Under what circumstances can air resistance exercises ignored?

Answer:

To find the work done in moving the particle from the origin to x = 2, we need to integrate the force over the given interval.

The work done (W) is calculated by integrating the force function with respect to displacement (dx) from the initial position (0) to the final position (2):

W = ∫(0 to 2) (10x³ - 5) dx

Integrating the force function, we get:

W = ∫(0 to 2) (10x³ - 5) dx = [2.5x⁴ - 5x] evaluated from 0 to 2

Now, substituting the upper limit (2) and lower limit (0) into the equation:

W = [2.5(2)⁴ - 5(2)] - [2.5(0)⁴ - 5(0)]

 = [2.5(16) - 10] - [0 - 0]

 = 40 - 10

 = 30

Therefore, the work done in moving the particle from the origin to x = 2 is 30 units of work.

Explanation:

(a)The force constant (k) is 700N/m.(b) Work done (W) while drawing the bowstring back is 252J.(c) speed of the arrow (v) while releasing from the bowstring is 35.49m/s.

It states that “ The applied force (F) is equal to constant k times the displacement or change in length.”

Mathematically,

F=kx

Where F= applied force in newton(N).

k= constant

x= displacement in m.

In the above question given,

Force F = 420N

Displacement x= 0.60m

And mass m= 0.20kg

a) For calculating k, applying Hooke’s law we get,

F=kx

k= F/x = 420/0.60=700N/m

b) We know work done is equal to the product of force and distance.

Now

W= Fx= 420*0.60=252J

c) Here the bow is pulled backward with a force of 420N so that the kinetic energy stored by the bow

is equal to the Kinetic energy given by the arrow.

Applying law conservation of energy

Initial total energy = final total energy

½ kx2=½ mv2

Now

v2= kx2/m

v=sqrt(kx2/m)

v= sqrt(700*(0.60)2 /0.20)

v=35.496m/s

Hence the force constant k is 700N/m and the work done while drawing the bowstring is 252J and the velocity of the arrow is 35.496m/s.

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The approximate time difference between the first P-wave and the first S-wave recorded at a seismic station located 8000 kilometers from the earthquake’s epicenter would be 11 minutes 20 seconds.

Given the distance from earthquake’s epicenter (d) = 8000km

The approximate time difference between a P-wave and an S-wave can be calculated using the following formula:

From the diagram given we can see that the speed of P-wave (v1)= 8km/s

The speed of S-wave (v2) = 4.75km/s

We know that the time is calculated as distance per speed.

Then time taken for P-wave (t1) = d/v1

Time taken for S-wave (t2) = d/v2

Time Difference (t) = t1 - t2

Then, \(t = d/v1 - d/v2 = d((v2 - v1)/v1*v2)\)

\(t = 8000 * (8 - 4.75/8 * 4.75)\)

t = 680.4 seconds

So, for an earthquake epicenter located 8000 km away, the time difference would be:

Time Difference = 11 minutes 20 seconds

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Answer:

1. B = 79.12 MeV

2. B = -4.39 MeV/nucleon

3. B = 2.40 MeV/nucleon

4. B = 7.48 MeV/nucleon

5. B = -18.72 MeV

6. B = 225.23 MeV            

Explanation:

The binding energy can be calculated using the followng equation:

\( B = (Zm_{p} + Nm_{n} - M)*931 MeV/C^{2} \)

Where:

Z: is the number of protons

\(m_{p}\): is the proton's mass = 1.00730 u

N: is the number of neutrons

\(m_{n}\): is the neutron's mass = 1.00869 u

M: is the mass of the nucleus

1. The total binding energy of \(^{12}_{6}C\) is:

\( B = (Zm_{p} + Nm_{n} - M)*931.49 MeV/u \)

\( B = (6*1.00730 + 6*1.00869 - 12.011)*931.49 MeV/u = 79.12 MeV \)

2. The average binding energy per nucleon of \(^{24}_{12}Mg\) is:

\( B = \frac{(Zm_{p} + Nm_{n} - M)}{A}*931.49 MeV/u \)

Where: A = Z + N

\( B = \frac{(12*1.00730 + 12*1.00869 - 24.305)}{(12 + 12)}*931.49 MeV/u = -4.39 MeV/nucleon \)                                  

3. The average binding energy per nucleon of \(^{85}_{37}Rb\) is:

\( B = \frac{(Zm_{p} + Nm_{n} - M)}{A}*931.49 MeV/u \)

\( B = \frac{(37*1.00730 + 48*1.00869 - 85.468)}{85}*931.49 MeV/u = 2.40 MeV/nucleon \)

4. The binding energy per nucleon of \(^{238}_{92}U\) is:

\( B = \frac{(92*1.00730 + 146*1.00869 - 238.03)}{238}*931.49 MeV/u = 7.48 MeV/nucleon \)

5. The total binding energy of \(^{20}_{10}Ne\) is:

\( B = (Zm_{p} + Nm_{n} - M)*931.49 MeV/u \)

\( B = (10*1.00730 + 10*1.00869 - 20.180)*931.49 MeV/u = -18.72 MeV \)

6. The total binding energy of \(^{40}_{20}Ca\) is:

\( B = (Zm_{p} + Nm_{n} - M)*931.49 MeV/u \)

\( B = (20*1.00730 + 20*1.00869 - 40.078)*931.49 MeV/u = 225.23 MeV \)

I hope it helps you!

