot chocolate with a temperature of 40 °C inside a freezer at -20 °C
Situation B - the same cup of hot chocolate at 90 °C in a room at 25°C

Answers

Answer:

More energy is transferred in situation A

Explanation:

Each of the situations are analyzed as follows;

Situation A

The temperature of the cup of hot chocolate = 40 °C

The temperature of the interior of the freezer in which the chocolate is placed = -20 °C

We note that at 0°C, the water in the chocolate freezes

The energy transferred by the chocolate to the freezer before freezing is given approximately as follows;

E₁ = m×c₁×ΔT₁

Where;

m = The mass of the chocolate

c₁ = The specific heat capacity of water = 4.184 kJ/(kg·K)

ΔT₁ = The change in temperature from 40 °C to 0°C

Therefore, we have;

E₁ = m×4.184×(40 - 0) = 167.360·m kJ

The heat the coffee gives to turn to ice is given as follows;

E₂ = m·\(H_f\)

Where;

\(H_f\) = The latent heat of fusion = 334 kJ/kg

∴ E₂ = m × 334 kJ/kg = 334·m kJ

The heat required to cool the frozen ice to -20 °C is given as follows;

E₃ = m·c₂·ΔT₂

Where;

c₂ = The specific heat capacity of ice = 2.108 kJ/(kg·K)

Therefore, we have;

E₃ = m × 2.108 ×(0 - (-20)) = 42.16

E₃ = 42.16·m kJ/(kg·K)

The total heat transferred = (167.360 + 334 + 42.16)·m kJ/(kg·K) = 543.52·m kJ/(kg·K)

Situation B

The temperature of the cup of hot chocolate = 90 °C

The temperature of the room in which the chocolate is placed = 25 °C

The heat transferred by the hot cup of coffee, E, is given as follows;

E = m×4.184×(90 - 25) = 271.96

∴ E = 271.96 kJ/(kg·K)

Therefore, the total heat transferred in situation A is approximately twice the heat transferred in situation B and is therefore more than the heat transferred in situation B

Energy transferred in situation A = 543.52 kJ/(kg·K)

Energy transferred in situation B = 271.96 kJ/(kg·K)

Energy transferred in situation A ≈ 2 × Energy transferred in situation B

∴ Energy transferred in situation A > Energy transferred in situation B.

Cart A has a mass of 2 kilograms and a speed of
3 meters per second. Cart B has a mass of 3
kilograms and a speed of 2 meters per second.
Compared to the inertia and magnitude of
momentum of cart A, cart B has

Answers

Cart B has more inertia and the same amount of momentum compared to Cart A's inertia and magnitude of momentum.

What impact does the cart's bulk have on how it moves?

The cart moves more slowly because a greater mass with higher inertia must be moved by the same force. This cart's momentum also rises as a result of its increasing bulk. Due to its larger momentum, it pushes the other cart harder.

How is impulse determined?

p is equal to F net t. The impulse-momentum theorem refers to the relationship between the expressions F net t and F net t. We can observe that the impulse is equal to the average net external force times the length of time that force is in effect.

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can Somebody Explain Please
Introduction to Newton's law of gravitation

Answers

Answer: so basically, Newtons Law states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Explanation: newtons law simplified in my opinion is a physical law that describes the attraction between two objects with mass.

hope this helps.

Answer:

Explanation:

she rieat

the total energy of a system is 300j. if the potential energy is 40j what is the kinetic energy if the object started 300m above the ground?

Answers

Answer:

43.3 m/s.

Explanation:

Assuming the potential energy is due to the gravitational potential energy, we can use the conservation of energy to find the kinetic energy:

Total energy = Potential energy + Kinetic energy

Kinetic energy = Total energy - Potential energy

Kinetic energy = 300 J - 40 J = 260 J

However, we need to know the mass of the object to convert the kinetic energy to velocity. We can use the potential energy to find the mass:

Potential energy = mgh

40 J = m(9.81 m/s^2)(300 m)

m = 0.137 kg

Now we can use the kinetic energy to find the velocity:

Kinetic energy = (1/2)mv^2

260 J = (1/2)(0.137 kg)v^2

v^2 = (2*260 J) / 0.137 kg

v = 43.3 m/s (rounded to one decimal place)

Therefore, the kinetic energy is 260 J and the velocity of the object when it reaches the ground is 43.3 m/s.

Evaluate the phases of change management and describe your
reflection on the material.

Answers

The phases of change management typically include initiation, planning, execution, and evaluation.

Change management is a structured approach to transitioning individuals, teams, and organizations from a current state to a desired future state. The phases of change management help guide the process and ensure its effectiveness.

