Dispersion in wave theory is the phenomena where a wave's phase velocity changes depending on its frequency. The article can explore different definitions. This is the typical definition for dispersion (waves).
When sinusoidal waves with various wavelengths propagate at various speeds, a wave packet with mixed wavelengths has a tendency to disperse in space. Dispersion in wave theory is the phenomena where a wave's phase velocity changes depending on its frequency.
The article can explore different definitions. This is the typical definition for dispersion (waves).
A full set of approximate solutions to the one-electron Schrödinger equation are found in a three-dimensional atomic lattice that is randomly filled with atoms of different kinds and has, on average, the periodicity of a Bloch wave.
Equations are provided that enable the calculation of each wave's energy, average behavior, absent a phase factor, close to any sort of atom, and damping parameter.
A comparison is made between a periodic lattice with a complicated, energy-dependent potential and a random A-B lattice. The dispersion relation of the system is obtained by solving the eigenvalue problem in this potential using any of the established techniques for periodic potentials.
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Part E
Once you complete your outline, write a 500- to 750-word paper using word processing software. Add a works cited page at the end to give credit to your sources. Submit your completed paper along with this activity to your teacher for evaluation.
A Voyage to Proxima Centauri
Proxima Centauri is the second closest star to our solar system, which makes scientists curious to know more about it. What do we know about Proxima Centauri? How did we discover this information? Is it possible for humans to travel to this star? In this task, you will research and write a 500- to 750 word paper that answers these questions. Follow these steps to complete your research and writing. This guide about the research process can help.
Estimated time to complete: 3 hours
Part A
The goal of your paper is to describe the history of the discovery and research of Proxima Centauri. Another goal is to find the possibilities of traveling to this star. Some questions that your paper should answer are:
When was Proxima Centauri discovered?
How was Proxima Centauri discovered?
How have scientists researched Proxima Centauri?
What technologies have they used? What types of data do these technologies collect?
Have spacecraft ever reached this star?
What are the limitations of sending spacecraft to Proxima Centauri?
What accommodations would humans need to travel to Proxima Centauri?
Proxima Centauri otherwise known as Alpha Centauri C, is the closest star to our solar system, located about 4.24 light-years away. It was discovered in 1915 by Robert Innes, the director of the Union Observatory in South Africa. Innes identified Proxima Centauri as a possible member of the Alpha Centauri system after noticing that the star had a similar proper motion to Alpha Centauri A and B.
Proxima Centauri was first observed through telescopes, which allowed scientists to study the star's spectra and estimate its distance from Earth. In the following decades, scientists continued to study Proxima Centauri through telescopes, including the Hubble Space Telescope, which provided high-resolution images of the star.
In 2016, the European Southern Observatory announced the discovery of an exoplanet orbiting Proxima Centauri, called Proxima Centauri b. This discovery was made using the radial velocity method, which measures the star's small wobbles caused by the gravitational pull of an orbiting planet.
What are the major challenges facing the discovery of Proxima Centauri?Despite the advances in our understanding of Proxima Centauri, no spacecraft have ever reached this star. The distance between Proxima Centauri and Earth is so vast that it would take tens of thousands of years to reach the star using current propulsion technology.
One potential solution to this problem is the use of interstellar travel, which would allow humans to travel to Proxima Centauri within a human lifetime. There are several proposed methods for interstellar travel, including using a starship propelled by fusion engines or a massive light sail pushed by a beam of lasers. However, these technologies are still in the theoretical stage and have not yet been developed.
There are also many other challenges that must be overcome in order for humans to travel to Proxima Centauri. For example, humans would need to find a way to protect themselves from the high levels of radiation that they would be exposed to during the journey. They would also need to find a way to provide enough food, water, and other resources to sustain themselves for the duration of the trip.
Overall, while it is theoretically possible for humans to travel to Proxima Centauri, it would be a massive undertaking that would require significant technological advancements and the development of new solutions to many challenges.
