Answers
The nodal voltage is V and the currents are as defined in the diagram.
At the upper node, Kirchhoff's current law equation is I1+I5=I2+I3
What is Kirchhoff's rules?The voltage around a loop equals the sum of every voltage drop in the same loop for any closed network and equals zero. Put differently, the algebraic sum of every voltage in the loop has to be equal to zero and this property of Kirchhoff's law is called conservation of energy.Kirchhoff's circuit laws are two equalities that deal with the current and potential difference in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell.Kirchhoff's first rule—the junction rule. The sum of all currents entering a junction must equal the sum of all currents leaving the junction. Kirchhoff's second rule—the loop rule. The algebraic sum of changes in potential around any closed circuit path (loop) must be zeroTo learn more about Kirchhoff's rules refers to:
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Related Questions
what is the normal force on a 2000N refrigerator resting on the ground
Answers
The perpendicular force that a surface applies to an item is known as the normal force. FN = m ⋅ g
What is Normal force?The perpendicular force that a surface applies to an item is known as the normal force. For instance, if you place a book on a table, a gravitational force will cause it to fall. The table pulls on the book in order to counterbalance this force and keep it from dropping. The normal force, often known as the opposing force, is denoted by the symbols FN F N or NN. "N" stands for the normal force unit (Newton).
A common illustration of Newton's third rule of motion is the normal force.
When one object applies force to another, the other applies a force in the opposite direction and of equal magnitude to the first object (action equals reaction).
Therefore, the force applied by the item to the surface is equal to the normal force. The calculations change according to the surface's slope.
The formula is as follows for an object laying on a flat surface:
FN = m ⋅ g
where
The mass of an object is m.
Gravitational acceleration is denoted by g.
The normal force (FN F N ) for an item on a flat surface is equal to its gravitational force, according to Newton's third law ( WW).
The formula is as follows for an object laying on a flat surface:
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4. How many excess electrons does a balloon that was rubbed on a child's hair and
now has a charge of 4.0 x 107 Coulombs?
Answers
Hope this helps!
An appeal of a state appellate court ruling can next be made to:
• A. a state trial court.
• B. the state supreme court.
• C. the U.S. Supreme Court.
• D. a U.S. Court of Appeals.
Answers
The decision of the country's highest court may then be appealing to that Supreme Court of both the U. S., but only in cases where the issue involves federal law.
Why is Supreme renowned?In particular, followers of hip-hop, surfing, and post - punk culture will find their clothing appealing. Every person who appreciates streetwear will discover the ideal item thanks to Supreme's wide range of clothing.
Why is Supreme so expensive?Rebellious and distinctive brand image! Despite giving a venture - capital group a 50% ownership in the company, Supreme has been able to keep its skater roots and fan base. To top it all off, the Supremes' emblem is distinctive, outstanding, and simple to recognize.
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8:11
GCSE Science - Physics
22 of 25
14 67%
A cat accelerates from rest to 10 m/s
when it sees a dog. This takes 2
the cat?
seconds What is the acceleration of the cat ?
Answers
the acceleration of the cat is 5m/s square
In this case, the initial velocity (u) is 0 m/s (since the cat starts at rest), the final velocity (v) is 10 m/s, and the time (t) is 2 seconds. Plugging these values into the formula, we get:
a = (10 m/s - 0 m/s) / 2 s
= 10 m/s / 2 s
= 5 m/s^2
So the acceleration of the cat is 5 m/s^2.
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.
Answers
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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Corn plants and milkweed plants grow in the same area. Over several years, the milkweed plants have taken over the field and the corn plants no longer have space to grow.
This best demonstrates which type of an interaction between the plants?
cooperation
parasitism
commensalism
competition
Answers
The interaction between the Corn plants and milkweed plants demonstrates as competition.
What is competition in Plants community?Competition is typically considered to refer to the detrimental consequences that neighbors' presence has on a plant's fitness or growth, typically through lowering the resources available.
In addition to resources, disturbance, herbivory, and mutualisms, competition can be a significant factor in controlling plant populations. The resource involved is depending on the species and the region, as all plants require a few fundamental ingredients.
