Answer:
2m.s¹ left
Explanation:
( Mblock1 x V initial ) + (Mblock2 x V initial) = ( M1 +M2)×0
(1×2) + (1× V initial) = 0
V initial = -2
* I consider right as positive(+)*
Is air in a balloon solid or gas?
gas is the answer for this question
can you make me a brainlist
The moon is significantly smaller than the sun. Why is the moon able to fully block the sun from our view on
Earth?
Answer:
The moon is 400x smaller but it's also 400x closer so it looks the same size even though it's not
Explanation:
To solve this we must be knowing each and every concept related to moon. Therefore, the moon is able to fully block the sun from our view on earth as it is 400 times.
What is moon?Any celestial object that revolves around a planet, such as the eight main planets, dwarf planets, or minor planets, is referred to as a moon. In order to distinguish the moon from other celestial bodies that circle other bodies, the term "natural satellite" may also be used to describe the moon.
The Galilean moons orbiting Jupiter, called after astronomer as well as discoverer Galileo Galilei, were the first moons found outside of the moon of Earth. The moon is significantly smaller than the sun. The moon is able to fully block the sun from our view on earth as the moon appears the same size despite the fact that it's 400 times smaller because it is 400 times closer and hence smaller.
Therefore, the moon is able to fully block the sun from our view on earth as it is 400 times.
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determine the force of gravitational attraction between a 78 kg boy sitting 2 meters away from a 65 kg girl. circle your answer and include units
Answer:
The force of gravitational attraction is 8.454 x 10⁻⁸ N.
Explanation:
Given;
mass of the boy, m₁ = 78 kg
mass of the girl, m₂ = 65 kg
distance between the boy and the girl, r = 2 meters
The force of gravitational attraction is given as;
\(F = \frac{Gm_1m_2}{r^2}\)
where;
G is gravitational constant = 6.67 x 10⁻¹¹ Nm²/kg²
r is the distance between two masses, m₁ and m₂
\(F = \frac{Gm_1m_2}{r^2} \\\\F = \frac{(6.67 \times 10^{-11})(78 \times 65)}{2^2}\\\\F = 8.454 \times 10^{-8} \ N\)
Therefore, the force of gravitational attraction is 8.454 x 10⁻⁸ N.
a mountain 9.0 km from a person exerts a gravitational force on him equal to 2.20% of his weight. calculate the mass of the mountain.
A mountain 9.0 km from a person exerts a gravitational force on him equal to 2.20% of his weight. The mass of the mountain is 8,72,181.35 * \(10^{11}\).
Firstly, we know that gravitational force is 2.20% of weight. So,
Let the gravitational force = \(F_{g}\)
weight of the person = w
So, now we know that
\(F_{g}\) = 0.022 w
We know that weight = mass * g = mg, here m is the mass of person
\(F_{g}\) = 0.022 mg
Now, we also know that
\(F_{g}\) = (G m M)/r²,
where G is gravitational constraint = 6.6743 × 10-11 m³ kg-1 s-²
M = mass of the mountain
and r is the distance between person and mountain = 9km = 9000 m
So,
0.022 mg = (G m M)/r²
[0.022 * g * r²]/ G = M
[0.022 * 9.8 * (9000)²] / 6.6743 × \(10^{-11}\) = M
= [0.2156 * 27000000] / 6.6743 × \(10^{-11}\) = M
= 5821200 / 6.6743 × \(10^{-11}\) = M
= 8,72,181.35 * \(10^{11}\) = M
So, the mass of the mountain is 8,72,181.35 * \(10^{11}\).
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based on your answer,what idea comes in to your mind?
Answer:
Homework · Free food · Loosing and robbing pencil · Forgetting book at home · Waiting for a Play time · My first bit · Lunch sharing · Assembly lines- standing in last just ...
Explanation:
Atom X has an atomic number of 10. Atom Y has an atomic number of 4. All of these statements about atoms X and Y are correct except
A . atom X has 8 valence electrons
B. atom Y is less reactive than atom X
C. atom Y has 2 valence electrons
D atom X has the same number of energy levels as atom Y
1. A 5 kg block is pulled across a table by a horizontal force of 40 N with a frictional force of 8 N
opposing the motion. Calculate the acceleration of the object.
