you walk 9.6km in 4.5h , what the average speed​

Answers

Answer 1
the answer would come to: 2.13 km/h

Related Questions

A 3.09 x 10-4 T magnetic field points directly east. A loop of area 0.0471 m2 faces directly northeast. What is the magnetic flux through the loop?

Answers

Answer:

1.03 * 10^-5

Explanation:

The magnetic flux through the loop is approximately 1.317 × \(10^{(-5)\)T·m².

To calculate the magnetic flux through a loop, we use the formula:

Φ = B × A × cos(θ)

Where:

Φ is the magnetic flux

B is the magnetic field strength

A is the area of the loop

θ is the angle between the magnetic field and the normal to the loop

Given:

Magnetic field strength (B) = 3.09 × \(10^{(-4)\) T (east direction)

Area of the loop (A) = 0.0471 m²

The loop faces directly northeast

To find the angle θ,  determine the angle between the magnetic field direction (east) and the normal to the loop (northeast).

Since the loop faces northeast, the angle between the normal to the loop and the east direction is 45 degrees (90 degrees divided by 2).

Now calculate the magnetic flux:

Φ = B  × A  × cos(θ)

Φ = (3.09 × \(10^{(-4)\) T) × (0.0471 m²) × cos(45°)

Using the value of cos(45°) as 0.7071:

Φ = (3.09 × \(10^{(-4)\) T) × (0.0471 m²) ×0.7071

Φ = 1.317 × \(10^{(-5)\) T·m²

Therefore, the magnetic flux through the loop is approximately 1.317 × \(10^{(-5)\) T·m².

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HELP!!!!!!! if you were to ride a bicycle on a rocky pathway, how much friction would there be and what would be the thermal and friction energy level?

Answers

Answer: The equation for calculating friction is fr=FR/N

Explanation:

Fr (retentive force : friction) divided by N (normal/perpendicular force) equals fr (friction)

which material appears continuous to the unaided eye rather than discrete?

Answers

When we say that something appears continuous to the unaided eye, it means that we can't see any distinct boundaries or breaks between different parts of that material. In other words, it looks like one smooth and uninterrupted surface. This is in contrast to a material that appears discrete, where we can clearly see separate components or units.

One example of a material that appears continuous to the unaided eye is water. When we look at a body of water like a lake or a river, we don't see any apparent separations between different molecules or particles. Instead, the water seems to flow seamlessly from one point to another. This is partly because water molecules are tiny and closely packed together, but also because of how light interacts with the surface of the water. Other materials that might appear continuous to the unaided eye include glass, certain types of plastic, and some metals. However, it's worth noting that this perception can vary depending on factors like lighting conditions, surface texture, and individual differences in visual perception. In some cases, what appears continuous to one person may appear more discrete or textured to another. In summary, a material that appears continuous to the unaided eye is one that lacks any apparent breaks or separations between different parts. Water is one example of such a material, but there are others depending on various factors.

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What is the mass of the object being measured?
A triple beam balance is shown. The first slider is at the 70 gram mark. The second slider is at the 300 gram mark. The third slider is at the 5 gram mark.

Answers

Answer:

m = 375 [gram]

Explanation:

A triple Beam balance is an instrument very easy to use, since we only have to perform the arithmetic sum of each of the weights that are recorded in each beam

m = 300 + 70 + 5 = 375 [gram]

For a better understanding, the following image is attached, with values on each beam, which should be read.

The largest mass is in the indicator of 100 [gram], the second mass is in the indicator of 20 [gram] and the third is in the indicator of 5.8 [gram]. Thus the arithmetic sum corresponds to:

M= 100 + 20 + 5.8 = 125.8 [gram]

Note: it is important that when the instrument is in balance, the opposite end of the beam should indicate a position of zeros.

What is the mass of the object being measured?A triple beam balance is shown. The first slider is at

Thanks + BRAINLIST

Please need correct answer asappp

Thanks + BRAINLIST Please need correct answer asappp

Answers

Answer:

Standing waves can be thought of as a sin wave and a cos wave overlapping each other. They go in different direction hence C is correct Wave interference can be thought of as the opposite of destructive ---> constructive anda hencd meet and interact on the same medium such that answer B is correct

a fragment of bone is discovered during an archaeological dig. the bone contains carbon-14 isotopes of the element carbon. the bone is approximately 23000 years old. calculate what proportion of the carbon-14 isotopes remains. give your answer to the nearest whole fraction. the half life of carbon-14 is 5730 years.

