The position of a 55 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds. determine the velocity at t=0.40s

Answers

Answer 1
For this problem, we combine the concepts learned in physics and in calculus. The velocity, by definition, is the total distance travelled per time elapsed. It can also be expressed in Δx/Δt, This is also a definition in calculus where dx/dt is equal to velocity. Therefore, to solve the velocity, differentiate the equation in terms of t.

x = 2 cos(10t)
dx/dt = 2*(-sin(10t))*(10)
dx/dt = -20sin (10t)

We are asked to find the velocity at 0.40 seconds. Thus, we substitute t = 0.40 to the equation

dx/dt = -20sin(10*0.4)
dx/dt = v = -1.395 m/s

Therefore, the velocity at t=0.04 seconds is -1.395 m/s. The negative sign connotes that the direction of the motion is south or to the left based on the sign convention.
Answer 2

The velocity of the oscillating mass at time [tex]t = 0.40\,{\text{s}}[/tex] is [tex]\boxed{15\times{10^{-2}}\,{\text{m/s}}}[/tex] or [tex]\boxed{15\,{\text{cm/s}}}[/tex] or [tex]\boxed{0.15\,{\text{m/s}}}[/tex].

Further explanation:

Velocity of a particle or a mass at any instant is defined as the rate of change of position of particle with respect to time.  

Mathematically,

[tex]V\left( t \right) = \dfrac{d}{{dt}}\left( {X\left( t \right)} \right)[/tex]

If position of a particle or mass is a function of time then velocity of mass at any instant will change with respect to time.

Given:

The position of an oscillating mass varies according to the function  [tex]X(t)=({2.0\text{ cm}}})\cos({10t})[/tex].

Mass of an oscillating object is [tex]55\text{ g}[/tex].

Concept:

The velocity of mass at any instant is calculated by using the following relation

[tex]\begin{aligned}V(t)&=\frac{{dX\left( t \right)}}{{dt}}\\&=\frac{d}{{dt}}\left[{\left( {2.0{\kern 1pt} {\text{cm}}} \right)\cos \left( {10t} \right)} \right]\\&=-\left( {20\,{\text{cm/s}}}\right)\sin\left( {10t}\right)\\\end{aligned}[/tex]

Therefore the velocity of the mass at any instant is given by

[tex]V\left( t \right)=-\left( {20{\kern 1pt} {\text{cm/s}}} \right)\sin \left( {10t} \right)[/tex]                                                                          

From the above expression of velocity it can be observed that velocity is changing with time according to the sin function.

Substitute [tex]0.40\,{\text{s}}[/tex] for t in the above expression

[tex]\begin{aligned}V\left( {0.4\,{\text{s}}} \right)&=-\left( {20\,{\text{cm/s}}} \right)\sin \left( 4 \right)\\&=-\left( {20\,{\text{cm/s}}} \right)\left( { - 0.757} \right)\\&=15.14\,{\text{cm/s}}\\\end{aligned}[/tex]

 

Thus, the velocity of the oscillating mass at time [tex]t = 0.40\,{\text{s}}[/tex] is [tex]\boxed{15\times{10^{-2}}\,{\text{m/s}}}[/tex] or [tex]\boxed{15\,{\text{cm/s}}}[/tex] or [tex]\boxed{0.15\,{\text{m/s}}}[/tex].

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Answer Details:

Grade: College

Subject: Physics

Chapter: Force

Keywords:

position, oscillating, 55 g, mass, time, x(t)=(2.0cm)cos(10t), t=4 s, determine, velocity, 15 cm/s, 0.15 m/s, rate, change in position.

The Position Of A 55 G Oscillating Mass Is Given By X(t)=(2.0cm)cos(10t), Where T Is In Seconds. Determine

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An incandescent light bulb is shown in the picture. The filament is the one labelled with number 3. This is a wire made usually of tungsten where the current passes to complete the flow of the electrons from the source to itself as the load. The tungsten material offers a quantity of resistance in ohms. The relationship between the current (I) , resistance (R) and voltage (V) is expressed by the Ohm's Law: V=IR. The voltage across the bulb is directly proportional to the current passing through it with the resistance of the material as its constant of proportionality. 