The acceleration of the block is 6.4 m/s².
To calculate the acceleration of the block, we need to consider the forces acting on it.
The applied force is 40 N, and since it is the only horizontal force in the direction of motion, it is the net force acting on the block.
The frictional force opposing the motion is 8 N.
The acceleration, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = ma).
The net force is the difference between the applied force and the frictional force:
40 N - 8 N = 32 N.
Now, we can plug the values into Newton's second law:
32 N = 5 kg × a.
Solving for the acceleration (a), we get
a = 32 N / 5 kg
a = 6.4 m/s².
Therefore, the acceleration of the block is 6.4 m/s².
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The Washington Monument is 169 meters tall.
A worker assigned to the restoration of the Washington Monument is checking the condition of the stone at the very top of the monument. A nickel with a mass of 0.005 kg is in her shirt pocket.
Q: If the nickel accidentally falls out of her pocket, what will happen to the gravitational potential energy (GPE) of the nickel as it falls to the ground?
The gravitational potential energy (GPE) of the nickel will increase as it falls to the ground due to the force of gravity acting on it.
When an object falls, it gains kinetic energy, which is the energy of motion. As an object falls, it gains kinetic energy at the expense of its potential energy.
The amount of GPE gained will be equal to the mass of the nickel multiplied by the acceleration due to gravity and the change in height from the worker's pocket to the ground. Specifically, the change in GPE = 0.005 kg \(* 9.8 m/s^2 * 169\)* m. As the nickel falls it will accelerate and its kinetic energy will increase as well. The nickel will convert the potential energy into kinetic energy and also will gain velocity as it falls, reaching a terminal velocity.
When the nickel reaches the ground, all of its potential energy will have been converted into kinetic energy.
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A. Tick (1) the best alternatives. 1. What is the acceleration due to gravity on the surface of moon ? (a) 9.8m/s (b)1.6m/s2 (c) 6.67x10-1m/s (d) 9.8m/s?
Answer:
\( \green{ \sf \: \: 1.6 \: m {s}^{ - 2} \: \: \: is \: the \: correct \: answer}\)
Explanation:
\( \sf \: \huge{g } _{ \small{moon}} = \frac{ {\huge{g}}_{earth}}{6} \\ \\ \sf \implies \: \sf \: \huge{g } _{ \small{moon}} = \frac{ 9.8}{6} = 1.6 \: \: m {s}^{ - 2} \)
Which liquid substance Would evaporate most quickly in the open air at 25 celius
Assume that it is now January 1, 2022. Wayne-Martin Electric Inc. (WME) has developed a solar panel capable of generating 200% more electricity than any other solar panel currently on the market. As a result, WME is expected to experience a 14% annual growth rate for the next 5 years. Other firms will have developed comparable technology by the end of 5 years, and WME's growth rate will slow to 5% per year indefinitely. Stockholders require a return of 12% on WME's stock. The most recent annual dividend (Do), which was paid yesterday, was $1.75 per share. a. Calculate WME's expected dividends for 2022, 2023, 2024, 2025, and 2026. Do not round intermediate calculations. Round your answers to the nearest cent. D2022 = $ X D2023 = $ D2024 = $ X D2025 = $ D2026 = $ b. Calculate the value of the stock today, Po. Proceed by finding the present value of the dividends expected at the end of 2022, 2023, 2024, 2025, and 2026 plus the present value of the stock price that should exist at the end of 2026. The year end 2026 stock price can be found by using the constant growth equation. Notice that to find the December 31, 2026, price, you must use the dividend expected in 2027, which is 5% greater than the 2026 dividend. Do not round intermediate calculations. Round your answer to the nearest cent. X S C. Calculate the expected dividend yield (D2/Po), capital gains yield, and total return (dividend yield plus capital gains yield) expected for 2022. (Assume that Do = P, and recognize that the capital gains yield is equal to the total return minus the dividend yield.) Do not round intermediate calculations. Round your answers to two decimal places. D1/Po = X % Capital gains yield = % Expected total return = % Then calculate these same three yields for 2027. Do not round intermediate calculations. Round your answers to two decimal places. D/Ps = % Capital gains yield = % Expected total return = %
a) D2022 = $1.9975, D2023 = $2.27715, D2024 = $2.60554, D2025 = $2.98868, D2026 = $3.43243
b) Po = $13.63
c) Dividend yield = 13.85%, Capital gains yield = 74.52%, Expected total return = 88.37%. Dividend yield = 17.89%, Capital gains yield = -23.29%, Expected total return = -5.40%.
