Describe a longitudinal wave for particle motion and energy motion

(a) The magnitude of the angular momentum of the system is 5,252 kg m²/s.

(b) The rotational energy of the system is 2,826 J.

(c) The new moment of inertia is 31.25 Kgm².

(d) The new speed of each astronaut is 420.15 m/s.

(e) The new rotational energy of the system is 65.82 kJ.

(f) The work is done by the astronauts in shortening the rope -45,317,098 KJ.

(a) To calculate the magnitude of the angular momentum of the system, we can use the following equation:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. Since we are treating the astronauts as particles, we can assume they are point masses and use the formula for the moment of inertia of a point mass:

I = mr²

where m is the mass of each astronaut and r is the distance between them. The angular velocity can be found from the linear velocity and the distance between the astronauts:

ω = v/r

Putting in the given values, we get:

r = 5.00 m

m = 90.5 kg

v = 5.80 m/s

I = 2(mr²) = 2(90.5 kg)(5.00 m)²

              = 4,525 kg m²

ω = v/r = 5.80 m/s / 5.00 m

           = 1.16 rad/s

L = Iω = (4,525 kg m²)(1.16 rad/s)

          = 5,252 kg m²/s

Therefore, the magnitude of the angular momentum of the system is 5,252 kg m²/s.

(b) To calculate the rotational energy of the system, we can use the following equation:

E = (1/2)Iω²

Putting in the values for I and ω that we found in part (a), we get:

E = (1/2)(4,525 kg m²)(1.16 rad/s)²

  = 2,826 J

Therefore, the rotational energy of the system is 2,826 J.

(c) When the distance between the astronauts is shortened to 5.00 m, the moment of inertia of the system changes. We can calculate the new moment of inertia using the parallel axis theorem:

I = Icm + md²

where Icm is the moment of inertia about the center of mass (which remains the same), m is the mass of each astronaut, and d is the distance between each astronaut and the center of mass (which is half the original distance, or 2.50 m).

The new moment of inertia is:

I = Icm + 2md²

 = 2(m(2.50 m)²)

 = 31.25 kg m²

Therefore the new moment of inertia is 31.25 Kgm².

(d) To find the new speeds of the astronauts, we can use the conservation of angular momentum:

L = Iω = L'

where L is the initial angular momentum (which we found in part (a)) and L' is the new angular momentum (which we can find using the new moment of inertia and the new distance between the astronauts, which is 5.00 m).

Solving for ω', we get:

ω' = L' / I = L / I'

Putting in the values, we get:

L' = L = 5,252 kg m²/s

I' = 31.25 kg m²

ω' = 5,252 kg m²/s / 31.25 kg m² = 168.06 rad/s

The new speed of each astronaut is the tangential velocity at a distance of 2.50 m from the center of mass, which can be found using the formula:

v = ω'r

where r is the distance from the center of mass. Putting in the values, we get:

v = 168.06 rad/s * 2.50 m = 420.15 m/s

Therefore, the new speed of each astronaut is 420.15 m/s.

(e) To find the new rotational energy of the system after the astronauts have shortened the rope to 5.00 m, we can use the conservation of angular momentum:

L = Iω

where L is the angular momentum of the system, I is the moment of inertia of the system, and ω is the angular speed of the system. Since the rope is assumed to have negligible mass, we can treat the system as two point masses moving in a circle around their center of mass. The moment of inertia of this system can be calculated as:

I = 2mr²/5

where m is the mass of each astronaut and r is the distance between them. Initially, the moment of inertia of the system is:

I = 2 * 90.5 kg * (10.0 m / 2)² / 5

= 3638 kg m²

The initial angular momentum of the system is:

L = Iω = 3638 kg m² * (5.80 m/s) / (10.0 m / 2)

          = 4213.6 kg m²/s

After the astronauts have shortened the rope to 5.00 m, the moment of inertia of the system is:

I' = 2 * 90.5 kg * (5.00 m / 2)² / 5

  = 1352.5 kg m²

Since the angular momentum of the system is conserved, the new angular speed of the system is:

ω' = L/I' = 4213.6 kg m²/s / 1352.5 kg m² = 3.115 rad/s

E' = (1/2)I'ω'² = (1/2) * 1352.5 kg m² * (3.115 rad/s)²

                    = 65,817.6 J

                    = 65.82 kJ

Therefore, the new rotational energy of the system is 65.82 kJ.