Answers

When a fragment of bone containing carbon-14 isotopes of the element carbon is discovered during an archaeological dig, and it is estimated to be approximately 23,000 years old, one can calculate the proportion of the carbon-14 isotopes that remains.

The half-life of carbon-14 is 5,730 years. Carbon-14 has a half-life of 5,730 years, which implies that half of the carbon-14 atoms will decay every 5,730 years. This property of carbon-14 may be used to determine the age of ancient artefacts and fossils. By determining the proportion of carbon-14 remaining in a sample, we may determine how old it is.According to the problem, the bone is around 23,000 years old. We can utilize the following formula to calculate the proportion of carbon-14 isotopes that remain: Proportion remaining = (1/2)^(number of half-lives)We can first calculate the number of half-lives that have occurred since the bone was alive. The number of half-lives is calculated as follows:Number of half-lives = (time elapsed) / (half-life)Number of half-lives = 23,000 / 5,730Number of half-lives = 4.016So the number of half-lives that have occurred since the bone was alive is 4.016. We can now use this number to calculate the proportion of carbon-14 isotopes that remains:Proportion remaining = (1/2)^(4.016)Proportion remaining = 0.105Therefore, the proportion of carbon-14 isotopes that remains is 0.105, or approximately 1/10 (to the nearest whole fraction).

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An alcohol-related motor vehicle crash in the U.S. kills one person every 3.5 hours. TRUE FALSE​

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An alcohol-related motor vehicle crash in the U.S. kills one person every 3.5 hours. This statement is FALSE.

An alcohol-related motor vehicle crash in the U.S. does not necessarily kill one person every 3.5 hours. The frequency and impact of alcohol-related motor vehicle crashes can vary, and the number of fatalities can change over time and across different regions. It is important to consider up-to-date statistical data and specific circumstances to accurately assess the frequency of alcohol-related motor vehicle crash fatalities.

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An electron moving at 4.10 ✕ 103 m/s in a 1.45 T magnetic field experiences a magnetic force of 1.40 ✕ 10−16 N. What angle does the velocity of the electron make with the magnetic field? There are two answers between 0° and 180°. ° (smaller value) ° (larger value)

Answers

ANSWER

\(8.46\degree;\text{ }171.54\operatorname{\degree}\)

EXPLANATION

Parameters given:

Speed of electron, v = 4.10 * 10^3 m/s

Magnetic field, B = 1.45 T

Magnetic force, F = 1.40 * 10^(-16) N

To find the angle that the velocity of the electron makes with the magnetic field, apply the formula for magnetic force:

\(F=qvB\sin\theta\)

where θ = angle

q = electric charge = 1.6 * 10^(-19) C

Make θ the subject of the formula:

\(\begin{gathered} \sin\theta=\frac{F}{qvB} \\ \\ \theta=\sin^{-1}(\frac{F}{qvB}) \end{gathered}\)

Therefore, the angle that the velocity makes is:

\(\begin{gathered} \theta=\sin^{-1}(\frac{1.4*10^{-16}}{1.6*10^{-19}*4.1*10^3*1.45}) \\ \\ \theta=\sin^{-1}(0.1472) \\ \\ \theta=8.46\degree \end{gathered}\)

To find the second angle, subtract the angle from 180 degrees:

\(\begin{gathered} 180-8.46 \\ \\ 171.54\degree \end{gathered}\)

The angles are:

\(8.46\operatorname{\degree};\text{ }171.54\operatorname{\degree}\)

what happens to the depth and width of the pit as the golf balls fall into the center near the bowling ball? (imagine putting lots of golf balls in.)

Answers

As the golf balls fall into the center near the bowling ball, the depth of the pit increases while the width remains constant.

As more golf balls fall into the center near the bowling ball, the depth of the pit increases, and the width of the pit decreases. The weight of the golf balls creates a depression in the elastic fabric, and as more balls are added, they push against the fabric, causing it to stretch downward and the pit to become deeper. At the same time, the fabric is pulled inward by the weight of the golf balls, causing the width of the pit to decrease. Overall, the shape of the pit becomes more pronounced, with a deeper center and steeper sides.

