Consider a system consisting of three particles: m1 = 4 kg, vector v1 = < 10, -5, 15 > m/s, m2 = 9 kg, vector v2 = < -15, 5, -3 > m/s, m3 = 3 kg, vector v3 = < -24, 36, 18 > m/s.
a) what is the total momentum of this system?
b) what is the velocity of the center of mass of this system?
c) what is the total kinetic energy of this system?
d) what is the translational kinetic energy of this system?
e) what is the kinetic energy of this system relative to the center of mass?
one way to calculate krel is to calculate the velocity of each particle relative to the center of mass, by subtracting the center-of-mass velocity from the particle's actual velocity to get the particle's velocity relative to the center of mass, then calculating the corresponding kinetic energy, then adding up the three relative kinetic energies. however, there is a much simpler way to determine the specified quantity, without having to do all those calculations; think about what you know about the relationships among the various kinds of kinetic energy in a multiparticle system.

Answers

Answer 1

The answers to your questions are as listed below

A) The total momentum of the system is :  < - 167, 133, 87 >   kg m/s

B) Velocity of the center of mass of this system : < - 10.44 , 8.31, 5.44 > m/s

C) Total kinetic energy of the system : 5159.5 J  

D) Translational kinetic energy of the system :  1660.84 J

E) kinetic energy relative to the center of mass : 3498.66 J

Given data :

m₁ = 4 kg ,   V₁ = < 10, -5, 15 > m/s

m₂ = 9 kg,   V₂ = < -15, 5, -3 > m/s

m₃ = 3 kg    V₃ = < -24, 36, 18 > m/s.

A) Determine the total momentum of the system

Total momentum = Σ mv

= < 4*10 + 9*(-15) + 3*(-24), 4*(-5) + 9*5 + 3*36, 4*15 + 9 (-3) + 3*18 >

= < - 167, 133, 87 >   kg m/s

B) Velocity at the center of mass of this system

Velocity = < - 167 / 16 , 133/ 16, 87/ 16 >

              =  < - 10.44 , 8.31, 5.44 > m/s

C) Determine the total kinetic energy of the system

Total Kinetic energy = 1/2 m₁v₁² + 1/2 m₂v₂²  + 1/2 m₃v₃²  --- ( 1 )

where : v² = v₁² + v₂² + v₃²

therefore

Total kinetic energy = 700 + 1165.5 + 3294

                                  = 5159.5 J  

D) Determine the translational kinetic energy of the system

Translational kinetic energy ( Kcm ) = 1/2 ( m₁ + m₂ + m₃ ) * Velocity²

                                                           = 1/2 ( 16 ) * (  - 10.44² + 8.31² + 5.44² )

Hence translational kinetic energy = 1660.84 J

E) The Kinetic energy of the system relative to the center of mass

Krel = Ktotal - Kcm

       = 5159.5 - 1660.84

       = 3498.66 J

Hence we can conclude that the answers to your questions are as listed above.

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Related Questions

A student wants to make a scientific explanation regarding the wave model of electromagnetic radiation. Which of the following would be part of the scientific explanation?(1 point)

claims


opinions

historical events

procedures

Answers

Answer:

Explanation:

I can say claims

Electromagnetic radiation are a group of waves which are are produced by the vibrations of electromagnetic fields.

What is electromagnetic waves?

Electromagnetic radiation are a group of waves which are are produced by the vibrations of electromagnetic fields. Electromagnetic waves/radiation possess the ability to travel through vacuum (i.e. they do not require a material medium for their propagation) while also carrying radiant energy.

Electromagnetic fields which are the sources of electromagnetic radiation, exist as a result of the combination and interaction of travelling electric and magnetic field forces.

Electromagnetic radiations consists of the following waves: radio waves, infrared waves, visible light, ultraviolet rays, X-rays, and gamma rays.

These waves have differing and unique properties such as wavelength, frequencies, ionizing properties, penetrating ability, sources as well as well as uses. However, they have a common property of velocity- they travel with the speed of light, 3.0 * 10⁸ m/s.

In addition to having the same velocity, all electromagnetic radiation exhibit interference and diffraction.

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How do you think an object's mass relates to its weight?