As corn plants and milkweed plants grow in the same area, the interaction between the Corn plants and milkweed plants demonstrates competition.
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After Victor returns to the house in chapters 21-continuation of Frankenstein, he looks out the window and sees the monster standing outside grinning. How does Victor react
to seeing him?
A. He invites him in to have a talk.
B. He runs outside to embrace him.
C. He draws his pistol and shoots at him.
Answers
Victor reacts when he sees him and threatens to call the police if he doesn't leave. Therefore, choice C is correct.
How does Frankenstein play out?When the court learns of Victor's residence on the Orkney Islands, Kirwin presents a compelling defense of Victor at the trial and is successful in securing Victor's release. Victor's absence from his lab in the Orkneys at the time of the murder is evidence that he did not commit the crime. Victor is taken home by Alphonse.
At the conclusion of Frankenstein, what happens to Victor?Victor Frankenstein wishes he could kill the monster he created when he dies in Frankenstein. Frankenstein is visited by the Monster. He informs Walton that he intends to kill himself and expresses regret for the murders he has committed.
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Full Question = After Victor returns to the house in chapters 21-continuation of Frankenstein, he looks out the window and sees the monster standing outside grinning. How does Victor react
to seeing him?
A. He invites him in to have a talk.
B. He draws his pistol and shoots at him.
C. He threatens to call the police if he doesn't go away.
D. He runs outside to embrace him.
Q.2. Assertion: When distance between two bodies is doubled and also mass of each body is doubled. then the gravitational force between them remains the same. Reason: According to Newton's law of gravitation, force is directly proportional to the product of mass of the two bodies and inversely proportional to square of the distance between them. ent to
Answers
Answer:
True:
F1 = G M1 M2 / R^2
F2 = G (2 M1) * (2 M2) / (2 R)^2
F1 = F2
describe wht happends to the motion of the moving object when there is no resultant force acting on it
Answers
Answer:
it keeps moving until a force disturbs it
Explanation:
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?
Answers
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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Read the following poem by Lola Ridge. Then, respond to the prompt that follows.
Wild Ducks
By Lola Ridge
That was a great night we spied upon
See-sawing home,
Singing a hot sweet song to the super-stars
Shuffling off behind the smoke-haze …
Fog-horns sentimentalizing on the river …
Lights dwindling to shining slits
In the wet asphalt …
Purring lights …red and green and golden-whiskered …
Digging daintily pointed claws in the soft mud …
…But you did not know …
As the trains made golden augers
Boring in the darkness …
How my heart kept racing out along the rails,
As a spider runs along a thread
And hauls him in again
To some drawing point …
You did not know
How wild ducks' wings
Itch at dawn …
How at dawn the necks of wild ducks
Arch to the sun
And new-mown air
Trickles sweet in their gullets.
In a well-written paragraph of 5–7 sentences, analyze the ambiguous nature of "Wild Ducks." Your response should include:
an explanation of your interpretation of the poem's meaning
evidence from the poem (PReP) that supports your interpretation
an explanation of how another reader could interpret the poem differently
evidence from the poem to support an alternative interpretation
Answers
Due to the possibility of misinterpretation, the poem "Wild Duck" can be read as either the speaker leaving her lover or the lover leaving her.
What does the poem discuss?Lola Ridge's poem "Wild Duck" allows for more than one interpretation of the speaker's meaning. As a result, it is ambiguous. The ambiguity of the poem can be examined, and the following response to the prompt:
You could say that according to your interpretation of the poem, the speaker is telling us about a night when she bid her lover farewell.
You could argue that the metaphor comparing the speaker to wild ducks and the speaker's statement that her heart "races along the train rails" are examples from the poem that support your claim.
You could argue that a different reading would imply that the speaker is the one being dumped by her lover.
You could cite the second stanza, which is not included here, where the speaker claims that the "known you" have emptied her soul, as proof for your claim.
But it's crucial to remember that the first interpretation appears to be the most plausible one. The metaphor involving the wild duck and the personification of the heart that runs on rails are quite clear, even though the poem does leave some room for ambiguity. The person who wants to leave someone behind is the speaker.