In short, the voltage and current are related through the filament's resistance according to Ohm's Law.

Sort the following hypothetical discoveries into the appropriate bins as follows:consistent with theory: the statement describes a discovery that we could reasonably expect to find if the nebular theory is correct.not consistent with theory: the statement describes a discovery that would force us to modify or discard the nebular theory.

Answers

Here are the three observable facts that are explained by the nebular theory:
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Here are the missing statements and its appropriate labels:

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Which of the following scenarios will cause the current to stop flowing within a circuit?

A. Insulating materials within the circuit are replaced with conducting materials.
B. A wire connected to the voltage source runs from the negative to the positive terminal.
C. The switch within the closed circuit is opened.
D. The circuit is closed.

Answers

C is correct. Only a closed circuit can carry current, opening a switch disconnects the circuit and stops current from flowing. Remember, all current flows in loops, if you can't make a loop out of it, current can't flow, and opening a switch, assuming no other paths for current exist, will completely stop the current.
The correct answer is C

A potter's wheel decelerates from 50 rev/min to 30 rev/min in 5.0 s, with a constant deceleration. what is the magnitude of the deceleration?

Answers

Final answer:

The magnitude of the deceleration of the potter's wheel is 0.419 rad/s².

Explanation:

To find the magnitude of the deceleration of the potter's wheel, we can use the formula for angular acceleration: a = (ωf - ωi) / t. Given that ωi (initial angular velocity) is 50 rev/min, ωf (final angular velocity) is 30 rev/min, and t (time) is 5.0 s, we can calculate the magnitude of deceleration as follows:

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Since 1 rev/min is equal to 0.1047 rad/s, we can convert the magnitude of deceleration to rad/s²:

a = (-4 rev/min²) * (0.1047 rad/s / 1 rev/min) = -0.419 rad/s²

Therefore, the magnitude of the deceleration is 0.419 rad/s².

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How long does it take the sun to melt a block of ice at 0∘c with a flat horizontal area 1.0 m2 and thickness 1.0 cm ? assume that the sun's rays make an angle of 37 ∘ with the vertical and that the emissivity of ice is 0.050?

Answers

The first step in solving this problem is to calculate for the volume of ice: 
V = A w

V = 1 m^2 (0.010 m)

V = 0.010 m^3

 
At 0°C, the density of solid block of ice is: d = 917 kg / m^3 

Therefore the mass of the solid ice is:

m = 917 kg / m^3  * 0.010 m^3

m = 9.17 kg


The heat of fusion of ice is equivalent to 333.55 kJ/kg, therefore: 
Phase change enthalpy = 333.55 kJ/kg (9.17 kg)

Phase change enthalpy = 3,058.65 kJ = 3,058,650 J

 
Using 1kW/m^2 insolation energy: 
1kW/m^2 * (.05) * sin(90°-37°) = 39.93 Watts = 39.93 Joule/s m² 

 

Therefore the time required to melt the ice is:

t = (3,058,650 J) / [39.93 Joule/s m² * (1 m^2)]
t = 76,600.3 s = 21 hours 16 min 40 seconds

Final answer:

To calculate the time it takes for the sun to melt the block of ice, we need to calculate the amount of heat transfer. The heat used to melt the ice is given by Q = mLf, where Q is the amount of heat transfer, m is the mass of the ice, and Lf is the latent heat of fusion of the ice.

Explanation:

To calculate the time it takes for the sun to melt the block of ice, we need to calculate the amount of heat transfer. The heat used to melt the ice is given by Q = mLf, where Q is the amount of heat transfer, m is the mass of the ice, and Lf is the latent heat of fusion of the ice.

First, we need to calculate the mass of the ice using the formula m = ρV, where ρ is the density of ice and V is the volume of the ice. Since the thickness of the ice is given as 1.0 cm and the area is 1.0 m², the volume can be calculated as V = A × h, where A is the area and h is the thickness.