Answers

Explanation:

w = m.g

g is Gravity acceleration . on surface of Earth it's

9.8 m/s² ≈ 10 m/s²

how many kids under the age of 21 are drinking and smoking in the us and California combined

Answers

Answer:

Well I don't think there is a specific answer for that, but a lot of under the age children do drink and smoke,because these days,their parents either don't care, and some just don't know about it. Many kids drink and smoke these days and I don't think there is a on point percentage.

Explanation: Hope this helps and have a good day!!!

Answer:

See the chart below! :)

Explanation:

See the chart below! :)

you have to choose more than one on this

Answers

b/c bc it’s just b and c

Use the electron arrangement interactive to complete the table

Answers

The number of electrons that is needed to fill the following sublevels are:

1s = 2 electrons. 2s = 2 electrons. 2p = 6 electrons. 3s = 2 electrons.

What is the number of electrons needed to complete the table?

The formula to find this out is:

= 2 x (2 x Level +1)

1s = 0 levels

Number of electrons:

= 2 x (2 x 0 + 1)

= 2 electrons

2s = 0 levels

= 2 x (2 x 0 + 1)

= 2 electrons

2p = 1 level

= 2 x (2 x 1 + 1)

= 6 electrons

3s = 0 levels

= 2 x (2 x 0 + 1)

= 2 electrons

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The completed table using the electron arrangement interactive is attached below. In this table for sublevel 1s, 2s, 2p and 3s electron needed is 2,2,6 and 2 respectively.

What is electron arrangement?

The electron arrangement is the way or process to arrange the electrons in an atom. The number of electron  needed per sublevel are expressed in following points.

The number of electron need to feel sublevel 1s is 2.The number of electron need to feel sublevel 2s is 2.The number of electron need to feel sublevel 2p is 6.The number of electron need to feel sublevel 3s is 2.

The image of the table which fill the sublevel is attached below. In this table all the electron is fulfilled with needed electrons.

Thus, the completed table using the electron arrangement interactive is attached below. In this table for sublevel 1s, 2s, 2p and 3s electron needed is 2,2,6 and 2 respectively.

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_____ is a measure of how closely packed particles of matter are in certain amount of space​

Answers

I think It’s Density

Sorry If I am wrong

Answer:

Density

Explanation:

The more dense something is, the more packed the particles are. The equation for density is m/v.

A 4000 kg freight car moving at 3 km/hr collides and couples with an 8000 kg freight car which is initially at rest. the final speed of the combined cars is

Answers

Answer: 0.28 m/s (1 km/hr)

Explanation:

This is an inelastic conservation of momentum question.

First, convert the speed to m/s: 3 km/hr (1000m/1km)(1hr/3600s) = .83 m/s

Then, Momentum before = Momentum after;

Momentum before = m1v1 + m2v2 = 4000(.83) + 8000(0)

Momentum after: (m1 + m2)v3 → (4000 + 8000)v3

Set these equal: 4000(.83) = 12000v3 and solve to get: v3=.28 m/s :)

Identify the reactions of the citric acid cycle that provide reducing power for the electron‑transport chain

Answers

The reactions of the citric acid cycle that provide reducing power for the electron‑transport chain are as follows:

Conversion of isocitrate to α-ketoglutarateConversion of succinate to fumarateConversion of α-ketoglutarate to succinyl-coA

What is citric acid cycle?

Citric acid cycle also known as kreb cycle is a series of biochemical reactions that involves the synthesis of reduced electron carrier and ATP.

The following steps in the citric acid cycle involves the provision of reducing power for the electron‑transport chain:

Conversion of isocitrate to α-ketoglutarate: Isocitrate is converted to α-ketoglutarate as catalyzed by isocitrate dehydrogenase. Conversion of α-ketoglutarate to succinyl-coA: α-ketoglutarate is converted to succinyl-coA as catalyzed by α-ketoglutarate dehydrogenase.

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The reactions of the citric acid cycle which provide reducing power for the electron‑transport chain are:

Conversion of isocitrate to α-ketoglutarateConversion of α-ketoglutarate to succinyl-coAConversion of succinate to fumarate.

Which citric acid cycle, provide reducing power?

Citric acid cycle, is the tricarboxylic acid cycle (TCA), which is the combination of chemical reaction. This reaction is necessary to produce the energy in aerobic organisms.

The reactions of the citric acid cycle which provide reducing power for the electron‑transport chain are:

Conversion of isocitrate to α-ketoglutarateConversion of α-ketoglutarate to succinyl-coAConversion of succinate to fumarate.