Sources of Works Cited include:
"Proxima Centauri." Wikipedia, Wikimedia Foundation, 5 Jan. 2021,
"Proxima Centauri b." Wikipedia, Wikimedia Foundation, 20 Nov. 2020,
"Interstellar Travel." Wikipedia, Wikimedia Foundation, 4 Jan. 2021,
Therefore, the correct answer is as given above
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While skiing in Jackson, Wyoming, your friend Ben (of mass 63.2 kg) started his de- scent down the bunny run. 11.5 m above the bottom of the run. If he started at rest and converted all of his gravitational potential energy into kinetic energy, what is Ben's kinetic energy at the bottom of the bunny run? Use g = 9.8 m/s Answer in units of J.
Answer:
Approximately [tex]7.1 \times 10^{3}\; {\rm J}[/tex] (given: [tex]g = 9.8\; {\rm m\cdot s^{-2}}[/tex].)
Explanation:
To find the change in the gravitational potential energy ([tex]\text{GPE}[/tex]), use the formula:
[tex]\begin{aligned}& (\text{change in GPE}) \\ &= (\text{mass})\, (g)\, (\text{change in height})\end{aligned}[/tex].
Assume that gravitational field strength [tex]g[/tex] is constant (e.g., [tex]g = 9.8\; {\rm m\cdot s^{-2}}[/tex].) For an object of mass [tex]m[/tex], if the altitude of the object changes by [tex]\Delta h[/tex], the [tex]\text{GPE}[/tex] of that object would change by [tex]m\, g\, \Delta h[/tex].
In this question, the mass of Ben is [tex]m = 63.2\; {\rm kg}[/tex]. It is given that [tex]g = 9.8\; {\rm m\cdot s^{-2}} = 9.8\; {\rm N\cdot kg^{-1}}[/tex] and is constant. Since change in the altitude of Ben is [tex]\Delta h = 11.5\; {\rm m}[/tex], the change in the ([tex]\text{GPE}[/tex]) of Ben would be:
[tex]\begin{aligned} m\, g\, \Delta h &= (63.2\; {\rm kg}) \, (9.8\; {\rm N\cdot kg^{-1}})\, (11.5\; {\rm m}) \\ &\approx 7.1\times 10^{3}\; {\rm N\cdot m} = 7.1\times 10^{3}\; {\rm J} \end{aligned}[/tex].
The position-versus-time plot of a boat positioning itself next to a dock is shown in the figure (Figure 1).
Rank the six points indicated in the plot order of increasing value of the velocity v, starting with the most negative. Rank the points in order of increasing value of the velocity. To rank items as equivalent, overlap them.
Incorrect: Try Again; 2 attempts remaining: no points deducted
The points in order of increasing value of the velocity can be ranked as:
B < C < A ≡ F < E < D.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
According to the figure:
The points in order of increasing value of the velocity can be written as:
B < C < A ≡ F < E < D.
As the displacement becomes from positive to negative near point B, it has the lowest velocity and as the displacement becomes from negative to positive near point D, it has the highest velocity
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Ball A with a mass of 0.280kg makes an elastic head-on collision with ball B initially at rest. After collision, ball B moves off with half the original speed of ball A. Is the momentum conserved in the collision? Why?
The mass of ball B and the final velocity of ball A can complement the conservation of linear momentum. The answer is yes.
What is Momentum ?Momentum can simply be defined as the product of mass and velocity. It is a vector quantity.
Given that ball A with a mass of 0.280kg makes an elastic head-on collision with ball B initially at rest. After collision, ball B moves off with half the original speed of ball A.
In an elastic head-on collision, momentum is mostly always conserved. That is, the sum of the momentum before collision will be equal to the sum of the momentum after collision.
Mathematically, MaUa = MaVa + MbVb
Is the momentum conserved in the collision?
The answer is yes!
Why?
Because we need to consider the mass of the ball B and the final velocity of the ball A.
Therefore, In consideration of the mass of the ball B and the final velocity of the ball A, we can say that the momentum is conserved.
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Please help me thank you
The gravitational potential energy of a body is determined by the equation U=mgh, where m is the body's mass, g is its gravitational force, and h is its height. The relationship between mechanical energy and gravitational potential energy is described by the equation E=U+K.
What is the kinetic energy equation?KE= 1/2 m v2
The relationship between kinetic energy and an object's mass and square of its velocity is direct: K.E. = 1/2 m v2.