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what energy transformation is preformed by a radio
Answers
Answer:
Chemical energy to sound energy to heat energy
Kam does 4000J of work in climbing a set of stairs. if he does work in 6 seconds, whi is his power output?
Answers
Answer:
666.7 W
Explanation:
Power = P = W/t = 4000 J/6 s = 666.7 W (watts)
The four conducting cylinders shown in the figure are all made of the same material, though they differ in length and/or diameter. They are connected to four different batteries, which supply the necessary voltages to give the circuits the same current, I.
Rank the four voltages. V₁, V₂, V₃, and V₄. in order of decreasing value. Rank from largest to smallest. To rank items as equivalent, overlap them.
This content in not available an your mobile device, but your work is still incomplete. Please use a different device to submit your solution for grading
Answers
The ranking of the voltages, V₁, V₂, V₃, and V₄ in the order of decreasing voltage value is; V₂ > V₃ > V₁ > V₄
What is the voltage of an electric circuit?A voltage is the difference in potential or pressure that pushes or causes the flow of electric current in a circuit or conducting loop.
The current flowing through the circuit can be found using the following formula;
[tex]I=\dfrac{V}{R}[/tex]
The formula for conductivity is presented as follows;
[tex]\sigma =\dfrac{l}{R\times A}[/tex]
Where;
σ = The conductivity of the material
l = The length
R = The resistance to electricity
A = The cross-sectional area of the conductor
Therefore;
[tex]R=\dfrac{V}{I}[/tex]
[tex]R=\dfrac{l}{A\times \sigma}[/tex]
[tex]\dfrac{V}{I} =\dfrac{l}{A\times \sigma}[/tex]
[tex]V=\dfrac{l \times I}{A\times \sigma}[/tex]
Based on the dimensions of the cylinders, obtained from a similar question, we get;
[tex]V_1=\dfrac{3\cdot L \times I}{\pi \cdot D^2\times \sigma} = 3\times \dfrac{ L \times I}{\pi \cdot D^2\times \sigma}[/tex]
[tex]V_2= \dfrac{2\cdot L \times I}{\pi \cdot \dfrac{D^2}{4} \times \sigma} = \dfrac{8\cdot L \times I}{\pi \cdot D^2\times \sigma} = 8\times \dfrac{ L \times I}{\pi \cdot D^2\times \sigma}[/tex]
[tex]V_3=\dfrac{L \times I}{\pi \cdot \dfrac{D^2}{4} \times \sigma} =\dfrac{4\cdot L \times I}{\pi \cdot D^2\times \sigma}= 4\times \dfrac{L \times I}{\pi \cdot D^2\times \sigma}[/tex]
[tex]V_4=\dfrac{L \times I}{\pi \cdot D^2\times \sigma} = 1\times \dfrac{ L \times I}{\pi \cdot D^2\times \sigma}[/tex]
Therefore;
V₁ = 3·V₄
V₂ = 8·V₄
V₃ = 4·V₄
The rank of the voltages in the order of decreasing value is therefore;
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An object has 100 J of kinetic energy. If the object’s mass doubles, what is its kinetic energy?
Answers
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.
Which one of the following statements about velocity is true?
O Velocity is the magnitude of speed.
O Velocity is the displacement of an object divided by the time interval.
O Velocity describes how fast an object is changing speed.
O Speed and velocity refer to the same vector quantity.
Answers
Answer:
Velocity is the displacement of an object divided by the time interval.
Explanation:
Let's consider each choices:
1. Velocity is not the magnitude of speed. Velocity is a vector quantity which means it consists of both direction and magnitude. Speed is the magnitude of velocity, not the other way around.
3. Velocity describes how fast an object is changing speed. If a speed changes each time interval, that is not a velocity but rather the magnitude of acceleration. Magnitude of acceleration is change in speed over time. Acceleration is the one that describes how velocity is changing through time.
4. Speed and velocity refer to the same vector quantity. Speed is not a vector quantity but a scalar quantity which only has magnitude. Speed is also considered as the magnitude of velocity as well.