Hence, the option 1,3 and 4 is correct.

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15. Which of the following describes the law of
conservation of energy?
A. Energy cannot be created or destroyed.
B. Energy can only be released through
transformation.
C. When energy is conserved, it always
changes form.
D. Energy increases when it is transferred
from one object to another.

Answers

Answer:

Energy cannot be created or destroyed (it can only change forms).

Explanation:

This is the definition of the law of conservation of energy.

A block of mass 3. 0 kg is hung from a spring, causing it to stretch 12 cm at equilibrium, as shown above. The 3. 0 kg block is then replaced by a 4. 0 kg block, and the new block is released from the position shown above, at which the spring is unstretched. How far will the 4. 0 kg block fall before its direction is reversed?.

Answers

Answer: 32 cm

Explanation:

What is the wavelength in nm of a light whose first order brightband forms a diffraction angle of 19.0°, and the diffraction grating has 600.0 lines per mm? round to the nearest whole number. nm

Answers

The wavelength of light will be 195.34 nm.

What is wavelength?

The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.

The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.

The wavelength from the diffraction grating formula is found as;

[tex]\rm m \lambda= d sin\theta \\\\ \lambda= \frac{dsin \theta }{m}\\\\ \lambda= \frac{600 \times sin 19^0 }{1} \\\\ \lambda= 195.34\ nm[/tex]

Hence the wavelength of light will be 195.34 nm.

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Answer:543nm

Explanation:

becuase

50 points
lab report guide (4).docx What do the results tell you about your hypothesis(es)? Results will tell you which hypothesis is true How do the data support your claim above?

Answers

Answer: Put simply, a hypothesis is a specific, testable prediction. More specifically, it describes in concrete terms what you expect will happen in a certain circumstance. A hypothesis is used to determine the relationship between two variables, which are the two things that are being tested.

Explanation:

HELP Due right now

A 1345-kg car moving east at 15.7m/s is struck by a 1923-kg car moving north. They stick together and move with a velocity of 14.5m / s at theta = 63.5 degrees Was the north-moving car exceeding the 20.1m / s speed limit?​

Answers

Answer:

so here the initial momentum was all in the X direction. This is Equalling the mass. I'm someone multiplied by visa one initial Equalling 1345 kilograms multiplied by 15.7 meters per second. This is Equalling 2.11 times 10 to the fourth kilograms meters per second. Now the car stick together and we can say that the final momentum is Equalling. I'm someone plus himself to multiplied by the final velocity. This is gonna be equal to 1345 kilograms plus 1900 23 kilograms. This is multiplied by 14 0.5 meters per second. And we find that the final month Thomas Equalling 4.74 times 10 to the fourth kilograms meters per second. Now the y component of the final momentum, we can say that he's sub final. Why would be equaling two 4.74 times 10 to the fourth kilograms meters per second? This would be equally rather multiplied by sign of 63.5 degrees. This is Equalling 4.24 times 10 to the fourth kilograms meters per second. By law, of the conservation of momentum. We can say that the Y component of the final momentum equals the why component of the initial momentum. This is equaling EMS up to visa to initial and be some to initial is found to be equal to the final. The white component of final momentum divided by the second cars mass and so this would be 4.24 times tend to the fourth kilograms meters per second, divided by M sub 2 1923 kilograms and this is giving us 22.0 meters per second. And of course this is greater than 20 whether 20.1 meters per second. And so we can say that yes, this car is exceeding the speed limit. 

Explanation:

mark me brainliest!!

What is the Earth’s atmosphere composed of, and why is it important?

Answers

Answer:

i hope this helps you have a good day i hope you get an 100% on you quiz!

Explanation:

The atmosphere is a mixture of nitrogen (78%), oxygen (21%), and other gases (1%) that surrounds Earth. High above the planet, the atmosphere becomes thinner until it gradually reaches space. The atmosphere is an important part of what makes Earth livable.

Which concept is exemplified by being able to distinguish a slight change in light when a dimmer is used to adjust the brightness

Answers

Answer:

The just-noticeable concept.

Explanation:

Do u think heaven is real?