We compute kinetic energy because...It provides information on how a substance's mass impacts its velocities. Take this as a case study. A lorry and a sleek vehicle powered by the same engine cannot go at the same pace because to their different designs.
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5. If a jump rope is shaken fast enough to produce a wave with a wavelength of 0.5 m and
the crest of the wave passes a specific point 6 times per second, what is the velocity of the
wave?
Answer:
After solving the equation the wave is traveling at a velocity of 3 m/s.
What is velocity?Velocity is a vector quantity that describes the rate at which an object changes its position. It is a measure of both the speed and the direction of an object. Velocity is typically expressed in terms of meters per second (m/s). When an object is in uniform motion, its velocity is constant, meaning that it is not changing in magnitude or direction. If an object is accelerating, its velocity is changing over time, either in magnitude, direction, or both.
The velocity of the wave can be calculated using the following equation:
Velocity = Wavelength x Frequency
In this case, the wavelength is 0.5 m and the frequency is 6 Hz (6 cycles per second). So, the velocity of the wave is:
Velocity = 0.5 m x 6 Hz = 3 m/s
This means that the wave is traveling at a velocity of 3 m/s.
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What is the average time for the toy car to move 1.0 m on cement?
Answer:
24.4
Explanation:
you would add all the numbers , 25.5+24.4+24.2= 73.1/3=24.36 and you round up you get 24.4
Which of the following is not a safety tip for outdoor activities
The following which is not a safety tip for outdoor activities is to go alone for a sense of oneness with nature and is therefore denoted as option A.
What is Safety?This is referred to as the condition of being protected from harm or other danger and it involves the use of various methods and activities and an example is to ensure that a basic first aid kit is available so as to help in the incident of an injury.
However going alone for a sense of oneness with nature is not a safety tip as should in case any issue arises there will be no one to support and rescue such individual.
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The full question is:
Which of the following is not a safety tip for outdoor activities
a. go alone for a sense of oneness with nature
b. bring a basic first aid kit
c. bring a flashlight or headlamp
d. pack plenty of water and energy-dense food
A lawnmower is pushed with a force of 72 Newtons at an angle of 40 degrees from the horizontal. How much work is done to the mower if it moves 740 meters?
The work done to the mower is the product of force and the distance covered by the object which is equal to 40,811 Joules.
What is Work done?Work done can be defined as the product of external force and the distance over which the force is being applied. Work is done on an object when a force is applied to an object and the object is moved through a particular distance.
From this we can see that:
X-Component:
cos(θ) = x/F
Then,
X= F cos(θ).…..(1)
Now putting the values of F and θ in equation (1) we get,
X = 72 N × cos(40)
X = 72 N × 0.766
X= 55.15 N this is the x-component force
The work done to the mower is:
W = F × d
W = 55.15 × 740
W = 40,811 Joules
The work done to the mower is 40811 Joules.
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brandon buys a new seadoo. he goes 12km north from the beach he jumps wakes for 6km to the east what distance did he cover what was his displacement
Total distance covered by Brandon is 18 km and total displacement covered by him is 13.41 km.
Displacement: What is it?The definition of displacement is the changing of an object's position. It has a magnitude and direction and is a vector quantity. It is shown as an arrowhead that travels from the initial location to the end. An object's position changes, for instance, if it moves from position A to position B.
Distance covered by Brandon is-
12 + 6 = 18 km
Displacement covered by Brandon is-
d²= 12² + 6²
= 144 + 36
d²= 180
d = √180
d = 13.41 km.
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How long will a boy sitting near the window of a train travelling at 36 km h see a train passing by in the opposite direction with a speed of 18 km h^-1.The length of the slow- moving train is 90 m.
Answer:
5/18 is used to convert km/hr into m/s
1 km = 1000 m
1 hr = 3600 sec
1 km/hr to m/s
1*1000/1*3600
1000/3600metre/sec
10/36metre/sec
5/18 metre/sec
Explanation:
srry if this is wrong!
How long does it take the Earth to spin on its axis once?