Once we have the mass of the ice, we can use the formula Q = mLf to calculate the amount of heat transfer. Finally, we can calculate the time it takes for the ice to melt by dividing the amount of heat transfer Q by the rate of heat transfer P, which can be calculated using the equation P = BEA(T1 - T2), where B is the angle factor, E is the emissivity of ice, A is the area, and (T1 - T2) is the temperature difference between the sun and the ice.

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Part A. The formula relating electric power, voltage and current is:

P = I V

I = P / V

I = 4,100 W / 240 V

I = 17.08333 A

I = 17.08 A

 

Part B. The maximum amount of current an electrical wire can conduct is measure in terms of Ampacity. For a 12-gauge wire the Ampacity is greater than 20 A. Therefore the answer to this is “Yes”.

 

Part C. The formula for resistance is:

R = V / I

R = 240 V / 17.08 A

R = 14.05 Ω

 

Part D. The cost per hour is:

(11 cents / kwh) (4.1 kw) = 45.1 cents / hr

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(1)   Through the Second Law of motion, the equation  for Force is:

                                 F = m x a

Where m is mass and a is acceleration (deceleration)

 

(2)   Distance is calculated through the equation,

                             D = Vi^2 / 2a

Where Vi is initial velocity

(3)   Work is calculated through the equation,

                          W = F x D

 

Substituting the known values,

Part A:

(1)     F = (85 kg)(2 m/s^2) = 170 N

(2)     D = (37 m/s)^2 / (2)(2 m/s^2)  = 9.25 m

(3)     W = (170 N)(9.25 m) = 1572.5 J

 

Part B:

(1)    F = (85 kg)(4 m/s^2) = 340 N

(2)   D = (37 m/s)^2 / (2)(4 m/s^2) = 4.625 m

(3)    W = (340 N)(4.625 m) = 1572.5 J

A roller coaster travels 200 feet horizontally and then rises 135 feet at an angle of 30 degrees above the ground. What is the magnitude of the resultant vector?

Answers

Final answer:

The roller coaster's path is represented by two vectors: a horizontal and an inclined one. The inclined path is further broken into its vertical and horizontal components. By summing up the squares of the total horizontal and vertical distances (after calculating these components) and taking the square root, the magnitude of the resultant vector equates to 323.95 feet.

Explanation:

The question relates to the calculation of the magnitude of a resultant vector, which is a concept in physics. The roller coaster's path can be represented as two vectors - the horizontal and the inclined path. The magnitude of the resultant vector can be calculated using the Pythagorean theorem, which is commonly used in physics to determine the resultant of perpendicular vectors.

The horizontal displacement is 200 feet. However, the vertical displacement is part of the inclined path, which needs to be broken down into its components to get the vertical and horizontal distances. The vertical distance covered in the inclined path can be calculated as 135 sin(30) = 67.5 feet and the horizontal distance as 135 cos(30) = 116.7 feet. Thus, the total horizontal distance becomes 200 + 116.7 = 316.7 feet.

The resultant vector, which represents the total path covered by the roller coaster, can be calculated by adding the squares of the total horizontal and vertical distance and then taking the square root of the sum. Using the Pythagorean theorem, the magnitude of the resultant vector becomes √(316.7² + 67.5²) = 323.95 feet.

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A ball of mass 0.5 kg is released from rest at a height of 30 m. How fast is it going when it hits the ground? Acceleration due to gravity is g = 9.8 m/s²

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The answer is attached.

In order to distinguish between wavelengths independent of light intensity, one must have at least _____visual pigment(s).?

a. ?three

b. ?two

c. ?four

d. one?

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When a perfume bottle is opened, some liquid changes to gas and the fragrance spreads around the room. Which sentence explain this?

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This would be evaporation. Evaporation occurs when a liquid changes to a gas. Also, bonus facts:
When a gas changes to a liquid, this is called condensation. When a liquid changes to a solid, this is called freezing. When a solid changes to a liquid, this is called melting. When dry ice turns into carbon dioxide gas, this is called sublimation. Most other solids could probably do this, but dry ice is the most common example.

