What is the magnitude of the torque about the origin of the force (−3i^ 3 j^ 4 k^) n if it is applied at the point whose position vector is r⃗ =(−2i^ 4j^) m.

Answers

Answer 1

The torque vector τ has magnitude

|τ| = |F| |r| sin(θ)

where θ is the angle made by the force vector F and position vector r.

Recall the dot product identity,

F • r = |F| |r| cos(θ)

and use to find the measure of the angle in question.

F = (-3 i + 3 j + 4 k) N

r = (-2 i + 4 j) m

F • r = (6 + 12 + 0) N•m = 18 N•m

|F| = √((-3 N)² + (3 N)² + (4 N)²) = √34 N

|r| = √((-2 m)² + (4 m)²) = √20 m

So, we have

cos(θ) = (18 N•m) / ((√20 m) (√34 N)) = 9/√170

⇒   θ = arccos(9/√170) ≈ 46.3°

Now just find |τ| :

|τ| = (√34 N) (√20 m) sin(arccos(9/√170))

|τ| = (√680 N•m) sin(arccos(9/√170))

|τ| = (√680 N•m) √(89/170)

|τ| = 2√89 N•m ≈ 18.9 N•m


Related Questions

How do electromagnetic and mechanical waves compare?

Answers

Transmit energy
Doesn’t transmit matter

Answer:

Transmit energy

Explanation:

Answer:
Use the table below to answer questions 5-6.

Answer:Use the table below to answer questions 5-6.

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Answer:

its also difficult for me.

a. What is electric cell? Mention its types.​

Answers

An electric cell, also known as a battery, is a device that converts stored chemical energy into electrical energy.

There are two main types of electric cells:

Primary cells: These cells are designed to be used once and discarded. They cannot be recharged. Examples of primary cells include alkaline batteries and zinc-carbon batteries.

Secondary cells: These cells are rechargeable and can be used multiple times.

SPEED THAT
INCLUDES THE
DIRECTION is ____

Answers

Answer:

Velocity

Explanation:

No two electrons in an atom can have the same four quantum numbers. This is a statement attributed to.

Answers

No two electrons in an atom can have identical four quantum numbers. This is a statement that is attributed to the Pauli Exclusion Principle.

It states that in an atom or molecule, no two electrons can possess the same four electronic quantum numbers. As an orbital can accommodate a maximum of only two electrons, the two electrons must have opposite spins. This means if one electron is allotted a spin-up electron, the other electron must be a spin-down electron.

The adequacy of an orbital to accommodate electrons is decided by Pauli's exclusion principle. According to this principle, for an electron belonging to the same orbital, the spin quantum number must be different since the other three quantum numbers are the same.

The spin quantum number can have two values: +1/2 and -1/2.

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The following figures give the approximate distances of five galaxies from Earth. Rank the galaxies based on the speed with which each should be moving away from Earth due to the expansion of the universe, from fastest to slowest.
5 billion light-years, 2 billion light-years, 800 million light-years, 230 million light-years, 70 million light-years

Answers

The ranking of the galaxies from the fastest speed to slowest speed is 5 billion light years,  2 billion light years, 800 million light years, 230 million light years, and 70 million light-years.

What is the speed with which galaxies move away from Earth?

Hubble's law gives insight in observation of physical cosmology, that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth.

That is, the galaxy with the greatest distance from Earth will have the highest speed with which it moves away from Earth.

The ranking of the galaxies based on their distance from Earth from the largest to the smallest include;

5 billion light years = 5,000 million light years2 billion light years = 2,000 million light years800 million light years230 million light years70 million light-years

Thus, the ranking of the galaxies from the fastest speed to slowest speed is;

5 billion light years 2 billion light years 800 million light years230 million light years70 million light-years

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If an object that was held steady (0 speed) and then dropped, how many meters would it fall in one second?