The correct answer is B. According to Newton's law of universal gravitation, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

In simpler terms, as objects get closer together, the gravitational force between them increases.

When the distance between two objects decreases, the denominator of the equation (distance squared) becomes smaller, resulting in a larger force. Conversely, when the distance increases, the denominator becomes larger, resulting in a smaller force.

It is important to note that the mass of an object does not directly affect the strength of the gravitational force between two objects. However, a higher mass will lead to a greater gravitational force when compared to a lower mass, but only because the force is being exerted on a more massive object. The mass of an individual object doesn't directly affect the gravitational force it experiences from another object. option B

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Answer:

The mass of the ball is 1.360 kilograms.

Explanation:

By Work-Energy Theorem, gravitational potential energy (\(U\)), in joules, is the product of weight of the ball (\(W\)), in newtons, and height (\(h\)), in meters. Please notice that weight is the product of the mass of the ball (\(m\)) and gravitational acceleration (\(g\)), in meters per square second. Then, the formula for the mass of the ball is:

\(m = \frac{U}{g\cdot h}\) (1)

If we know that \(U = 1000\,J\), \(g = 9.807\,\frac{m}{s^{2}}\) and \(h = 75\,m\), then the mass of the ball is:

\(m = \frac{U}{g\cdot h}\)

\(m = 1.360\,kg\)

The mass of the ball is 1.360 kilograms.

Answer:

The lower mantle is the liquid inner layer of the earth from 400 to 1,800 miles below the surface.

Explanation:

  The Direct Imaging technique used to detect exoplanets has biases associated with it. It is heavily biased towards finding exoplanets that are very large and very far from their parent star.

  The Direct Imaging technique involves directly capturing the light from an exoplanet, which is challenging due to the brightness of the parent star. This technique is more likely to succeed in detecting exoplanets that are large in size, as their signal is relatively easier to separate from the glare of the parent star. Therefore, the Direct Imaging technique is biased towards finding very large exoplanets.

  Additionally, this technique is better suited for detecting exoplanets that are located farther away from their parent star. When an exoplanet is situated at a significant distance from its star, the contrast between the planet's light and the star's light is more pronounced, making it easier to distinguish and image the exoplanet. Hence, the Direct Imaging technique is biased towards finding exoplanets that are very far from their parent star.

  On the other hand, this technique is not well-suited for detecting exoplanets that are moving very slowly or located very close to their parent star. Slow-moving exoplanets might be difficult to distinguish from background noise or other sources of motion, while planets close to their parent star might be obscured by the star's brightness, making it harder to directly image them using this technique.

  Therefore, the Direct Imaging technique is not biased towards finding exoplanets that are moving very slowly or very close to their parent star.

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The distance traveled at the point where the magnitudes of the centripetal and tangential accelerations are equal is approximately 1742.69 meters.

To determine the distance traveled at this point, we need to find the time it takes for the Porsche to reach the velocity where the centripetal and tangential accelerations are equal.

We convert the given velocity of 51.4 mph to meters per second (m/s), which is 22.983 m/s. The time required to reach this velocity is 5.94 seconds.

Next, we calculate the centripetal acceleration using the formula a_c = v²/r, where v is the velocity and r is the radius of the circular track. Substituting the values, we find a_c = (22.983 m/s)² / 466 m = 1.131 m/s².

Since the centripetal acceleration and tangential acceleration are equal at the desired point, we can equate the two: a_c = a_t. The tangential acceleration is given by a_t = Δv/Δt, where Δv is the change in velocity and Δt is the change in time.

Rearranging the equation, we have Δv = a_c * Δt.

Substituting the values, we find Δv = 1.131 m/s² * 5.94 s = 6.7224 m/s.

To calculate the distance traveled, we use the equation d = v_i * Δt + 0.5 * a_t * (Δt)², where v_i is the initial velocity and Δt is the change in time. Substituting the values, we find d = 5.27 m/s * 5.94 s + 0.5 * 6.7224 m/s * (5.94 s)² = 1742.69 meters.