Explanation:
it takes the earth 24 hours to spin on it's axis once
Please help with this
A unit vector must have length equal to 1. By calculating the length of (1, 1), we discover that (12 + 12) = 2 = 1.414, which is not the same as 1, is the length.
How do you write unit vector notation?I,J notation is a way to describe a vector. In Cartesian coordinates, a unit vector is a vector with length 1. The unit vectors along the axis are denoted by the letters I and j, respectively. The form ai+bj an I + b j can be used to represent any two-dimensional vector.Numerous operations, including addition, subtraction, and vector multiplication, can be carried out with the aid of the vector form of representation. A=xi+yj+zk is the vector form of the cartesian representation of the three points (x, y, and z). A is equal to x I y j, and z k.Vy = Vyj, Vz = Vz k, and Vx = Vxî. V = Vx + Vy + Vz = Vxî+ Vyj+ Vz k is the result of applying the triangle rule to vector addition twice. The unit vector notation is used in this situation.To learn more about vector refer to:
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A barefoot field-goal kicker imparts a speed of 22 m/s to a football initially at rest. If the football has a mass of 0.42 kg and the time of contact with the ball is 0.023 s, what is the magnitude of the force exerted by the ball on the kicker’s foot? Answer in units of N
Explanation:
Mass of the football = 0.49 kg
Initial velocity of the ball ,u= 0 m/s
Final velocity of the ball ,v= 44 m/s
time of contact ,t = 0.028 seconds
First law of motion:
v=u+at
44 m/s=0+a\times 0.028 sec44m/s=0+a×0.028sec
a=1,571.42 m/s^2a=1,571.42m/s
2
force=mass\times acceleration=0.49 kg\times 1,571.42 m/s^2=769.99Nforce=mass×acceleration=0.49kg×1,571.42m/s
2
=769.99N
The magnitude of the force exerted by the ball on the kicker's foot is of 769.99 Newtons.
The largest flowers in the world are the Rafflesia Arnoldii, found in Malaysia. A single flower is almost a meter across and has a mass up to 11.0 kg. Suppose you cut off a single flower and drag it along the flat ground. If the coefficient of kinetic friction between the flower and the ground is 0.39, what is the magnitude of the frictional force that must be overcome?
The magnitude of the frictional force that must be overcome is 42.04 N.
What is the magnitude of the frictional force?
The magnitude of the frictional force that must be overcome is calculated by applying Newton's second law of motion as follows;
Mathematically, the formula for the frictional force is given as;
F = μmg
where;
μ is the coefficient of frictionm is the mass of the flowerg is acceleration due to gravityThe magnitude of the frictional force that must be overcome is calculated as;
F = 0.39 x 11 kg x 9.8 m/s²
F = 42.04 N
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The type of heat transfer responsible for your computer leaving your desk very hot after you've used it for awhile?
Answer:
Conduction
Explanation:
Conduction is a process whereby heat is transfer through solid state.
What will be the change in temperature if 600 g of water absorbs 5200 J of heat?
The change in temperature of the 600 g of water, given that the water aborbs 5200 J of heat energy is 2.07 °C
How do I determine the change in temperature of the water?First, we shall list out the given parameters from the question. This is given below:
Mass of water (M) = 600 gHeat absorbed (Q) = 5200 JChange in temperature (ΔT) = ?Calorimetry suggest the following formula:
Q = MCΔT
Where
Q is the heat transferred M is the mass C is the specific heat capacity ΔT is the change in temperatureUsing the above formula, the change in temperature of the water can be obtained as follow:
Note: Specific heat capacity of water (C) = 4.184 J/gºC
Q = MCΔT
5200 = 600 × 4.184 × ΔT
5200 = 2510.4 × ΔT
Divide both sides by 2510.4
ΔT = 5200 / 2510.4
ΔT = 2.07 °C
Thus, we can conclude from the above calculation, that the change in temperature of the water is 2.07 °C
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What is the power of a lightbulb that has a current of 0.480 A at 120.0 V?
Answer:
The power is 57.6 watts
Explanation:
We can use the Electric Power Equation to evaluate the power.
Electric Power Equation
[tex]P=IV[/tex]
[tex]P[/tex] is the power in watts
[tex]I[/tex] is the current in amps
[tex]V[/tex] is the voltage in volts
Our lightbulb has current of 0.480 A and a voltage of 120.0 V.