a) Dividend is the distribution of earnings to shareholders. Expected dividend for each year can be calculated as follows:
D2022 = D0 (1 + g) = $1.75 (1 + 0.14) = $1.9975
D2023 = D2022 (1 + g) = $1.9975 (1 + 0.14) = $2.27715
D2024 = D2023 (1 + g) = $2.27715 (1 + 0.14) = $2.6055415
D2025 = D2024 (1 + g) = $2.6055415 (1 + 0.14) = $2.98868161
D2026 = D2025 (1 + g) = $2.98868161 (1 + 0.14) = $3.432429195
b) The present value of dividends expected in 2022, 2023, 2024, 2025 and 2026 can be calculated using the following formula:
PVD = D / (1 + r)t
where
PVD = present value of dividends expected
D = dividend expected in a future year
t = number of years from now
r = required rate of return
PVD2022 = $1.9975 / (1 + 0.12)¹ = $1.77700934579
PVD2023 = $2.27715 / (1 + 0.12)² = $1.88843867485
PVD2024 = $2.6055415 / (1 + 0.12)³ = $1.99719364693
PVD2025 = $2.98868161 / (1 + 0.12)⁴ = $2.10928913223
PVD2026 = ($3.432429195 + ($3.432429195 * 1.05)) / (1 + 0.12)⁵ = $2.25661605368
The present value of the stock price that should exist at the end of 2026 can be calculated using the constant growth equation:
Po = D1 / (r - g)
where
Po = price of stock today
D1 = dividend expected at the end of 2026r = required rate of return
g = expected growth rate
Po = $3.60484320761
Total present value of all dividends expected plus the present value of the stock price at the end of 2026 can be calculated using the formula:
Total PV = PVD2022 + PVD2023 + PVD2024 + PVD2025 + PVD2026 + PoTotal PV = $1.77700934579 + $1.88843867485 + $1.99719364693 + $2.10928913223 + $2.25661605368 + $3.60484320761 = $13.6333900619
The value of the stock today, Po, is $13.63.
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the position of a particle is m. determine its velocity and acceleration as a function of time. ( 0 3 ) m/s ( 4 0 0 ) m/s2 what are its velocity and acceleration at time ?
At time t = 0, the velocity and acceleration of an object are represented by the equations a. (t) = 8 hati + 0 hatj - 0 hatk, and a. (0) = 8 hati + 0 hatj - 0 hatk.
The particle position is given as
\underset{r}{\rightarrow}(t) = 4 t2\hat{i} + 2.4 \hat{j} - 5.6 t \hat{k}
velocity is given as the derivative of position relative to time
1 (t) = dx(t)/dt
1 (t) = (d/dt) (4 t2\hat{i} + 2.4 \hat{j} - 5.6 t \hat{k})
1 (t) = (8t) \hat{i} + 0 \hat{j} - 5.6 \hat{k}
acceleration is given as the derivative of velocity relative to time
a. (t) = d1 (t)/dt
a. (t) = (d/dt) ((8t) \hat{i} + 0 \hat{j} - 5.6 \hat{k})
a. (t) = 8 \hat{i} + 0 \hat{j} - 0 \hat{k}
velocity is given as
1 (t) = (8t) \hat{i} + 0 \hat{j} - 5.6 \hat{k}
at t = 0
1 (0) = (8(0)) \hat{i} + 0 \hat{j} - 5.6 \hat{k}
1 (0) = 0\hat{i} + 0 \hat{j} - 5.6 \hat{k}
acceleration is given as
a. (t) = 8 \hat{i} + 0 \hat{j} - 0 \hat{k}
at t = 0
a. (0) = 8 \hat{i} + 0 \hat{j} - 0 \hat{k}
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explain how to find the surface area of a rectangular pyramid
...................
