degeneracy pressure results from the uncertainty principle. general relativity. special relativity. the exclusion principle.

Raw iron will rust more quickly in salt water when we add it to the first two test tubes, which will be filled with fresh and salt water, respectively.

The iron in the third and fourth test tubes will rust more quickly if oxygen or water are removed from them, respectively. Iron is susceptible to rusting, a form of corrosion. When iron is exposed to oxygen and water, rusting happens because hydrated iron(III) oxide is created. This means that any action we take to keep iron away from oxygen or water will delay the rusting process. When iron is exposed to salts or a low pH, the rusting process is also sped up. There is no water in a tube with simply air, but the nail is exposed to the air. Since air contains some water vapour, water will eventually find its way inside the tube. In tap water, there is always a little amount of dissolved oxygen gas. This indicates that the tube already contains water and oxygen.

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Jupiter: largest planet Saturn: has the most conspicuous rings Uranus: has the most highly inclined rotation axis Neptune: has the medium-sized moon Triton in orbit

Jupiter is the largest planet in the Solar System, with a diameter of over 140,000 kilometers and a mass about 318 times that of Earth. It is the fifth planet from the Sun and is known for its strong magnetic field and large number of moons, including the four Galilean moons - Io, Europa, Ganymede, and Callisto - which were discovered by Galileo Galilei in the 17th century.

Saturn is the second-largest planet in the Solar System and is known for its beautiful and prominent ring system, which is composed of ice, rock, and dust particles. The rings are tilted relative to the planet's equator, and the width of the rings varies from about 10 meters to over 20,000 kilometers.

Uranus is the seventh planet from the Sun and is notable for its unusual orientation, with its axis of rotation tilted at an angle of about 98 degrees relative to its orbit around the Sun. This means that Uranus experiences extreme seasons, with each hemisphere experiencing about 42 years of daylight and darkness.

Neptune is the eighth and outermost planet in the Solar System and is known for its bright blue appearance and strong winds. It has a medium-sized moon called Triton, which orbits the planet in a retrograde direction (opposite to the planet's rotation). Triton is thought to be a Kuiper Belt object that was captured by Neptune's gravity and is the only large moon in the Solar System that orbits in this direction.

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In a black hole, the pull of gravity is so great that not even the most powerful electromagnetic waves can make their way out. According to general relativity, a black hole can arise if a massive object is so compact that it warps spacetime.

The event horizon is the threshold beyond which it is impossible to travel. According to general relativity, there are no locally observable features despite the fact that crossing them might drastically change the course of an object's life. A black hole is very similar to a perfect black body in that it does not reflect any light.

What's more, the same spectrum as a black body with a temperature inversely proportional to its mass is predicted by quantum field theory in curved spacetime for the radiation that event horizons generate. Stellar black holes have temperatures on the order of billionths of a Kelvin, making direct observations nearly impossible.

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The specific gravity of the other fluid in the bottle with a mass of 53.22 g is determined to be 0.8879.

The ratio of a material's density to a predetermined reference substance is the substance's specific gravity. If anything has a specific gravity, it will either float or sink. When tested against water, the specific gravity of a solid or liquid is compared; if it is less than one, it will float, and if it is greater than one, it will sink. Then, the specific gravity of a material is given by, [tex]RD = \frac{\rho_{\text{substance}}}{\rho_{\text{reference}}}[/tex].

The mass of water in the bottle is 95.94 g -  36.00 g = 59.94 g. And the mass of another fluid in the bottle is 89.22 g - 36.00 g = 53.22 g. Then,

[tex]\begin{aligned}\text{specific gravity of other fluid}&=\frac{\rho_{\text{fluid}}}{\rho_{\text{water}}}\\&=\frac{\frac{m_f}{V}}{\frac{m_w}{V}}\\&=\frac{m_f}{m_w}\\&=\frac{53.22}{59.94}\\&=0.8879\end{aligned}[/tex]

The answer is 0.8879.

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The top page will receive the current in the loop, and the bottom page will receive it out of the loop.

(a) Because B is constant and there is a constant magnetic Feld, we may recast the change in flux as shown above. Since A is positive, the loop will have a negative emf, which corresponds to an induced magnetic moment on the page that points to the left. The loop's current will flow into and out of the page in opposite directions. V=-Δφ/ Δt = -B·ΔA/ Δt

(b) Individual electrons in the wire loop can be imagined travelling radially outward as the loop's radius grows. We'll take into account one at the top of the loop (which is moving up the page). The Lorentz force Law is F=q(v)=qvB(yx)=-qvB.