[tex]I=0.480\\V=120.0[/tex]
Now we can evaluate power.
Substitute our values in for the variables.
[tex]P=0.480*120[/tex]
[tex]P=57.6[/tex]
What will be the final temperature of a sample of water, if 32 kJ of heat is removed to lower 836
g of water starting with an initial water temperature of 25*C?
The final temperature of a sample of water is 15.89 ⁰C.
What will be the final temperature of the sample of water?
The final temperature of the sample of water is calculated by using the formula for heat capacity of water.
Q = mcΔθ
where;
Q is the heat capacity of the water = 32 kJm is the mass of the water = 836 gc is the specific heat capacity of water = 4200 J/kgCΔθ is the change in the temperature of the water = ?Δθ = Q / mc
The change in the temperature of the sample of water is calculated as follows;
Δθ = ( 32,000 ) / ( 0.836 x 4200 )
Δθ = 9.11 ⁰C
The final temperature of the water when heat is removed is calculated as follows;
T₂ = 25 ⁰C - 9.11 ⁰C = 15.89 ⁰C
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you are in the year where the earth has no more land available for houses you decide to build an apartment up and need things to survive in each earths 5 layers (troposphere,stratosphere, mesosphere, thermosphere, exosphere) Question: what things would you need to survive the mesosphere
PLS I RLLY NEED SOME HELP
The things would which would be needed to survive the mesosphere include the following below:
Food and waterOxygen supply.What is a Mesosphere?This is refereed to as the third layer of the atmosphere which is present above the stratosphere and directly below the thermosphere.
It has a low density of gas and water vapor present in the area which is why it is no place for human life as there is a shortage of oxygen and other gases needed for some biochemical reactions in the ecosystem. This is therefore the reason why things such as food, water and oxygen supply is neeeded tio survive in the mesosphere.
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Net work W would accelerate an object from rest to velocity v. What net work is needed to accelerate the object from rest to velocity 2v?
The net work that is needed to accelerate a 2.0 kg mass from rest to velocity 2v is 4.0 m/s.
What is net work done?When a force acts on a body at rest or at uniform motion in a straight line, then it starts to accelerate.
Given that, the velocity is 5.0
Time is 2 sec
The given mass is 2.0 kg
First, we calculate the acceleration
Acceleration = v / t = 10 / 5.0 = 2
From Newton's second law, we know that
force = mass x acceleration
F = ma
F = 2.0 x 2 = 4.0 m/s
Therefore, the net work that is needed to accelerate a 2.0 kg mass from rest to velocity 2v is 4.0 m/s.
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The question is incomplete. Your most probably complete question is given below:
What net force is needed to accelerate a 2.0 kg mass from rest to a velocity of 10 m/s in 5.0 s?
A 30kg metal ball is dropped from a height of 12.5 m.
a. Find the final velocity when the ball hits the ground.
b. Find the time it takes for the ball to hit the ground.
From conservation of linear momentum, the final velocity is 15.7 m/s and the time taken is 1.6 s
What is Velocity ?Velocity can be defined as a distance travel in a specific direction per time taken. It is a vector quantity.
Given that 30kg metal ball is dropped from a height of 12.5 m.
a. Find the final velocity when the ball hits the ground.
The maximum K.E of the ball at it final velocity will be equal to its maximum P.E at height 12.5 m. That is,
K.E = P.E
1/2mv² = mgh
Where
m = 30 Kgg = 9.8 m/s²h = 12.5 mv = ?Substitute all the parameters
1/2 × 30 × v² = 30 × 9.8 × 12.5
v² = 245
v = √245
v = 15.65 m/s
b. The time it takes for the ball to hit the ground can be found through
h = ut + 1/2gt²
but u = 0
h = 1/2gt²
Substitute all the necessary parameters
12.5 = 1/2 × 9.8 × t²
12.5 = 4.9t²
t² = 12.5/4.9
t² = 2.55
t = √2.55
t = 1.6 s
Therefore, the final velocity when the ball hits the ground is 15.65 m/s and the time it takes for the ball to hit the ground is 1.6 s
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Gravity on earth is 9.8
Jaydens mass is 50 kilograms his weight is
a boy is swinging a toy on apiece of string in a vertical circle. the toy has mass 150g and the radius of circle is 0.8m. a) he swings the toy with a linear velocity 2m/s. will the top move in a circle? explain your answer.