Diffusion is the process by which perfume molecules spread out in the room after a bottle is opened.

Diffusion is the process by which molecules move from an area of high concentration to an area of low concentration until equilibrium is reached. When a perfume bottle is opened, the liquid evaporates, and the fragrance molecules spread out through the room via diffusion, explaining how the scent permeates the entire space.

Convective cooling cools rocks much more rapidly than heat conduction. hydrothermal circulation represents convective cooling at ocean ridges and is well known from things like black smokes, but only occurs close to the spreading ridge axis. when geophysicists measure the geothermal gradient in areas along ridges where there is no hydrothermal activity, the thermal gradient is far below what you would predict theoretically, but near hydrothermal vents it is far more than you would predict. why would this be?

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When geophysicists measure the geothermal gradient in areas on the ridges where there is no activity hydrothermally, the gradient is far below than what is predicted theoretically, but when measured near hydrothermal vents it is more than what is predicted. This is because most of the heat is being carried through convection by hydrothermal systems so that the average gradient when measured far from the circulation would be depressed or lower.

Two manned satellites approaching one another at a relative speed of 0.450 m/s intend to dock. The first has a mass of 4.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. If the two satellites collide elastically rather than dock, what is their final relative velocity? Adopt the reference frame in which the second satellite is initially at rest and assume that the positive direction is directed from the second satellite towards the first satellite.

Answers

Final answer:

The final relative velocity after an elastic collision between two satellites, where one has initially been at rest, would be reversed from the initial relative velocity. Therefore, the direction would slide from the first satellite towards the second, with the speed remaining at 0.450 m/s.

Explanation:

In your question about the collision of two manned satellites, you're dealing with a physics problem related to the conservation of momentum in elastic collisions. The approach requires the understanding of the principle of conservation of momentum, which states that the total momentum of a system is conserved if there is no net external force acting on it.

In the case of two satellites approaching each other, the total momentum before the collision is represented by (m1 * v1) + (m2 * v2) = 0, with m1 and m2 as the masses of the satellites and v1 and v2 as their respective velocities. Given that the second satellite is initially at rest, v2 = 0. Because the collision is described as elastic, kinetic energy is also conserved. In an elastic collision, the relative velocity of the two objects after collision is the negative of the relative velocity before the collision. In this case, the final relative velocity would be -0.450 m/s, with the direction reversed (from the first satellite towards the second).

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Albert uses as his unit of length (for walking to visit his neighbors or plowing his fields) the albert (a), the distance albert can throw a small rock. one albert is 88 meters. how many square alberts is equal to one acre? (1 acre = 43,560 ft2 = 4050 m2)

Answers

To solve this problem, we know that:

1 Albert = 88 meters

1 A = 88 m

The first thing we have to do is to square both sides of the equation:

(1 A)^2 = (88 m)^2

1 A^2 = 7,744 m^2

Since it is given that 1 acre = 4,050 m^2, so to reach that value, 1st let us divide both sides by 7,744:

1 A^2 / 7,744 = 7,744 m^2 / 7,744

(1 / 7,744) A^2 = 1 m^2

Then we multiply both sides by 4,050.

(4050 / 7744) A^2 = 4050 m^2

0.523 A^2 = 4050 m^2

Therefore 1 acre is equivalent to about 0.52 square alberts.

A person walks first at a constant speed of 5.10 m/s along a straight line from point circled a to point circled b and then back along the line from circled b to circled a at a constant speed of 2.75 m/s. (a) what is her average speed over the entire trip? 3.57 correct: your answer is correct. m/s

Answers

Average speed = total distance / time

1) Distance from A to B

Distance = velocity * time  = V1 * t1 = 5.10 t1

2) Distance from B to A

Distance = velocity * time  = V2*t 2 = 2.75 t2

Distance from A to B = distance from B to A => 5.10t1 = 2.75t2

=> t2 = 5.10t1 / 2.75

3) Average speed = total distance / total time =

total distance = 2 * 5.10 t1 = 10.20 t1

Average speed = [10.20 t1] / [t1 + 5.10 t1 / 2.75]

As you see t1 is factor for the three terms, so you can simplify it

=> Average speed = [10.20 ] / [1 + 5.10/2.75] = 3.57 m/s

Answer: 3.57 m/s

 


You need to include:

An explanation of gravity
An explanation of how mass determines (or affects) the force of gravity
An explanation of the part air resistance plays
An example of the force of gravity (be creative)

Answers

Gravity, the force that attracts a body toward the center of the earth. 

