The effect wind has on an airplane can be modeled by using a wind tunnel. What is one limitation of this model

Answer:

An elastic collision is a collision in which there is no net loss in kinetic energy in the system as a result of the collision. Both momentum and kinetic energy are conserved quantities in elastic collisions.

Suppose two similar trolleys are traveling toward each other with equal speed. They collide, bouncing off each other with no loss in speed. This collision is perfectly elastic because no energy has been lost.

In reality, examples of perfectly elastic collisions are not part of our everyday experience. Some collisions between atoms in gases are examples of perfectly elastic collisions. However, there are some examples of collisions in mechanics where the energy lost can be negligible. These collisions can be considered elastic, even though they are not perfectly elastic. Collisions of rigid billiard balls or the balls in a Newton's cradle are two such examples.

The process of charging a capacitor consists of transferring charge from the plate at lower potential to the plate at higher one (higher potential).

When a battery is connected in series with a resistor and capacitor, a large initial current flows when the battery moves charge from one capacitor plate to the other. As the capacitor charges to the battery voltage, the charging current asymptotically decreases until it is zero.

Therefore, a unidirectional flow of electric charge is known as direct current. When the voltage from the power source matches the voltage at the capacitor terminals, the capacitor is fully charged. When the electrical circuit's current stops flowing, the charging phase of the capacitor is complete.

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The time it takes the stone to fall from a height of 7.11 m is 1.2 seconds.

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

To calculate the time it takes the stone to drop from an height of 7.11 m, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for t.

Hence, the time it takes the stone to fall is 1.2 seconds.

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During the Vietnam War, journalists often referred to the military's press briefings as "five o'clock follies" because they felt that the information provided was often incomplete or misleading.

The two choices that are correct are:

•Called the military's press briefings "five o'clock follies"

•Did not witness any combat on a firsthand basis.

. Additionally, due to the dangers of the conflict, many journalists did not have the opportunity to witness combat on a firsthand basis.

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(1) The distance of the image formed by the lens is determined as 6 cm.

(2) The image formed is real.

The distance of the image formed by the lens is calculated by applying the following formula as follows;

1/f = 1/v + 1/u

where;

The distance of the image formed by the lens is calculated as;

1/v = 1/f - 1/u

1/v = 1/2 - 1/3

1/v = 1/6

v = 6 cm

Since the sign of the image of the image is positive, the image formed is real.

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Answer:

Explanation:

a(t)= -2.00 m/s^2 + (3 m/s^3)t.

dv / dt =  -2.00 m/s^2 + (3 m/s^3)t.

dv = (-2.00 m/s^2 + (3 m/s^3)t.)dt

v  = - 2t + 3 t² / 2 + c , where c is a constant

for initial velocity t = 0

v0 = c

v  = - 2t + 3 t² / 2 + v0

ds / dt =  - 2t + 3 t² / 2 + v0

ds =  (- 2t + 3 t² / 2 + v0)dt

s = - 2t²/2 + 3 t³/6 + vot + c₁

At t = 0

s = c₁

At t = 4

s = -16 + 32 + 4v0 + c₁

=  4v0 + c₁ + 16

Given

4v0 + c₁ + 16  = c₁

v0 = - 4 m /s

Putting this value in the equation of velocity

v  = - 2t + 3 t² / 2 - 4

At t = 4

v = -8 + 24 - 4

= 12 m / s

Answer:

force=12000

Explanation:

F=m*a aka force equals mass times acceleration so 800*15=12000

Answer:

12000 N

Explanation:

The equation for Force is:

\(Force=mass*acceleration\)

We can plug in the given values into the equation:

\(Force=800kg*15m/s^2\\Force=12000N\)

The statement regarding the electric forces on the objects is true: f: ab 5 2f: ba.

As the space between two charged items grows, so do the electric forces between them. With more charge on the objects, there are greater electric forces between the charged things. Each object's charge has a direct impact on electrostatic force. Therefore, if the charge of one object is doubled, the force will increase by two times.

There is either a push or a pull. The effects of forces include moving an object, altering its speed, altering its shape, or changing the volume of a body.

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The force constant of the spring is determined as 14,222.2 N/m.

Apply the principle of conservation of energy,

K.E = U

where;

¹/₂mv² = ¹/₂kx²

mv² = kx²

k = mv²/x²

Where;

k = (2000 x 8²)/(3²)

k = 14,222.2 N/m

Thus, the force constant of the spring is determined as 14,222.2 N/m.