Answers

Answer:

h = 4.905 m

Explanation:

In order to find the distance covered by the object in 1 second, we can use the second equation of motion:

\(h = v_i t + \frac{1}{2}gt^2\\\)

where,

h = distance covered = ?

vi = initial speed = 0 m/s

g = acceleration due to gravity = 9.81 m/s²

t = time = 1 s

Therefore,

\(h = (0\ m/s)(1\ s)+\frac{1}{2}(9.81\ m/s^2)(1\ s)^2\\\\\)

h = 4.905 m

IF SOMEONE CAN'T FIND THE ANSWER I WILL COMMIT ARSON PLEASE HELP MEE
Brainliest + random amount of points please help me It's a crossword

IF SOMEONE CAN'T FIND THE ANSWER I WILL COMMIT ARSON PLEASE HELP MEEBrainliest + random amount of points

Answers

Answer:

Freefall

Explanation:

Hi the answer is freefall, hope this helps :)

Following are a number of distinguishing characteristics of spiral and elliptical galaxies. Match each characteristic to the appropriate galaxy type.
Spiral galaxies, Elliptical Galaxies

--contain primarily old, low-mass stars
--contain many bright, hot stars
--significant ongoing star formation
--have flattened disk of stars
--contains abundant clouds of gas & dust
--are rare in central regions of galaxy clusters
--more reddish in color

Answers

Characteristics:

1. Spiral galaxies - contain primarily old, low-mass stars

2. Spiral galaxies - contain many bright, hot stars

3. Spiral galaxies - significant ongoing star formation

4. Spiral galaxies - have flattened disk of stars

5. Spiral galaxies - contain abundant clouds of gas & dust

6. Elliptical galaxies - are rare in central regions of galaxy clusters.

7. Elliptical galaxies - more reddish in color

Matching the characteristics to the appropriate galaxy type:

1. Spiral galaxies - contain primarily old, low-mass stars

2. Elliptical galaxies - contain many bright, hot stars

3. Spiral galaxies - significant ongoing star formation

4. Spiral galaxies - have flattened disk of stars

5. Spiral galaxies - contain abundant clouds of gas & dust

6. Elliptical galaxies - are rare in central regions of galaxy clusters.

7. Elliptical galaxies - more reddish in color

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A circular loop ( radius = 0.5 m) carries a current of 3.0 A and has unit normal vector of (2i - j +2k)/3 what is x component of the torque on this loop when it is placed in a uniform magnetic field of (2i-6j) T

Answers

Answer:

\(T=9.42Nm\)

Explanation:

From the question we are told that:

Radius \(r= 0.5 m\)

Current \(I= 3.0 A\)

Normal vector \(n=\frac{(2i - j +2k)}{3}\)

Magnetic field \(B= (2i-6j) T\)

Generally the equation for Area is mathematically given by

 \(A=\pi r^2\)

 \(A=3.1415 *0.5^2\)

 \(A=0.7853 m^2\)

Generally the equation for Torque is mathematically given by

 \(T=A(i'*B)\)

Where

 \(i'*B= \begin{bmatrix}2&-1&2\\2&-6&0\end{bmatrix}\)

 \(X\ component\ of\ i'*B= [(-1 * 0)-(2*-6)]\)

 \(X\ component\ of\ i'*B=12\)

Therefore

 \(T=0.7853*12\)

 \(T=9.42Nm\)

True or false: " The rotation of the earth and revolution of the earth mean essentially the same thing."

Answers

Answer:

FALSE

Explanation:

Rotation is spinning on its axis

Revolution is spinning around the sun

False. This is because one rotation is one day and one revolution is one year

What phenomenon in hearing is analogous to spatial frequency channels in vision?
A. critical bands
B. tonal suppression
C. auditory adaptation
D. the volley principle

Answers

The phenomenon in hearing that is analogous to spatial frequency channels in vision is critical bands. Hence, the correct option is A: Critical bands.

Critical bands are regions of the audible frequency range in which a complex sound is divided into individual, discrete frequency bands by the human auditory system.

For instance, when different frequencies in a complex sound, such as a musical instrument or a human voice, are picked up by the ear, they are sent to the brain via various channels that respond to specific frequencies.

These channels are referred to as critical bands. The frequency range of these bands varies depending on the loudness of the sound.

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The phenomenon of echo of sound waves is due to:
a. Reflection
b. Interference
c. Diffraction
d. All of the above


Answers

The phenomenon of echo of sound waves is due to reflection. The correct answer is Option A.


Echo is the reflection of sound waves off a surface. When sound waves hit a surface, they bounce back or reflect off that surface, creating an echo. This is similar to how light reflects off a mirror.

The reflected sound waves can be heard as an echo if the distance between the source of the sound and the reflecting surface is large enough for the reflected sound to be heard after the original sound. The reflection of sound waves is also what allows us to hear our own voices when we speak in a room with hard surfaces, such as a bathroom or an empty room.