(c) Circular orbits will emerge from constant forces pointing into the center of the loop (around the wire). We can tell we have positive current there since the force is pointing into the middle of the loop (into the page).

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The projectile's impulse is equal to the bowling pin's impulse in the negative, which in turn is equal to the projectile's change in momentum in the negative.

Impulse is commonly denoted by the letter J and is equivalent to the change in momentum ( p Delta p p). According to the impulse-momentum theorem, an object will experience an impulse that is equal to the change in its momentum. An object's impulse during a collision is always equal to the change in momentum. If a collision does not cause the system to lose any net kinetic energy, it is referred to as elastic. In elastic collisions, momentum and kinetic energy are both conserved.

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The 15 ° is the  the angle of projection, if the shells are fired with a velocity of 100 m/s.

What is angle of projection ?

Angle of projection: The angle created between the projection's direction and the horizontal line drawn there.

What is velocity ?

The velocity of the body or object determines its direction of motion. Speed is frequently a scalar number. In its most basic form, velocity is a vector quantity. It gauges how rapidly a distance changes. It is the pace at which displacement is altering.

Given V=100ms and Range R=500m and g=10m/s²

Let the angle of projection is θ with the horizontal.

Horizontal velocity Vh =Vcosθ=100cosθ

Vertical velocity Vv =Vsinθ=100sinθ

∴ Time of flight = 2Vv/g = 2×100sinθ/g

⇒ Range =Vh ×Time of flight

⇒ 100cosθ×2×100sinθ/g =500  ⇒sin2θ=1/2

⇒2θ=30° ⇒θ=15 °

Therefore, 15 ° is the  the angle of projection, if the shells are fired with a velocity of 100 m/s.

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ε = 2πfNabB sin2πft = εsin2πft this is the proved equation for the emf induced in the coil as a function of time t.

Electromagnetic radiation-induced electric and magnetic forces. Researchers are examining whether the electromagnetic fields (EMFs) produced by electrical equipment, wireless and cellular cellphones, and power lines might result in cancer or other negative health effects. likewise known as electromagnetic field.

Since, the coil of conducting wire is placed in a magnetic field,

number of turns = N

frequency = f

area = A

now, angular velocity of coil, ω = 2πf

in time t coil is rotated by θ angle, θ = ωt

Magnetic field through coil, φ = ΦB. dA = ΦB.dAcosθ

dA = area of N turns = NA

φ = NABcosθ

After putting value of θ, φ = NABcosωt

ε = dφ/dt

ε = d/dt×NABcosωt

  = -NAB [-ωsinωt]

  = NABωsinωt

ε = NAB2πft

area of rectangular coil, A = a×b

ε = Nab2πfsin2πft

sin2πft = 1, emf will be maximum

εmax = ε' = NabB2πf

ε = ε'sin2πft

ε = 2πfNabB sin2πft = εsin2πft

Hence proved that the emf induced in the coil is given as a function of time t.

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The linear speed of the cart is determined as 6 m/s.

The speed of the cart is calculated by applying the formula for centripetal acceleration as shown below;

Mathematically, the formula for centripetal acceleration is given as;

a = v² / r

where;

v² = ar

v = √ ( ar )

F = ma

a = F / m

a = 24 N / 2 kg

a = 12 m/s²

Substitute the given parameters and solve for the speed of the cart as shown below;

v = √ ( ar )

v =  √ ( 12 x 3  )

v = 6 m/s

Thus, the speed of the cart is a function of centripetal acceleration and the radius of the circular path.

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Answer: The mass of the first object is less than that of the second object.

Explanation:

ΣF = ma

a = ΣF/m

Thus, given two objects acted on by the same ΣF, a is inversely proportional to m. If a is larger, m must be smaller and vice-versa.

0.325 m far from the bar on the the right can the painter walk before the plank starts to fall.

Calculation :

balancing the moment of forces about right bar

22kg * g* L = 81* g * L

 d = (22/81)*L

 d =  (22/81)*1.2

 d = 0.325 m

The word "force" has a precise meaning. At this level it is appropriate to describe the force as pushing or pulling. A force does not contain or "have within" an object. A force is applied from one object to another. The concept of force is not limited to living things and inanimate things

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The potential gradient along the wire is 0.208Vm⁻¹

We are given that,

Resistance of wire = R = 20Ω

Internal resistance = r = 18Ω

length of wire = L = 10m

E.M.F = ∈ =5V

Thus to find the value of potential gradient of the wire, we can use the equation,

i =  (∈)/(R+r)

i = 5v/ (20Ω +18Ω)

i = 0.104 A

Vr = iR =(0.104 A)(20Ω) =

Vr = 2.08 volt

Thus the potential gradient of the wire is given as,

potential gradient = V/L =  (2.08volt)/(10m)

potential gradient = 0.208Vm⁻¹

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What Is Climate Change?