Answer:
So let's first start with the base which is a rectangle remember that the formula to solve the area
Explanation:
To steadily (constantly) increase the velocity of something requires a steadily increasing force. decreasing force. constant net force. none of the above
To steadily increase the velocity of something, it requires c. constant net force.
According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, this is represented as F = ma, where F is the net force, m is the mass, and a is the acceleration. When a constant net force acts on an object, it causes the object to accelerate at a constant rate. This acceleration leads to a steady increase in the object's velocity.
It is important to note that a steadily increasing force would result in an object experiencing an increasing acceleration, which would cause the velocity to increase at an increasing rate rather than steadily. On the other hand, a decreasing force would result in a decreasing acceleration, causing the velocity to increase at a slower rate or even decrease. In conclusion, to steadily increase the velocity of an object, a constant net force must be applied to it. This constant force leads to a constant acceleration, which in turn results in a steady increase in the object's velocity.
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Your friend has a rubber band stretched between two fingers. When you pluck the rubber band, it vibrates and makes sound. What would you have to do to make the sound a higher pitch?
To make a higher pitch, stretch the rubber band more.
To make a higher pitch, pluck the rubber band less hard.
To make a higher pitch, stretch the rubber band less.
To make a higher pitch, pluck the rubber band harder.
Answer:
I think it is To make a higher pitch, stretch the rubber band more
Explanation:
I'm not too sure. Sry if u got it wrong
Answer:
To make a higher pitch ,pluck the rubber band more
a rock is vertically upward with a velocity of 10 m/s. calculate the maximum height it reaches and time taken to reach that height.
Answer:
maximum height: p(t) = Vo * t - 1/2 * g * t^2
p’(t) = v(t) = 0 = Vo - g*t. So, maximum height occurs when t = Vo / g
p(Vo / g) = Vo^2/g - 1/2 * g * (Vo/g)^2
Vo = 10 m / s. Let’s approximate g = 10 m / s^2
p(Vo / g) = 10^2 / 10 - 1/2 * 10 * (10/10)^2 = 10 - 5 = 5 meters (approximately)
Calculation of time:
v = u + gt
0 = 10√2 + (-10)t
-10√2 = -10t
2 = √2s
1. Write the goal of the lab or the question you tried to answer.
Answer:
Type your answer here.
Lab report density and buoyancy
The goal of the lab is to investigate the relationship between density and buoyancy. The lab aims to determine how different objects or substances behave in fluids and understand the principles of density and buoyancy through experimental observations and calculations.
The goal of the lab or the question being addressed in the lab report is to investigate and understand the concepts of density and buoyancy. Density refers to the measure of how much mass is contained within a given volume, while buoyancy refers to the upward force exerted on an object submerged in a fluid, such as water or air.
The lab report aims to explore the relationship between density, mass, and volume by conducting experiments and analyzing data. It may involve measurements of different objects or substances, determining their masses and volumes, and calculating their densities. The report may also involve experiments related to buoyancy, such as determining the buoyant force on an object and investigating factors affecting buoyancy.
By conducting the lab and analyzing the obtained results, the lab report aims to provide a deeper understanding of these fundamental concepts in physics and to demonstrate the principles of density and buoyancy through practical experimentation. The report may also include discussions of the significance and applications of density and buoyancy in various fields, such as engineering, architecture, and fluid dynamics.
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Tool
Scientists are searching for planets that orbit stars outside Earth's solar system by collecting data from different technology tools. A student lists a few tools and their cases that would provide clients
with information about these planets in a table, as shown
Use
spectroscope
gathers information about the
planets in any weather conditions
space probe
collects data from the planets that
would otherwise not be available
identifies different elements present
reflector telescope
around the planets
radio telescope produces images of the planets
Which tool is paired correctly with its intended use?
space probe
Opectroscope
radio telescope
reflector telescope
Answer:
9758 how many significant figures
Engineers often build a prototype perfectly. It is rare that they have to improve their product.
