a) To estimate c1 and c2 using linear least squares fitting, we first need to set up the system of equations A^T Ac = A^Tb. Here, A is a matrix with columns corresponding to the sine and cosine terms in the equation y(t), and b is a column vector containing the displacement values at the given times. Specifically, we have:
A = [sin(ωt1), cos(ωt1); sin(ωt2), cos(ωt2); ... ; sin(ωt6), cos(ωt6)]
b = [y(t1); y(t2); ... ; y(t6)]
Plugging in the given values for ω and y(t), we get:
A = [0.932039, 0.362358; -0.932039, -0.362358; ... ; -0.487163, 0.874347]
b = [-0.746945; -2.27601; ... ; -2.27083]
Next, we can solve for c by computing the matrix product (A^T A)^-1 A^T b, where (A^T A)^-1 denotes the inverse of the matrix A^T A. This gives:
c = (c1, c2) = (-0.979, 0.382)
Therefore, c1 ≈ -0.979 and c2 ≈ 0.382 are the estimated values of the constants in the vibrating bridge equation.
b) To estimate ω, c1, and c2 using nonlinear least squares fitting, we need to minimize the sum of squared errors between the actual displacement values and the predicted values from the equation y(t) = c1sin(ωt) + c2cos(ωt). This can be done using an optimization algorithm, such as the Levenberg-Marquardt algorithm.
Using this approach, we obtain:
ω ≈ 1.213
c1 ≈ -0.974
c2 ≈ 0.385
Therefore, the estimated values of ω, c1, and c2 from the nonlinear least squares fit are slightly different from the linear fit, but still very close. This suggests that the vibrating bridge equation is a good model for the given displacement values, and that the constants c1, c2, and ω can be estimated accurately using either approach.
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Suppose the ski patrol lowers a rescue sled and victim, having a total mass of 90.0 kg, down a p slope at constant speed, as shown below. The coefficient of friction between the sled and the snow is 0.100. (a) How much work is done by friction as the sled moves 30.0 m along the hill
The work done by friction to move the sled is - 1,323 J.
What is Coefficient of friction?The friction coefficient is the ratio of the normal force pressing two surfaces together to the frictional force preventing motion between them.Typically, it is represented by the Greek letter µ. In terms of math, is equal to F/N, where F stands for frictional force and N for normal force.The coefficient of friction has no dimensions because both F and N are measured in units of force (such as newtons or pounds). For both static and kinetic friction, the coefficient of friction has a range of values.When an object experiences static friction, the frictional force resists any applied force, causing the object to stay at rest until the static frictional force is removed. The frictional force opposes an object's motion in kinetic friction.Solution:
Given that
Coefficient of friction (µ) = 0.10
Mass (m) = 90kg
distance covered (d) = 30m
We use the formula:
friction work = -µmgdcos∅
friction work = -0.100 × 90 kg × 9.8 m/s² × 30 m × cos 60°
friction work = - 1,323 J
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Ungrounded alternating-current systems from 50v to 1,000v or less that are not required to be grounded in accordance with article 250.20(b) shall have___________.
Ungrounded alternating-current systems from 50v to 1,000v or less that are not required to be grounded in accordance with article 250.20(b) shall have ground detectors installed.
What is current system analysis?The current systems is known to be a kind of techniques that are often used to examine the current systems and know the extent of support given to the set of business activities.
A ground detector is known to be a tool that is often use to be able to know or detect conductor insulation that are said to be resistance to ground.
Note that the ground detection is also a sensing equipment that is linked as close as possible to where the system gets its supply and as such, Ungrounded alternating-current systems from 50v to 1,000v or less that are not required to be grounded in accordance with article 250.20(b) shall have ground detectors installed.
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Hydrostatic equilibrium in the Sun means that Choose one: A. energy produced in the core per unit time equals energy emitted at the surface per unit time. B. pressure balances the weight of overlying layers. C. the Sun absorbs and emits equal amounts of energy. D. the Sun does not change over time.
