Is it reasonable that a 30-kg child could run fast enough to have 100 J of kinetic energy?
(A). Yes, this is reasonable
(B). No, this is not reasonable

Answers

Answer 1

Answer:

A.) Yes, this is reasonable

Explanation:

The formula for kinetic energy states [tex]E_k=\frac{1}{2}mv^2[/tex]:

[tex]E_k=100J\\m=30kg[/tex]

Rewrite the formula to solve for v:

[tex]v=\sqrt(\frac{2E_k}{m})\\v=\sqrt(\frac{(2)(100J)}{30kg})\\v=\sqrt(6.67\frac{m^2}{s^2})\\v=2.58\frac{m}{s}[/tex]

[tex]2.58\frac{m}{s}[/tex] translates to approximately 5.77 mph.  Which seems reasonable enough for a child.


Related Questions

A bicycle with 0. 80-m-diameter tires is coasting on a level road at 5. 6 m/s. A small blue dot has been painted on the tread of the rear tire.

Answers

The speed of the blue dot when it is 0.80 m above the road is 11.2 m/s

Calculation1:

d = diameter of tire = 0.80 m

r = radius of tire = (0.5) d = (0.5) (0.80) = 0.40 m

v = speed of bicycle = 5.6 m/s

w = angular speed of the tire

Speed of cycle is given as

v = r w

5.6 = (0.40) w

w = 14 rad/s

Radians per second. ω ω = 14 rad/s

Calculation2:

v' = speed of blue dot

Speed blue of dot is given as

v' = v + rw

v' = 5.6 + (0.40) (14)

v' = 11.2 m/s

The speed of the blue dot when it is 0.80 m above the road is 11.2 m/s

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Question:

Express your answer in radians per second. ω ω = 14 rad/s Previous Answers Correct Part B What is the speed of the blue dot when it is 0.80 m above the road?

Our solar system was created by the gravitational collapse of the _____.

Answers

Answer:

Solar Nebula?

Explanation:

Our solar system formed about 4.5 billion years ago from a dense cloud of interstellar gas and dust. The cloud collapsed, possibly due to the shockwave of a nearby exploding star, called a supernova. (I thought everyone knew this.)

Salt water is more dense than fresh water. A ship floats in both fresh water and salt water. Compared to the fresh water, the volume of salt water displaced by the ship A.is less than the volume of fresh water. B.is greater than the volume of fresh water. C.is the same as the volume of fresh water. D.cannot be compared without knowing the mass & volume of the ship.

Answers

Answer:

Buoyant force B = V * ρ        volume * density

Since the buoyant force is the same in both cases (salt & fresh)

a smaller volume is required when the density of the displaced water is greater

(A) is correct

Correctly identify the bones of the skull. Frontal bone Sphenold bone Vomer Temporal bone Inferior concha Parietal bone Mandible Zygomatic bone Lacrimal bone Ethmoid bone Frontal bone Maxilla Nasal bone Nasal bone

Answers

The bones of the skull includes the following:

Frontal boneSphenoid boneTemporal bone Parietal bone Ethmoid bone

What is the frontal bone?

The frontal bone in an adult is an unpaired bone that is a part of the boney structure that forms the anterior and superior portions of the skull.

The frontal bone consists of two parts which are

the vertically oriented squamous part, and the horizontally oriented orbital part,

These two parts makes up the bony part of the forehead, part of the bony orbital cavity holding the eye, and part of the bony part of the nose respectively.

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what is example of energy in the form of motion

Answers

Answer:

The wind is an example of motion energy. A dramatic example of motion energy is a car crash—a car comes to a total stop and releases all of its motion energy at once in an uncontrolled instant.

Explanation:

Please give the brainliest.

a 1 mci source of 60co is placed in the center of a cylindrical water-filled tank with an inside diameter of 20 cm and depth of 100 cm. the tank is made of iron with a wall thickness of 1 cm. what is the uncollided flux density at the outer surface of the tank nearest the source? you will need data from appendix d of the course text. making the right assumption(s) simplifies the calculation.