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The amount of force applied to the 7kg object that caused it to accelerate at 8m/s² is 56 newtons.

A force is simply a push or a pull of an object resulting from the object's interaction with another object.

From newton's second law;

Force = mass × acceleration

Given the data in the question;

Plug the given values into the formula to determine the applied force.

Force = mass × acceleration

Force = 7kg × 8m/s²

Force = 56kgm/s²

Force = 56 N

Therefore, the applied force is 56 newtons.

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The vector sum is the algebraic sum if the two vectors have the same direction.

The sum vector is zero if the two vectors have the same magnitude and opposite direction

Vector addition is a process that can be performed graphically using the parallelogram method, see  attached, where the second vector is placed at the tip of the first and the vector sum goes from the origin of the first vector to the tip of the second.

There are two special cases where the vector sum can be reduced to the algebraic sum if the vectors are parallel

case 1. if the two vectors are parallel, the sum vector has the magnitude of the sum of the magnitudes of each vector

case 2. If the two vectors are antiparallel and the magnitude of the two vectors is the same, the sum gives zero.

In summary in the sum of vectors If the vectors are parallel it is reduced to the algebraic sum, also in the case of equal magnitude and opposite direction the sum is the null vector

a) Magnitudes: \(\| \vec A\| \ge 0\), \(\|\vec B\| \ge 0\), \(\|\vec C\| \ge 0\); Directions: \(\theta_{A} \in (-\infty, +\infty)\) for \(\|\vec A\|\ne 0\). Undefined for \(\|\vec A\| = 0\), \(\theta_{B} \in (-\infty, +\infty)\) for \(\|\vec B\|\ne 0\). Undefined for \(\|\vec B\| = 0\), \(\theta_{C} \in (-\infty, +\infty)\) for \(\|\vec C\|\ne 0\). Undefined for \(\|\vec C\| = 0\).

b) Magnitudes: \(\|\vec A\| \ge 0\), \(\|\vec B\| \ge 0\), \(\|\vec C\| = 0\); Directions: \(|\theta_{A}-\theta_{B}| = 180^{\circ}\), \(\theta_{C}\) is undefined.

a) Let suppose that \(\vec A \ne \vec O\), \(\vec B \ne \vec O\) and \(\vec C \ne \vec O\), where \(\vec O\) is known as Vector Zero. By definitions of Dot Product and Inverse Trigonometric Functions we derive expression for the magnitude and directions of \(\vec A\), \(\vec B\) and \(\vec C\):

Magnitude (\(\vec A\))

\(\|\vec A\| = \sqrt{\vec A\,\bullet\,\vec A}\)

\(\| \vec A\| \ge 0\)

Magnitude (\(\vec B\))

\(\|\vec B\| = \sqrt{\vec B\,\bullet\,\vec B}\)

\(\|\vec B\| \ge 0\)

Magnitude (\(\vec C\))

\(\|\vec C\| = \sqrt{\vec C\,\bullet \,\vec C}\)

\(\|\vec C\| \ge 0\)

Direction (\(\vec A\))

\(\vec A \,\bullet \,\vec u = \|\vec A\|\cdot \|u\|\cdot \cos \theta_{A}\)

\(\theta_{A} = \cos^{-1} \frac{\vec A\,\bullet\,\vec u}{\|\vec A\|\cdot \|u\|}\)

\(\theta_{A} = \cos^{-1} \frac{\vec A\,\bullet\,\vec u}{\|\vec A\|}\)

\(\theta_{A} \in (-\infty, +\infty)\) for \(\|\vec A\|\ne 0\). Undefined for \(\|\vec A\| = 0\).

Direction (\(\vec B\))

\(\vec B\,\bullet \, \vec u = \|\vec B\|\cdot \|\vec u\| \cdot \cos \theta_{B}\)

\(\theta_{B} = \cos^{-1} \frac{\vec B\,\bullet\,\vec u}{\|\vec B\|\cdot \|\vec u\|}\)

\(\theta_{B} = \cos^{-1} \frac{\vec B\,\bullet\,\vec u}{\|\vec B\|}\)

\(\theta_{B} \in (-\infty, +\infty)\) for \(\|\vec B\|\ne 0\). Undefined for \(\|\vec B\| = 0\).