The top move will in a circle because there is tension at the top which will add up with the weight of the toy to maintain equal centripetal force providing the circular motion.
What is tension of the top of the vertical circle?
The tension experienced by the top of the vertical circle is calculated by using the following formula.
T = Fc - W
where;
Fc is the centripetal force of the toyW is the weight of the toyT = mv²/r - mg
where;
m is the mass of the toyv is the linear speed of the toyg is acceleration due to gravityr is the radius of the vertical circleThe tension experienced by the toy at the top of the vertical circle is calculated as follows;
T = ( 0.15 x 2² / 0.8 ) - ( 0.15 x 9.8 )
T = 0.75 - 1.47
T = -0.72 N
Thus, with the negative tension at the top of the vertical circle, the sum of the tension force and the weight of the toy will be equal to the centripetal force to maintain the orbit of the toy in a circular path.
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A man is attempting to train his dog. He is pulling on the dog with a force of 52.4 Newtons at an angle of 35.1 degrees above the horziontal. Fimd the X and Y component of the applied Force
The formula for the horizontal component (Fx), which is the angle the force makes with the horizontal, is Ftens•cosine(). Ftens• sine() can be used to compute the upward component (Fy), where is the angle that the force produces with the horizontal.
What is the force's horizontal component?The portion of a force that works horizontally with regard to a body is known as its horizontal component. Its vertical component is known as its vertical component.
Why is moving the box with the rope horizontal easier?The pulling of the box is with the rope horizontal. When the rope is angled Because Is less than, the horizontal component (= F cos ) is less. As a result, it is the proper response.
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Teddy is playing with toy cars on his driveway. He rolls two cars directly at each other so that they will have a head-on collision. Their momentums before and after the collision are shown in the table below.
Momentum Before Momentum After
Car 1 9 g · m/s -2 g · m/s
Car 2 -6 g · m/s 4 g · m/s
Which of the following is true?
A.
This situation does not show a closed system.
B.
The situation shows a closed system.
C.
Car 2 has more mass than Car 1.
D.
Car 2 had a greater velocity before the collision than Car 1 had.
The true statement is " this situation does not show a closed system" because the linear momentum is not conserved.
option A is the correct answer.
What is the principle of conservation of linear momentum?
The principle of conservation of linear momentum states in a closed or isolated system, the total momentum of the system is always conserved.
Mathematically, the formula for the conservation of linear momentum is given as;
Pi = Pf
where;
Pi is the sum of the initial momentum of the systemPf is the sum of the final momentum of the systemm₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where;
m₁ is the mass of the first objectm₂ is the mass of the second objectu₁ is the initial velocity of the first objectu₂ is the initial velocity of the second objectv₁ is the final velocity of the first objectv₂ is the final velocity of the second objectThe given momentum of the toy cars before and after collision;
Momentum Before Momentum After
Car 1 9 g m/s -2 g m/s
Car 2 -6 gm/s 4 g m/s
Sum of the momentum before the collision = 9 gm/s - 6 g m/s = 3 g m/s
Sum of the momentum after the collision = -2 gm/s + 4 gm/s = 2 g m/s.
The above does not show conservation of linear momentum, hence the system is closed because of the momentum is lost.
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A 10 kg box is on an inclined plane that is 40 degrees above the horizontal. It is sliding
down with a constant velocity.
a. Draw a free body diagram with Fg, FN, F₂ and Ff.
b. What is the weight of the box?
What is the normal force of the box?
c. What is the force of friction acting on the box?
d. What is the net force acting on the box?
A horizontal force of 10.0 N is acting on a 10 kg box that is sliding to the right along the floor with velocity v.
What are the assumptions for drawing a free-body diagram?Most people make the common assumptions of rigid body action and ignoring air resistance and friction. In statics, all forces and moments must balance to zero; if they don't, the body is accelerating and the laws of statics do not apply, according to the physical interpretation.
