When a car of mass 1079 kg accelerates from 3.00 m/s to some finals speed, 2.00x10^5 J of work are done. Find the final speed

The dragonfly must generate approximately 4.8 × 10^-4 Joules of energy to spin itself at a rate of 1100 rpm.

Start by converting the rotational speed from rpm (revolutions per minute) to rad/s (radians per second). Since 1 revolution is equal to 2π radians, we can use the conversion factor:

Angular speed (ω) = (1100 rpm) × (2π rad/1 min) × (1 min/60 s)

ω ≈ 115.28 rad/s

The moment of inertia (I) is given as 2.0 × 10^-7 kg⋅m².

Use the formula for rotational kinetic energy:

Rotational Kinetic Energy (KE_rot) = (1/2) I ω²

Substituting the given values:

KE_rot = (1/2) × (2.0 × 10^-7 kg⋅m²) × (115.28 rad/s)²

Calculate the value inside the parentheses:

KE_rot ≈ (1/2) × (2.0 × 10^-7 kg⋅m²) × (13274.28 rad²/s²)

KE_rot ≈ 1.331 × 10^-3 J

Round the result to the proper number of significant figures, which in this case is three, as indicated by the given moment of inertia.

KE_rot ≈ 4.8 × 10^-4 J

Therefore, the dragonfly must generate approximately 4.8 × 10^-4 Joules of energy to spin itself at a rate of 1100 rpm.

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Answer:

C

Explanation:

Answer:

Explanation:

(m1 + m2)*V1 = m2*V2 + m1*Vx

Vx = ((m1 + m2)*V1 -  m2*V2) / m1

Vx = ((82 + 48)*7.4 - 48*8.6) /82 = 6.7 m/s

Option C. The heat absorbed or lost by a substance while it's changing state  correctly describes latent heat

Latent heat is the heat absorbed or lost by a substance while it is changing state.

The latent heat is a type of heat that is transferred during phase change, i.e., while a substance undergoes a change of state.

For example, when ice melts into liquid water, or when liquid water evaporates into water vapor, heat is absorbed from the surroundings.

Latent heat is not associated with a temperature change; rather, it's associated with a change of state.

For instance, the temperature of water remains at 100°C while boiling.

When water is boiling, the latent heat of vaporization is absorbed and utilized to break the hydrogen bonds holding water molecules together to change water from the liquid phase to the gaseous phase.

When the water is boiling, adding more heat won't increase the water's temperature, instead, the extra heat will be absorbed to change the phase of water molecules.

Therefore, the correct answer to the given question is option C: The heat absorbed or lost by a substance while it is changing state.

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Answer:

A)  4.95 m

B)  1.48225 m

Explanation:

Constant Acceleration Equations (SUVAT)

\(\boxed{\begin{array}{c}\begin{aligned}v&=u+at\\\\s&=ut+\dfrac{1}{2}at^2\\\\ s&=\left(\dfrac{u+v}{2}\right)t\\\\v^2&=u^2+2as\\\\s&=vt-\dfrac{1}{2}at^2\end{aligned}\end{array}} \quad \boxed{\begin{minipage}{4.6 cm}$s$ = displacement in m\\\\$u$ = initial velocity in ms$^{-1}$\\\\$v$ = final velocity in ms$^{-1}$\\\\$a$ = acceleration in ms$^{-2}$\\\\$t$ = time in s (seconds)\end{minipage}}\)  

When using SUVAT, assume the object is modeled as a particle and that acceleration is constant.

Consider the horizontal and vertical motion of the projectile separately.

The horizontal component of velocity is constant, as there is no acceleration horizontally.

Resolving horizontally, taking → as positive:

\(u=9.00\quad v=9.00 \quad a=0\quad t=0.550\)

\(\begin{aligned}\textsf{Using} \quad s & = \left(\dfrac{u+v}{2}\right)t:\\\\s&= \left(\dfrac{9+9}{2}\right)(0.550)\\s&= (9)(0.550)\\ \implies s&= 4.95\:\sf m\\\end{aligned}\)

As the projectile is fired horizontally, the vertical component of its initial velocity is zero.