Direction (\(\vec C\))

\(\vec C \,\bullet\,\vec u = \|\vec C\|\cdot\|\vec u\|\cdot \cos \theta_{C}\)

\(\theta_{C} = \cos^{-1}\frac{\vec C\,\bullet\,\vec u}{\|\vec C\|\cdot\|\vec u\|}\)

\(\theta_{C} = \cos^{-1} \frac{\vec C\,\bullet\,\vec u}{\|\vec C\|}\)

\(\theta_{C} \in (-\infty, +\infty)\) for \(\|\vec C\|\ne 0\). Undefined for \(\|\vec C\| = 0\).

Please notice that \(\vec u\) is the Vector Unit.

b) Let suppose that \(\vec A \ne \vec O\) and \(\vec B \ne \vec O\) and \(\vec C = \vec O\). Hence, \(\vec A = -\vec B\). In other words, we find that both vectors are antiparallel to each other, that is, that angle between \(\vec A\) and \(\vec B\) is 180°. From a) we understand that \(\|\vec A\| \ge 0\), \(\|\vec B\| \ge 0\), but \(\|\vec C\| = 0\).

Then, we have the following conclusions:

Magnitude (\(\vec A\))

\(\|\vec A\| \ge 0\)

Magnitude (\(\vec B\))

\(\|\vec B\| \ge 0\)

Magnitude (\(\vec C\))

\(\|\vec C\| = 0\)

Directions (\(\vec A\), \(\vec B\)):

\(|\theta_{A}-\theta_{B}| = 180^{\circ}\)

Direction (\(\vec C\)):

Undefined

Answer:

A.

Position-time graph:

The position-time graph for the ball punted vertically will be a parabolic curve, with the vertex at the highest point of the ball's trajectory. Since the initial position is zero, the curve will go through the origin.

Velocity-time graph:

The velocity-time graph will be a straight line that starts at the initial velocity and decreases linearly until it reaches zero at the highest point of the ball's trajectory. After that, the velocity increases linearly in the negative direction until the ball hits the ground.

Acceleration-time graph:

The acceleration-time graph will be a constant negative value, representing the acceleration due to gravity.

Motion map:

A motion map is a diagram that shows the position of an object at several specific times during its motion. For the ball punted vertically, the motion map would look like this:

|O|------|-------|------|-------|------|H|

O represents the initial position, and H represents the highest point of the ball's trajectory. The "|" symbols represent the position of the ball at regular intervals of time.

B.

To find the initial velocity of the ball, we can use the hang time and the acceleration due to gravity.

Hang time = 3.8 seconds

Acceleration due to gravity = -9.8 m/s^2

At the highest point of the ball's trajectory, the velocity is zero. Therefore, we can use the following kinematic equation to find the initial velocity:

hang time = (final velocity - initial velocity) / acceleration

Solving for initial velocity:

initial velocity = final velocity - (hang time x acceleration)

final velocity = 0 m/s

hang time = 3.8 s

acceleration = -9.8 m/s^2

initial velocity = 0 - (3.8 x -9.8)

initial velocity = 37.64 m/s

Therefore, the initial velocity of the ball was 37.64 m/s.

The time interval between the man clapping and hearing his echo is approximately 1.75 seconds.

An echo is a repetition or reflection of a sound or signal. It can be caused by sound waves bouncing off a surface, signal interference, or the repetition of a message in communication.

The speed of sound in air at room temperature is approximately 343 meters per second. When a person claps, the sound waves propagate outward in all directions and reach the school building, where they bounce off and return to the person as an echo. The time it takes for the sound to travel the distance to the building and back to the person is the time interval between the clap and the echo.

To calculate the time interval, we can use the following formula:

time = distance / speed

where distance is the total distance traveled by the sound (twice the distance from the person to the school building), and speed is the speed of sound in air.

distance = 2 x 300m = 600m

speed = 343 m/s

time = 600m / 343 m/s = 1.75 seconds (rounded to two decimal places)

Therefore, the time interval between the man clapping and hearing his echo is approximately 1.75 seconds.