Therefore, the only correct choice is 2. Velocity is the displacement of an object divided by the time interval. This is true since velocity is change in position (displacement) over time.
A boat has a speed of 20m/s in still waters. what is the speed in a river flowing due east with a velocity of 5m/s if the boat is heading north. How far from a point directly north on the other side of the river will the boat arrive if the width of the river is 10m.
Answers
The boat will arrive 2.5 meter in east far from a point directly north on the other side of the river.
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.
A boat has a speed of 20m/s in still waters.
The velocity of river is 5m/s in east.
The width of the river is = 10 meter.
Hence, time taken by the board to cross the river = 10/20 second
= 0.5 second.
In this time, the board will move in east direction = 5×0.5 meter = 2.5 meter.
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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.
Answers
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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Maritza's school provides a laptop to each student to use in the classroom and for
homework. What is the BEST way for her to use the laptop in her science class?
A.to look up bands who are coming to town?
B.to take notes as her teacher talks?
C.to complete her English assignment?
D.to email her friend in another class?
Answers
The best way for her to use the laptop in her science class is to take notes as her teacher talks
How can a laptop be used in a classroom?Fostering online collaboration with other students.Providing curriculum support and additional information to students.Promoting better organization: Laptops help students keep track of their assignments and utilize an online school calendar.Laptops allow students to collaborate with their classmates inside and outside the classroom. They can ask questions, compare notes and share what they have learned more readily. They can also work together on group projects even if they are not in the same locationIn the last several years, schools across the country have experimented with providing each student with a laptop to facilitate learning. In 2016, Michigan State University studied the results from a number of these programs to determine if providing laptops influenced academic performance. The researchers, led by Michigan State University’s Assistant Professor Binbin Zheng, looked at nearly 100 studies of the use of laptops in the classroom, known as “one-to-one computing environments.”To learn more about laptop refers to:
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1. What does Louis de Broglie's principle propose about electrons?
They have energy and momentum.
They behave as a wave and a particle.
They contain high-energy and low-energy photons.
They interact with other electrons to form new substances.
Answers
Louis de Broglie's principle of electrons states that (b) They behave as a wave and a particle.
The de Broglie equation is one of the equations that is commonly used to define the wave properties of matter. It basically describes the wave nature of the electron.Electromagnetic radiation, exhibit dual nature of a particle (having a momentum) and wave (expressed in frequency, wavelength). Microscopic particle-like electrons also proved to possess this dual nature property.Louis de Broglie in his thesis suggested that any moving particle, whether microscopic or macroscopic will be associated with a wave character. It was called ‘Matter Waves’. He further proposed a relation between the velocity and momentum of a particle with the wavelength, if the particle had to behave as a wave.Particle and wave nature of matter, however, looked contradictory as it was not possible to prove the existence of both properties in any single experiment. This is because of the fact that every experiment is normally based on some principle and results related to the principle are only reflected in that experiment and not the other.To know more about electrons visit:
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Concluding statement about electricity like a sentence or two
Things are:
Wind turbines
Hydroelectric
Geothermal heat
Write it in like a concluding statement feel
Answers
Wind turbines, hydroelectric, and geothermal heat have been relied upon for decades to provide a renewable and clean energy source to people around the world. These alternative energy technologies provide optimal clean and renewable energy sources for many communities and countries striving for sustainable development.
A crane exerts 56000 Newtons of force over a distance of 4.5 meters. how much power was generated if it took 4.2 seconds to accomplish this?
Answers
Answer:
E = F * S definition of energy
P = E / t = F * S / t definition of power
P = 5.6E4 N * 4.5 m / 4.2 s = 60,000 watts
An astronaut weights 8x10^2
Answers
Answer:
800
Explanation:
10^2 = 100
8 x 100 = 800
A student pours a spoonful of dirt into a cup of water. The water and dirt are stirred together. The water turns a light brown color. Some dark pieces float to the top of the cup and another dark layer forms on the bottom of the cup. Which statement BEST describes the contents of the cup?
Answers
The statement that is correct is that the contents of the cup form a mixture.