Basically, the larger the mass the greater the pull of gravity. Weight is actually a measurement of gravitational force between two masses

Gravity is a force attracting two masses, with strength depending on their mass and distance apart. Air resistance affects how objects fall, especially lighter ones. A creative example is traveling by balloons, where releasing air and gravity interact to influence descent.

Explanation of Gravity

Gravity is a fundamental force that causes two objects with mass to be attracted to one another. It is why objects fall to the ground when released, and it keeps planets in orbit around stars. The force of gravity depends on the mass of the objects and the distance between them. According to Newton's law of gravity, the more mass an object has, the more powerful its gravitational pull. According to Einstein's theory of general relativity, gravity is the result of massive objects causing a curvature in spacetime.

Effect of Mass on Gravity

The force of gravity is directly proportional to the mass of the objects involved, meaning that larger masses will exert a stronger gravitational pull. If you were to calculate the gravitational pull between two objects, you would use the equation F = G (m1 * m2) / r², where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers of mass.

Role of Air Resistance

Air resistance acts against the force of gravity, especially on light or low-density objects. It is this resistance that explains why a feather falls more slowly than a bowling ball, despite gravity pulling on all objects equally. Air resistance depends on the speed and surface area of the falling object, as well as the density of the air.

Creative Example of the Force of Gravity

Imagine a world where everyone travels by balloons. The only way to move downward is by releasing some of the air from your balloon. Here, the force of gravity and the mass of the person in the balloon interact to determine how quickly they descend, with air resistance playing a part depending on the size and shape of the balloon.

A 230.0 kg bear grasping a vertical tree slides down at constant velocity. What is the friction force between the tree and the bear?

Answers

Well, it's equal to the weight of the bear, which is 230*10=2300 N
Hi there! Thanks for asking here on Brainly. ✉

Solving the dynamic equilibrium: 

Friction = Gravity = ma
(230.0 kg)*(10 m/s2) =
23000 N

So the friction force between the tree and bear is 2300 N.

Hope that helps! ★ If you have further questions about this question or need more help, feel free to comment below or leave me a PM. -UnicornFudge aka Nadia

What is the maximum amount by which the wavelength of an incident photon could change when it undergoes compton scattering from an atom or molecule with a 36.0 u mass? (1 u = 1.66 × 10-27 kg)?

Answers

Final answer:

The maximum amount by which the wavelength of an incident photon could change in Compton scattering depends on the angle of scattering and can be calculated using the given formula.

Explanation:

In Compton scattering, the wavelength of an incident photon can change. The maximum change in wavelength, or shift, can be determined by using the formula:

Change in wavelength (Δλ) = Compton wavelength (λc) * (1 - cosθ)

Where λc is the Compton wavelength, given by:

In this formula, h is Planck's constant, m is the mass of the scattering particle (in this case, the atom with a mass of 36.0 u), and c is the speed of light.

The maximum amount by which the wavelength of an incident photon could change depends on the angle of scattering (θ) and can be calculated using the formula mentioned above.

An object has a mass of 5 kg what force is needed to accelerate it at 6 m/s ?

Answers

Hello there! I'd like to thank you for taking the time to ask your question here at Brainly. I will be assisting you with answering this problem, and how to deal with it in the future on your own.

First, let's look at our problem;

"An object has a mass of 5 kg. What force is needed to accelerate it at 6 m/s^2?" (Units for acceleration must be squared)

To solve for this, we need to apply a formula. You may or may not have heard of "F = M • A", or "Force is equal to mass times acceleration".

We have our unit of mass, kg, and our acceleration, m/s^2. So, let's plug these into the "F= M • A" formula.
Replace "M" with 5 kg, and replace "A" with 6 m/s^2.