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Identify the materials that are made from nonmetallic resources. Choose one or more: A. granite countertops B. electrical wire C. nuts and bolts D. concrete E. drywall

Answers

Answer:

D. Concrete & E. Drywall

Explanation:

With a light shone upon the materials, Concrete and Drywall neither have a metallic sheen.

The materials that are made from non-metallic resources are granite countertops, concrete, and drywall. Hence, the correct options are A, D, and E.

Non-metallic materials are materials that lack magnetic properties like good electrical conductivity and thermal conductivity. They lack the properties like luster, rigor, and malleability. These materials are essential for many industries and are used for industrial purposes.

Non-metallic minerals do not have any metal substance in them. There is no new product is formed by the process of melting of non-magnetic materials. They do not have any shine or luster and they can break down easily. Eg: sand, gravel, etc.

From the given,

The materials that are made from non-metallic resources are Granite countertops, concrete, and drywall.

Hence, the ideal solutions are options A, D, and E.

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what has more momentum a large truck stopped at a stop sign or a motorcycle moving down the road.

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I'm pretty sure it's"a motorcycle moving down the road."The truck isn't moving so the truck cannot have momentum.Momentum is basically "mass in motion."Please let me know if I am wrong.

a domestic hot water tank contains 200 kg of warer at 20°C. how much energy must be supplied to heat this water to 70°C (specific heat capacity of water =4200J/kg°C

Answers

Answer: 4.2 × 10⁷

Explanation:

E = mcΔT

E = (200 kg)(4200 J/kg°C)(20 - 70°C)

E = 42000000 J

Calculate the force generated by a car that hits the wall at an
acceleration of 4 m/s^2 and has a mass of 45 kg? (INCLUDE UNITS)

Answers

This is a defective question. It was WRITTEN by someone who is unclear on the concepts.  DON'T try and answer it.

It's trying to get us to use Newton's second law ... F = m • a.

But that only tells us how much force must act ON THE CAR in order to accelerate it. (45 kg) • (4 m/s^2) = 180 newtons.

This is NOT the force exerted BY the car when it hits something. THAT force depends on its speed WHEN it hits, AND how long it takes for the wreckage to actually come to rest, AND how hard or soft the wall is.

DON'T try to answer this question. Your answer will be wrong, you won't understand why, and the teacher you try to argue with probably won't either.

============================================

More explanation:

Think about jumping off of a ladder in your back yard.  Several times.

Your mass is the same every time.  Your acceleration is the same every time . . . 9.8 m/s² down, the acceleration of Earth gravity, every time.

BUT ...

-- I'll bet you would rather land on wood than on concrete. The force of landing would be less.

-- I'll bet you would rather land on dirt than on wood. The force of landing would be less.

-- I'll bet you would rather land on grass than on dirt. The force of landing would be less.

-- I'll bet you would rather land on a pile of blankets than on dirt. The force of landing would be less.

-- I'll bet you would rather land on a trampoline than on a pile of blankets. The force of landing would be less.

-- I'll bet you would rather jump from a short ladder than from a tall one.  Your speed would be less when you landed, and the force of landing would be less.

==> Your mass is the SAME every time, and your acceleration is the SAME every time.  But the force when you hit is DIFFERENT every time.

The mass and acceleration of the car DON'T tell us the force of the hit when the car hits a wall.  

Which of the following is a way that trees have been negatively impacted by human use? a. Deforestation b. Pollution c. Reduction d. All of the above Please select the best answer from the choices provided A B C D.

Answers

Answer:

D

Explanation:

Trees are obviously effected from deforestation.

Pollution effects the things trees need to grow (water, air).

Reduction removes parts of the tree, some parts being needed.

Answer: D

Explanation:Trees are obviously effected from deforestation.

Pollution effects the things trees need to grow (water, air).

Reduction removes parts of the tree, some parts being needed.

Chet plans an experimental investigation to see how well a new fertilizer works on daisies. The fertilizer must be dissolved in water and delivered to the plants by spraying it onto the leaves and stems.


To set up his control group for the experiment, Chet should leave out what

Answers

Answer:

The answer is D or Fertilizer, sorry for the late answer

Explanation:

Answer:

D Fertilizer hope this helps ..