(f) The work done by the astronauts in shortening the rope is:

W = ∫F dl = (F' - F) ∫dl

   = (6,043,064.25 N - 630.56 N) * (-7.50 m)

   = -45,317,098 KJ

Therefore, the work is done by the astronauts in shortening the rope -45,317,098 KJ.

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We have that the time in seconds, minutes, and hours is

\(t=1.083*10^{-4}s\)

\(T_{min}=1.805*10^{-6}min\)

\(T_{hours}=3.0083*10^{-8}hours\)

From the Question we are told that

Velocity \(v=13.0m/s\)

Distance \(d=120 km\)

Generally the equation for the Time  is mathematically given as

\(t=\frac{13}{120*10^3}\\\\t=1.083*10^{-4}s\)

Therefore

\(T_{min}=1.083*10^{-4}s/60\)

\(T_{min}=1.805*10^{-6}min\)

And

\(T_{hours}=T_{min}/60\)

\(T_{hours}=3.0083*10^{-8}hours\)

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Answer:

It is the force that opposes motion between two surfaces touching each other. ( OR ) The force between two surfaces that are sliding or trying to slide across each other.

Explanation:

Answer:

a constant force that acts on objects that rub together

Explanation:

a constant force that acts on objects that rub together

Answer:

Speed = 100 km/h

Explanation:

Given:

Speedometer reading = 100 kph for one lap

Assume;

Time taken to complete one lap = 1 hour

Computation:

Speed =  Distance / Time

Speed =  100 / 1

Speed = 100 km/h

The acceleration and distance:

a2 =  2,168 m/s²

In general, the following tactic constitutes the overall strategy:

(I) To begin, you will need to determine the child's velocity v at the point of impact.

(II) after that, determine the amount of deceleration based on the stopping distance.

These two equations, which originate from the explanation of what it means to "accelerate," are used in both calculations:

v = at (1) (1)

s = at²/2 (2) (2)

where

a stands for acceleration.

t is the amount of time needed to go from having no velocity to having a certain velocity, or vice versa.

The value s represents the total distance covered during the allotted time t.

Let's get ready to perform the algebraic operations that are listed below.

From (2) t = √(2s/a)                                            (3)

From (1) and (3) v = a√(2s/a) = √(2sa)               (4)

From (4) a = v²/2s                                               (5)

Let

s1 = 0.42 m be the distance of the fall,

s2 = 1.9 mm or 1.2 cm be the stopping distance,

t1 will be an unknown value representing the amount of time it takes to fall,

t2 will be an unknown value representing the amount of time it takes to decelerate, v will be an unknown value representing the velocity at impact, and a1 will be the gravitational acceleration (experienced during fall)

a2 is an unknown value that represents the deceleration felt during the impact.

(I)

To calculate v, use equation (4) substituting s = s1, a = a1

Then

v = √(2s1a1)                                                                                  (6)

(II)

To calculate a2 and t2, substituting s = s2, a = a2, and v from (6).

Then using (5) and (6)

a2 = v²/2s2 = 2s1a1/2s2 = (s1/s2)a1

Using (3)

t2 = √(2s2/a2) = √(2s2/((s1/s2)a1) = √(2s2²/(s1a1) = s2√(2/(s1a1))

Now substitute actual numbers:

The case of hardwood

a2 = (0.42/0.0019)×9.81 = 2,168 m/s²

t2 = 0.0019×√(2/(0.42×9.81) =  0.0013 s = 1.3 ms

The case of carpet

a2 = (0.42/0.021)×9.81 = 196 m/s²

t2 = 0.021×√(2/(0.42×9.81) = 0.015

s = 15 ms

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Given:

Piston 1 has an area

and the force applied on this piston is

The force on piston 2, which is the weight of the car, is

Required: The area of piston 2.