Acceleration due to gravity = 9.8 ms⁻²

Resolving vertically, taking ↓ as positive:

\(u=0\quad a=9.8\quad t=0.550\)

\(\begin{aligned}\textsf{Using} \quad s & = ut+\dfrac{1}{2}at^2:\\\\s&= (0)(0.550)+\dfrac{1}{2}(9.8)(0.550)^2\\s&= 0+(4.9)(0.3025)\\\implies s&= 1.48225\:\sf m\\\end{aligned}\)

The order of the average surface temperature of the given planets as Mercury, Earth, Mars, Jupiter, and Neptune based on their distance from the sun.

The Solar System can be described as the gravitationally bound system of the Sun and the plants are the objects that orbit it. The solar system is formed 4.6 billion years ago from the gravitational collapse of a giant interstellar cloud.

Most of the mass of the solar system is contained in the Sun and the remaining mass is in the planet Jupiter. The four inner planets Mercury, Venus, Earth, and Mars are terrestrial planets, made primarily of rock and metal.

The two largest planets Jupiter and Saturn, are gas giants, made mainly of hydrogen and helium. The next two, Uranus and Neptune, are ice giants, made of volatile substances with hydrogen and helium, such as ammonia, water, and methane.

The average surface temperature of Mercury is 333°F (167°C), Earth 59°F (15°C), Mars -85°F (-65°C), Jupiter -166°F (-110°C), and Neptune -330°F (-200°C)

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Answer:

A

Explanation:

Answer: a or e

Explanation:

Answer:

\(\boxed {\boxed {\sf 6,000 \ Newtons}}\)

Explanation:

Force is the product of mass and acceleration.

\(F=ma\)

The mass of the Kia Soul is 1200 kilograms and its acceleration is 5 meters per square second.

\(m= 1200 \ kg \\a= 5 \ m/s^2\)

Substitute the values into the formula.

\(F= 1200 \ kg * 5 \ m/s^2\)

Multiply.

\(F= 6000 \ kg*m/s^2\)

\(F= 6000 \ N\)

Answer:

Force

We know that

F = ma

F = Force

m = mass

a = acceleration

F = 1200 × 5

F = 6000 N

\( \\ \)

Answer: Since the train travels with a constant speed, it does not experience any acceleration. The magnitude of the train's acceleration is 0 m/s^2.

The distance the train travels during this time can be calculated using the formula d = vt, where d is the distance, v is the velocity, and t is the time. Plugging in the values given, we have:

d = 20.0 m/s * 8.00 s = <<20*8=160>>160 m

Therefore, the train traveled a distance of 160 meters during this time.

Answer:

Option e is correct.

Explanation:

An object of mass m moves horizontally, increasing in speed from 0 to v in a time t.

We know that,

Work done = change in kinetic energy

\(W=\dfrac{1}{2}m(v^2-u^2)\)

Here, u = 0

So,

\(W=\dfrac{1}{2}mv^2\)

Also,

Power = work done/time

So,

\(P=\dfrac{\dfrac{1}{2}mv^2}{t}\\\\=\dfrac{mv^2}{2t}\)

So, the correct option is (e).

In order to measure the angle of incidence and the angle of refraction using Tracker's protractor tool (the green angle in the video frame), the following steps should be followed:

Step 1: Open the video in Tracker software.

Step 2: Click on the "Measure" button on the toolbar at the top of the software.

Step 3: From the dropdown menu, select "Angle".

Step 4: Click on the "protractor tool" icon (the green angle in the video frame).

Step 5: Position the vertex of the protractor exactly at the origin of the coordinate axis and move the arms of the protractor so that one arm is on the vertical axis (above or below, as appropriate) and the other on the light ray.

Step 6: Measure the angle of incidence and the angle of refraction for the frame numbers specified in the table below by using the step buttons on the right to advance the video a frame at a time.

Step 7: Record the measured angles in the table below. Note that the angle of incidence should be measured on the incident ray (the ray that is coming from the left), and the angle of refraction should be measured on the refracted ray (the ray that is coming from the right).In conclusion, by following these steps, one can measure the angle of incidence and the angle of refraction using Tracker's protractor tool.

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The change in motion, visible effects of the collision, and temperature increase would all serve as evidence that energy was transferred during the collision between the cart and the track after the removal of electrostatic forces.

If the electrostatic forces on the cart and track were suddenly removed and the cart hits the track, there would be several pieces of evidence indicating that energy was transferred during the collision.Firstly, there would be a noticeable change in the motion of the cart. The cart would decelerate as it collides with the track, and its velocity would decrease due to the loss of energy. This change in motion demonstrates that energy has been transferred from the cart to the track.