The specific situation and the presumptions used will determine how many forces and moments are displayed. Most people make the common assumptions of rigid body action and ignoring air resistance and friction.
In statics, all forces and moments must balance to zero; if they don't, the body is accelerating and the laws of statics do not apply, according to the physical interpretation. The resultant forces and moments in dynamics can have non-zero values.
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A model rocket flies horizontally off the edge of a cliff at a velocity of 50.0 m/s. If the canyon below is 100.0 m deep, how far from the edge of the cliff does the model rocket land?
My teacher provided the equations:
x= vt and y = (Vi * t)1/2* a * t^2
Yes! The second one is one of the constant acceleration equations. We know that our X and Y values are independent of each other, which is why Y doesn't matter here. We only care about the X position value since X and Y are independent! (This is an extremely important rule, trust me)
Therefore, we don't need to calculate a Y velocity or anything like that. We only need Y because we need to find time t. We can use Y to calculate time because although X and Y are independent of each other, they do share the same time traveled!
We know that [tex]V_{0,y}[/tex] = 0, since the car wasn't moving vertically initially. We also know Y initial is 100 and Y final is 0 when it hits the ground! The last thing we know is that the acceleration of any item in free fall is (usually) -9.81. Therefore, using the original Y equation that your teacher gave, we can plug things in and solve for time!
[tex]y_f=y_i+v_it+\frac{1}{2}at^2\\0=100+(0)t+\frac{1}{2}(-9.81)t^2\\-100=-4.905t^2\\t^2=20.39\\t=4.52[/tex]t = 4.52s
(Your teacher simplified the Y equation a little, so it may look slightly different from mine. I started at the original Y equation)
Now we have time! So now we can use the other equation your teacher provided. Again, remember, even though the car is now traveling through the air vertically, that does not affect its x velocity! The car is still traveling at 50m/s!
Therefore, we can just plug and chug!:
x = vt
x = (50)(4.52)
x = 226m
I hope this helps!
A force of 20 Newtons moves a box 2.0 meters and does 40 N*m of work. How many Joules is this?
1 N*m = 1 Joule
40 N*m = 40 joules
An object has 100 J of kinetic energy. If the object’s mass doubles, what is its kinetic energy?
An object has 100 J of kinetic energy. If the object’s mass doubles, then its kinetic energy will be 200J and is denoted as option C.
What is Kinetic energy?This is referred to as the type of energy that it possesses due to its motion and can also defined as the work which is needed to accelerate a body of a given mass from rest to its stated velocity.
The unit is in Joules and the formula is 1/2mv² where m is the mass and v is the velocity of the body or object. In a scenario where the mass is doubled or tripled and the velocity is constant then the kinetic energy will also be doubled or tripled respectively.
For instance, lets assume initial mass is 50kg and the v² is 50m/s then the kinetic energy is 1/2mv² which is 1/2 × 50 × 50 = 1250J. When the mass is doubled it becomes 100kg which 1/2 × 100 × 50 = 2500J which depicts that it was also doubled.
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The options are:
A. 50 Joules.
B. 100 Joules.
C. 200 Joules.
D. 400 Joule
Assuming an object has 100 Joules of kinetic energy. If the object’s mass doubles, its kinetic energy would be equal to: C. 200 Joules.
What is kinetic energy?In Science, kinetic energy can be defined as a type of energy that's possessed by a physical object or body, especially due to its motion or a change in velocity (acceleration).
This ultimately implies that, a physical object or body would gain more of kinetic energy as it falls back toward the Earth because it is in motion.
How to calculate kinetic energy?Mathematically, kinetic energy can be calculated by using this formula:
K.E = 1/2 × mv²
Where:
K.E represents the kinetic energy.m represents the mass.v represents the speed or velocity.Since the mass of the object doubles, its kinetic energy would be twice that of its initial kinetic energy;
Kinetic energy = 2 × initial kinetic energy
Kinetic energy = 2 × 100
Kinetic energy = 200 Joules.
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Complete Question:
A. 50 Joules.
B. 100 Joules.
C. 200 Joules.
D. 400 Joules.