1. Initiation: This phase involves recognizing the need for change, identifying the scope and goals of the change, and securing support from key stakeholders. It is crucial to establish a clear vision and communicate it effectively to gain buy-in from those affected by the change.

2. Planning: In this phase, a detailed plan is developed to outline the actions, resources, and timeline required for implementing the change. This includes identifying potential risks and developing strategies to mitigate them. Stakeholders are engaged, and their roles and responsibilities are defined.

3. Execution: The execution phase involves implementing the change plan. It requires effective communication, training, and support to help individuals navigate through the transition. Monitoring progress, addressing resistance, and making necessary adjustments are key activities during this phase.

4. Evaluation: Once the change has been implemented, the evaluation phase assesses its outcomes and effectiveness. This includes gathering feedback, measuring performance against the desired goals, and identifying areas for further improvement.

The phases of change management provide a structured framework to navigate through the process of change effectively. Each phase plays a vital role in ensuring successful change implementation, from recognizing the need for change to evaluating its outcomes. Reflecting on the material, change management is a valuable approach that helps organizations navigate the complexities of change while minimizing resistance and maximizing the chances of successful outcomes.

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In the figure, the magnitude of vector a⃗ is 18. 0 units, and the magnitude of vector b⃗ is 12. 0 units. What vector c⃗ must be added to the vectors a⃗ and b⃗ so that the resultant of these three vectors points in the − x direction and has a magnitude of 7. 50 units?

Answers

The magnitude of vector C is 15.5. The angle with positive x axis is 209.4°.

The vector A is given as

\(\vec{A}\) = \(A_x\)Î + \(A_y\)Ĵ

   = 0Î + AĴ

   = 18Ĵ

The vector B is given as,

\(\vec{B}\) = \(B_x\) Î + \(B_y\)Ĵ

= B cos (90° - 30°)î-B sin (90° -30°) Ĵ

= B cos 60°Î - B sin 60°Ĵ

= 12 cos 60°Î  - 12 sin 60°ĵ

= 6Î - 10.39Ĵ

The vector A+B is given as

\(\vec{A}+\vec{B}\) = 18Ĵ + 6Î - 10.39Ĵ

          = 6Î + 7.61Ĵ

The resultant of vectors A, B, and C is 7.50 units along the -x axis. Then the y component of C vector must be equal and opposite to the y component of vector A+B. That is,

\(C_y= A_y + B_y\)

    = -7.61

Then the sum of the x component of all three vectors will be equal to -7.5. Then the x component of vector C is determined as follows:

\(A_y+B_x+C_x = -7.5\\0+6+C_x=-7.5\\C_x=-13.5\)

The magnitude of vector C is given as,

\(C=\sqrt{C_x^2+C_y^2}\\C = \sqrt{(-13.5)^2+(-7.61)^2}\\C=15.5\)

The angle \(\phi\) is given as,

\(\phi = tan^{-1}(\frac{-7.61}{-13.5})\\\phi = 29.4\\\)

The angle with positive x axis is given as,

\(\phi'=\phi\) + 180°

=29.4° +180°

= 209.4°

A vector is a mathematical object that has both magnitude and direction. A vector is typically represented as an arrow in a coordinate system, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Vectors can be used to describe various physical quantities such as velocity, acceleration, force, and displacement. They are commonly used in calculus, linear algebra, and geometry. In linear algebra, vectors are used to represent points in a space, and they can be added and multiplied by scalar values to create new vectors. This allows for the creation of vector spaces, which are important in many areas of mathematics and physics.

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Complete Question:-

In this figure, the magnitude of vector A is 18.0 units, and the magnitude of vector B is 12.0 units. What vector C must be added to the vectors A and B in Fig. 1.3 so that the resultant of these three vectors points in the -x-direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector C by giving its magnitude and the angle it makes with the x-axis taking counter clockwise to be positive.

In the figure, the magnitude of vector a is 18. 0 units, and the magnitude of vector b is 12. 0 units.

In a simple model of the hydrogen atom, the electron moves in a circular orbit of radius 0.053nm around a stationary proton. How many revolutions per second does the electron make?
Could you also explain where your different values cam from? Thank you.

Answers

The number of revolutions per second that the electron makes is equal to the frequency, or 1.22 x \(10^{14}\) revolutions per second.

The number of revolutions per second that an electron makes in a circular orbit around a stationary proton in a simple model of the hydrogen atom can be calculated using the formula

v = (2πr)/T, where v is the velocity of the electron, r is the radius of the orbit, and T is the period of the orbit. Using this formula and the given radius (0.053nm), we can calculate the velocity of the electron to be 2.45 x \(10^{6}\) m/s.

Since the period of a circular orbit is equal to one over the frequency, we can calculate the frequency of the electron's orbit to be 1.22 x \(10^{14}\) Hz.

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