Answers

The uncollided flux density at the outer surface of the tank nearest the source is Ψ• = 3.4 x 10^4 MeV/cm^2.s

In this formula, C represents the source's activity at that precise moment, and 24rCE= is the energy fluence.

We must ascertain what level of activity passes through the shielding since it will diminish when the gamma rays pass through the water and iron.

Using 1.25 MeV as the average 60Co energy will make things simpler. With regard to water and iron, the attenuation coefficients for 1.25 MeV  is the energy fluence are 0.06 cm2/g and 0.058 cm2/g, respectively. first figuring out the intensity, then the iron

I =  1 x 10^-3 x 3.3 x 10^10 x e^(-0.06x1.1) x e^-0.058x7.861

I = 2.6x 10^7 Bq

That is what the cylinder is producing. Using a total radius of 11 cm to calculate the uncollided flux density energy fluence

Ψ• = CE/4πr^2 = 2.6 x 10^7 x 2 x 1.25/4π x 11^2

Ψ• = 3.4 x 10^4 MeV/cm^2.s

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What is the most numerous type of receptor? Multiple Choice Tactile receptors Chemoreceptors Photoreceptors Proprioceptors

Answers

Tactile receptors are the most numerous type of receptors.

Tactile receptors are the most numerous type of sensory receptors that includes mechanoreceptors (in skin) and mucous membranes.A mechanoreceptor, is a sensory receptor that responds to mechanical pressure or distortion. Mechanoreceptors are innervated by sensory neurons that convert mechanical pressure into electrical signals that, in animals, are sent to the central nervous system.There are three classes of mechanoreceptors: tactile, proprioceptors, and baroreceptors. Mechanoreceptors sense stimuli due to physical deformation of their plasma membranes. They contain mechanically-gated ion channels whose gates open or close in response to pressure, touch, stretching, and sound.

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the perception of flashing lights on a christmas tree as continuous movement can be explained by the optical illusion

Answers

The perception of flashing lights on a christmas tree as continuous movement is due to optical illusion.

Perceptual Illusions: the misinterpretation of a real external, sensory experience. The action of deceiving, especially by appearances. An instance of the sense perception of an external object suggesting a false belief as to its nature.

Induced Motion: an illusion of motion, experienced because we have a strong tendency to assume that the object moves, while the background is stationary.Optical Illusions: an instance of something having an appearance so resembling something else as to deceive the eye; mental misapprehension caused by this. An illusion of vision usually affecting “spatial” relations. Also referred to as ‘visual illusions.’Somatic Illusions: tricks used to make parts of your body feel like they are growing, shrinking, bending, etc. Examples (include) ‘Pinocchio,’  ‘Shrinking Waist,’  ‘Doorframe,’ and ‘Rubber Hand.’

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What would be the height of the atmosphere if the air density (a) were uniform and (b) decreased linearly to zero with height? Assume that at sea level the air pressure is 1.0 atm and the air density is 1.3 kg/

Answers

The height of the atmosphere would be 7951.33 m.

We are given that,

Pressure = P = 1 atm

Air density = ρ = 1.3 kg/m³

Therefore, the height of the atmosphere when the density is constant can be calculated by,

P = ρ g h

We know that pressure at sea level = 1 atm = 101300 Pa

Thus , putting the values in the above equation,

h = (101300 Pa)/(1.3 kg/m³)(9.8m/s²)

h = 7951.33 m

Therefore, the height of the atmosphere would be 7951.33 m, when the air density is constant.

Note : the correct order of the question is,

Assume that at sea-level the air pressure is 1.0 atm and the air density is 1.3 kg/m3.(a) What would be the height of the atmosphere if the air density were constant?(b) What would be the height of the atmosphere if the air density decreased linearly to zero with height?

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a scale from which a rock is suspended reads 5 n when the rock is out of water and 3 n when the rock is submerged. buoyant force on the rock is

Answers

A rock suspended by a weighing scale weighs 3 N when submerged in water and 5 N out of water. F= N1-N2. Substitute 5N for F1 and 3n for F2 above the expression to get F. F=5N-3N = 2N.