Climate change refers to long-term shifts in temperatures and weather patterns. These shifts may be natural, such as through variations in the solar cycle. But since the 1800s, human activities have been the main driver of climate change, primarily due to burning fossil fuels like coal, oil and gas.

Burning fossil fuels generates greenhouse gas emissions that act like a blanket wrapped around the Earth, trapping the sun’s heat and raising temperatures.

Examples of greenhouse gas emissions that are causing climate change include carbon dioxide and methane. These come from using gasoline for driving a car or coal for heating a building, for example. Clearing land and forests can also release carbon dioxide. Landfills for garbage are a major source of methane emissions. Energy, industry, transport, buildings, agriculture and land use are among the main emitters.

The Earth is feeling the heat.

Greenhouse gas concentrations are at their highest levels in 2 million years

And emissions continue to rise. As a result, the Earth is now about 1.1°C warmer than it was in the late 1800s. The last decade (2011-2020) was the warmest on record.

Many people think climate change mainly means warmer temperatures. But temperature rise is only the beginning of the story. Because the Earth is a system, where everything is connected, changes in one area can influence changes in all others.

The consequences of climate change now include, among others, intense droughts, water scarcity, severe fires, rising sea levels, flooding, melting polar ice, catastrophic storms and declining biodiversity.

The Earth is asking for help.

People are experiencing climate change in diverse ways

Climate change can affect our health, ability to grow food, housing, safety and work. Some of us are already more vulnerable to climate impacts, such as people living in small island nations and other developing countries. Conditions like sea-level rise and saltwater intrusion have advanced to the point where whole communities have had to relocate, and protracted droughts are putting people at risk of famine. In the future, the number of “climate refugees” is expected to rise.

Every increase in global warming matters

In a series of UN reports, thousands of scientists and government reviewers agreed that limiting global temperature rise to no more than 1.5°C would help us avoid the worst climate impacts and maintain a livable climate. Yet policies currently in place point to a 2.8°C temperature rise by the end of the century.

The emissions that cause climate change come from every part of the world and affect everyone, but some countries produce much more than others. The 100 least-emitting countries generate 3 per cent of total emissions. The 10 countries with the largest emissions contribute 68 per cent. Everyone must take climate action, but people and countries creating more of the problem have a greater responsibility to act first.

Photocomposition: an image of the world globe looking worried to a thermometer with raising temperatures

We face a huge challenge but already know many solutions

Many climate change solutions can deliver economic benefits while improving our lives and protecting the environment. We also have global frameworks and agreements to guide progress, such as the Sustainable Development Goals, the UN Framework Convention on Climate Change and the Paris Agreement. Three broad categories of action are: cutting emissions, adapting to climate impacts and financing required adjustments.

Switching energy systems from fossil fuels to renewables like solar or wind will reduce the emissions driving climate change. But we have to start right now. While a growing coalition of countries is committing to net zero emissions by 2050, about half of emissions cuts must be in place by 2030 to keep warming below 1.5°C. Fossil fuel production must decline by roughly 6 per cent per year between 2020 and 2030.

Growing coalition

Adapting to climate consequences protects people, homes, businesses, livelihoods, infrastructure and natural ecosystems. It covers current impacts and those likely in the future. Adaptation will be required everywhere, but must be prioritized now for the most vulnerable people with the fewest resources to cope with climate hazards. The rate of return can be high. Early warning systems for disasters, for instance, save lives and property, and can deliver benefits up to 10 times the initial cost.

We can pay the bill now, or pay dearly in the future

Climate action requires significant financial investments by governments and businesses. But climate inaction is vastly more expensive. One critical step is for industrialized countries to fulfil their commitment to provide $100 billion a year to developing countries so they can adapt and move towards greener economies.

Climate finance

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The average velocity of the body is 12.8ft/s and the speed of the body when t is 8 seconds is 256 ft/s.

We are ignoring the air resistance and the body is falling whose side is changing with the time as,

x(t) = 16t²

Where,

x is in feet,

t is in seconds.