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physics




what are the two correct choices??



choice1
- insulating
- neutral
- large
- conductive


choice2
- potential energy
- potential difference
- charge
- electric potential


physics what are the two correct choices??choice1- insulating- neutral - large- conductivechoice2- potential

Answers

Answer:

answers are conductive and electric potential

Explanation:

Charges are equally spaced over the surface of a conductive sphere and the electric potential across any two points on the sphere is zero

A stalled car is pushed with a force of 342 N from rest. How far does the car travel in 12 seconds if its mass is 989 kg? ​

Answers

Answer:

Roughly 25 meters

Explanation:

Use the formula D=1/2*a*t^2 where d=distance, a=acceleration, and t=time

Plug in all the variables we know...

D=1/2*a*12^2

in order to solve for acceleration, we use the formula  F=ma where F=force, m=mass, and a=acceleration.

Plug in known variables,

342N=989kg*a

solve for a and we get...

342N/989kg=a

Now that we know the acceleration, we can plug that into our original equation and solve for distance.

D=1/2*342N/989kg*12s^2

Simplify,

D=72s^2*342N/989kg

D=72s^2*342kgm/s^2/989kg

D=72s^2*342m/s^2/989

D=72*342m/989

D=24624/989 meters, or 24.898meters which rounds up to 25.

Describe a situation in which all four spheres of the Earth interact with each other.

Answers

Answer:

All the spheres interact with other spheres.

Explanation:

Rain (hydrosphere) falls from the clouds in the atmosphere to the lithosphere and then forms streams and and rivers that provide drinking water for wildlife and humans and water for plants and crops to grow.

Sonar stands for ""sound navigation and ranging."" What assumption was proved wrong after the invention of sona

Answers

The invention of sonar, which stands for "sound navigation and ranging," revolutionized underwater navigation and detection by using sound waves. Before the development of sonar, there was an assumption that sound traveled in a straight line underwater, similar to how it does in air. However, this assumption was proved wrong after the invention of sonar.

Sonar works by emitting sound waves into the water and then measuring the time it takes for the sound waves to bounce back after hitting an object. By analyzing the returned sound waves, sonar systems can determine the distance, direction, and shape of underwater objects or features. This technique was initially based on the assumption that sound waves would travel in a straight line underwater, just as they do in the air.

However, sonar experiments and observations revealed that sound waves in water are affected by various factors, such as temperature, salinity, and pressure. These factors can cause sound waves to refract (bend) and reflect off underwater surfaces, leading to complex paths and interactions. As a result, the assumption of straight-line sound propagation was proven wrong.

The understanding of sound behavior underwater and the corrections made to sonar techniques allowed for more accurate mapping of underwater environments, detection of underwater objects, and navigation of submarines and ships. By accounting for the effects of refraction and reflection, modern sonar systems can provide precise and reliable information about underwater conditions, contributing to a wide range of applications in marine exploration, navigation, and scientific research.

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Morgan has an equal amount of Sand and Salt. They take the two piles of material and combine them together. Morgan says that this combination of Sand and Salt is a Compound. Do you agree with Morgan?

Answers

Answer: I DISAGREE with Morgan

Explanation:

A compound is made up of two or more elements which are usually chemically bonded together. Such elements can only be separated by a chemical process and not by physical processes like filtration and decantation.

Examples of compounds includes:

--> Table salt(NaCl) this is a chemical compound which contains elements such as sodium and chlorine which are chemically bonded together.

--> water(H2O): this contains elements such as hydrogen and oxygen chemically bonded together

But substances such as sand is not a compound but a mixture which contains natural deposits of silicon dioxide, small rocks and other organic substances which are not chemically bond together.

Therefore, the combination of equal parts of salt and sand will lead to the formation of a HETEROGENEOUS MIXTURE not a compound.

This is a type of mixture in that made up of different compositions.

identify the phases of the moon if at sunset in the northern hemisphere the moon is in each of the following positions.

Answers

The phases of the moon if at sunset in the northern hemisphere the moon is in each of the following positions: Near the eastern horizon: Full moon; High in the southern sky: First quarter; In the southeastern sky: Waxing gibbous ; In the southwestern sky: Waning gibbous.

The moon's phases are determined by the position of the moon relative to the sun. At sunset, the moon is always on the opposite side of the Earth from the sun. So, the phase of the moon will depend on how much of the moon's illuminated side is facing the Earth.

If the moon is near the eastern horizon at sunset, then the entire illuminated side of the moon is facing the Earth. This means that the moon is full.