What is the rock's buoyant force?

The weight of the water volume that the submerged object displaces is what creates the buoyant force. The buoyant force is the weight of water that has the same volume as the rock because the boulder is totally submerged. The buoyant force is still present even though the rock is sinking; it is merely smaller than the rock's weight.

What is seen on the weighing scale's reading when the lift accelerates its descent?

Your perceived weight is equal to the normal force. Therefore, when the elevator accelerates upward or downward, you truly feel a little heavier than usual and a little lighter than usual.

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Jupiter's _____ _____ ______ is a giant storm about three times wider than the diameter of Earth and at least 100 years old.

Answers

Jupiter's great red spot is a giant storm about three times wider than the diameter of Earth and at least 100 years old.

A massive storm larger than Earth that has been raging for hundreds of years is Jupiter's famous Great Red Spot.

Numerous moons orbit Jupiter around it. Jupiter also has a number of rings, but they are much fainter and made of dust rather than ice, unlike the well-known rings of Saturn.

It is mostly Jupiter's fault that it is difficult to comprehend the Great Red Spot. Jupiter is a gas-dominated planet that is a thousand times larger than Earth. Its core is surrounded by a liquid ocean of hydrogen, and the atmosphere is primarily made up of helium and hydrogen.

Jupiter's clouds also make it difficult to make precise observations of its lower atmosphere. While some studies of Jupiter have looked at regions in its lower atmosphere, orbiting telescopes and probes studying the Great Red Spot can only see clouds dispersed high in the atmosphere.

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An Object's Moment Of Inertia Is 2.0kg?M2 . Its Angular Velocity Is Increasing At The Rate Of 3.8rad/S Per Second. What Is The Net Torque On The Object?

Answers

The Net Torque On The Object =7.6 N-m.

The force will cause a torque. The net torque is the sum of the person torques. Rotational Equilibrium is similar to translational equilibrium, where the sum of the forces are same to zero. In rotational equilibrium, the sum of the torques is equal to zero.

The individual torques upload to provide a internet torque approximately the axis. when the ideal sign (fine or bad) is assigned to the magnitudes of character torques approximately a designated axis, the internet torque approximately the axis is the sum of the character torques: →τnet=∑i|→τi|.

Solution:-

Torque= momentInertia*angularacceleration

=> torque= 2.0 x 3.8

=>torque =7.6 N-m

here,

Angular acceleration ,

a  = 3.8rad/s^2

then

Torque  = I * a  = 2 * 3.8  = 7.6 N.m

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PLEASE ANSWER WILL MARK BRAINLIEST IF YOU EXPLAIN HOW YOU GOT THE ANSWER!!!!!!

I’m not sure if the answer I chose is correct or not

Answers

If there is a decrease in the angle of inclination, the acceleration would decrease accordingly.

What is the acceleration?

We know that the acceleration is the change in the velocity of the object with time. Given that the mass of the pulley remains the same and the puly is being moved up the incline as we can see.

We have to also recall that we have been told that the incline is frictionless and as a result we are not going to consider the frictional force. In any case, the force that moves the pully along the incline stull depends on the angle of inclination.

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a spehere with a mass m and a radius r rolls down a ramp that makes an angle theta with the horizontal

Answers

The acceleration of the roll ramp is a = mR² sinθ / I + mR²

The mass of the given object is m

And the radius of the given object is r

the angle of the ramp is given as θ

The expression to calculate the given equilibrium of the object :

mgsinθ - f = ma

this implies f = m( a + gsinθ)

Here we can write

I a' = fR

a' = ( m ( a + gsinθ) ) R / I

The expression without the value of friction can be written as

a = Ra'

Substitute the values in the above expression and we will get:

I a = mR² ( a + gsin θ )

On further solving it by opening the brackets we get

a = mR² sinθ / I + mR²

The acceleration of the roll ramp is a = mR² sinθ / I + mR²

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which sublevels are in each of the following principal energy levels? (a) n = 1 (b) n = 2 (c) n = 3 (d) n = 4

Answers

The outermost energy shell of the atom, where the electrons are situated in relation to the nucleus. the energy levels are-  1 (only"s"), 2 ("s","p"), 3 ("s","p","d"), 4 ("s", "p", "d", "f").