Answer: Hydrostatic equilibrium in the Sun means that pressure balances the weight of overlying layers.
Explanation: To find the answer, we have to know more about the Hydrostatic equilibrium in sun.
What is Hydrostatic equilibrium in sun?Hydrostatic equilibrium in sun means that, the sun is neither expanding not contracting.We can say that the forces that control the sun are precisely balanced.The structure of the sun is in such a way that it can balance the pressure outward and the force of gravity inward.This balance is known as hydrostatic equilibrium.Thus, we can conclude that, the Hydrostatic equilibrium in the Sun means that pressure balances the weight of overlying layers.
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Intelligence test. If you get it right ,you are a critical thinker. You were in the garden,there are 34 people in the yard. You killed 30. How many people are in the garden.
The riddle is solved by knowing that there is only one person left in the garden and that is you.
How many people are in the garden?We are told that there were a total of 34 people in the yard. We do not know if these people are in the garden or somewhere around the yard. The next information we have is that a total of 30 persons were killed.
Since you killed them in the garden, the others may still be lurking somewhere in the yard thus there is only one person left in the garden and that is you.
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Please give detailed explanation
Answer:
» (a)
Explanation:
Velocity is the rate of change in displacement.
[tex]{ \rm{velocity = \frac{ \triangle displacement}{time} }} \\ [/tex]
The change from one position to another is displacement or distance between the points.
[tex] = { \rm{ \frac{22000}{200} }} \\ \\ = { \tt{110 \: m {s}^{ - 1} }}[/tex]
PLSLPSLLPSLPSLPS HELP I ONLY HAVE 5 MINS PLEASE
a bus slows down from 50.0 km/h to 36.5/h in the school zone. determine the magnitude of the vehicle's acceleration if it took 19.5 seconds to slow down.
Answer:
0.19m/s²
Explanation:
Initial velocity(u) = 50×1000/60×60
=13.88 m/s
Final velocity(v) = 36.5×1000/60×60
=10.13 m/s
Acceleration(a) = v-u/t
=10.13-13.88/19.5
a= -0.19m/s²
-a = 0.19m/s²
The magnitude of retar dation is 0.19m/s²
Answer:
[tex]\sf 0.192\:ms^{-2}\:\:(3\:s.f.)[/tex]
Explanation:
Given:
initial velocity (u) = 50.0 km/hfinal velocity (v) = 36.5 km/htime (t) = 19.6 secondsFirst, convert the velocities into meters per second by dividing by 3.6:
[tex]\implies \sf 50.0\: km h^{-1}=\dfrac{50.0}{3.6}\:ms^{-1}= \dfrac{125}{9}\:ms^{-1}[/tex]
[tex]\implies \sf 36.5\: km h^{-1}=\dfrac{36.5}{3.6}\:ms^{-1}= \dfrac{365}{36}\:ms^{-1}[/tex]
To find the vehicle's acceleration, use one of the constant acceleration equations with the given values:
[tex]\implies \sf v=u+at[/tex]
[tex]\implies \sf \dfrac{365}{36}=\dfrac{125}{9}+19.5a[/tex]
[tex]\implies \sf \dfrac{365}{36}-\dfrac{125}{9}=19.5a[/tex]
[tex]\implies \sf 19.5a=-3.75[/tex]
[tex]\implies \sf a=-\dfrac{3.75}{19.5}[/tex]
[tex]\implies \sf a=-0.1923076923...\:ms^{-2}[/tex]
Therefore, the magnitude of acceleration is:
[tex]\implies \sf |a|=|-0.19230...|=0.192\:ms^{-2}\:\:(3\:s.f.)[/tex]
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irius, the brightest star in the sky, is 2.6 parsecs (8.6 light-years) from Earth, giving it a parallax of 0.379 arcseconds. Another bright star, Regulus , has a parallax of 0.042 arcseconds. What is its distance in parsecs
The actual distance of Regulus from Earth is 23.81 parsecs.
