Give a common example of Newton's first law of motion and why (include inertia in your answer)

30 pts

Plz help me ✌

To solve, this PDE using the Fourier series we have to follow the below process

We know that u(x,t) can be represented in the Fourier series as:

u(x, t) = Σn=1∞ {An sin( nπx) + Bn cos( nπx)}\( \times \left ( Cn cos(n\pi t)+Dn sin(n\pi t)\right )\)

Where An, Bn, Cn, and Dn are constants that depend on the given function f(x) and g(x).

Next, we differentiate u(x, t) twice with respect to t and once with respect to x, and then we plug it into the given wave equation to get:

∑n=1∞ (Cn sin(nπx) - Dn cos(nπx))[(nπ)^2 + 1]cos(nπt) = ∑n=1∞ An sin(nπx) (nπ)^2 [Cn cos(nπt) + Dn sin(nπt)]

To find An, we multiply both sides of the above equation by sin(nπx) and integrate it with respect to x.

∫[0,1] sin(nπx)[∑n=1∞ (Cn sin(nπx) - Dn cos(nπx))[(nπ)^2 + 1]cos(nπt) dx] = ∫[0,1] sin(nπx) [∑n=1∞ An sin(nπx) (nπ)^2 [Cn cos(nπt) + Dn sin(nπt)] dx]

Using the orthogonality property of sine and cosine,

we get An (nπ)^2 [Cn cos(nπt) + Dn sin(nπt)] = ∫[0,1] sin(nπx) [∑n=1∞ (Cn sin(nπx) - Dn cos(nπx))[(nπ)^2 + 1]cos(nπt) dx]

We can find the constants Cn and Dn by using the initial conditions:u(x, 0) = f(x), x ∈ [0, 1], and ut(x, 0) = g(x), x ∈ [0, 1].

Applying Fourier series to initial conditions:

u(x, 0) = f(x) = ∑n=1∞ An sin(nπx) Cn cos(nπt) + Dn sin(nπt)ut(x, 0) = g(x) = ∑n=1∞ An sin(nπx) nπ [Cn cos(nπt) + Dn sin(nπt)]

Therefore, we have to solve the four equations given by:

An (nπ)^2 [Cn cos(nπt) + Dn sin(nπt)] = ∫[0,1] sin(nπx) [∑n=1∞ (Cn sin(nπx) - Dn cos(nπx))[(nπ)^2 + 1]cos(nπt) dx]f(x)

= ∑n=1∞ An sin(nπx) Cn cos(nπt) + Dn sin(nπt)g(x) = ∑n=1∞ An sin(nπx) nπ [Cn cos(nπt) + Dn sin(nπt)]u(0, t) = 0u(1, t) = 0

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The overall force acting on an object, taking into account all the individual forces that are affecting it. The net force is equal to the sum of all the forces acting on an object, and it determines the direction and magnitude of the object's motion.

The net force is also known as the resulting force and it is calculated by subtracting the forces that are in the opposite direction from the forces that are acting in the same direction. The net force is an important concept in physics and is used to describe the interactions between objects and the physical laws that govern motion. force of anything is the measure of the body to create a pressure to pull or push something from its position and we can do it. The net force is equal to the sum of all the forces acting on an object

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Answer:

C

Explanation:

I took the test

Answer:

Hope it helps

Explanation:

C

Answer:

A. 0.5m/s².

B. –0.5m/s².

C. –0.5m/s².

D. 100m.

Explanation:

A. Determination of the acceleration in the first 20s.

Initial velocity (u) = 0

Final Velocity (v) = 10m/s

Time (t) = 20secs.

Acceleration (a) =..?

Acceleration = change in Velocity /time

a = (v – u)/t

a = (10 – 0)/20 = 10/20

a = 0.5m/s²

Therefore, the acceleration of the cyclist in the first 20secs is 0.5m/s²

B. Determination of the acceleration between 20 and 30s. This can be obtained as follow:

Initial velocity (u) = 10m/s

Final Velocity (v) = 5m/s

Time (t) = 30 – 20 = 10s

Acceleration (a) =..?

Acceleration = change in Velocity /time

a = (v – u)/t

a = (5 – 10)/10 = –5/10

a = –0.5m/s²

Therefore, the acceleration of the cyclist between the 20 and 30secs is

–0.5m/s².

C. Determination of the acceleration in the last 10s.

Initial velocity (u) = 5m/s

Final Velocity (v) = 0

Time (t) = 10s

Acceleration (a) =..?

Acceleration = change in Velocity /time

a = (v – u)/t

a = (0 – 5)/10 = –5/10

a = –0.5m/s²

Therefore, the acceleration of the cyclist between the last 10secs is

–0.5m/s².