The velocity of the body can by found as,

v(t) = 32t

Now, the average velocity between t = 8 seconds to t = 8.4 seconds is,

v(t) = 32(8.4 - 8)

v(t) = 32 x 0.4

v(t) = 12.8 ft/s.

Now, the velocity at the instance, when  t= 8 seconds.

v(t) = 32t

Putting t = 8 seconds,

v(t) =  32(8)

v(8) = 256ft/s.

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The ratio of intensities of the signal and the background noise for each device is 7943.2 and 316.2 respectively.

The signal-to-noise ratio (SNR) is a measure of the strength of the desired signal relative to the background noise. It is usually expressed in decibels (dB).

A higher SNR indicates a stronger signal relative to the background noise, and therefore a higher quality of sound. To find the ratio of intensities of the signal and the background noise for each device, you can use the formula:

Intensity ratio = 10^(SNR/10)

For the cassette player with an SNR of 62 dB, the intensity ratio would be:

Intensity ratio = 10^(62/10) = 316.2

This means that the intensity of the signal is 316.2 times stronger than the intensity of the background noise.

For the CD player with an SNR of 98 dB, the intensity ratio would be:

Intensity ratio = 10^(98/10) = 7943.2

This means that the intensity of the signal is 7943.2 times stronger than the intensity of the background noise. Therefore, the CD player has a much higher intensity ratio and a higher quality of sound compared to the cassette player.

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J- shaped tube is a device used to observe the relationship between volume and number of moles at constant pressure and temperature.

This is based on Boyle's law: A gas law known as Boyle's law asserts that a gas's pressure is inversely proportional to its volume when it is held at a fixed temperature and of a given mass.

To put it another way, as long as the temperature and volume of the gas remain constant, the pressure and volume of the gas are inversely proportional to one another. The Anglo-Irish chemist Robert Boyle proposed Boyle's law in the year 1662.

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The largest atom of period 4 is Potassium (K).

One of the chemical elements in the fourth row (or period) of the periodic table of the elements is known as element of period 4. The periodic table is organized into rows to show recurrent (periodic) tendencies in the chemical behavior of the elements as their atomic number rises.

One element is present in each of the eighteen groups, making up the fourth period's 18 elements, which start with potassium and end with krypton. d-block, which includes transition metals, makes its first appearance in the table.

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The graph is incorrect because; the title has the incorrect order for the variables. Option D

We know that a graph is made up of two parts. It has two axes and these are what we call the parts of the graph. It is common that we would have the independent variable on the x axis and then we have the dependent variable on the y axis.

With this said, we would now have to look at the graph that has been attached so that we can be able to see what the error in the graph that has been plotted as shown is and how the error that is in the graph can be able to be correct as the student is trying to pass information by the use of a graph system.

The title of the graph can be seen to show that the volume rather than the mass is plotted on the y axis.

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Answer: To solve this problem, we can use the equations of static equilibrium to determine the forces acting on the particle P. In equilibrium, the sum of the forces and the sum of the moments must be zero.

Explanation:

(i) The normal component of the contact force on P is 0.58 N.

(ii) The frictional component of the contact force on P is 0.11 N.

(iii) The coefficient of friction between P and the plane is 0.19.

The forces operating on the particle P can be ascertained using the equations for static equilibrium. The total of the moments and the forces must be zero in an equilibrium state.

The contact force on P has a normal component of 0.58 N.

The 0.11 N frictional component of the contact force on P.

P and the plane experience 0.19 coefficient of friction.

Friction between two surfaces causes kinetic energy to be converted into thermal energy when they move in relation to one another (that is, it converts work to heat). The utilization of friction produced by rubbing pieces of wood together to start a fire serves as an example of how this attribute can have dramatic effects.

When a viscous fluid is agitated, for instance, kinetic energy is transformed into thermal energy. Wear, which can result in component damage or performance degradation

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And p(2)=poexp(-x/L) describes how its resistivity changes along a rod. The rod's end at r=0 has a potential Vo that is higher than the end at x=L.Ohm's law is followed by the substance,  

Solution p(x)=p₀ exp(-x/L)

(a) we know that R=PL/A

dR=ρ(x)dx/A=p₀ e[tex]^{-x/L}[/tex] dx/A

R=p₀/A[tex]\int\limits^L_0 e^{-x/L} \, dx[/tex]

R=(p₀L/A)(1-e⁻¹)

(b)I=V₀/R=V₀A/p₀L(1-e⁻¹)