Describe the concept of energy levels.

An atom's energy level is the set distance between its nucleus and any potential location for electrons. Additionally, energy levels might be compared to a staircase's steps.

What exactly does low energy mean?

Most major diseases, including heart disease, many types of cancer, autoimmune diseases like lupus and multiple sclerosis, and anemia, commonly manifest with a lack of energy (too few red blood cells). Another typical indicator of depression and anxiety is fatigue. Additionally, a side effect of several drugs is weariness.

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(fill in the blank) is the use of reliable knowledge for a practical purpose. (fill in the blank) is the study of the natural world through observation and experimentation. reset next

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Technology is the use of reliable knowledge for practical purposes.

Ecology is the study of the natural world through observation and experimentation.

Technology refers to the application of scientific knowledge for practical purposes. This is how science and technology are connected. Scientific knowledge develops through observations about the natural world. Observations can raise scientific questions that can lead to hypotheses.

The hypothesis can be tested by experiment. Experimental results lead to changes in scientific knowledge. Science is any body of knowledge dealing with the physical world and its phenomena that requires unbiased observation and systematic experimentation. To be reliable experimental observations must be reproducible.

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Answer:

Second one is Science

Explanation:

It takes a snail 10 seconds to move 1 centimeter. Clear check how far can the snail move in 2 seconds? centimeters how long will it take the snail to move 2. 5 centimeters? seconds.

Answers

A centimeter will be moved by the snail in 10 seconds as opposed to a centimeter being moved in 2 seconds. Accordingly, the snail advances 1 centimeter every 10 seconds.

Why is travel important to life?

Traveling is important because it will expose you to a different way of being and living. You'll encounter different people, places, and cultures when traveling, which can give you a wider perspective. A lot of learning and personal growth may occur while traveling.

Why do you love to travel?

Nothing is more thrilling than traveling to discover new things and create enduring memories, whether it be by vehicle or by airline. The most fulfilling aspect of traveling is meeting individuals from all around the world. The discussions will increase understanding and might create more significant prospects.

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A chef drop a pumpkin pie of ma 1. 7kg from a height of 1. 875 meter. How long doe it take the pie to hit the ground?

Answers

If a chef drops a pumpkin pie of mass 1.7 kg from a height of 1.875 meter, the time taken by the pie to hit the ground is 0.62 s

According to equations of motion,

s = ut + 1 / 2 at²

s = Distance

u = Initial velocity

t = Time

a = Acceleration

Since it is dropped,

u = 0

g = 9.8 m / s²

s = 1.875 m

s = ut + 1 / 2 at²

1.875 = 0 + ( 1 / 2 * 9.8 * t² )

t² = 1.875 / 4.9

t² = 0.385

t = 0.62 s

Therefore, the time taken is 0.62 s

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Planets a and b are both the same size, but planet b has three times the mass of planet a. How does the weight of an object compare on the two planets?.

Answers

A comparison of an object's weight between the two worlds An object's weight is the same on both planets.

Why do objects of the same mass weigh differently on various planets?

The weight of an object is determined by its mass and how strongly gravity pushes on it. How far apart two objects are from one another determines how strong gravity is. Because of this, the same thing weights differently on several planets.

What connection between the planets' weight and sizes do you notice?

The gravity of planets, moons, and stars is the same. Depending on their size, they have different amounts of gravity. Therefore, gravity is different for larger and smaller planets. A human with more mass has greater gravitational pull, just like the planets.

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a planet orbiting another star is made primarily of hydrogen and helium and has approximately the same mass as jupiter but is the same size as neptune.
a. true
b. false

Answers

When a planet orbiting another star is made primarily of hydrogen and helium and has approximately the same mass as jupiter but is the same size as neptune, it is a false statement.

What is a planet?

A planet is defined as the solar body that revolves round the sun. There are various types of planets which include the following:

Mercury: The radius of this planet is 2,440km which is about 1/3 the size of Earth.