D. Determination of the distance travelled by the cyclist when he was moving at a constant speed.

Velocity (v) = 5m/s

Time (t) = 50 – 30 = 20secs

Displacement (d) =?

Velocity = Displacement /Time

v = d/t

5 = d/20

Cross multiply

d = 5 x 20

d = 100m

Therefore, the distance travelled by the cyclist at constant speed is 100m

Answer:

Doubling the mass of both objects

Explanation:

If you double the mass of both objects, the gravitational force will quadruple, if you move the objects away from each other, the gravitational force will decrease

The gravitational force of attraction is increased by doubling the mass of both objects.

According Newton's law of Universal gravitation force, two objects in the universe attracts each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of distance between them.

\(F = \frac{Gm_1 m_2}{R^2}\)

where;

Thus, we can conclude that by doubling the mass of both objects or reducing the distance between them, the gravitational force of attraction increases.

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The method you do an exercise to target particular muscle groups is known as technique.

When workouts are performed properly, the muscles and joints that are being particularly targeted by the movement get the load. When an exercise is performed improperly, it frequently results in the loading of other joints and muscles as well as a reduction in the benefit to the target muscles.

Whatever your weightlifting objectives, using perfect form is the first and most crucial step. Technique has a greater influence than weight used, whether you're trying to bulk up or tonify. Bad form simply won't yield the same outcomes.

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The two options that help explain why the rotation of a conducting loop between the poles of a magnet generates a potential difference are:

(A) The magnetic field changes its direction relative to the loop.

(D) The angle between the loop and the magnetic field changes.

In a simple generator, a conducting loop rotates between the poles of a magnet, resulting in the generation of a potential difference. Two factors contribute to this phenomenon.

Firstly, as the loop rotates, the magnetic field lines passing through it change their direction relative to the loop (option A). This change in the magnetic field induces a changing magnetic flux through the loop.

According to Faraday's law, this changing magnetic flux induces an electromotive force (EMF) or a potential difference across the loop. Secondly, as the loop rotates, the angle between the loop and the magnetic field changes (option D).

This change in angle alters the component of the magnetic field perpendicular to the loop, further contributing to the generation of a potential difference.

Together, these changes in the magnetic field and the angle between the loop and the magnetic field lead to the generation of a potential difference, enabling the functioning of the generator.

Therefore the correct options are (A) The magnetic field changes its direction relative to the loop and (D) The angle between the loop and the magnetic field changes.

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To calculate the change in potential energy of an energetic 80 kg hiker who makes it from the floor of Death Valley to the top of Mt. Whitney, we need to use the formula of potential energy.What is potential energy?Potential energy is the energy an object has due to its position or state.

It is the energy that a system possesses due to its configuration relative to some zero position. The gravitational potential energy is a type of potential energy that is possessed by an object due to its position in a gravitational field.

The formula for potential energy is given by: Potential Energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)PE = mghwhere m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object from the reference level.In this question, the mass of the hiker is given as 80 kg. We also know that the hiker has climbed from the floor of Death Valley to the top of Mt. Whitney.

Let's assume the reference level as the floor of Death Valley and calculate the height difference. The elevation of the floor of Death Valley is approximately -282 feet, while the elevation of the top of Mt. Whitney is 14,505 feet. Therefore, the height difference is:Δh = 14,505 ft - (-282 ft)Δh = 14,787 ft.

Now, we can calculate the change in potential energy using the formula:PE = mghPE = (80 kg) × (9.81 m/s²) × (4,509.6 m)PE = 3,524,203 J. Therefore, the change in potential energy of the hiker is 3,524,203 J (Joules) as they climbed from the floor of Death Valley to the top of Mt. Whitney.

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The weak nuclear force is responsible for the beta decay, therefore the false statement about strong and weak nuclear forces would be that both promote beta decay, therefore the correct answer is option C.

The ability of some unstable atoms to emit nuclear radiation spontaneously, typically in the form of alpha or beta particles frequently accompanied by gamma rays, is known as radioactivity.

The weak nuclear force is among the two nuclear forces that are responsible for beta decay.

The weak nuclear force is what causes beta decay, hence the incorrect statement regarding the strong and weak nuclear forces is that they both encourage beta decay. Therefore, option C is the best response.

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The correct answer is: All of these answers are correct.

All the provided explanations can be plausible reasons for the low adoption of a cookstove intervention in rural Bangladesh. It is important to consider factors such as technology maintenance, regional cooking preferences, and the suitability of the chosen stove for the user's level of education.