If the moon is high in the southern sky at sunset, then half of the illuminated side of the moon is facing the Earth. This means that the moon is in its first quarter phase.

If the moon is in the southeastern sky at sunset, then more than half of the illuminated side of the moon is facing the Earth. This means that the moon is in its waxing gibbous phase.

If the moon is in the southwestern sky at sunset, then less than half of the illuminated side of the moon is facing the Earth. This means that the moon is in its waning gibbous phase.

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a window of a car is found to be covered with 0.6cm of ice. if the area of the window is 1 m2, and the ice is at -12 degrees celsius, what is the minimum heat required to melt all the ice? take the density of ice to be 900 kg/m3, the specific heat capacity of ice to be 0.5 cal/g*k, and the latent heat of fusion to be 80 cal/g. answer in kcal.

Answers

The total heat required to melt all the ice is 46.44 kcal.

To melt the ice, we need to first raise its temperature to 0 degrees Celsius, at which point it will start to melt. The mass of the ice on the window is given by the formula

m = (density)(volume) = (900 kg/m3)(0.6 cm)(1 m2) = 0.54 kg.

To raise the temperature of this ice to 0 degrees Celsius, we need to transfer a certain amount of heat to it. The heat required is given by the formula

Q = (mass)(specific heat capacity)(temperature change) = (0.54 kg)(0.5 cal/g*K)(12 K) = 3.24 kcal.

Once the ice has reached 0 degrees Celsius, it will start to melt. The heat required to melt the ice is given by the formula

Q = (mass)(latent heat of fusion) = (0.54 kg)(80 cal/g) = 43.2 kcal.

Therefore, the total heat required to melt all the ice is 3.24 kcal + 43.2 kcal = 46.44 kcal.

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A hematocrit is the process of stopping bleeding
O True
O False

Answers

True, a diminished hematocrit may contribute to the bleeding tendency already present in patients with thrombocytopenia.

A change in the momentum of an object caused by exerting a force on it for a period of time t is called a(n):________

Answers

The change in the momentum of an object caused by exerting a force on it for a period of time t is called impulse.

What is the momentum of a body?

The momentum of a body is the product of the mass of the body and its velocity.

Momentum = mass * velocity.

Momentum of a body ca change when an external force is applied over a period of time.

The change in the momentum of an object caused by exerting a force on it for a period of time t is called impulse.

In conclusion, the momentum of a body is the product of its mass and velocity.

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fill in the blank. a sine wave will hit its peak value ___ time(s) during each cycle.

Answers

A sine wave is a mathematical curve that oscillates between positive and negative values over time. It represents a smooth, periodic oscillation.

In each cycle of a sine wave, which is a complete repetition of the wave's pattern, the wave reaches its highest positive value (peak) and its lowest negative value (trough). Therefore, the sine wave will hit its peak value once during each cycle.

The number of times a sine wave completes a full cycle per unit of time is determined by its frequency. Higher frequencies mean more cycles occur in a given time period, but regardless of the frequency, the wave will always have one peak value per cycle.

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Free fall with an initial horizontal velocity is also called:
a.
parabolic motion
c.
kinematic motion
b.
projectile motion
d.
all of the above

Answers

Answer:

B. Projectile motion is the correct one

A sample of gas x initially has a higher temperature than a sample of gas y . the molecules of gas x have more mass than the molecules of gas y . the samples are mixed together in an insulated container. which of the following claims best describes the collisions between gas x and gas y molecules?
a. The gas X molecules will always lose momentum and kinetic energy, and the gas Y molecules will always gain momentum and kinetic energy b. The gas X molecules wit always gain momentum and kinetic energy, and the one Y molecules will always lose momentum and kinetic energy с. Neither paa molecules will have a change in momentum, but the pa X molecules will always love kinetic energy, and the gas y molecules will always goin kinetic energy d. Molecules of both gases will sometimes gain and sometimes lose momentum, and sometimes gain and sometimes lote kinetic energy

Answers

Molecules of both gases will sometimes gain and sometimes lose momentum, and sometimes gain and sometimes lose kinetic energy. The correct option is d which claims best the collisions between gas x and gas y molecules.

When the samples of gas X and gas Y are mixed together, their molecules will collide with each other. During these collisions, momentum and kinetic energy can be transferred between the molecules.