Explanation:

The formula that can be obtained by balancing the pressures is

On substituting the values, the area of the second piston will be

Final Answer: The area of the piston lifting the car is 0.975 meter-squared.

If the block's mass is m, block's initial velocity is v and the spring constant is k, the maximum compression in the spring is  sqrt(mv² /k)

Applying the law of conservation of energy, since it is a frictionless surface, all the kinetic energy of the block will be converted to the potential energy of the spring.

The kinetic energy of the block:

Ek = 1/2 . mv²

Where:

m = mass of block

v = block's initial velocity

The potential energy of the spring:

Ep = 1/2 . kx²

Where:

k = spring constant

x = maximum compression in the spring

It holds:

Ek = Ep

1/2 . mv² =  1/2 . kx²

x = sqrt(mv² /k)

Hence, the maximum compression in the spring is sqrt(mv² /k)

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Answer:

Narendra Modi

Explanation:

The answer depends on what year you are talking about on, Narendra Modi was a prime minister of india since 2014. If you are missing information on your question tell me so I can try and tell you the answer,

Hope this helped,

have a good day :]

The addition of vectors allows us to find that the resulting vector is

         c = 17.73 N  with an angle of θ = 21.1º

Giving parameters

To find

Vector magnitudes have magnitude and direction, so their addition must be done using the vector aliebre.

Analytical method is one of the easiest ways to use vectors, it consists of the following parts:

Let's decompose the two vectors into a coordinate system with the horizontal x axis and the vertical y axis, in the attachment we can see a diagram of the vectors

Vector A

            cos 30 = \(\frac{A_x}{A}\)

            sin 30 = \(\frac{A_y}{A}\)

            Aₓ = A cos 30

            \(A_y\) = A sin 30

            Aₓ = 10 cos 30

           A_y = 10 sin 30

            Aₓ = 8.66 N

            A_y = 5.00 N

Vector B

            cos 10 = \(\frac{B_x}{B}\)

            sin 10 = \(\frac{B_y}{B}\)

            Bₓ = B cos 10

            \(B_y\) = B sin 10

            Bₓ = 8 cos 10 = 7.878 N

            B_y = 8 sin 10 = 1.389 N

We perform the algebraic sum

x-axis

            x = Aₓ + B_y

            x = 8.66 +7.878

            x = 16.54 N

y-axis

           y = A_y + B_y

           y = 5.00 + 1.389

           y = 6.39 N

We construct the resulting vector

For the module we use the Pythagoras' theorem

           c = \(\sqrt{x^2+y^2}\)

           c =\(\sqrt{16.54^2 + 6.39^2}\)  

         c = 17.73 N

For the direction we use trigonometry

         tan θ =  \(\frac{y}{x}\)  

         θ = tan⁻¹  \(\frac{y}{x}\)

         θ = tan⁻¹  \(\frac{6.39} { 16.54}\)

         θ = 21.1º

measured counterclockwise from the positive side of the x-axis

In conclusion using vector addition we can find the resulting vector is

         c = 17.73 N     with an angle of θ = 21.1º

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Galaxies were originally found to rotate at a rate that was too fast for said amounts of gravity that might be produced by the luminous mass. This led to the discovery of dark matter.

The force that pulls items toward the center of a planetary or other entity is called gravity. Each one of the planets are kept in orbits around the sun by gravity.

Albert Einstein discovered the solution in 1915 when he released his general relativity theories. All entities with mass, including our Earth, really bend and curve spacetime, which is what causes gravity to pull you toward the ground.

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According to the question, the impact of an electric car to reach its top speed is found to be 51 sec.

Acceleration may be defined as the process of the rate of change of the velocity of an object with respect to time. It is a vector quantity as it has both magnitude and direction.

According to the question,

The acceleration of an electric car = 1.6 m/s²

The speed of an electric car = is 296 km/hour = 1000 m/hour. = 82.2 m/sec.

The acceleration of any moving object is calculated with the help of the following formula:

         1.6 m/s²            =  82.20 - 0/t

           t = 51.45 sec ≅ 51 seconds.

Therefore, the impact of an electric car to reach its top speed is found to be 51 sec.