Explanation:

Is the substance an atom or a molecule?

Answers

Answer:

A pair of oxygen atoms is a molecule of oxygen. A molecule is the smallest particle of a substance that exists independently. Molecules of most elements are made up of only one of atom of that element. Oxygen, along with nitrogen, hydrogen, and chlorine are made up of two atoms.

Explanation:

Transcribed image text: y Part A Consider a hydrogen atom in the ground state. Determine the circumference of the electron orbit. Express your answer in meters to three significant figures. 10 AED DAME ? C- m Submit Request Answer Part 8 Determine the speed of the electron Express your answer in meters per second to three significant figures. Vo AEC ? m/s Submit Request Answer Consider a hydrogen atom in the ground state. Part C Determine the total energy of the electron Express your answer in electronvolts to three significant figures. ? SU V AED eV E: - Submit Request Answer Part D Determine the minimum energy required to remove the electron completely from Express your answer in electronvolts to three significant figures. 10 AED ? E- eV Submit Request Answer

Answers

Part A: Circumference of electron orbit in ground state: Approximately 6.63 × \(10^(-10)\) meters.

Part B: Speed of electron in hydrogen atom: Approximately 2.19 × \(10^6\)meters per second.

Part C: Total energy of electron in ground state: Approximately -13.6 electronvolts.

Part D: Minimum energy to remove electron from hydrogen atom: Approximately 10 electronvolts.

How to determine electron orbit circumference?

Part A: The circumference of the electron orbit in a hydrogen atom can be calculated using the formula for the circumference of a circle, which is given by 2πr, where r is the radius of the orbit. In the ground state of a hydrogen atom, the radius of the orbit is equal to the Bohr radius, which is approximately 5.29 × \(10^-11\)meters. Therefore, the circumference of the electron orbit is 2π(5.29 × \(10^-11\)) meters.

How to determine electron speed?

Part B: The speed of the electron in the hydrogen atom can be calculated using the formula for the orbital speed, which is given by v = (kQ\(e^2\))/(mr), where k is the Coulomb constant, Qe is the elementary charge, m is the mass of the electron, and r is the radius of the orbit. Plugging in the values, the speed of the electron is approximately 2.19 × \(10^6\) meters per second.

How to determine total energy?

Part C: The total energy of the electron in the ground state of a hydrogen atom can be calculated using the formula for the energy of an electron in an orbit, which is given by E = -13.6 eV/\(n^2\), where n is the principal quantum number. In the ground state, n = 1, so the total energy of the electron is -13.6 eV.

How to determine minimum energy to remove electron?

Part D: The minimum energy required to completely remove the electron from a hydrogen atom is equal to the ionization energy. In the ground state, the ionization energy of a hydrogen atom is 13.6 eV.

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in two-slit diffraction, the bright fringes are located at angles given by the equation sinθm=mλ/d . what is m in this equation?a- Massb- Integerc- Index of refractiond- Meters

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in two-slit diffraction, the bright fringes are located at angles given by the equation sinθm=mλ/d . what is m in this equation ,In the equation sinθm = mλ/d, m represents an integer.

In two-slit diffraction, light passing through two narrow slits creates a pattern of bright and dark fringes on a screen placed behind the slits. The equation given, sinθm = mλ/d, relates the position of the bright fringes (represented by the integer m) to the wavelength of the light (λ), the distance between the slits (d), and the angle at which the bright fringe is observed (θm).

The integer m represents the order of the bright fringe, with m=0 corresponding to the central bright fringe and m=1,2,3,... corresponding to the first, second, third, etc. order bright fringes on either side of the central fringe. Each order of bright fringe corresponds to a different angle of diffraction, given by the equation sinθm = mλ/d. The integer m can be positive or negative, depending on whether the bright fringe is to the right or left of the central fringe.