True or false
Answer:
false
Explanation:
most prototypes are and perfect and they are build to find our mistakes
If part of the magnet develops resistance and liquid helium boils away, rendering more and more of the magnet nonsuperconducting, how will this quench affect the time for the current to drop to half of its initial value
When a magnet experiences a quench due to resistance and loss of superconductivity, the time for the current to drop to half of its initial value will be significantly reduced.
The loss of superconductivity in a magnet occurs due to resistance, which results in increased heating. This heat causes the liquid helium surrounding the magnet to boil away, leading to a loss of the superconducting state. As the superconducting state is lost, the magnet's ability to carry current efficiently decreases. Consequently, there is a rapid decline in the current flowing through the magnet. This phenomenon highlights the importance of maintaining the low-temperature environment necessary for superconductivity to prevent the loss of the superconducting state and ensure the magnet operates optimally.
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An airplane's speed increased from 100m/s to 160m/s, at the average rate of 15m/s^2. How long did it take for the plane to complete this increase in speed?
Answer:
4s
Explanation:
Using the formula of motion as follows:
V = u + at
Where;
V = final velocity (m/s)
U = initial velocity (m/s)
a = acceleration (m/s)
t = time (s)
Based on the provided information, v = 160m/s, u = 100m/s, a = 15m/s², t = ?
V = u + at
160 = 100 + 15t
160 - 100 = 15t
60 = 15t
t = 60/15
t = 4seconds.
Therefore, the time it takes for the plane to complete this increase in speed is 4s.
figure show the directions of magnetic field vector and magnetic force vector. find the velocity vector in each case for a positively charged particle
The directions of the magnetic field vector and the magnetic force vector can be determined using the right-hand rule. When you extend your right hand so that your thumb points in the direction of the particle's velocity vector, and your fingers curl in the direction of the magnetic field vector, the palm of your hand will indicate the direction of the magnetic force vector.
For a positively charged particle, the magnetic force vector will be perpendicular to both the velocity vector and the magnetic field vector. The velocity vector will remain unchanged in each case, as the magnetic field does not affect the speed of the particle. However, the direction of the velocity vector may be altered due to the influence of the magnetic force.
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why is angular momentum conserved in these collisions (parts i and ii)? note that linear momentum is not conserved in part ii. how then is angular momentum conserved?
Angular momentum is conserved in collisions due to the principle of conservation of angular momentum. This principle states that the total angular momentum of a closed system remains constant, provided no external torques are acting upon it.
In both parts i and ii, we consider closed systems where external torques are not present. In part i, we have a collision where both linear and angular momentum are conserved. This occurs in a situation like an isolated spinning object or when two objects collide elastically without any friction between them.
In part ii, linear momentum may not be conserved, possibly due to friction or other external forces acting on the objects. However, angular momentum is still conserved. This happens because, despite the change in linear momentum, the net torque acting on the system remains zero. Therefore, the total angular momentum of the system is conserved, as dictated by the principle of conservation of angular momentum.
In summary, angular momentum is conserved in both parts i and ii because the principle of conservation of angular momentum holds true, as long as no external torques are acting upon the closed system. Even when linear momentum is not conserved, the total angular momentum remains constant due to the absence of net external torques.
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Si el sonido no atraviesa las paredes entonces, ¿por qué se escuchan las voces de los vendedores dentro de nuestra casa aún cuando las puertas y las ventanas estén cerradas?
Answer:
DE HECHO EL SONIDO DÍ PUEDE ATRAVESAR LAS PAREDES, PERO
CUANDO ENTRA EN LA PARED, EL SONIDO VIAJA MÁS RÁPIDO QUE EN EL
AIRE Y CUANDO SALE DEL OTRO LADO, EL SONIDO VA A UNA
VELOCIDAD ALTA, POR ESTO LSA VOCES SE ESCUCHAN AUNQUE NO
MUY CLARAS.
Explanation:
Nellie whirls a tether ball in a horizontal circular path over her head. if the action force is nellie pulling on the string, the reaction force is?
The reaction force is string pulling on the Nellie when a tether ball in a horizontal circular path over her head .
A reaction force is a force that acts in the opposite direction to an action force. i.e. Newton's third law of motion describes action and reaction forces and the law states that for every action force, there is an equal and opposite reaction force.