Given:
Parallax of Regulus, p = 0.042 arc seconds
Calculation:
When an observer changes their position, an apparent change in the object's position takes place. This change can be calculated using the angle ( or semi-angle) made by the observer and object i.e. the angle made between the two lines of observation from the object to the observer.
Thus from the relation of parallax of a celestial body we get:
S = 1/ tan p ≈ 1 / p
where S is the actual distance between the object and the observer
p is the parallax angle observed
Here for Regulus, we get:
S = 1 / p
= 1 / (0.042) [ 1 parsecs = 1 arcseconds ]
= 23.81 parsecs
We know that,
1 parsecs = 3.26 light-years = 206,000 AU
Converting the actual distance into light years we get:
23.81 parsecs = 23.81 × (3.26 light yrs) = 77.658 light-years
Therefore, the actual distance of Regulus from Earth is 23.81 parsecs which is 77.658 in light years.
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In our Solar System, the inner planets are rocky because Choose one: A. warm temperatures in the inner disk caused the inner planetesimals to be formed of mostly rocky material. B. the original cloud had more rocky material near the center. C. the hydrogen and helium atoms were too low mass to remain in the inner disk. D. the inner disk filled a smaller volume, making it denser.
The inner planets are rocky because The warm temperatures in the inner disk caused the inner planetesimals to be formed of mostly rocky material.
What are rocky planets?
Rocky planets are the planet in which constituents are mostly silicate rocks or metal. They are also regarded as a planet with a solid surface.The formation of rocky planets is said to have occurred billions of years ago and its process of formation is termed accretion. Through accretion are its constituents formed as the more it goes bigger, the higher the rising temperature and pressure in its core and the elements which have to undergo accreted heat up, melt, and spread. Through this process, heavier elements go deeper into the core of the planet and lighter elements float toward the surface. In the formation of rocky planets, the inner portions of the disk are said to be warm from the protostar thereby resulting in the production of the heavy elements that stay there.Examples of rocky planets are Earth or MarsHence, from the above, we can say that,
The warm temperatures in the inner disk caused the inner planetesimals to be formed of mostly rocky material.
Here,
Option A is correct.
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The tub of a washing machine goes into its spin cycle, starting from rest and gaining angular speed steadily for 8.00 s, at which time it is turning at 6.00 rev/s. At this point, the lid of the washing machine is opened, and a safety switch turns it off. The tub then smoothly slows to rest in 11.0 s. Through how many revolutions does the tub rotate while it is in motion
Through 57 revolutions the tub rotate while it is in motion.
What is angular speed?
Angular speed is defined as the rate of change of angular displacement, It is a scalar measurement of rotating object.
It is expressed as follows: ω = θ / t.
Here,
Initially tub is at rest so,
ω(i) = 0 rev/s
ω(f) = 6 rev/s
time taken, t = 8 second
Now the total number of revolutions,
N = t * ( ω(i)+ ω(f) ) / 2
N1 = 8* ( 0+6 ) / 2
N1 = 24 rev
Now, when the lid is opened it's safety switch is off due to which it is uniformly decelerated and comes to rest in 11 s
N2 = 11* ( 0+6 ) / 2
N1 = 33 rev
So,
Total number of revolutions:
N = N1 + N2
N = 24 + 33
N = 57 revolutions
Thus,
Through 57 revolutions the tub rotate while it is in motion.
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The mississippi river delta is one in which the primary source of local current energy is ____.
Answer:potential energy
Explanation:
A peregrine falcon in a tight, circular turn can attain a centripetal acceleration 1.5 times the free-fall acceleration.
The acceleration of a body traveling in a circular route is known as centripetal acceleration. The radius of the turn if the falcon will be 19.7 m.
What is Centripetal acceleration?The acceleration of a body traveling in a circular route is known as centripetal acceleration. Because velocity is a vector quantity. It has both a magnitude and a direction.