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Answer:

B. increase as the depth increase

The magnitude of the average acceleration of the cart: a(CD) > a(AB) > a(DE) > a(BC). Therefore, option (d) is correct.

Acceleration can be defined as the rate of change of velocity and is denoted by ‘a. It is measured in the units of m/s². For a particular interval, the average acceleration is the change in velocity for that specific time interval.

Average acceleration is calculated by the following formula,

Average acceleration = Δv/Δt

Where Δ v is the change in velocity and Δt is the total time in the velocity is changing.

For the curve AB:

Average acceleration = \(a =\frac{v_f-v_i}{t_f-t_i}\)

a = (8 -0)/(0.6 - 0) = 13.3 m/s²

For the curve BC:

Average acceleration = \(a =\frac{v_f-v_i}{t_f-t_i}\)

a = (8 -8)/1 - 0.6) = 0 m/s²

For the curve CD:

Average acceleration = \(a =\frac{v_f-v_i}{t_f-t_i}\)

a = (0-8)/(1.2 -1.0) = -40 m/s²

For the curve DE:

Average acceleration = \(a =\frac{v_f-v_i}{t_f-t_i}\)

a = (-4-0)/(2.0 - 1.2) = 5 m/s²

Therefore, the magnitude of the average acceleration of the cart: Acd > Aab > Ade > Abc

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A 50.0-kg wagon is pulled with a constant force of 380 N. Neglecting friction, the wagon's acceleration will be 7.6 m/s².

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Answer:

See below

Explanation:

For a right triangle, remember that tan = opposite leg / adjacent leg:

The angle will be found by using the inverse tangent function

arctan ( .3/1.4)  = 12°

The measure of the angle, in degrees, between the resultant and the 1.40-kilometer displacement vector is 12.

In physics, a vector is a quantity with both magnitude and direction. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity.

A vector does not have position, while having magnitude and direction. In other words, a vector's shape is unaltered if it is shifted parallel to itself as long as its length is unaltered.

Ordinary quantities with a magnitude but no direction are referred to as scalars in contrast to vectors. For instance, while speed (the amount of velocity), time, and mass are scalars, displacement, velocity, and acceleration are vector quantities.

Therefore, The measure of the angle, in degrees, between the resultant and the 1.40-kilometer displacement vector is 12.

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Answer:

A. Reversibility

Explanation:

Because if you don't progress then you do the opposite, you reverse.

Sorry if my explanation is confusing it made sense in my head i just didn't know how to put it.

hope this help. ;)

Answer:

A. Reversibility

Explanation:

Answer:

Explanation:

As the sum of the two right directed forces match exactly the left directed force, the only unbalanced force, and thus the net force, is the upward 25 N force.

Answer:

W =  343.2 J

Explanation:

Given that,

Mass of bale of hay = 26 kg

Horizontal force exerted = 88 N

Distance moved, d = 3.9 m

Work done, W = Fd

Put all the values,

W = 88 N × 3.9 m

= 343.2 J

So, the work done is 343.2 J.  

The image only shows the path of the ball and its different positions at different times during the flight.

To determine the speed of the ball at each position, additional information such as the time elapsed between each position and the distance traveled would be needed. Only with this information would it be possible to calculate the speed at each position and determine where the ball is traveling the fastest.

Speed is the measure of the distance traveled by an object over a specified period. It is a scalar quantity and is typically expressed in units of distance per unit of time, such as miles per hour, kilometers per hour, or meters per second. Speed can be calculated as the ratio of the distance covered by an object to the time taken to cover that distance. It is an important concept in physics and plays a critical role in determining the motion of objects, particularly in the field of mechanics.

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We can infer from the Variable Radius table that as the radius grows, the centripetal force decreases.

The centripetal force and radius have an inverse connection, which means that as one quantity changes, the other changes proportionally.

The mathematical formula for the functional form of this connection is F = k/r, where F is the centripetal force, k is a proportionality constant, and r is the radius.

The centripetal force equation, which describes this relationship, is a key idea in comprehending circular motion.