F = 5 • 6 is our formula/equation.
So, to simplify for the force, F, we must multiply 5 by 6.

5 • 6 = 30.

We are now left with:
F = 30

We are not done yet, though. We need to apply the proper unit of force to our solution.
Force is measured in "Newtons", or with the symbol "N".

We are left with our solution:
F = 30N.

I hope this helps you!

A spring tide occurs ________. twice a year at the new or full moon closest to the vernal and autumnal equinox once a month, or 12 times a year about 26 times per year, at every full and new moon once a year at the first full moon after the vernal equinox

Answers

Answer: Option (1)

Explanation: A spring tide occurs when the sun, earth and the moon are collinear. It is the condition in which the gravitational pull is exerted on earth by both the sun as well as the moon, from opposite sides. Due to this, there occurs a high tide, in comparison to the regular tide, because of the combination of both the gravitational force. It occurs two time a year on each of the lunar month.

Thus, the correct answer is option (1).

Final answer:

A spring tide, characterized by higher tides due to the alignment of the Sun, Moon, and Earth, occurs about 26 times a year at every full and new moon. Neap tides occur when the Moon is at first or last quarter, resulting in lower than usual tides.

Explanation:

A spring tide occurs about 26 times per year, at every full and new moon. The term 'spring tides' is connected not to the season but to the idea that higher tides 'spring up'. During a spring tide, the Sun, Moon, and Earth are aligned, causing the Sun's and Moon's gravitational pulls to reinforce each other. This creates higher than usual tides as tidal bulges occur on both sides of the Earth.

In contrast, when the Moon is at first or last quarter (at right angles to the Sun's direction), neap tides occur. At this time, the Sun's tides partially cancel out the Moon's tides, resulting in lower than usual tides. The actual magnitude of these tides can be affected by the distances from the Earth to the Moon and Sun.

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A river flows due south with a speed of 1.4 m/s . you steer a motorboat across the river; your velocity relative to the water is 4.7 m/s due east. the river is 660 m wide. part a what is the magnitude of your velocity relative to the earth? express your answer with the appropriate units.

Answers

Refer to the diagram shown below.

The river flow south at a velocity of 1.4 m/s.
The motorboat moves east with velocity of 4.7 /s

The velocity of the motorboat relative to the earth, v, is the vector sum of the two velocities. Its magnitude, by the Pythagorean theorem, is
v = √(4.4² + 1.4²)
   = 4.904 m/s

Its direction south of east, is at an angle, θ, given by
tan θ = 1.4/4.7 = 0.298
      θ = tan⁻¹ 0.298 = 16.6°

Answer:
The velocity of the motorboat is 4.9 m/s, at 16.6° south of east.

Final answer:

The magnitude of your velocity relative to the Earth when steering a motorboat across a river with given velocities is 4.9 m/s, calculated using the Pythagorean theorem on the perpendicular vector components.

Explanation:

To calculate the magnitude of your velocity relative to the Earth as you steer a motorboat across a river, you need to consider the velocities in the southern and eastern directions as vectors. The velocity of the river is 1.4 m/s south, while the velocity of the boat relative to the water is 4.7 m/s east. Applying the Pythagorean theorem to these perpendicular vector components, we find the total velocity relative to the Earth by calculating the magnitude of the resultant vector:

Vtot = \\(v_x^2 + v_y^2\\)

Where Vx is 4.7 m/s (eastward component of boat velocity) and Vy is 1.4 m/s (southward component of river velocity).

Vtot = \\(4.7^2 + 1.4^2\\)^{0.5} = \\sqrt{22.09 + 1.96} = \\sqrt{24.05} = 4.9 m/s

The magnitude of your velocity relative to the Earth is 4.9 m/s.

Calculate the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom undergoes the transition from the energy level n = 4 to the level n = 2.