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Identify the factors that cause melting and thus the formation of magma.

a. Continental rift

b. Continental shelf

c. Transformm fault

d. Hot spot volcano

e. Mid ocean ridge

f. Subduction zone

Answers

Melting and the formation of magma can be caused by several factors related to plate tectonics:

a. Continental rifts: These occur when tectonic plates pull apart, allowing mantle material to rise and partially melt as it decompresses. This can result in the formation of basaltic magma. b. Continental shelves: The weight of a continental shelf can cause the underlying mantle to partially melt and form magma. c. Transform faults: These are areas where two plates slide past each other, which can cause frictional heating and the partial melting of rock. d. Hot spot volcanoes: These are areas of intense volcanic activity that are not associated with plate boundaries. They occur as a result of a mantle plume rising from deep within the Earth. e. Mid-ocean ridges: These are areas where new oceanic crust is formed as magma rises from the mantle and solidifies. This occurs as a result of decompression melting. f. Subduction zones: These occur where one tectonic plate is forced beneath another, causing it to partially melt as it descends into the mantle. This can result in the formation of andesitic and rhyolitic magma. In summary, melting and the formation of magma can occur due to a variety of plate tectonic processes, including rifts, hot spots, mid-ocean ridges, and subduction zones.

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1. Una bola de 0.510 kg de masa se mueve al este (dirección +x) con una rapidez de 4.80 m/s y choca frontalmente con una bola de 0.220 kg en reposo. Si la colisión es perfectamente elástica, ¿cuál será la rapidez y dirección de cada bola después de la colisión?

Answers

Responder:

3,37 m / s, + ve x - dirección

Explicación:

Utilizando la ley de conservación de la cantidad de movimiento expresada por la fórmula;

m1u1 + m2u2 = (m1 + m2) v

m1 y m2 son las masas de los objetos

u1 y u2 son sus velocidades iniciales

v es su velocidad común

Dado

m1 = 0,519 kg

u1 = 4,80 m / s

m2 = 0,220 kg

u2 = 0 m / s (cuerpo en reposo)

Necesario

Velocidad común v

Sustituir en la fórmula los valores dados;

0,519 (4,8) + 0,22 (0) = (0,519 + 0,220) v

2,4912 + 0 = 0,739 v

2,4912 = 0,739v

Dividir ambos lados por 0,739

2,4912 / 0,739 = 0,739 / 0,739

v = 3,37 m / s

Por lo tanto, la rapidez de ambas bolas después de la colisión es de 3.37 m.s hacia la dirección x positiva, ya que m1> m2 y la velocidad común es positiva.

The melting of methane hydrates on the seafloor can lead to a sharp rise in global temperatures because methane is a powerful greenhouse gas (true or false)

Answers

The melting of methane hydrates on the seafloor can lead to a sharp rise in global temperatures because methane is a powerful greenhouse gas. The statement is true.

Methane is a powerful greenhouse gas, with a global warming potential that is estimated to be about 25 times greater than that of carbon dioxide over a 100-year time horizon. Methane hydrates are solid, crystalline compounds that contain a large amount of methane gas trapped within water molecules. These hydrates are stable under certain temperature and pressure conditions, but if they become destabilized, they can release large amounts of methane into the atmosphere.

The melting of methane hydrates on the seafloor is a concern because it has the potential to release vast amounts of methane into the atmosphere, which could significantly contribute to global warming and climate change. This process could be triggered by rising ocean temperatures, changes in ocean currents, or other factors that alter the stability of the hydrates. While the exact extent and impact of this phenomenon are still uncertain, it is an area of active research and concern among climate scientists.

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Scientists have changed the model of the atom as they
What experimental evidence led to the development of
have gathered new evidence. One of the atomic models
this atomic model from
the one before it?
iS shown below.
O A few of the positive particles aimed at a gold foil
seemed to bounce back.
The colors of light emitted from heated atoms had
very specific energies.
Experiments with water
vapor showed that elements
combine in specific proportions.
Cathode rays were bent in the same way whenever a
magnet was brought near them.

Answers

The experimental evidence led to the development of have gathered new evidence. One of the atomic models this atomic model from the one before it is the colors of light emitted from heated atoms had very specific energies.

As scientific knowledge about the structure of the atom has changed, so have models of the atom.

The Rutherford planetary model, which depicts electrons travelling around the nucleus like planets move around the sun in the solar system, is the direct precursor of the model illustrated in the figure attached.

This model was created as a result of the study of light hues released by heated atoms with highly particular energies.

The Bohr model of the atom is so named because Niels Bohr had a major role in developing it. The passage of electrons between energy levels caused the light hues released by heated atoms. Electrons are grouped in shells or energy levels.