The Variable Radius table reveals that there is an inverse proportionality between the centripetal force and radius. The centripetal force reduces as the radius grows, and vice versa.

The centripetal force equation, F = k/r, where F is the centripetal force, k is a proportionality constant, and r is the radius, describes this relationship.

The travel of planets around the sun or the movement of cars around a curve are only two examples of how comprehending this relationship is crucial to understanding circular motion.

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For example

Answer:

D) A magnesium atom donates two electrons to the fluorine atoms → Each fluorine atom accepts one of the electrons → The magnesium atom becomes a +2 ion → Each fluorine atom becomes a -1 ion

Explanation:

sorry if its a bit late

The correct steps in the formation of an ionic bond are A magnesium atom donates two electrons to the fluorine atoms → Each fluorine atom accepts one of the electrons → The magnesium atom becomes a +2 ion. The correct option is D.

The electrical attraction between two ions with opposing charges creates an ionic bond, also known as an electrovalent bond, in a chemical molecule.

Ionic compounds are created by ionic bonds, while covalent bonds create covalent compounds. Ionic bonds are created by a complete transfer of electrons, whereas covalent bonds are created by sharing electrons.

Covalent bonds are weaker than ionic ones. Ionic compounds have higher melting and boiling points.

Therefore, the correct option is D.

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Answer:

K = 202.5 J

Explanation:

Given that,

Mass of pie is 5 kg

Velocity of pie is 9 m/s

We need to find the kinetic energy of a pie. The kinetic energy of an object is due to its motion. It can be given by the formula as follows :

\(K=\dfrac{1}{2}mv^2\\\\K=\dfrac{1}{2}\times 5\times (9)^2\\\\K=202.5\ J\)

So, the kinetic energy of the pie is 202.5 J.

Answer:

3.6 arcsec

Explanation:

 angular diameter = diameter / distance

diameter is constant

so angular diameter ∝ 1 / distance

angular diameter = k / distance

For first case ,

18 = k / .5

for second case let angular diameter be D .

D = k / 2.5

dividing ,

D / 18 = .5 / 2.5 = 1 / 5

D = 18 / 5 = 3.6 arcsec

3.6 arcsec is the answer .

The density of the metal is ρ = 8.0g/cm³.

The measure of material how densely it is packed together is called density. As the mass per unit volume, it has that definition. Symbol for density: D or Formula for Density: When is the density, m is the object's mass, and V is its volume, the equation is: = m/V.

Because it enables us to predict which compounds will float and which will sink in a liquid, density is a crucial notion. As long as an object's density is lower than the liquid's density, it will often float.

To the given equation we have :

mass of the bar = 256g

volume of metal bar = 32cm³

So according to the formula of density

ρ = m/V

So, putting values

ρ = 256g /32cm³

ρ = 8.0g/cm³

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In response to questions (a) and (b), I will say that wave speed each component of the rope must help to sustain the rope's weight, and as a result, tension will tend to rise with height.

A wave's speed increases as a string's tension does, increasing the frequency (for a given length). By applying pressure in various locations, you may alter the string's length, the standing wave's wavelength, and consequently, its frequency.

If the rope does not expand, take note that the increase is linear. Thus, when height rises, the wave speed v= √ T/μ

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Question:-

(a) If a long rope is hung from a ceiling and waves are sent up the rope from its lower end, why does the speed of the waves change as they ascend? (b) Does the speed of the ascending waves increase or decrease? Explain.

The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.

The p-waves travel with a constant velocity of 7 km/s

The time can be calculated by using the formula

t = d / v

where

T1 =  10:05 a.m

d is the distance they take to travel from the epicenter

v is the speed of the p-waves

On average, the speed of p-waves is

v = 7 km/s

d = 5600 km (given)

Substituting the values in the formula;

t = d / v

t = 5600 ÷ 7

t = 800 seconds

Converting into minutes,

t = 800 ÷ 60

t = 13.3

≈ 13 mins

T1 -  13 mins = T2

10:05 - 13 mins = 9.52 am

It means the earthquake occurred prior 13 minutes, that is at 9.52 am.

Therefore, the earthquake occurred at 9.52 am.

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