Given:
a is the centripetal acceleration = 1.5g
v is the velocity = 17 m/sec
To Find:
r is the radius of circular turn = ?
Mathematically centripetal acceleration is given as
a = v^2/r
r = v^2/a. = (17)^2/1.5 x 9.81
r = 19.7 m
Hence the radius of the turn if the falcon will be 19.7 m.
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True or false: power output can be increased by increasing the rate at which work is done.
By speeding up the process of doing work, power production may be enhanced. The following statement is true.
Description:
Work is completed at a rate determined by power. It is the ratio of work to time. It may be calculated mathematically using the next equation.
Power = Work / Time
or, P = W / T
If the amount of effort/work increases and the amount of time decreases, power will grow. To complete a task in a short amount of time, a lot of force is used.
The Watt is the common metric unit of power. A quantity of power is one unit of labor divided by one unit of time, as the expression for power suggests. As a result, one Watt is equal to one Joule/second. The term "horsepower" is sometimes used to describe a machine's output of power for historical reasons. The equivalence of horsepower is around 750 Watts.Therefore it is concluded that the questioned statement is true.
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PLS GIVE RIGHT ANSWER
I GIVE UP
YOU WILL GET 100 PTS or MORE
Answer:
it is in explanation part
Explanation:
9
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3
2
5
8
1
11
14
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13
Answer:
Explanation:
4. Which is the best season for shearing? Why?
Answer:
During dry season /Spring
Explanation:
Shearing is the removal of wool from a sheep. When you remove wool from sheep, you subject the sheep to cold since nothing is covering the entire body. Therefore, the most suitable season is during dry periods/ Spring since you won't subjects the sheep to cold but warm environment. Thus important to consider that.
Hi I need help with the question in the image, step by step. ASAP!, thank you.
The heating curve is a representation of temperature change for a body with time as shown on cartesian axes.
What is a heating curve?The heating curve is a representation of temperature change for a body with time as shown on cartesian axes.
The point A represents the steady increase in the temperature of the solid. The point B shows the point of fusion, at this point, the solid is transformed into liquid. The point C shows the temperature rise with time as the liquid is heated. The point D shows the process of vaporization which converts the liquid to gas. The point E shows when the substance now exists in the gas phase.
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He wavelengths of the sounds produced by two horns are 6.0 m and 7.0 m, respectively. what beat frequency is heard when the horns are sounded on a day when the speed of sound is 340 m/s?
The beat frequency will be 8.1 Hz when the horns are sounded on a day when the speed of sound is 340 m/s
frequency = speed / wavelength
f1 = 340 / 6 = 56.67 Hz
f2 = 340 / 7 = 48.57 Hz
Beat frequency = fb = | f2 - f1 |
= | 48.57 - 56.67 |
= 8.1 Hz
The beat frequency will be 8.1 Hz when the horns are sounded on a day when the speed of sound is 340 m/s
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A billiard ball at rest is struck by another billiard ball of the same mass whose speed is 6.0 m/s. After an elastic collision the striking ball goes off at an angle of 25° with respect to its original direction of motion. Find the angle the struck ball makes with this direction and the final speeds of both balls.
The angle that the stuck ball makes with the direction of motion and the velocity of both the billiard balls are 65°, 2.6 m/s and 5.5m/s respectively.
To find the answer, we need to know about the linear momentum and angle made in elastic 2 dimensional collision.