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Using the correct IUPAC nomenclature, what is the correct name, formula,
and classification of a compound that contains two nitrogen atoms and one
oxygen atom?
O A. Mononitrogen dioxide, N20, covalent compound.
B. Nitrogen dioxide, NO2, ionic compound.
O C. Dinitrogen monoxide, N20, covalent compound.
D. Nitrogen oxide, No, ionic compound.

Answers

Answer: C is right

Explanation:

N and O are no-metals and forms covalent bonds.

Usually they need a. Prefix whic tells number of atoms in compound

What factor affects the speed of the motion of a roller coaster the most?A.massB.heightC,Size of the wheels D.Spring constant

Answers

Answer:

Height

Option B is correct

Explanation:

The roller coaster is a railway with a large height and steep inclines that is basically found in the amusement park for carrying a train of people for a fun ride.

The speed of the roller coaster is determined by a number of factors such as the energy input, drag force, temperature, mass, etc.

The height at which the roller coaster is released when launched determines greatly the speed of the motion of the roller coaster

A sample of hydrogen (H2) gas was collected over water at 60°C. If the total volume of gas collected was 55.6 mL and the atmospheric pressure was 1.1 bar, what mass (in g) of hydrogen gas was collected above the water? The vapour pressure of water at 60°C is 150 torr.

Answers

First, calculate the partial pressure of H2 by considering the total pressure:

\(P_{\text{tot}}=P_{H2}+P_{H20}\)

where,

Ptot = 1.1bar

PH20 = 150Torr

Convert the previous values to atm:

Ptot = 1.1 bar = 1.085 atm

PH20 = 150 Torr = 0.197 atm

Then, for PH2 you obtain:

\(P_{H2}=P_{\text{tot}}-P_{H20}=1.085\text{atm-}0.197\text{atm}=0.888atm\)

Next, use the following equation for ideal gases:

\(PV=\text{nRT}\)

where,

V: volume = 55.65mL = 0.05565 L

R: gas constant = 0.082 atm*L/mol*K

T: temperature = 60 + 273 = 333K

P: partial pressure of H2 = 0.888atm

Solve the equation for n and replace the values of the other parameters:

\(n=\frac{PV}{RT}=\frac{(0.888atm)(0.05565L)}{(0.082atm\cdot\frac{L}{\text{mol}\cdot K})(333K)}=0.00181mol\)

Next, use the atomic weight to determine the mass of H2:

\(M=(\frac{2.0141g}{\text{mol}})(0.00181mol)=0.0036g\)

Hence, there are 0.0036 g of H2 collected above the water

Which is the temperature that Fahrenheit and Celsius thermometers would
read as the same number?
A. -40° c
B. -273° c
c. 100°C
D. 0° C

Answers

Answer:

–40o

Explanation:

Which is the temperature that Fahrenheit and Celsius thermometers wouldread as the same number?A. -40

Si tomamos como referencia el recipiente uno y se aplican 5 gramos de tinta y el agua se moviera a una velocidad de 10m/s cual seria la energia cinetica de la solucion

Answers

Answer:

Kinetic energy = 0.25 J

Explanation:

The question is "If we take container one as a reference and apply 5 grams of ink and the water moves at a speed of 10m / s, what would the kinetic energy of the solution be?"

We have,

Mass of ink, m = 5 grams = 0.005 kg

Speed of water, v = 10 m/s

We need to find the kinetic energy of the solution of water and ink. Kinetic energy is associated with the motion of an object. Its formula is given by :

\(K=\dfrac{1}{2}mv^2\\\\K=\dfrac{1}{2}\times 0.005\times (10)^2\\\\K=0.25\ J\)

So, the kinetic energy of the solution is 0.25 Joules.

A typical jar that has been tightened to a reasonable degree requires 2.0 N⋅m to open. If you grab a 8.2-cm-diameter jar lid with one hand so that your thumb and fingers exert equal magnitude forces on opposite sides of the lid, what is the magnitude of each of the forces?