Since gas X initially has a higher temperature than gas Y, its molecules have higher average kinetic energy. When the molecules of gas X collide with the molecules of gas Y, they can transfer some of their kinetic energy to the gas Y molecules. This transfer of kinetic energy can result in gas Y molecules gaining momentum and kinetic energy.

On the other hand, gas Y molecules can also collide with gas X molecules and transfer some of their kinetic energy to them. This transfer of kinetic energy can cause gas X molecules to lose momentum and kinetic energy.

The specific outcomes of these collisions will depend on factors such as the masses and velocities of the individual molecules involved in each collision. Some collisions may result in a net gain of momentum and kinetic energy for gas X molecules, while others may lead to a net loss. Similarly, gas Y molecules may sometimes gain momentum and kinetic energy, while in other collisions they may lose them.

Overall, it is not accurate to claim that one gas will always gain momentum and kinetic energy while the other always loses. The collisions between gas X and gas Y molecules will be a dynamic process with a mixture of different outcomes, including both gains and losses of momentum and kinetic energy for molecules of both gases.

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what is the kinetic energy of a 200kg boulder that has fallen 500m off a 1000m cliff ?

Answers

Answer:

Ek =  981000 [J]

Explanation:

To solve this problem we must use the principle of energy conservation, where kinetic energy is transformed into potential energy or vice versa. In this special case we take the reference level of potential energy in the soil (potential energy equivalent to zero). When the potential energy is zero, this energy has been transformed into kinetic energy and the velocity will be maximum.

\(E_{k} =\frac{1}{2}*m*v^{2}\)

\(E_{p}=m*g*h\)

where:

Ek = kinetic energy [J]

Ep = potential energy [J]

m = mass = 200 [kg]

h = elevation = 500 [m]

\(E_{p}= E_{k}\) (energy conservation)

Ep = 200*9.81*500

Ep = 981000 [J]

And the kinetic energy is equal to:

Ek = Ep =  981000 [J]

how does a simple cell work

Answers

Answer:

A simple cell can be made by connecting two different metals in contact with an electrolyte

A simple cell consists of two solid electrodes placed in an electrolyte connected together by an electrical conductor such as wire. The two electrodes must be two different metals. The electrolyte can be acid solution, alkaline solution, salt solution or even a fruit such as orange or lemon.

if a test charge of magnitude twice as large as the original test charge were placed at point a, how would the force it feels compare to the force felt by the original test charge when it was placed at point a?

Answers

The force felt by the larger test charge would be twice as large as the force felt by the original test charge.

This is because the force felt by a test charge in an electric field is directly proportional to the magnitude of the test charge. The electric field is a vector field and the force experienced by a test charge is given by the product of the charge of the test particle and the electric field at that point.

So, when the magnitude of the test charge is doubled, the force experienced is also doubled. Therefore, if a test charge of magnitude twice as large as the original test charge were placed at point a, it would feel twice the force that the original test charge felt when it was placed at that same point.

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Which describes the greenhouse effect? 1. Earth continues to get warmer over time because it is slowly moving closer to the sun. 2. Earth's atmosphere blocks the sun's ultraviolet light. 3. Pollution gets into the air, causing trees to not get enough oxygen. 4. Energy given off by earth is reflected off of earth's atmosphere back down to the surface.

Answers

Answer: The green house effect is best described by option 4 (Energy given off by earth is reflected off of earth's atmosphere back down to the surface).

Explanation:

The green house effect can be described as the energy given off by earth is reflected off of earth's atmosphere back down to the surface.

When energy from the sun passes through the atmosphere, some are absorbed which keeps the earth surface warm. While the rest is reflected back largely by cloud.

The energy which is emitted from the earth surface is called the infrared radiation. Some of the infrared radiation passess through the atmosphere but most is absorbed and re- emitted in all directions by the greenhouse gas molecules and clouds. This effect warms the earth surface and the lower atmosphere. Therefore this statement (Energy given off by earth is reflected off of earth's atmosphere back down to the surface) is correct about greenhouse effect.

For the greenhouse effect to occur, greenhouse gas molecules are mostly needed. Examples of these gases include:

--> Carbon dioxide (CO2),

--> Water vapor (H2O), and

--> Methane (CH4)

Over the years, the excessive human activities has lead to increase in the greenhouse gas molecules which has negatively affected the greenhouse effects.

what is magnetic field​

Answers

Answer:

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field.

Explanation:

Answer:

Explanation:

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. ... Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time.

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