There are Newton's three law of motion which can be describe as ,
The first law is can be stated as, an object will not change its motion unless a external force acts on it.
The second law is describe as, the force on an object is equal to its mass times its acceleration. i.e.
F = ma
In above equation F is force , m is mass and a is acceleration on an object.
The third law can be explained as, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.
Therefore , from the above discussion can be said as Nellie whirls a tether ball in a horizontal circulars path over her head. if the action force is nellie pulling on the string, the reaction force is string pulling on the Nellie.
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An engine using 1 mol of an ideal gas initially at 15.7 L and 272 K performs a cycle consisting of four steps:1) an isothermal expansion at 272 K from 15.7 L to 29.3 L; 2) cooling at constant volume to 105 K: 3) an isothermal compression to its original volume of 15.7 L; and 4) heating at constant volume to its original temperature of 272 K. Find its efficiency. Assume that the heat capacity is 21 J/K and the universal gas constant is 0.08206 L atm/mol/K 8.314 J/mol/K.
The efficiency of the engine is zero, since the net work done by the engine is zero.
What is the efficiency of the heat engine?The efficiency of the heat engine is calculated as follows;
During the isothermal expansion, the work done by the gas is calculated as;
W₁ = nRT ln(V₂/V₁)
where;
V₂ is final volumeV₁ is initial volumen is number of molesR is gas constantT is constant temperatureW₁ = (1 mol)(0.08206 L.atm/mol/K)(272 K) ln(29.3 L/15.7 L)
W₁ = 13.93 L.atm
1 L.atm = 101.325 J
13.93 L.atm = ?
= 13.93 x 101.325 J
= 1,411.5 J
The heat absorbed by the gas is equal to the work done, since it is isothermal process.
Q₁ = -W₁ = -1,411.5 J
The heat lost by the gas is calculated as follows;
Q₂ = nCvΔT
Q₂ = (1 mol)(21 J/K)(105 K - 272 K)
Q₂ = -3,507 J
During the compression process, the work done on the gas is calculated as;
W₃ = -nRT ln(V₂/V₁)
W₃ = -(1 mol)(0.08206 L.atm/mol/K)(272 K) ln(29.3 L/15.7 L)
W₃ = -13.93 L.atm
W₃ = -1,411.5 J
So the heat rejected by the gas is equal to the work done on the gas.
Q₃ = -W₃ = 1,411.5 J
The heat absorbed by the gas during constant volume is calculated as:
Q₄ = nCvΔT
Q₄ = (1 mol)(21 J/K)(272 K - 105 K)
Q₄ = 3,507J
The net work done by the engine during the cycle is calculated as;
W(net) = W₁ + W₃
W(net) =1,411.5 J - 1,411.5 J = 0
The net heat absorbed by the engine during the cycle is calculated as;
Q(in) = Q₁ + Q₄
Q(in) = - 1,411.5 J + 3,507J
Q(in) = 2,095.5 J
The efficiency of the engine is calculated as;
eff. = W(net)/Q(in) x 100%
eff. = 0/2,095.5 J x 100%
eff. = 0%
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Starting at the origin of coordinates, the following displacements are made in the xy-plane. 60mm in the +y
direction, 30mm in the -x direction, 40mm at 150 degrees, and 50mm at 240 degrees. Find the resultant vector
both graphically and algebraically.
The vectors addition allows finding that the answer for the addition of a series of vectors by vector and analytical methods is
R = 96.86 mm θ = 157.26º
Vectors are magnitudes that have modulus and direction, so the addition must be done with vector algebra.
There are graphical and analytical methods to perform the vectors addition
A graphic method of adding vectors is to start a vector and place each of the other vectors at the tip of the previous one and the resulting vector is drawn by drawing a result vector from the origin of the first vector to the tip of the last, in the attachment we can see a diagram of this method.
The analytical method consists of decomposing each vector into a coordinate system, summing each component and then constructing the resulting vector.
We decompose the vectors in the coordinate system that we see as the adjoint.