Venus: The radius of this planet is 6,052km only which is slightly smaller than Earth.

Earth: The earth has approximately 6,371km radius.

Mars: The radius of this planet is 3,390km which is about half the size of Earth.

Jupiter: The radius of this planet is 69,911km which is about 11x Earth’s size.

Saturn: The radius of this planet is 58,232km which is about 9x larger than Earth.

Uranus. : The radius of this planet is 25,362km which is about 4x Earth’s size.

Neptune: The radius of this planet is 24,622km which is only slightly smaller than Uranus.

Pluto: Sometimes not regarded as a planet.

The statement about the planet is a false statement because it is contradictory. This is so because, in order to be smaller than Jupiter, a hydrogen-helium planet would have to be more gravitationally compressed, so it would have to have a larger mass than Jupiter, also a planet with that size and mass would be too dense to be made of hydrogen and helium.

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Energy efficiency strategies are based on the assumption that consumers will be willing to pay more in exchange for reduced energy use.

Answers

On the premise that consumers will be prepared to pay more in exchange for using less energy, energy efficiency measures are based.

What do you think of the American Council for an Energy Efficient's strategy?

Energy efficiency policies, programs, technologies, investments, and habits are advanced by ACEEE through research and outreach. In the future, we want energy efficiency to contribute to the US's economic success, energy security, and environmental sustainability.

How is utilizing multiple policy instruments more effective than use just one?

How is utilizing multiple policy instruments more effective than use just one? Wider coverage is possible when many policy instruments are used. Cotton was created by Eli Whitney.

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identify a control commonly used by organizations during the output design phase of the physical systems design stage of developing a new system to avoids expensive time delays later in the SDLC process

Answers

requesting users' signatures on a document confirming their acceptance of the output form and content design

Which task in the physical design phase of the systems development life cycle (SDLC) takes the longest?

Program Development: One of the SDLC's most time-consuming tasks is program development. It is best to use an organized programming process.

The last step in the systems development life cycle is which of the following?

Once the implementation phase is over, the last step begins. The system has a defined support approach in place for the maintenance phase.

Which of the following activities takes place during the software development life cycle's system planning and designing phase?

The system planning and designing phase of the SDLC includes the parallel run, sizing, and specification freeze phases.

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21. The coefficient of friction acting upon a 1500 kg car is 0.75. The car is making a 180-degree turn around a curve with
a radius of 25 meters. Determine the maximum speed with which the car can make this turn.
a. 187.5 m/s
b. 209.44 m/s

c. 13.69 m/s
d. 7.5 m/s

Answers

The maximum speed with which the car can make the turn is 13.69 m/s (Option C)

How do I determine the maximum speed?

We'll begin by obtaining the force. This can be obtained as follow:

Mass (m) = 1500 KgAcceleration due to gravity (g) = 10 m/s²Normal reaction (N) = mg = 1500 × 10 = 15000 NCoefficient of friction (μ) = 0.75Force (F) = ?

F = μN

F = 0.75 × 15000

F = 11250 N

Finally, we shall determine the maximum speed. Details below:

Radius (r) = 25 metersMass of car (m) = 1500 KgForce (F) = 11250 NMaximum speed (v) =?

F = mv²/r

11250 = (1500 × v²) / 25

Cross multiply

1500 × v² = 11250 × 25

Dive both sides by 1500

v² = (11250 × 25) / 1500

Take the square root of both sides

v = √[(11250 × 25) / 1500]

v = 13.69 m/s

Thus, the maximum speed is 13.69 m/s (Option C)

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A mass of 0.30 kg on the end of a spring oscillates with a period of 0.45 s and an amplitude of 0.15 m. Part A Find the velocity when it passes the equilibrium point. Express your answer with the appropriate units. 0 HA ? V= Value Units Submit Request Answer Part B Find the total energy of the system. Express your answer with the appropriate units. HA ?

Answers

The answer is k = 58.486.