(c)ρ=E/J

E=ρJ

E(x)=Ip₀e[tex]^{-x/L}[/tex]/A=V₀Ap₀ e[tex]^{-x/L}[/tex]/p₀L(1-e⁻¹)A

Hence E(x)=V₀ e[tex]^{-x/L}[/tex]/L(1-e⁻¹)

(d)R(x)=∫dR=p₀/A[tex]\int\limits^x_r e^{-x/L} \, dx[/tex]

R(x)=Lp₀/A(1-e[tex]^{-x/L}[/tex])

starting from left end of rod ,there is potential drop IR(x) at distance x

∴V(x)=V₀-IR(x)

V(x)=V₀( e[tex]^{-x/L}[/tex] -e⁻¹)/(1-e⁻¹)

The current through a conductor between two places is directly proportional to the voltage across the two points, according to Ohm's law. The typical mathematical equation that captures this relationship is reached by including the resistance as the constant of proportionality.

where I denotes the current flowing through the conductor, V is the voltage applied across the conductor, and R denotes the conductor's resistance. The R in this relationship is constant and independent of the current, according to Ohm's law. Although the previous equation cannot be referred to as Ohm's law if the resistance is not constant, it can still be used to define static/DC resistance. The conductivity of the great majority of electrically conductive materials is accurately described by Ohm's law, an empirical relation.

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There is a flow of electrons from charged to uncharged whenever a charged capacitor is connected to an uncharged capacitor, and this flow continues until a steady state is reached. As a result, there is no further charge transfer and both capacitors are in equilibrium.

When we say a capacitor is uncharged, we imply that there are an equal amount of positively and negatively charged ions and electrons on each of its plates.

The capacitor's starting voltage is zero.

The capacitor's charge Q and voltage across it are both 0 before the switch is closed.

The charge has not had a chance to accumulate before the switch is closed.

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The capacitance per unit is 1.292 X 10⁻¹⁰.

The radius of inner part of the conductor = r = 2.6 X 10⁻³ m

The radius of outer part of the conductor = R = 4 X 10⁻³ m

Length of the capacitor = l = 2.1 X 10⁻³ m

Capacitance is purely geometrical property. It depends only on length, radius of conductor.

From the formula of cylindrical capacitor,      

= C = (2πεl) / ln(R/r)

where ε = 8.85 X 10⁻¹²

But we need capacitance per unit length so,

= C/l = (2πε) / ln(R/r)

= C/l = (2 X 3.14 X 8.85 X 10⁻¹²) / ln ( 4 X 10⁻³ / 2.6 X 10⁻³)

= C/l = 55.58 X 10⁻¹² / 0.43

= C/l = 1.292 X 10⁻¹⁰

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Clocks at rest in a reference frame where the two events occur are used to calculate the proper time between the events.

A. take place simultaneously B. take place at the same coordinates C. are separated by the maximum distance a light signal can travel in the given amount of time.

E On the x axis of reference frame S, there are two simultaneous events, one at x = a and the other at x = +a. An observer going in the direction of positive x says.

They are seen in reference frame S, which is travelling at a positive x-motional speed of 0.95c. The clocks of S are zeroed when the sources of the two frames coincide at time t = 0.

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The time it takes the block and the sphere to reach the bottom of the plane, uniform sphere and a block are placed at rest is 3 second

a=gsinθ1+K2R2

I=25MR2=MK2

K^2/R^2=2/5

θ=g×sin30∘1+25

a=5/7g×12

=57×9.8×12

=3.5m/s2

s=ut+12at2,

15.75=0+12×3.5×t2

t^2=15.75×23.5=9

t=3s

Time is described by physicists as the progression of events through the past, present, and future. A system is essentially timeless if it doesn't change. Time may be viewed as the fourth dimension of reality when describing events that occur in three-dimensional space. Time is something we cannot see, touch, or taste, but we can calculate how much of it has passed. Time is constant everywhere in classical mechanics. The timekeeping mechanisms continue to be accurate. Time is relative, however, as demonstrated by Einstein's special and general theories of relativity. It depends on the viewpoint of the observer. According to the theory of time dilation, intervals between events lengthen as one gets closer to the speed of light (dilates).

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When a particle may pass through a potential energy barrier with an energy greater than its kinetic energy, this process is known as tunnelling in quantum mechanics. This remarkable characteristic of tiny particles is crucial in the explanation of a number of scientific processes, including radioactive decay.

An atom or subatomic particle might appear on the other side of a barrier that should be impossible for it to cross due to a phenomena known as quantum tunnelling. It's as though you were out walking when you came across.