Therefore, the distance traveled at the point where the centripetal and tangential accelerations are equal is approximately 1742.69 meters.

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Complete question here:

A Porsche drives with an initial velocity of 5.27 m/s on a circular track of radius 466 m. The Porsche starts to accelerate at its maximum constant acceleration. A Porsche 911 reached 51.4 mph within 5.94 s. Determine the distance traveled at the point where the magnitudes of the centripetal and tangential accelerations are equal.

Answer:

Explanation:

Given:

V₁ = V₂ = V

R₁ = 7 m

n = 7

R₂ = R₁ / n = 7 / 7 = 1 m

____________

aₙ₂ / aₙ₁ - ?

aₙ₁ = V₁² / R₁ = V² / 7

aₙ₂ = V₂² / R₂ = V² / 1 = V²

aₙ₂ / aₙ₁- =  V²  /  (V²/7) = 7

Centripetal acceleration increased by 7 times

An atom with only 1 to 3 valence electrons will tend to lose/subtract those valence electrons. That is option D.

Valence electrons are those electrons that are located at the outermost layer of an atom.

During a chemical reaction, elements that have 1 or 2 or 3 valence electrons donate or give out their electron to form a chemical bond with another aton if an element.

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Answer:

0.75N/kg

Explanation:

coefficient of force=force/mass

so 15N/20kg

=0.75N/kg

thanks!!

The speed with which they threw the bundle is  14 m/s.

We know that the speed of the bundle can be obtained from the use of the equations of kinematics. Now we can use the equation of the upward motion under gravity here.

Using;

v^2 = u^2 - 2gh

v = final velocity

u = initial velocity

g = acceleration due to gravity

h = height

Now;

v = 0 m/s at the maximum height

u^2 = 2gh

We now have;

u = √2gh

u = √ 2 * 9.8 * 10

u = 14 m/s

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The orbital period of a planet can be directly determined using all three methods, and the distance to the planet can then be determined using Newton's interpretation of Kepler's third rule.

The tilt of a planet's orbit affects the amount of the Doppler shift that humans can see. Planetary Motions According to Kepler's Law: Orbits, Areas, and Periods According to Kepler's Law, the sun is in the center of the elliptical orbits that the planets follow around it. Kepler's Laws are divided into three categories. Law of Areas, Periods, and Orbits.

The Doppler approach searches for recurring Doppler changes to detect planetary motion. It works best for finding large planets with nearby orbits. All orbital inclinations of planets are detected, excluding face-on. When the orbital inclination to Earth is unknown, it necessitates the use of huge telescopes and only offers the bare minimum mass.

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Answer:

Explanation:

The acceleration of an object given it's mass and the force acting on it can be found by using the formula

\(a = \frac{f}{m} \\ \)

m is the mass

f is the force

From the question we have

\(a = \frac{70}{7} = 10 \\ \)

We have the final answer as

Hope this helps you

The term energy density tells us that the difference between the particle model and the energy interaction model lies in how the energy is distributed or spread out within a system.What is Energy Density?The amount of energy per unit volume that a substance or system contains is known as energy density.

Energy density is a measure of how much energy is stored in a given volume or mass of a substance or system. It is a vital physical property that affects how a system behaves and how much energy can be extracted from it.Particle Model Vs. Energy Interaction Model The particle model of matter refers to the view of matter as being composed of tiny, indivisible particles that are in constant motion and have kinetic energy. In this model, the behavior of matter is primarily determined by the interactions between these particles.The energy interaction model, on the other hand, views matter as being composed of different forms of energy that can be transferred or transformed from one form to another.

In this model, the behavior of matter is primarily determined by the interactions between different forms of energy.The primary difference between these two models lies in how they distribute or spread out energy within a system. In the particle model, energy is primarily distributed among the particles, while in the energy interaction model, energy is primarily distributed among the different forms of energy that are present in the system. This difference in energy distribution can have significant implications for how a system behaves and how much energy can be extracted from it.

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Answer:

The first case requires more force to spin de bucket.

Explanation:

As we know, the centripetal force is directly proportional to the mass, the equation is given by:

\(F_{c}=ma_{c}\)

The first case has a quarter more water than the second case, therefore the first case requires more force to spin de bucket.

I hope it helps you!

Answer:

F=mass x acceleration

1000= 2000 x a

a=1000/2000

a=1/2 m/sec^2

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Answer:

the time taken for the box to stop is 3.6 s.

Explanation:

Given;

initial speed with which the box was pushed, u = 5 m/s

time taken for the box to stop, t = 1.5 s

Assuming the box is moving at constant acceleration, a;

\(a = \frac{u}{t} \\\\a = \frac{5}{1.5} \\\\a = 3.33 \ m/s\)

When the box is pushed a speed of 12 m/s, the time taken for the box to stop is calculated as;

\(t = \frac{v}{a} \\\\t = \frac{12}{3.33} \\\\t = 3.6 \ s\)

Therefore, the time taken for the box to stop is 3.6 s.