All of these factors can significantly impact the acceptance and adoption of a new cooking technology.It would hinder their ability to effectively use and benefit from the intervention.

Considering these factors collectively provides insight into why the adoption rate remained low. Addressing these issues is crucial to improving the acceptance and success of cookstove interventions in rural communities.

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Answer:

Weight is a measure of the force of gravity pulling down on an object. It depends on the object's mass and the acceleration due to gravity, which is 9.8 m/s2 on Earth. The formula for calculating weight is F = m × 9.8 m/s2, where F is the object's weight in Newtons (N) and m is the object's mass in kilograms.

Explanation:

Answer:

b. between 2 s and 4 s

Explanation:

2-4 was both 3m/s

b. 1.

Explanation

Having a mechanical advantage means the force applied by the system is greater than the force you put in. In a pulley system, this means the pulley can lift the object with a greater amount of force than you apply to the rope

The mechanical advantage of a pulley is system is equal to the number of ropes supporting a movable pulley

hence, the force advantage is equal to the number of ropes

therefore

we can see the input force equals the output, so

therefore, the answer is

b. 1.

I hope this helps you

Answer:

shorter,higher

Explanation:

The spectrum observed from the Sun (or any star) would exhibit an absorption spectrum. This is because the outer gaseous atmosphere of the star absorbs specific wavelengths of light, resulting in dark absorption lines in the spectrum.

In the cooler, lower-density outer atmosphere, where white light from the star travels, some atoms or molecules in the atmosphere absorb photons with particular energy. In the spectrum, these absorptions show up as black lines at specific wavelengths. The specific set of absorption lines that each element or molecule generates results in a distinctive pattern that can be used to identify the elements that are present in the star's atmosphere.

The absorption spectrum offers insightful data on the chemical make-up and physical characteristics of the star. Astronomers can ascertain the elements present, their abundances, and other characteristics like the temperature, pressure, and velocity of the star's atmosphere by examining the absorption lines.

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Answer:

yes

Explanation:

moving earth makes us stand on ground

Answer:

the rotation of the earth can affect your weight but not gravity

For a human jumper to reach a height of 110 cm, the person will need to leave the ground at a speed of 4.65 m/s.  

We can calculate the initial speed to reach 110 cm of height with the following equation:

\( v_{f}^{2} = v_{i}^{2} - 2gh \)

Where:

\( v_{f}\): is the final speed = 0 (at the maximum height of 110 cm)

\( v_{i}\): is the initial speed =?

g: is the acceleration due to gravity = 9.81 m/s²

h: is the height = 110 cm = 1.10 m

Hence, the initial velocity is:

\( v_{i} = \sqrt{v_{f}^{2} + 2gh} = \sqrt{2*9.81 m/s^{2}*1.10 m} = 4.65 m/s \)

Therefore, the initial speed that the person must have to reach 110 cm is 4.65 m/s.

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The force F1 is equal and opposite to the downward force thus, F1 is equal to 60 N. The force F2 is inclined to 30 ° from leftward force and it is equal to 38.97 N in magnitude.

Force is an external agent acting on a body to deform it or to change its state of motion or rest. Force is a vector quantity and it is characterised by its magnitude and direction.

If two forces acting on a body from the same directions, then the net force will be the sum of these two forces. If they are acting from opposite directions, they will cancel each other in magnitude.

The force F1 is equal and opposite to the force acting downward. Thus its magnitude is 60 N. The force F2 is inclined to 30 ° from horizontal direction.

F2 = 45 cos 30 = 38.9 N.

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The average density of the Sun is high even though its composition is 99.9 % by atoms, 98.5% by mass, Hydrogen and Helium gases because of the immense gravitational forces acting on its massive core.

However, due to its enormous size and mass, the gravitational force at its core is substantial. This force compresses the gases within the Sun, causing them to become denser and hotter. As a result, the pressure and temperature at the core of the Sun are extreme, reaching millions of degrees Kelvin. These conditions facilitate nuclear fusion, a process that converts Hydrogen nuclei into Helium, releasing a tremendous amount of energy in the form of light and heat.

The energy generated by nuclear fusion keeps the Sun in a state of hydrostatic equilibrium, which is a balance between the inward gravitational force and the outward pressure exerted by the gases. This equilibrium maintains the Sun's high average density, despite its predominantly gaseous composition. In summary, the Sun's average density is high due to the immense gravitational forces compressing the Hydrogen and Helium gases in its core and the high pressure and temperature that facilitate nuclear fusion. These factors contribute to the Sun's hydrostatic equilibrium, which sustains its high density.