What is the nature of the cup?Though the question is incomplete but I would try to give you a good explanation as much as I can. We must recall that when we talk about a mixture, we have to note that the term mixture would refer to the combination of two or more substances that do not chemically react together.
In this case, we have been told that we have a water that was pure and then we add dirt to it. It is clear that the water and the dirt do not react in any way hence what we have formed is a mixture.
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please answer fast it doesn't have to be long please :)
Juan drives his car around a curve at a speed of 17.0 m/s. Assume the curve can be approximated by an arc of a circle of radius 122.0 m. If a force of 7380 N is required to maintain the car’s circular motion, what is the car’s mass?
Answers
The mass of the car moving with a velocity of 17 m/s is 3115.4 kg.
What is mass?Mass is the quantity of matter a body contains. The S.I unit of mass is kilogram
To calculate the mass of the car, we use the formula below
Formula:
m = Fr/v²...................... Equation 1Where:
m = Mass of the carF = Forcer = Radiusv = VelocityFrom the question,
Given:
F = 7380 Nr = 122 mv = 17 m/sSubstitite these values into equation 1
m = (7380×122)/17²m = 3115.4 kgHence, the mass of the car is 3115.4 kg.
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The momentum of an object is determined to be 7.2×10-3 kg⋅m/s. Express this quantity as provided or use any equivalent unit. (Note: 1 kg = 1000 g
Answers
The mass of the moving item is referred to as momentum. There is magnitude and direction to momentum. The object has a momentum of 7.2 g-m/s.
What is the momentum of an object?Momentum is a vector quantity that is created during motion by an object's mass and velocity. Thus, momentum will be expressed in units of kg-m/s.
Considering that item has motion. Likewise, 1 kilogram equals 1000 g. Therefore, the momentum will transform into units of grams when we enter the value of 1 kg.
Momentum = 7.2 x 10⁻³ 1000g-m/s
Momentum = 7.2 g-m/s.
Thus, we may deduce that the object's momentum, measured in grams per second, is 7.2 g-m/s.
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16. A car A is moving at a speed of 6m/s due north and car B is moving at a speed of 8m/s due east. Find the magnitude and direction of the velocity of car A relative to car B
Answers
Since car A is moving due north and car B is moving due east, the x-component of the velocity of car A is 0 and the y-component is 6 m/s, while the x-component of the velocity of car B is 8 m/s and the y-component is 0. Plugging these values into the formula, we get:
v = √((0 - 8)^2 + (6 - 0)^2)
= √(64 + 36)
= √100
= 10 m/s
To find the direction of the velocity, we can use the inverse tangent function (arctan) to calculate the angle between the velocity vector and the positive x-axis. The angle is given by the formula θ = arctan((vy_A - vy_B)/(vx_A - vx_B)). In this case, we get:
θ = arctan((6 - 0)/(0 - 8))
= arctan(-6/8)
= -53.13 degrees
So the magnitude of the velocity of car A relative to car B is 10 m/s, and the direction is 53.13 degrees counterclockwise from the positive x-axis.
Determine the parallel and perpendicular components of the force of gravity for a 369 N object on a 28.4 degree incline
Answers
The parallel component of the force of gravity is the net force. The perpendicular component of the force of gravity is directed opposite the normal force and as such balances the normal force.
What is the perpendicular component of the force of gravity?In order to balance the normal force, the perpendicular component of gravity is pointed in the opposite direction. No other force can counteract the parallel component of the gravitational force.
What is the parallel component of the force of gravity?The presence of an imbalanced force will then cause the object to accelerate downward along the inclined plane. This acceleration is brought on by the parallel part of the gravitational force. The net force is a parallel part of the gravitational force.