Answers

Answer:

Yes, heaven is for real – and it is heaven, indeed, because we have the hope and assurance of meeting Jesus face-to-face. In the meantime, let’s not just read books and watch movies about the reality of heaven – let’s tell as many people as we can, as often as we can, about the place that will be greater than we can possible imagine.

if the impulse acting on an object is 100n waht is force acting on it if the time 1 s

Answers

force = 100 N

Impulse ( N.s ) : Force ( N ) * Time ( s )

100 N.s = force * 1 s

force = 100/1

force = 100 N

Answer :-

The required Force is 100 Newton .

Explanation :-

As per the provided information in the given question, we have been given that the Impulse of the Object is 100 Ns . It's Time is given as 1 sec . And, we have been asked to calculate the Force .

For calculating the Force , we will use the Formula :-

[tex] \bigstar \: \: \: \boxed {\sf { \: Force \: = \: \dfrac {Impulse}{Time} \: }} [/tex]

Therefore , by Substituting the given values in the above Formula :-

[tex] \dag \: \: \: \sf {Force \: = \: \dfrac {Impulse}{Time}} [/tex]

[tex] \Longrightarrow \: \: \: \sf {Force \: = \: \dfrac {100}{1}} [/tex]

[tex] \Longrightarrow \: \: \: \textbf {\textsf {Force \: = \: 100}} [/tex]

Hence :-

Force = 100 Newton .

[tex] \underline {\rule {180pt}{4pt}} [/tex]

Air in a piston cylinder assembly undergoes a process from state 1 where t1=300k

Answers

For a process where T1 = 300K, P1 = 100 kPa, and where T2 = 500K, P2 = 650 kPa,  the change in entropy is mathematically given as

S1-S2=-0.0288KJ/Kgk

What is the change in entropy between the two states, in kJ/kg-K?

Generally, the equation for the entropy   is mathematically given as

S1-S2=mcp*lnt2-t1-Rlnt2/t1

Therefore

S1-S2=1+1.004*ln(500/300)-0.287*ln(650/100)

S1-S2=-0.0288KJ/Kgk

In conclusion, Entropy

S1-S2=-0.0288KJ/Kgk

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Complete Question

Air in a piston-cylinder assembly undergoes a process from state 1, where T1 = 300K, P1 = 100 kPa, to state 2, where T2 = 500K, P2 = 650 kPa. Using the ideal gas model for air, determine the change in entropy between the two states, in kJ/kg-K

The change in entropy between the two states, in a piston cylinder assembly, undergoes a process from state 1 where t1=300k is 2.36 kJ/kg K.

How to find change in entropy?

The change in entropy can be find out using the following formula,

[tex]S1-S2=s^oT_1-R\ln \dfrac{p_2}{p_1}[/tex]

Here, (p1 and p2) are the pressure at state 1 and 2 and R is the gas constant. The value of R is,

R=(8.314/28.97).

Air in a piston-cylinder assembly undergoes a process from state 1, where T1 = 300 K, p1 = 100 kPa, to state 2. where T2 = 500 K, p2 = 650 kPa.

Put these values,

[tex]S_2-S_1=1.70203_1-\dfrac{8.314}{28.97}\ln \dfrac{10\text { bar}}{1\text { bar}}\\S_2-S_1=2.36\rm\; kJ/kg K[/tex]

Thus, the change in entropy between the two states, in a piston cylinder assembly undergoes a process from state 1 where t1=300k is 2.36 kJ/kg K.

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Which statement describes characteristics of a convex lens? A convex lens diverges light and curves inward. A convex lens diverges light and curves outward. A convex lens converges light and curves inward. A convex lens converges light and curves outward.

Answers

Answer:

D, A convex lens converges light and curves outward.

Explanation:

edge

A convex lens converges light and curves outward.

What is a convex lens ?

A lens that is thin at the bottom and upper edges and somewhat thick in the middle is referred to as a convex lens. The edges are not bent inside, but rather outward.

Here,

In a convex lens, the light rays travelling parallel to its principal axis are converged by it (i.e., the incident rays are directed towards the principal axis).

Since all of the light rays that are refracted by a convex lens eventually converge at a single point, where the image is created, the convex lens is also known as a converging lens.

A converging lens produced a virtual image when the object is placed in front of the focal point.

Hence,

A convex lens converges light and curves outward.

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A wave pulse on a spring is 5.40 cm high and oriented upward. This pulse meets another pulse of the same shape which is 1.10 cm high but oriented downward.
At the moment when the two pulses come together, what is the amplitude of the resulting pulse? Note: if the pulse is oriented upward, make its amplitude positive. If it is oriented downward, make its amplitude negative.