Answers

The wavelength of the spectral lline produced is about 4.87 × 10⁻⁷ m

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Further explanation

The term of package of electromagnetic wave radiation energy was first introduced by Max Planck. He termed it with photons with the magnitude is :

[tex]\large {\boxed {E = h \times f}}[/tex]

E = Energi of A Photon ( Joule )

h = Planck's Constant ( 6.63 × 10⁻³⁴ Js )

f = Frequency of Eletromagnetic Wave ( Hz )

Let us now tackle the problem !

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Given:

initial shell = n₁ = 4

final shell = n₂ = 2

Asked:

λ = ?

Solution:

Firstly, we will use this following formula to calculate the change in energy of the electron:

[tex]\Delta E = R (\frac{1}{(n_2)^2} - \frac{1}{(n_1)^2})[/tex]

[tex]\Delta E = 2.18 \times 10^{-18} \times ( \frac{1}{2^2} - \frac{1}{4^2})[/tex]

[tex]\Delta E = 2.18 \times 10^{-18} \times ( \frac{1}{4} - \frac{1}{16} )[/tex]

[tex]\Delta E = 2.18 \times 10^{-18} \times \frac{3}{16}[/tex]

[tex]\boxed{\Delta E \approx 4.0875 \times 10^{-19} \texttt{ J}}[/tex]

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Next, we will calculate the wavelength of the light:

[tex]\Delta E = h \frac{c}{\lambda}[/tex]

[tex]4.0875 \times 10^{-19} = 6.63 \times 10^{-34} \times \frac{3 \times 10^8}{\lambda}[/tex]

[tex]\boxed{\lambda \approx 4.87 \times 10^{-7} \texttt{ m}}[/tex]

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Learn morePhotoelectric Effect : https://brainly.com/question/1408276Statements about the Photoelectric Effect : https://brainly.com/question/9260704Rutherford model and Photoelecric Effect : https://brainly.com/question/1458544

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Answer details

Grade: College

Subject: Physics

Chapter: Quantum Physics

Final answer:

The wavelength of the spectral line produced when an electron in a hydrogen atom undergoes the transition from the energy level n = 4 to the level n = 2 is approximately 121.57 nm.

Explanation:

The wavelength of the spectral line produced when an electron in a hydrogen atom undergoes the transition from the energy level n = 4 to the level n = 2 can be calculated using the equation:

wavelength = hc / (E2 - E1)

Here, hc is the product of Planck's constant (h) and the speed of light (c), and E2 - E1 is the energy difference between the two levels.

For this transition, the energy difference can be calculated as:

E2 - E1 = -13.6 eV * [(1/n^2) - (1/m^2)]

Substituting the values, we have:

E2 - E1 = -13.6 eV * [(1/2^2) - (1/4^2)]

E2 - E1 = 10.2 eV

Now, substituting the values of hc and E2 - E1 into the equation for wavelength, we get:

wavelength = (1240 eV.nm) / 10.2 eV

wavelength = 121.57 nm

Therefore, the wavelength of the spectral line is approximately 121.57 nm.

Dielectric materials used in the manufacture of capacitors are characterized by conductivities that are small but not zero. therefore, a charged capacitor slowly loses its charge by "leaking" across the dielectric. if a certain capacitor leaks charge such that the potential difference decreases to one third its initial value in 5.60 s, what is the equivalent resistance of the dielectric? round your answer to three significant figures.

Answers

To find the equivalent resistance  of the dielectric material in the capacitor, we can use the formula for the charging or discharging of a capacitor through a resistor.

V(t) = V_0 * e^(-t / RC) , where:

V(t) is the potential difference across the capacitor at time t,

V_0 is the initial potential difference across the capacitor,

e is the base of the natural logarithm (approximately 2.71828),

t is the time elapsed (in seconds),

R is the equivalent resistance of the dielectric (in ohms), and

C is the capacitance of the capacitor (in farads).

We are given that the potential difference decreases to one-third (1/3) of its initial value, which means V(t) = (1/3) * V_0 at time t = 5.60 s.