Part A. V = 2.094 m/sec

Part B. E = 0.6579 J

Solution:

T = 2√m/k

T² = 4n²m/k

k = 4n²m/T² = 4n² x 0.30/(0.45)²

k = 58.486.

The total energy of a system is the sum of kinetic energy and gravitational potential energy, and this total energy is conserved in one orbital motion. A minimum velocity is required for an object to leave the planet and not return. The total energy operator is called the Hamiltonian operator H and consists of the kinetic energy operator and the potential energy operator. The total energy at any stage of a moving fluid is the sum of the internal static velocity and potential energies at that stage.

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we've seen that squid can escape from predators by ejecting water. some squid do this at the surface of the ocean, thus launching themselves into the air-a particularly effective escape strategy. (figure 1) suppose a 36 kg squid (not including water) at rest at the surface of the water brings in and quickly ejects 3.0 kg of water to achieve a takeoff speed of 3.5 m/s; these are typical numbers.

Answers

The squid eject the water at the speed of 42 m/s.The maximum horizontal range that the squid can achieve before splashing down is 1.25 m.Explain law of conservation of momentum.

The law of conservation of momentum states that when two or more bodies act on each other in an isolated system, their total momentum remains constant unless an external force acts on them. Therefore, it can neither be created nor destroyed.

m₁v₁ = m₂v₂

For the given question:

m₁ = mass of squid (36 kg)

v₁ = velocity of squid (3.5 m/s)

m₂ = mass of water (3.0 kg)

v₂ = velocity of water

Substitute the values:

36 × 3.5 = 3.0 × v₂

v₂ = 42 m/s

The maximum range:

R = (v₂)²/ g

where,

g = 9.8 m/s² and launch angle 45°

R = 3.5²/9.8

R = 1.25 m

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The complete question is as follows:

We've seen that squid can escape from predators by ejecting water. Some squid do this at the surface of the ocean, thus launching themselves into the air-a particularly effective escape strategy. Suppose a 36 kg squid (not including water) at rest at the surface of the water brings in and quickly ejects 3.0 kg of water to achieve a takeoff speed of 3.5 m/s; these are typical numbers.

At what speed does the squid eject the water?

If we ignore lift and drag forces as the squid flies through the air, what is the maximum horizontal range that the squid can achieve before splashing down?

A reasonably uniform magnetic field over a limited region of space can be produced with the Helmholtz coil, which consists of two parallel coils centered on the same axis. The coils are connected so that they carry the same current I. Each coil has N turns and radius R, which is also the distance between the coils.
(a) Find the magnitude of the magnetic field at any point on the z-axis shown in the accompanying figure. (Use any variable or symbol stated above along with the following as necessary: z and µ0. Assume the origin is located halfway between the coils.)
(b) Show that dB/dz and d 2B/dz2 are both zero at z = 0. (These vanishing derivatives demonstrate that the magnetic field varies only slightly near z = 0.)

Answers

According to the formula, 2 moles of Co will magenetic produce 2 mole of CO2 and 1 mole of O2 prednisone will produce 2 moles of CO2. This is 602 for 1 mole. 0.5 mol of O2 is consumed. 0.344/2 = 0.172 mol

mol O2 is required, so O2 has a limiting reagent, so O2 mol has 0.172 mol, 0.344, therefore Co

: mol CO₂ production= 0.196 Particles

grams CO₂ production = 0.196 • Hook x 44.01 g CO₂ = 8.6259 g.Co₂

grams CO₂ 2.63 g = 863

5.50G 5.50G

MOL VON LA H 5,50 x I Mol 5,998 15.444

444 444

444

444

444

444

44

२८०२

mol CO = massmolar mass 5,50 g xX I mol

28-018 444 4 =4 mol 4

mols of la H 5.50 x × I mols

5.998 15.

0.344 mol. It represents the absolute or relative direction or magnitude that an object is moving in the sense of motion. Used to describe the size or extent of something. In physics, size generally refers to entities.