Answers

Answer: 24.39 N

Explanation:

Given

Torque required to open the lid is \(\tau =2\ N.m\)

diameter of lid \(d=8.2\ cm\)

Force exerted by fingers and thumb forms a couple. So, torque can be written as

\(\Rightarrow \tau= F\times 2r\\\Rightarrow 2=F\times 8.2\times 10^{-2}\\\\\Rightarrow F=\dfrac{200}{8.2}\\\\\Rightarrow F=24.39\ N\)

Thus, the magnitue of each force is 24.39 N

3. a). Using Newton's second law of motion, set up a model or ODE for the velocity as a function of time, v(t), for a falling body that is acted on by the force of gravity and air resistance. Determine the expression for v(t) assuming the air resistance is proportional to the square of the velocity, the ratio of the proportionality constant and the mass of the body is unity, and an initial velocity of 12 m/s when dropped. What would be the limiting velocity? b). The temperature of the cake from your oven was 300 ∘ F. Five minutes later, it was 200 ∘ F. Although you are hungry and cannot wait, you do not want to end up in the hospital with mouth burns. How long will it take the cake to cool off to a manageable warm temperature of 75 ∘ F for you to enjoy it if the room temperature is 70 ∘ F ?

Answers

a) The model for the velocity of a falling body with air resistance can be described using Newton's second law of motion. The equation can be written as:

m * dv/dt = mg - k * v^2

where m is the mass of the body, g is the acceleration due to gravity, k is the proportionality constant for air resistance, and v is the velocity of the body.

Assuming the ratio of k to m is unity, we can rewrite the equation as:

dv/dt = g - v^2

To solve this first-order ordinary differential equation, we can separate variables and integrate:

∫ 1/(g - v^2) dv = ∫ dt

After integration, we obtain:

atan(v/sqrt(g)) = t + C

Solving for v, we have:

v(t) = sqrt(g) * tan(t + C)

Given an initial velocity of 12 m/s, we can determine the value of C. Plugging in the values, we have:

12 = sqrt(g) * tan(C)

Now, we can solve for C using the given information.

b) To determine how long it will take for the cake to cool off to 75 °F, we can use Newton's law of cooling, which states that the rate of temperature change of an object is proportional to the difference between its temperature and the surrounding temperature. The equation can be written as:

dT/dt = -k(T - T_room)

where dT/dt is the rate of temperature change, T is the temperature of the cake, T_room is the room temperature, and k is the proportionality constant.

Separating variables and integrating, we get:

∫ 1/(T - T_room) dT = -k ∫ dt

After integration, we have:

ln|T - T_room| = -kt + C

Solving for T, we obtain:

T(t) = T_room + Ce^(-kt)

Given that the initial temperature is 300 °F and the desired temperature is 75 °F, we can determine the value of C. Plugging in the values, we have:

300 = 75 + Ce^0

Solving for C, we find:

C = 225

Now, we can determine the time it takes for the cake to cool to 75 °F by solving for t when T = 75 and plugging in the values.

Please note that the specific values of the proportionality constants and units are not provided in the question, so the final numerical results will depend on those values.

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The electron drift speed in a copper wire of diameter 1.8 mm is 3.6×10−4ms−1 The number of free electrons per unit volume for copper is 8.5×1028m−3 Estimate the current in the wire.

Answers

The current in the wire is 0.00274 A.

Given, the electron drift speed in a copper wire of diameter 1.8 mm is 3.6 × 10⁻⁴ms⁻¹

The number of free electrons per unit volume for copper is 8.5 × 10²⁸m⁻³

To estimate the current in the wire we use the relation, `I = nAvq`.

Where,I is the currentn is the number of free electrons per unit volumeV is the volume of the conductorq is the charge on a single electrona is the cross-sectional area of the conductor.

The volume of the conductor is given byV = πr²LWhere,r is the radius of the wire andL is the length of the wire.

The cross-sectional area of the conductor is given bya = πr².

Substituting the values, we getV = π(0.9 × 10⁻³m)²(1m)

                                 V = 2.54 × 10⁻⁶m³a = π(0.9 × 10⁻³m)²

                                    a = 2.54 × 10⁻⁶m²q = 1.6 × 10⁻¹⁹C

Using the above formula, I = nAvq

                                    I= 8.5 × 10²⁸m⁻³ × (2.54 × 10⁻⁶m³) × (3.6 × 10⁻⁴ms⁻¹) × (1.6 × 10⁻¹⁹C)

                                      I = 0.00274 A

Therefore, the current in the wire is 0.00274 A.

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