Now, we can rewrite the equation as:

(1/3) * V_0 = V_0 * e^(-5.60 / RC)

Next, we can cancel V_0 from both sides of the equation:

(1/3) = e^(-5.60 / RC)

To find the value of RC, we can take the natural logarithm of both sides:

ln(1/3) = ln(e^(-5.60 / RC))

ln(1/3) = -5.60 / RC

Now, we can solve for RC:

RC = -5.60 / ln(1/3)

RC ≈ 10.27

Finally, we can find the equivalent resistance by dividing RC by the capacitance (C) of the capacitor. Since we do not have the value of C, we cannot provide a specific value for Resistance. However, if you have the capacitance value (in farads), you can calculate the equivalent resistance using the equation R_eq = RC / C. Make sure to use the appropriate units for capacitance (farads) and time (seconds) to get the correct answer in ohms. Round your final answer to three significant figures as requested.

To know more about equivalent resistance:

https://brainly.com/question/31788815

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If he throws the ball (with mass 0.07 kg) with a speed of 28 m/s and there is no air resistance, how high does the ball go?

Answers

Since the problem did not state any angle of inclination, I assume that the motion was an object thrown up. There are already equation for motions of this kind that are all based from Newton's Laws of Motion. In this case, the maximum height reached by an object, denotes as Hmax, is

Hmax = v₀²/2g, where g is the acceleration due to gravity which is equal to 9.81 m/s and v₀ is the initial velocity of the ball. Substituting the values,

Hmax = (28m/s)²/2(9.81m/s)
Hmax = 39.96 m

Therefore, the ball thrown up could reach as high up to 39.96 meters.

What are some ways that scientists would collect data and make observations to help them learn more about the severity of the lion fish problem

Answers

experiments, tests, and trials

What speed is the surface current near tokyo, japan?

Answers

The Kuroshio current off Japan is a western boundary current. 

Final answer:

The speed of the surface current near Tokyo, Japan can vary depending on various factors such as tides and weather conditions. However, a typical range for surface currents in the ocean is around 1-2 meters per second or 2-4 knots.

Explanation:

The speed of the surface current near Tokyo, Japan can vary depending on various factors such as tides and weather conditions. However, a typical range for surface currents in the ocean is around 1-2 meters per second or 2-4 knots.

It's important to note that the speed of surface currents can change and is not constant. Factors such as the Earth's rotation, wind patterns, and the shape of the coastline can influence the speed and direction of surface currents.

Ultimately, it is recommended to consult local oceanographic data or resources for more precise and up-to-date information on the speed of the surface current near Tokyo, Japan.

Jumping up before the elevator hits. after the cable snaps and the safety system fails, an elevator cab free-falls from a height of 36 m. during the collision at the bottom of the elevator shaft, a 90 kg passenger is stopped in 5.0 ms. (assume that neither the passenger nor the cab rebounds.) what are the magnitudes of the (a) impulse and (b) average force on the passenger during the collision

Answers

There are two sections of solution to this problem. The first is the impulse and the second is the force.

A.) In physics, when two objects collide, there is a small interval of time when these objects are in contact with each other. The net force applied on the two objects as one system at that time is called the impulse. Its equation is

Impulse = 2mv/t, where m is the total mass of the system, v is the velocity at impact and t is the time when the objects are in contact

But first, we have to find the velocity of impact. For free-falling objects, there is a derived equation for the velocity of impact: v = √2gh, where g is equal to 9.81 m/s^2 and h is the height of fall. Thus,

v = √2(9.81)(36) = 26.58 m/s
Impulse = 2(90 kg)(26.58 m/s)/(5×10^-3 seconds)
Impulse = 956,880 Newtons

B.) According to Newton's second law of motion: F=ma, where F is the net force applied on the system, m is the mass and a is the acceleration. For free-falling objects, the acceleration is due to gravity which is equal to g=9.81 m/s^2. Thus,

F = (90kg)(9.81 m/s^2)
F = 882.9 Newtons

If you double the radius of the earth and keep the mass of the earth the same, the acceleration of gravity on the surface of the earth will be approximately ...

Answers

Even though the mass of the earth stays the same, the force gravity has on us will double because there is less space in the atmosphere for the gravity to pull anything in towards its center. Let me know if I'm correct!
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