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On one cookie containing 50 calories, you could potentially go approximately 298 meters

Given that one food calorie is equivalent to 4184 joules, we can calculate the total energy in joules contained in the 50 calorie cookie:

50 food calories * 4184 J/calorie = 209,200 joules

Assuming an average efficiency of around 25% (meaning 25% of the energy is effectively used for movement), and a body weight of 70 kilograms, we can use a rough estimation that it takes about 1 joule of energy to move 0.4 meters (based on the energy cost of walking).

Distance = (Energy obtained from the cookie * Efficiency) / (Energy cost per meter * Body weight)

Distance = (209,200 J * 0.25) / (1 J/m * 0.4 m/kg * 70 kg)

Distance ≈ 298 meters

Therefore, on one cookie containing 50 calories, you could potentially go approximately 298 meters

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The initial angular acceleration is 5.78 rad/s^2.

Since

A gymnast on the uneven parallel bars is at rest, tipped at a 45∘ angle from the vertical. The distance from her hands to her feet is 1.8 m.

So,

\(Torque \tau = r \times F\\\\ \tau = l\alpha\\\\so, r \times F = l\alpha\\\\mg\ cos\ 45 \times r = (1/3)mR^2 \times \alpha\\\\9.8\times cos\ 45 \times 0.9 = (1/3)\times (1.8)^2 \times \alpha\\\\\alpha = 5.78\ rad/s^2\)

hence, The initial angular acceleration is 5.78 rad/s^2.

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Answer:

2.753*10^-11N

Explanation:

According to Newton's law of gravitation, the force between the masses is expressed as;

F = GMm/d²

M and m are the distances

d is the distance between the masses

Given

M = 3.71 x 10 kg

m = 1.88 x 10^4 kg

d = 1300m

G = 6.67 x 10-11 Nm²/kg

Substitute into the formula

F = 6.67 x 10-11* (3.71 x 10)*(1.88 x 10^4)/1300²

F = 46.52*10^(-6)/1.69 * 10^6

F = 27.53 * 10^{-6-6}

F = 27.53*10^{-12}

F = 2.753*10^-11

Hence the gravitational force between the asteroid is 2.753*10^-11N

a. A high-pitch wave is characterized by a high frequency and a short wavelength. The frequency determines the pitch of the sound, with higher frequencies corresponding to higher pitches.

The wavelength is the distance between two consecutive peaks or troughs of the wave and is inversely proportional to the frequency. Therefore, a high-pitch wave has a shorter wavelength.

The amplitude of the wave, which is the height of the peak or the depth of the trough, is not directly related to the pitch of the sound, but it does determine the volume or intensity of the sound.

b. A high-volume wave is characterized by a high amplitude and a relatively long wavelength. The amplitude determines the volume or intensity of the sound, with higher amplitudes corresponding to louder sounds.

The wavelength of the wave does not directly affect the volume of the sound, but it can affect how the sound is perceived in different environments.

In general, longer wavelengths are more effective at traveling through obstacles such as walls and are better at penetrating long distances, whereas shorter wavelengths are more easily scattered and attenuated in the atmosphere.

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Answer:

convection currents

Explanation:

The distance mirror M2 must be moved so that one wavelength has produced one more new maxima than the other wavelength is;

L = 57.88 mm

We are given;

Wavelength 1; λ₁ = 589 nm = 589 × 10⁻⁹ m

Wavelength 2; λ₂ = 589.6 nm = 589.6 × 10⁻⁹ m

We are told that L₁ = L₂. Thus, we will adopt L.

Formula for the number of bright fringe shift is;

m = 2L/λ

Thus;

For Wavelength 1;

m₁ = 2L/(589 × 10⁻⁹)

For wavelength 2;

m₂ = 2L/(589.6)

Now, we are told that one wavelength must have produced one more new maxima than the other wavelength. Thus;

m₁ - m₂ = 2

Plugging in the values of m₁ and m₂ gives;

(2L/589) - (2L/589.6) = 2

divide through by 2 to get;

L[(1/589) - (1/589.6)] = 1

L(1.728 × 10⁻⁶) = 1

L = 1/(1.728 × 10⁻⁶)

L = 578790.67 nm

L = 57.88 mm

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Writing in an online journal is different from writing in a paper one in the following way: it is easier to communicate online (option B).

A journal is a newspaper or magazine dealing with a particular subject.

A journal is an efficient medium to communicate the findings or results of an investigation to the public.

However, a journal can be virtual (online) or paper (hard copy). In this 21st century, it is easier to communicate to the masses online because more audience will be captured.