Steps for Calculating the Force of Gravity on an Object Falling from an Inclined Plane: Determine the inclined plane's angle in the first step.Determine the object's mass on the inclined plane in step two.Determine and compute the gravitational force acting on the item.Determine and compute the parallel and perpendicular forces acting on the object.Formulas to Calculate the Force of Gravity on an Object Falling Down an Inclined Plane using Vocabularyincline plane: a wedged angle.Force of Gravitation the downward-moving gravitational force.Force that is parallel to the inclined plane's face is referred to as the perpendicular force.The force that is parallel to the inclined plane's face is known as the parallel force.Equation for Gravitational Force: The gravitational force is equal to the product of an object's mass and its gravitational acceleration.FGravity=m×g
where m is the object's mass and g is gravity's acceleration, which is 9.8 m/s2. In this case, the negative indicates that the force is downward-directed.
Equation for Perpendicular Force: The Perpendicular Force is equal to the gravitational force multiplied by the cosine of the angle of the inclined plane.FParallel=FGravity×Cos(Θ)
Equation for the Parallel Force: The Parallel Force is equal to the gravitational force multiplied by the sine of the inclined plane's angle.FParallel=FGravity×Sin(Θ)
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A 2kg block is attached to a spring for which K=200N/m it is held at an extension of 5 cm and then released at t=0.
A, the displacement as a function of time?
B, the acceleration when X=+A/2
C, the total energy when X=+A/2
D, the velocity when X=+A/2
Answers
The displacement, acceleration, energy and velocity of the simple harmonic motion of the mass attached to the spring are as follows;
A) x(t) = 0.05·sin(10·t + π/2)
B) The acceleration is; a(t) = -2.5 m/s²
C) The total energy is 0.0625 J
D) The velocity is ±√3/4 m/s
What is a simple harmonic motion?The restoring force of a body in simple harmonic motion is directly proportional to the displacement of the body from its mean or central position.
Mass of the block, m = 2 kg
The spring constant, k = 200 N/m
The extension of the spring = 5 cm
Time at which the spring is released, t = 0
A. The motion of the spring with the mass is a Simple Harmonic Motion
The angular velocity can be obtained using the formula;
ω = √(k/m)
Therefore;
ω = √(200/2) = 10
The angular velocity of the block on the spring is, ω = 10 rad/s
The period, T = The time to complete 2·π rad
Therefore; T = 2·π rad/(10 rad/s) = π/5 s
The amplitude, A, is the cistance of the mass from the at rest position, which is 5 cm = 0.05 m
The equation of the extension of the spring is therefore;
x(t) = 0.05·sin(10·t + c)
At t = 0, x(t) = 0.05, therefore;
sin(10 × 0 + c) = sin(c) = 1
c = π/2
The equation for the displacement as a function of time is therefore;
x(t) = 0.05·sin(10·t + π/2)B. The acceleration when x(t) = A/2 is obtained as follows;
x(t) = 0.05·sin(10·t + π/2)
A/2 = 0.05·sin(10·t + π/2)
A = 0.05
0.05/2 = 0.05·sin(10·t + π/2)
sin(10·t + π/2) = 1/2
10·t + π/2 = π/6
t = -π/30
cos(10×(-π/30) + π/2) = ±√3/2
v(t) = x'(t) = 0.05 × 10 × cos(10·t + π/2)
a(t) = v'(t) = -5·sin(10·t + π/2)
a(t) = v'(t) = -5·sin(10·t + π/2) = -5 × 1/2 = -2.5
The acceleration when X = + A/2 is -2.5 m/s²C. The energy in a pring = (1/2)·k·x²
When x = A/2, we get;
E = (1/2) × 200 × (0.05/2)² = 0.0625
The energy in the spring when x = A/2 is 0.0625 JD) The velocity when x = A/2 is; v(t) = x'(t) = 0.05 × 10 × cos(10·t + π/2)
v(t) = 0.5 × cos(10·t + π/2)
When x = A/2, sin(10·t + π/2) = 1/2, therefore;
cos(10·t + π/2) = ±√3/2
v(t) = 0.5 × ±√3/2 = ±√3/4
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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?
Answers
The work done to the mower is the product of the external force applied on the object and the distance covered by the object which is equal to 40,811 Joules.
What is Work done?Work done on an object can be defined as the product of external force applied on the object and the distance over which the force is being applied on the object. Work is done on an object when a force is applied to an object and the object is moved through certain distance.
From this we can see that the horizontal component of the force:
X-Component (horizontal 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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