Answers

The resulting positive amplitude of the two waves after the superimposition is 4.30 cm.

Amplitude of the waves

The amplitude of the waves is the maximum displacement of the wave. This is the vertical position of the wave measured from the zero origin.

After the superimposition of the two similar waves, the resulting amplitude will be less than the initial amplitude of the wave with the highest vertical height since the superimposition creates destructive interference.

Resulting amplitude of the two waves is calculated as;

A = 5.4 cm - 1.10 cm

A = 4.30 cm

Thus, the resulting positive amplitude of the two waves after the superimposition is 4.30 cm.

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Identify the names, charges, and location of three types of subatomic particles that make up an atom.

Answers

Answer:Proton (charge of +e, in the nucleus), Neutron (0 charge, in the nucleus), and Electron (charge of –e, outside the nucleus).Nov 13, 2015

Explanation: YA

Protons are positive and in the center ( nucleus)


Neutrons have no charge and are also in the center (nucleus)


Electrons are negative and orbit around the nucleus

The Kelvin scale is also know as the absolute zero
TRUE OR FALSE

Answers

The Kelvin scale is also called absolute zero scale

Explanation:

true

to be a social worker, you must have a master’s degree
A.True
B.False

Answers

Answer:

B --  False

Explanation:

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

Sigmund freud believed mental disorders were caused when an individual __________. a. recognized personal negative qualities b. masked painful feelings c. buried feelings in the unconscious d. distorted the present reality

Answers

Answer:

C. buried feelings in the unconscious

Explanation:

Hope that helps!

Sigmund Freud believed mental disorders were caused when an individual has buried feelings in the unconscious.

What exactly are mental disorders?

Mental disorders are illnesses that impact your thoughts, feelings, emotions, and behavior.

They might be short-term or long-term. They can have an impact on your capacity to interact with others and operate on a daily basis.

There are several sorts of mental illnesses. Panic disorder, obsessive-compulsive disorder, and phobias are examples of anxiety disorders.

Depression, bipolar illness, and other mood disorders are all examples of mood disorders.,

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Which planets are generally referred to as the ice giants?.

Answers

Answer:

The correct answer is Uranus and Neptune

What is the velocity of ab 8 kg lead shoot-out if it has 484 j

Answers

Answer:

attached image

Explanation:

true or false?

Electrons in a circuit move from the negative terminal of a battery toward the positive terminal.

Answers

Answer:

false

Explanation:

it moves from positive to negative

The kinetic energy of a javelin is 81 J, and its speed is 9.0 m/s. What is its mass?

A. 0.5 kg

В. 1.0 kg

C. 2.0 kg

D 9.0 kg

help asap

Answers

Explanation:

[tex]kinetic \: energy = \frac{1}{2} m {v}^{2} [/tex]

[tex]81 = \frac{1}{2}m {(9)}^{2} [/tex]

[tex] \frac{81 \times 2}{81} = m[/tex]

[tex]m = 2kg[/tex]

An archer shot a 0.04 kg arrow at a target. The arrow accelerated at 7,000 m/s2 to reach a speed of 60.0 m/s as it left the bow. How much force did the arrow have?

Answers

The force at which the arrow moved when an archer shot a 0.04 kg arrow at a target is 280 N.

What is force?

Force is the product of mass and acceleration.

To calculate the amount of force the arrow moves, we use the formula below.

Formula:

F = ma............ Equation 1

Where:

F = Force m = mass of the arrowa = acceleration of the arrow.

From the question,

Given:

m = 0.04 kga = 7000 m/s²

Substitute these values into equation 2

F = 0.04×7000F = 280 N

Hence, the force at which the arrow moved is 280 N.

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what 1columb=?
please help​

Answers

Explanation:

it's a unit used to measure charge (C)

1C=1000millicoulombs

1millicoulomb=1000microcoulumbs

Answer:

1 column - 3 x 10⁹ start columb

= 1 / 10 e mu

column is a bigger unit so in practice the smaller unit micro column is also used the smaller unit of charge

1 Milli column - 10-³

1 micro column 10-⁶

COLUMB LAW-

the force of attraction or illusion between the two point charge is directly proportional to the product of the magnitude and inversely proportional to the square of distance between them the direction of force along line joining the two charge

hope it's helpful

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