What's the angle made by the struck billiard ball with the direction of motion of the 1st ball?In the two dimensional elastic collision between two objects, the scattered objects make 90° angle between them.So, here the angle between the two billiard balls after collision is 90°.As the one billiard ball is making 25° with the initial direction of motion, so the another struck billiard ball makes 90°-25°= 65°.What's the conservation of linear momentum along vertical direction?Let m = mass of each billiard balls, v = velocity of scattered billiard ball, u = velocity of struck billiard ballBefore collision there's no vertical component of momentum. So it's zero.From figure, the total momentum along vertical direction is m×v×sin25°-m×u×sin65°From conservation of linear momentum,0= m×v×sin25°-m×u×sin65°
v×sin25°=u×sin65°
v= 2.1u
What's the conservation of momentum along horizontal direction as shown in figure?Total momentum before the collision along horizontal direction = m × 6 m/sFrom the figure, total momentum after collision is m×v×cos25° + m×u×cos65°So, m×6 = m×v×cos25° + m×u×cos65°6= 2.1u× cos25° +u×cos65°
= 2.33u
u = 6/2.33 = 2.6 m/sAnd v= 2.1×2.6= 5.5 m/sThus, we can conclude that the angle that the stuck ball makes with the direction of motion and the velocity of both the billiard balls are 65°, 2.6 m/s and 5.5m/s respectively.
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Calculate the force needed to give a car of mass 800 kg an acceleration of 2.0 ms−2. plss quick
The force needed to give a car of mass 800 kg an acceleration of 2.0 ms-² is 1600N.
How to calculate force?The force needed to push an object can be calculated by multiplying the mass of the object by its acceleration as follows:
Force = mass × acceleration
According to this question, a car of mass 800 kg has an acceleration of 2.0 ms−². The force is calculated as follows:
Force = 800kg × 2m/s²
Force = 1600N
Therefore, the force needed to give a car of mass 800 kg an acceleration of 2.0 ms-² is 1600N.
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A molecular cloud fragments as it collapses because Choose one: A. the interstellar wind is stronger in some places than others. B. the density increases fastest in the center of the cloud. C. the rotation of the cloud throws some mass to the outer regions. D. density variations from place to place grow larger as the cloud collapses.
The cause for a molecular cloud forming fragments when it collapses is indicated correctly by option D. density variations from place to place grow larger as the cloud collapses.
Molecular cloud:
A molecular cloud, also known as a stellar nursery, is a specific kind of interstellar cloud, whose density and size allow the development of molecules, absorption nebulae, and H II regions. In contrast, some regions of the interstellar medium mostly consist of ionized gas.
Molecular clouds are cold, dense areas of space where stars form. The cloud collapses into a proto-star when the gravitational force pulling it in outweighs the internal pressure pushing it in.
When a molecular cloud collapses, it is observed that the density varies from place to place with the variation increasing with collapse. As a result, the collapse is characterized by fragmentation of the cloud.
Thus the correct option is: D. density variations from place to place grow larger as the cloud collapses.
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Astronomers have realized that the surface of ida is older than the surface of gaspra. How do they measure this?
From counting craters on each asteroids , astronomers have realized that the surface of ida is older than the surface of gaspra.
Ida, and Gaspra are three objects located in the asteroid belt between Mars and Jupiter.
Crater counting is a method for estimating the age of a planet's surface based upon the assumptions that when a piece of planetary surface is new, then it has no impact craters; impact craters accumulate after that at a rate that is assumed known.
Counting how many craters of various sizes there are in a given area allows determining how long they have accumulated and consequently, how long ago the surface has formed. Hence , from counting craters on each asteroids ,astronomers have realized that the surface of ida is older than the surface of gaspra.
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Consider a two-dimensional projectile motion problem involving a ball starting and ending at the same height. the projectile leaves the ground with an initial velocity of 10 m/s at some angle theta with the horizontal, (a) what value of the angle theta (in degrees) makes the range of the projectile maximum? explain, (b) what is the range at this angle? (c) how long does it take for the ball to reach maximum height? (d) what is the maximum height?
The range of the projectile is maximum at angle 45°, the range is 10.2m, the time to reach the maximum height is 0.72 s and the maximum height is 2.6 m
What is a Projectile ?The stone, or object or anything projected in a trajectory path is known as a projectile.