Safety symbols, danger symbols, or safety labels are graphical symbols that warn of or indicate hazards linked with an area or object. Images, pictograms, forms, words, phrases, sentences, or statements placed on walls, boards, buildings, doors, entrances, machinery, equipment, tools, transportation, roadways, or any other visible location are examples of safety symbols. The symbol alerts people to the presence of hazardous products or substances, as well as a hazardous environment, and warns them on how to stay safe or the potential repercussions if not avoided.

The given symbol means hammer.

A hammer is a hand tool that consists of a weighted "head" attached to a long handle and swung to produce an impact to a limited region of an item. This may be used to drive nails into wood, shape metal, or crush rock.

While all of these hammers have a round head for driving nails, the claw end may be used for prying, splitting wood, ripping drywall, and other minor demolition chores. A claw hammer's claw is curved, whereas a framing hammer's claw is straight. These hammers are ideal for the following tasks: woodworking

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Answer:

Crops drain the soil of nutrients

Explanation:

i took the test:) yw

Answer:

1. By streching

2. false

3. building stronger muscles and bones

4. riding your bike

Explanation:

The routine of exercise begins with the usual basic step of stretching the body.

An essential component of a healthy lifestyle is exercise. Exercise can help you cope with stress and prevent health issues while also enhancing energy and strength. It can also help you control your appetite and keep your weight in a healthy range.

Here,

1. The routine of exercise begins with the usual basic step of stretching the body.

2. People don't have to necessarily go to the gym to get exercise, because exercise includes the activities from the basic one to difficult methods. So, you can do some kind of exercise at the home itself. So, the statement is false.

3. An advantage to exercising is building stronger muscles and bones.

4. Riding your bike is an example of exercise.

Hence,

The routine of exercise begins with the usual basic step of stretching the body.

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Answer:

Igneous Rock

Sedimentary Rock

Metamorphic Rock

Explanation:

Igneous Formed by lava

Sedimentary Form By other fragmented pieces of rock

Metamorphic rocks that have undergone physical changes  exposed to extreme presure.

Answer:

D. How inertia affects the motion of an object​

Explanation:

The first law is about inertia, the second is about forces, which are A and B. The third choice is about action and reaction, which is C.

Answer:

D

Explanation:

I think I looked it up tbh

Where are the answer choices

The rate of shortening of the elastic cord at r = 1.2 m is 6.25 m/s. The rate of shortening of the elastic cord at r = 1.2 m is 0.208 m/s

\(KE_i\)= (1/2)mv² = (1/2)(5 kg)(5 m/s)² = 62.5 J

PE = (1/2)k(r - \(r_0\))²

(1/2)mv² = (1/2)k(r - \(r_0\))²

Solving for v, we get:

v = √(k/m)(r - \(r_0\))²)

At r = 1.2 m, the speed of the disk is:

v = √((k/5 kg)(1.2 m - 0.5 m)²) = 3.83 m/s

\(L_i = Iw_i =\)(1/2)mr²(0) = 0

\(L_i = L\)

0 = (1/2)mr_i²\(w_i\)= (1/2)\(mr_f\)²\(w_f\)

Solving for ω_f, we get:

\(w_f = (r_i/r_f)w_i\)

\(v_r = rw_f = (r_i/r_f)r_iw_i\)

Substituting the given values, we get:

\(v_r\) = (1.5 m/1.2 m)(1.5 m)(5 m/s)/(1.5 m) = 6.25 m/s

At r = 1.2 m, we have:

dl/dt = (1.2 m - 1.5 m) / √[(1.2 m - 1.5 m)² + (1.0 m)²] × (v/r) = -0.208 m/s

An elastic cord refers to a flexible material that can stretch and then return to its original shape and length when a force is applied and then removed. The behavior of an elastic cord can be described by Hooke's law, which states that the force applied to an elastic material is proportional to the amount of stretch or compression produced.

The elastic cord has many practical applications, such as in bungee jumping, where the cord is stretched and then allowed to contract rapidly, producing a thrilling and exciting experience. It is also used in medical devices, such as braces and orthotics, to provide support and compression to the affected area. The elasticity of the cord depends on the material used and the thickness of the cord. Rubber and latex are common materials used to make elastic cords due to their high elasticity and ability to stretch without breaking.

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For this case, the relationship between the two forces is given by:

F1 = nF2

Where,

Then, replacing the values we have:

F1 = (2.2)(202)

Having the calculations we have:

F1 = 444.4N

Answer: The output force that only lifts the load is F1 = 444.4N.