Vector A
\(A_y\) = 60 j ^ mm
Aₓ = 0
Vector B
Bₓ = -30 i ^ mm
\(B_y\) = 0
Vector C
Module C = 40 mm
Angle θ = 150º
let's use trigonometry
cos 150 = \(\frac{C_x}{C}\)
sin 150 = \(\frac{C_y}{C}\)
Cₓ = C cos 150
\(C_y\) = C sin 150
Cₓ = 40 cos 150 = -34.64 mm
\(C_y\) = 40 without 150 = 20 mm
Vector D
Module D = 50 mm
Angle θ = 240º
cos 240 = \(\frac{D_x}{D}\)
sin 240 = \(\frac{D_y}{D}\)
Dₓ = D cos 240
\(D_y\) = D sin 240
Dₓ = 50 cos 240 = -25 mm
\(D_y\) = 50 without 240 = -43.30 mm
We perform the sum of each component
x-axis
Rₓ = Aₓ + Bₓ + Cₓ + Dₓ
Rₓ = 0 -30 -34.64 -25
Rₓ = -89.64 mm
y-axis
\(R_y = A_y + B_y + C_y + D_y\)
\(R_y\) = 60 + 0 + 20 -43.30
\(R_y\) = 36.7 mm
We construct the resulting vector
For the module we use the Pythagoras' theorem
R = \(\sqrt{R_x^2 +R_y^2}\)
R = \(\sqrt{89.64^2 + 36.7^2}\)
R = 96.86 mm
For the angle we use trigonometry
tab θ’= \(\frac{R_y}{R_x}\)
θ'= tan⁻¹ \(\frac{R_y}{R_x}\)
θ’= tan⁻¹ \(\frac{36.7}{89.64}\)
θ ’= 22.26º
Since the x component is negative, the angle is in the second quadrant
To measure from the positive side of the x axis
θ = 180 - θ '
θ = 180 -22.26
θ = 157.26º
In conclusion using the vectors addition we can find that the answer for the sum of a series of vectors by vector and analytical methods is
R = 96.86 mm
θ = 157.26º
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If work is done on an object, the object has more energy than it did before. This energy can come from increases in kinetic energy, potential energy, and/or _____.
If work is done on an object, the object has more energy than it did before. This energy can come from increases in kinetic energy, potential energy, and/or internal energy.
The energy transferred into an object by an external force is the work done on that object. The unit of work is the joule (J). Work can be expressed as a dot product of the force and the displacement, as given below:
W = F . d
Energy is the capacity of a system to do work. There are many different forms of energy, which can be classified as kinetic, potential, or internal energy.
Kinetic energy is the energy of motion. The kinetic energy of an object of mass m and velocity v is given by the equation below:
K = (1/2)mv²
Potential energy is the energy that a system possesses because of its position in a gravitational or electric field. A body's potential energy depends on its mass, height, and position. An object has gravitational potential energy when it is in a position that can potentially fall to a lower height. A system's electric potential energy is a result of the potential difference between two points.
Internal energy is the energy that a system possesses due to the motion of its atoms and molecules. The total energy of a system is the sum of its kinetic and potential energy. The internal energy of a system is the sum of the energy associated with the motion and position of its atoms and molecules. When energy is transferred to a system by an external force, some of that energy is converted to internal energy.
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A signal of frequency of 1/π Hz is passed through a first-order low-pass RC filter having a time constant of RC-5s. What is the expected phase lag?
The expected phase lag of the signal passing through the first-order low-pass RC filter with a time constant of RC-5s is -63.4 degrees.
The time constant (RC) and cutoff frequency of a first-order low-pass RC filter define it. By applying the formula = -tan1(2fRC), where f is the signal's frequency, one may determine the phase angle of the filter. The filter's time constant in this instance is RC-5s, and the frequency of the signal is 1/Hz. When we enter these variables into the calculation, we get the result = -tan1(2(1/)(5)) = -tan1(10). The phase angle is roughly -63.4 degrees, according to a calculation. In relation to the input signal, this means that the filter's output will be -63.4 degrees delayed.
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earth orbits the sun once every 365.25 days. find the average angular speed of earth about the sun.
earth orbits the sun once every 365.25 days. find the average angular speed of earth about the sun.
99×10−7 rad/s.