In the given two-dimensional projectile motion problem involving a ball starting and ending at the same height. the projectile leaves the ground with an initial velocity of 10 m/s at some angle Ф with the horizontal,
(a) The value of the angle Ф (in degrees) which will makes the range of the projectile maximum is angle 45° because Range = u²sin2Ф ÷ g
At Ф = 45
Range = u²sin90° ÷ g
where sin 90 = 1
So, Range = u² / g which is the maximum range.
(b) The range at this angle will be
Range = 10² ÷ 9.8
Range = 100 / 9.8
Range = 10.2 m
(c) To calculate how long it takes the ball to reach maximum height, we will use the formula
t = usinФ ÷ g
t = 10 sin 45 ÷ 9.8
t = 0.72s
(d) The maximum height will be
H = u²sin²Ф ÷ 2g
H = 10²(sin45)² ÷ 2 × 9.8
H = 100 × 0.5 ÷ 19.6
H = 50 ÷ 19.6
H = 2.55 m
Therefore, the range of the projectile is maximum at angle 45°, the range is 10.2m, the time to reach the maximum height is 0.72 s and the maximum height is 2.6 m
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When you lift twice the load twice as high, in half the time, the increase in potential energy is _______.
If you lift twice the load twice as high, in half the time then, the increase in potential energy is 4 times that of initial potential energy.
To find the answer, we need to know more about the gravitational potential energy.
What to find the potential energy?The form of mechanical energy possessed by a body by virtue of its position is called the potential energy.If the body is under the influence of gravitational field, then the energy possessed by the body is called gravitational potential energy.Given that,[tex]m'=2m\\h'=2h[/tex] where, m' and h' are the final mass and height.
We have the expression for potential energy as,[tex]U=mgh\\[/tex] , let us take this as the initial energy.
Then the final energy will be,[tex]U'=m'gh'=2m*g*2h=4mgh.\\U'=4U[/tex]
Thus, we can conclude that, the final potential energy is 4 times the initial.
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The final potential energy will be 4 times that of the initial, if we are twice the height and load.
To find the answer, we need to study about the gravitational potential energy.
Where can one find potential energy?Potential energy is the type of mechanical energy that a body possesses as a result of its position.The energy a body possesses is known as gravitational potential energy if it is being affected by a gravitational field.Due to that,[tex]m_f=2m\\h_f=2h[/tex]
where the final mass and height are denoted by mf and hf.
The phrase we use to describe potential energy is,[tex]U_i=mgh[/tex]
let's consider this to be the initial energy.
The final energy will then be,[tex]U_f=2m*2h*g=4mgh=4U_i[/tex]
As a result, we may say that the final potential energy is four times more than the original.
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An ear squeeze occurs when: Select one: The pressure inside the middle ear space is greater than ambient (surrounding) pressure. The pressure inside the middle ear space is less than ambient (surrounding) pressure. Divers forget to wear ear plugs. None of the above.
B. An ear squeeze occurs when the pressure inside the middle ear space is less than ambient (surrounding) pressure.
When external ear squeeze occursExternal ear squeeze occurs when gas trapped in the external ear canal remains at atmospheric pressure while the external water pressure increases during descent.
Thus, we can conclude that, an ear squeeze occurs when the pressure inside the middle ear space is less than ambient (surrounding) pressure.
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What does the length of a vector arrow represent?
O A. angle
OB. magnitude
C. direction
OD. force
what is the number of moles in 12.04×10²³ particles of NH3?
Answer:
[tex]\huge\boxed{\sf m = 2 \ moles}[/tex]
Explanation:
Given data:No. of particles = 12.04 × 10²³ particles
Avogadro's number = 6.02 × 10²³
Required:No. of moles = n = ?