Because in this straightforward system, if a particle's energy is below the potential, it will always bounce back, and if it has a higher energy, it will always pass.

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Nearsightedness that makes distant objects appear blurry.

Farsightedness (also called hyperopia) which makes nearby objects appear blurry.

Astigmatism which can make near and far objects appear blurry or distorted.

The acceleration of the crate is 1.82m/s2 and the upward force the ice exerts on the crate as it is pulled is 339.5N

The force Fx causing the acceleration is the horizontal component of the pull force F=90 Non the mass m=kg for the angle θ=36∘ to the horizontal.

Fx = F cos36 ∘

=90cos36∘

≈72.81N

According to Newton's second Law, the acceleration a due to the net force Fx=72.81N equals the force divided by the mass m of the crate, i.e.

a = F / m

=72.81 / 40kg

≈1.82m/s2

The upward force mentioned in the question is the normal reaction

N of the ice. It is equal to the weight of the crate mg minus the vertical component Fy of the pull force F i.e.

N = mg − Fy

= mg − F sin36∘

= 40kg*9.81m/s2 − 90sin36∘N

≈339.5N

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The force with which it pressing against the track is F= r^(−2cr+4er³ ) .

By energy conservation:

[tex]\frac{1}{2}mv_a^2 + mgH = \frac{1}{2}mv_b^2 + mgh[/tex]

[tex]\frac{1}{2}m*0^2 + mg*6R = \frac{1}{2}mv_b^2 + mg*2R[/tex]

[tex]4gR = \frac{1}{2}v_b^2[/tex]

[tex]\sqrt{8gR }=v_b[/tex]

Now by force balance at the top point

[tex]mg + F_N = \frac{mv_b^2}{R}[/tex]

[tex]mg + F_N = \frac{m*8gR}{R}[/tex]

[tex]F_N = \frac{8mgR}{R} - mg[/tex]

[tex]F_N = 7 mg[/tex]

2. [tex]U =cr^2 - er^4[/tex]

Force and potential energy is related by the following equation

[tex]F = - \frac{dU}{dr}[/tex]

[tex]F = - \frac{d}{dr}cr^2 - er^4[/tex]

[tex]F = \hat r (- 2cr + 4er^3)[/tex].

Forces are influences that can change the movement of an object. A force can change the velocity of an object with mass accelerating it. Forces can also be described intuitively by pushing or pulling. A force has both magnitude and direction and is a vector quantity. The word force has a precise meaning.

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Answer:

I agree as this is a very moving piece of information

we obtain  v0 =−xm ωsinϕ=3.06m/s.

What is  harmonic motion?

When the restoring force is proportionate to the displacement but acting in the opposite direction, an oscillating mass moves in a manner known as harmonic motion. The sine wave has a constant frequency and amplitude and can be used to describe harmonic motion because it is periodic.

What is mass?

The amount of matter in a particle or object is represented by its mass, which is denoted by the symbol m. In the International System (SI), the kilogram serves as the default unit of mass (kg).

ω= mK = 2.00kg/10100Nm

=7.07rad/s.

Energy methods provide one method of solution. Here, we use trigonometric techniques based on Eq.  x=x m cos(ωt+ϕ)  and Eq.  v=−ωx

msin(ωt+ϕ).

(a) Dividing Eq.  v=−ωxm

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sin(ωt+ϕ)  by  Eq.x=xmcos(ωt+ϕ),  we obtain  

xv=−ωtan(ωt+ϕ)  

So that the phase  (ωt+ϕ) is found from ωt+ϕ=tan−1( ωx−v )=tan −1( (7.07rad/s)(0.129m)

−3.415m/s).

With the calculator in radians mode, this gives the phase equal to  –1.31rad.  Plugging this back into Eq.x=xmcos(ωt+ϕ),  leads to  0.129m=xmcos(−1.31) ⇒xm=0.500m.

(b) Since  ωt+ϕ=–1.31rad  at  t=1.00s, we can use the above value of  ω  to solve for the phase constant  ϕ. We obtain  ϕ=–8.38rad  (though this, as well as the previous result, can have  2π  or  4π  (and so on) added to it without changing the physics of the situation). With this value of  ϕ, we find  x0=xmcosϕ=−0.251m.

(c) And we obtain  v0 =−xm ωsinϕ=3.06m/s.

Therefore, we obtain  v0 =−xm ωsinϕ=3.06m/s.

Learn more about simple harmonic motion from the given link.

https://brainly.com/question/2195012

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