Therefore, writing in an online journal is different from writing in a paper one in the following way: it is easier to communicate online.

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The three ways an emf can be induced in the loop are changing the magnetic field, changing the area of the loop and changing the angle between the field and the loop.

Faraday's first law of electromagnetic induction states that whenever a conductor is placed in a varying magnetic field, an electromotive force is induced.

Mathematically, the formula for Faraday's first law is given as;

E = - ( N dФ ) / ( dt )

where;

The three ( 3 ) ways an emf can be induced in the loop is listed below;

To induced an emf in a loop, there must be change in the magnetic flux of the loop.

Mathematically, the formula for magnetic flux is given as;

Ф = BA cosθ

where;

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Answer: Mount Nevado Huascarán

Explanation: Mount Nevado Huascarán in Peru has the lowest gravitational acceleration, at 9.7639 m/s2, while the highest is at the surface of the Arctic Ocean, at 9.8337 m/s2

The diameter of the smaller end of the pipe is approximately 0.78 meters.

To determine the diameter of the smaller end of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of water should remain constant throughout the pipe.

The mass flow rate is given by the equation:
Mass flow rate = density of water * cross-sectional area * velocity

Since the density of the water remains constant, we can write:
Cross-sectional area1 * velocity1 = Cross-sectional area2 * velocity2

Given that the velocity1 is 13 m/s, the diameter1 is 1.2 m, and the velocity2 is 30 m/s, we can solve for the diameter2 using the equation:
(pi * (diameter1/2)^2) * velocity1 = (pi * (diameter2/2)^2) * velocity2

Simplifying the equation:
(1.2/2)^2 * 13 = (diameter2/2)^2 * 30

Calculating the equation:
(0.6)^2 * 13 = (diameter2/2)^2 * 30

0.36 * 13 = (diameter2/2)^2 * 30

4.68 = (diameter2/2)^2 * 30

Dividing both sides by 30:
0.156 = (diameter2/2)^2

Taking the square root of both sides:
0.39 = diameter2/2

Multiplying both sides by 2:
0.78 = diameter2

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Answer:

d

Explanation:

middle of a current carrying solenoid creates Mutual inductance

Answer:

- 0.33 m/s

Explanation:

An illustration is shown above,

In this case, since the two objects move in opposite directions before collision, then move together, the formula to be used is,

m1u1 - m2u2 = (m1 + m2)v

Where,

m1 = mass of the first object

u1 = initial velocity of the first object

v1 = final velocity of the first object

m2 = mass of the second object

u2 = initial velocity of the second object

v2 = final velocity of the second object

Therefore,

(4.0 • 3.0) - (8.0 • 2.0) = (4.0 + 8.0)v

12 - 16 = 12v

-4 = 12v

Divide both sides by 12,

-4 / 12 = 12v / 12

-1 / 3 = v

v = -0.33 m/s

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Answer:

1. 125N

2. 200N

3. 280N

Explanation:

Force= mass × acceleration

1. force= 25×5

= 125N

2. Force= 50×4

=200N

3. Force=70×4

=280N

The torque that is produced at the center of the drum is 50 Nm.

The term torque has to do with a force that leads to a turning effect. I can use the example of a tap to show you what is meant by a torque. The force that is exerted on a tap causes the tap to turn and this is what we mean by saying that a torque would produce a turning effect.

We have the following;

Force = 250 N

Distance = 20 cm or 0.2 m

Torque = 250 N  *  0.2 m

= 50 Nm

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A bicycle with 26-inch diameter wheels is traveling at 20 mi/h. Find the angular speed of the wheels in rad/min.

______radians per minute

___revolutions per minuteω =  1320 rad/min, Revolution per minutes = 210.084

Diameter = 24 in

Radius r = 24/2 in = 12 in = 12 × 2.54 cm = 30.48‬ cm = 0.3048 m

Linear Speed v= 15 mi/hr = 15 * 1609.34 / 3600 m/s = 6.7056 m/s

Angular Speed ω = v / r = (6.7056 m/s) / (0.3048 m) = 21.999945

ω =  22 rad/s = 22× 60 rad/min = 1320 rad/min

∴ 1 revolution = 2π rad

⇒1 rad = 1 / 2π rev

so 1320 rad/min = 1320 / 2π  rev/min = 210.0845 rev/min

Revolution per minutes = 210.0845

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