Formula:[tex]\displaystyle No. \ of\ moles\ = \frac{no.\ of \ particles}{Avogadro's \ number}[/tex]
Solution:Put the given in the above formula
[tex]\displaystyle n =\frac{12.04 \times 10^{23}}{6.02 \times 10^{23}} \\\\n = 2 \times 1 \ moles\\\\m = 2 \ moles\\\\\rule[225]{225}{2}[/tex]
An athlete produced 840 watts of power in 0.6 seconds. How much work did this individual perform during the exercise
An athlete produced 840 watts of power in 0.6 seconds. And will produce 504 joule of work did this individual perform during the exercise.
Solution:
we know that power is the work done completed in a given interval of time.
Power = [tex]\frac{work}{time}[/tex]
also, Work = Power × Time
Work = 840 × 0.6 = 504 joule
What is Power?
The quantity of work that can be accomplished in a certain amount of time is measured by power.Power is expressed in joules per second (J/s) this is because work is denoted by the symbol J and time by the symbol s.This is the watt, which is also known as the power unit in SI (W). One joule of labor per second is equal to one watt.The number of watts that a device uses is indicated on labels for lightbulbs and other small appliances like microwaves.A force must be applied in order for work to be completed, and there must also be motion or displacement in the force's direction.The amount of force multiplied by the distance moved in the force's direction is known as the work done by a force acting on an item. Work has no direction and only magnitude. Work is a scalar quantity as a result.Know more about work power numerical https://brainly.com/question/181496
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The watermark can be of different types depending on the application. A watermark will resist manipulations of the media. However, a watermark will not resist tampering.
The first blank is robust watermark; a robust watermark will not resist tampering.
The second blank is fragile watermark; a fragile watermark will resist manipulations of the media.
What is a watermark?A watermark is a faint design made in paper during manufacture that is visible when held against the light and clearly identifies the maker.
The watermark can be of different types depending on the application and they include:
A robust watermark will not resist tampering.A fragile watermark will resist manipulations of the media.Thus, The first blank is robust watermark; a robust watermark will not resist tampering.
The second blank is fragile watermark; a fragile watermark will resist manipulations of the media.
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Why are temperatures in the thermosphere not strictly comparable to those experienced near earth's surface?
Temperatures in the thermosphere are not strictly comparable to those experienced near Earth's surface because the gases of the thermosphere are moving at very high speeds, and the temperature is very high.
The thermosphere lies among the exosphere and the mesosphere. “Thermo” way warmness and the temperature in this layer can reach as much as 4,500 tiers Fahrenheit. in case you have been to hang around inside the thermosphere, though, you'll be very cold because there are not sufficient fuel molecules to transfer the warmth to you.
The thermosphere is the outer layer of the Earth's surroundings, extending from about 53 miles to greater than 370 miles above the surface. The temperature increases rapidly in this layer due to the absorption of huge quantities of incoming excessive electricity sun radiation by using atoms of nitrogen and oxygen.
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Why is it important on diagrams to represent a force with an arrow? Why should mass NOT be represented by an arrow?
It is important on diagrams to represent a force with an arrow because force is a vector quantity but it is not important to represent a mass since it is scalar quantity.
Representing a force with arrow and not mass
Vector quantities are always represented with arrows because they have magnitude and direction.
Scalar quantities have only magnitude, and cannot be represented with arrows.
Thus, it is important on diagrams to represent a force with an arrow because force is a vector quantity but it is not important to represent a mass since it is scalar quantity.
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Suppose a fireworks shell explodes, breaking into three large pieces for which air resistance is negligible. How is the motion of the center of mass affected by the explosion
The center of mass isn't affected by the explosion.
To find the answer, we need to know about the trajectory of motion at zero external force.
How is the trajectory of an object changed when the net external force on it is zero?When there's no net external force acting on an object, its momentum doesn't change with time. As its momentum doesn't change, so it continues with the original trajectory.Why doesn't the trajectory of firework change when it's exploded?When a firework is exploded, its internal forces are changed, but there's no external force. So, although the fragments follow different trajectories, but the trajectory of center of mass remains unchanged.Thus, we can conclude that the center of mass isn't affected by the explosion.
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