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A force of 32N is applied to object of mass MKY which is at rest on a smooth horizontal surface if the product if 8M/S^2. find the value of M​

Answers

Answer:

m=4kg

Explanation:

F=32, m=?, a=8ms^-2

F=ma

32=8m

32/8=m

m=4kg

What three factors determine the amount of voltage induced into a conductor?
1.The turns of wire.
2.The strength of the magnetic field.
3.The speed of the cutting action.

Answers

Three factors that determine the amount of voltage induced into a conductor are : size of the magnetic field, active length of the conductor and speed at which the conductor passes through the field.

What are the factors that determine amount of voltage induced in a conductor?

Faraday's Law explains that inducing a voltage in conductor can be done by either passing it through a magnetic field or by moving the magnetic field past the conductor and if the conductor is part of a closed circuit, an electric current will flow.

Coils of wire are used to increase the induced voltage and current because the EMF generated is proportional to the time rate of change of magnetic flux as per Faraday's Law.

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why do we say that force is a vector quantity

Answers

Force is a vector quantity because its acceleration times a scalar constant (mass) equals the force (a vector quantity).

Why is force considered a vector quantity?

The product of an object's mass and acceleration is used to calculate the force acting on it. A vector quantity is acceleration. Since force is a scalar constant (mass) multiplied by acceleration, which is a vector quantity, force is also a vector quantity (a vector quantity).

Because it genuinely depends on the direction in which a force is applied, force can be thought of as a vector quantity. Physically, the force can be felt as a push or a pull. This is illustrated by many physical examples.

For instance, it makes sense that we must push an object upward in order to make it move upward. It simply remains fixed if we push it downward. Knowing which direction it is pushed is crucial.

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At what radial distance from the center of a toroid of 300 windings does the magnitude of the magnetic field equal that found inside a solenoid that has 400 turns per meter of length? Assume that the current is the same through both devices.The magnitude of the magnetic field inside a toroid of total Ntturns and carrying a current I is, Bt=μ0NtI2πs, where s is the distance of the field point from the center of the toroid. The magnitude of the magnetic field inside a solenoid of Ns turns per unit length and carrying a current I is Bs=μ0NI. So if for a value of s, the magnetic field inside a toroid and a solenoid are the same, then the value of s can be found by using the equation, μ0NtI2πs=μ0NsI.

Answers

The radial distance from the center of the toroid is 12 cm such that the magnitude of magnetic field through the toroid is equal to that found inside the solenoid.

It is given to us that -

The toroid has 300 windings

The solenoid has 400 turns per meter of length

We have to find out the radial distance from the center of the toroid if the magnitude of the magnetic field is equal to that found inside the solenoid.

We know that the magnitude of the magnetic field inside a toroid is given by -

[tex]B_{t} =[/tex] (μ₀[tex]N_{t}[/tex]I)/(2[tex]\pi[/tex]s) ------ (1)

where,

s = radial distance from the center of the toroid

I = current flowing through the toroid wire

[tex]N_{t}[/tex] = total turns in the toroid

We also know that the magnitude of magnetic field inside a solenoid is given by -

[tex]B_{s} =[/tex] μ₀[tex]N_{s}[/tex]I ----- (2)

where,

[tex]N_{s}[/tex] = turns per unit length of the solenoid

I = current flowing through the solenoid

Now, it is given to us that the magnitude of magnetic field at a radial distance of s inside the toroid is equal to the magnitude of magnetic field inside the solenoid.

=> [tex]B_{t} =[/tex] [tex]B_{s}[/tex]

=>  (μ₀[tex]N_{t}[/tex]I)/(2[tex]\pi[/tex]s) = μ₀[tex]N_{s}[/tex]I

Since it is given that the current is same through both toroid and solenoid, the above equation can be written as -

=> [tex]\frac{N_{t}}{2\pi s} =N_{s}[/tex]

[tex]= > \frac{300}{2\pi s} =400\\= > 800\pi s=300\\= > s = \frac{300}{800\pi } \\= > s = 0.11 m\\= > s = 12 cm[/tex]

Thus the radial distance from the center of the toroid is 12 cm such that the magnitude of magnetic field through the toroid is equal to that found inside the solenoid.

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