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Answer:

I think the answer is c

Explanation:

I had this problem once

Answer:

1)substance A will require 910 J of heat to increase the temperature by 10°C.

2) Substance B

3) Substance A

Explanation:

1) The meaning of the statement: "specific heat capacity of A is 910 J/kg °C" is that 1 kg of substance A will require 910 J of heat to increase the temperature by 10°C.

2) While heating equal mass of all the three substances supplied with equal amount of heat, Substance B will gain more temperature due to the fact that substances of lesser specific heat capacity always tend to gain or loose heat within a short period of time.

3) While keeping equal mass at the three substances heated for the same temperature of 100°C and kept on a wax slab, substance A will go down more in depth due to the fact that heat is preserved for a longer period of time for substances that have higher specific heat capacity.

Answer:

42.5 N

Explanation:

Here is a problem.

Problem:-

A car of mass 1700kg accelerated with a rate of 17m/s^2. find the force applied on it.

Extra:-

F=ma is. the famous formula of Sir Eizak Newton

Every photon has some energy within it and that energy is called photon energy.

The energy of photon is \(2.38\times10^{-18}\;\rm J\).

Given that, frequency of the photon is \(3.6\times10^{15}\;\rm Hz\) and Planck's constant is \(6.626\times {{10}^{-34}}\).

So the energy of the photon can be calculated by the given formula.

\(E=h\nu\)

Where \(h\) is plank's constant and \(\nu\) is the frequency of the photon.

By substituting the values in the above formula, the photon energy is,

\(E=6.626\times10^{-34}\times3.6\times10^{15}\;\rm J\)

\(E=2.38\times10^{-18}\;\rm J\)

The energy of photon is \(2.38\times10^{-18}\;\rm J\).

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If the lens in a person's eye is too highly curved, this person is suffering from: nearsightedness.

lens is a piece of transparent material (such as glass) that has two opposite regular surfaces either both curved or one curved and the other plane and that is used either singly or combined in an optical instrument for forming an image by focusing rays of light.

The lens is used to form an image of an object by focusing rays of light from the object.

Various types of lenses are :

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The total energy that can be stored in the spring bumpers is 43.8 J, or KE = 43.8.

The battery's power capacity is the amount of energy it can hold. Its power is commonly stated in Watt-hours (the symbol Wh) (the symbol Wh). A Watt-hour is equal to the voltage (V) and current (Amps) that a battery can produce for a specific period of time (generally in hours). Voltage * Amps * hours = Wh.

Block A's momentum before to the impact can be calculated using the formula p1 = m1v1 = (3.50 kg)(9.00 m/s) = 31.5 kgm/s.

Block B's initial momentum is p2 = m2v2 = 0, indicating that it is at rest.

Prior to the collision, the system's total momentum was equal to 31.5 kgm/p1 + p2.

\(p1 + p2 = (m1 + m2)v\)

\(31.5 kgm/s = (3.50 kg + 10.00 kg) * v\)

\(31.5 kgm/s = 13.50 kg * v\)

\(v = 31.5 kg*m/s / 13.50 kg = 2.33 m/s\)

The kinetic energy of block A before the collision is given by KE1 = (\(1/2)m1v1^2 = (1/2)(3.50 kg)(9.00 m/s)^2 = 141.8\) J

The kinetic energy of block B before the collision is KE2 = \((1/2)m2v2^2 = 0\)

The total kinetic energy before the collision is KE1 + KE2 = 141.8 J

\(ΔKE = KEf - KEi = (1/2)(m1 + m2)v^2 - KE1 - KE2\)

\(ΔKE = (1/2)(3.50 kg + 10.00 kg)(2.33 m/s)^2 - 141.8 J - 0\)

ΔKE = 43.8 J\(31.5 kgm/s = 13.50 kg * v\)

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Answer:

25

Explanation:

I just did this

A normal line is a line that is perpendicular to the boundary between two media. It is often used in optics to describe the behavior of light as it interacts with different surfaces.

When a light ray hits a boundary between two media at an angle, it will be refracted or reflected based on the angle of incidence and the properties of the media. The normal line is a reference line that is drawn perpendicular to the boundary at the point where the light ray hits it. This line helps to determine the angle of incidence and angle of reflection or refraction. It is important to note that the normal line is not always a straight line, but can be curved or angled depending on the shape of the surface it is interacting with. Therefore, the correct answer to the question is C) A line perpendicular to the boundary between two media.

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complete question:

What is a normal line? A) A line parallel to the boundary B) A vertical line separating two media C) A line perpendicular to the boundary between two media D) A line dividing incident ray from reflected or refracted ray E) Two of the above are possible