Secondly, there may be visible effects of the collision, such as deformation or damage to the cart or the track. This deformation or damage occurs because the energy transferred during the collision is transformed into other forms, such as heat or sound energy. These visible effects provide evidence of energy transfer.Additionally, there could be an increase in the temperature of the cart and/or the track due to the conversion of kinetic energy into thermal energy upon impact. This temperature change would be another indication that energy has been transferred.

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Answer:

a. The wooden cylinder b. the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.

Explanation:

a. Who reaches the bottom first

The kinetic energy of the objects is given by

K = 1/2mv² + 1/2Iω² where m = mass of object, v = velocity of object, I = moment of inertia and ω = angular velocity = v/r where r = radius of object

For the wooden cylinder, I = mr²/2 where m = mass of wooden cylinder and r = radius of wooden cylinder and v = velocity of wooden cylinder

So, its kinetic energy, K = 1/2mv² + 1/2(mr²/2)(v/r)²

K = 1/2mv² + 1/4mv²

K = 3mv²/4

For the steel hoop, I' = mr'² where m' = mass of steel hoop and r' = radius of steel hoop and v' = velocity of steel hoop

So, its kinetic energy, K' = 1/2m'v'² + 1/2(m'r'²)(v'/r')²

K' = 1/2m'v'² + 1/2m'v'²

K' = m'v'²

Since both kinetic energies are the same, since the drop from the same height,

K = K'

3mv²/4 = m'v'²

v²/v'² = 4m/3m'

v²/v'² = 4/3(m/m')

v/v' = √[4/3(m/m')]

Since the hoop weighs more than the cylinder m/m' < 1 and 4/3(m/m') < 4/3 ⇒ √ [4/3(m/m')] < √4/3 ⇒ v/v' < 1.16 ⇒ v'/v > 1/1.16 ⇒ v'/v > 0.866. Since 0.866 < 1, it implies v' < v.

Since v' = speed of steel hoop < v = speed of wooden cylinder, the wooden cylinder reaches the bottom first.

b. Why

Since the kinetic energy, K = translational + rotational

We find the translational kinetic energy of each object.

For the wooden cylinder,

K = K₀ + 1/2Iω² where K₀ = translational kinetic energy of wooden cylinder

K - 1/2Iω² = K₀

3/4mv² - 1/2(mr²/2)(v/r)² = K₀

3/4mv² - 1/4mv² = K₀

K₀ = 1/2mv²

For the steel hoop,

K' = K₁ + 1/2I'ω'² where K₁ = translational kinetic energy of steel hoop

K' - 1/2I'ω'² = K₁

m'v'² - 1/2(m'r'²)(v'/r')² = K₁

m'v'² - 1/2m'v'² = K₁

K₁ = 1/2m'v'²

So, K₀/K₁ =  1/2mv²÷1/2m'v'² = mv²/m'v'² = (m/m')(v²/v'²) = (m/m')4/3(m/m') = 4/3(m/m')².

Since (m/m') < 1 ⇒  (m/m')² < 1 ⇒ 4/3(m/m')² < 4/3 ⇒ K₀/K₁  < 1.33 ⇒ K₀ > K₁

So, the kinetic energy of the wooden cylinder is greater than that of the steel hoop.

So, the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.

a. The wooden cylinder b. the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.

The energy of the body due to its movement in a particular direction under the influence of a force like a free-falling body due to gravitaional force is called  Kinetic energy.

The kinetic energy of the objects is given by

\(K = \dfrac{1}{2}mv^2 + \dfrac{1}{2}Iw^2\)

where

m = mass of object,

v = velocity of object,

I = moment of inertia and

ω = angular velocity = v/r where r = radius of object

For the wooden cylinder, I = mr²/2 where m = mass of wooden cylinder and r = radius of wooden cylinder and v = velocity of wooden cylinder

So, its kinetic energy,

\(K = \dfrac{1}{2}mv^2 + \dfrac{1}{2}(\dfrac{mr^2}{2})\dfrac{v}{r}^2\)

\(K = \dfrac{3mv^2}{4}\)

For the steel hoop,

I' = mr'²

where

m' = mass of steel hoop and

r' = radius of steel hoop and

v' = velocity of steel hoop

So, its kinetic energy,

\(K' = \dfrac{1}{2}m'v'^2 + \dfrac{1}{2}(m'r'^2)\dfrac{v'}{r'}^2\)

\(K' = \dfrac{1}{2}m'v'^2 + \dfrac{1}{2}m'v'^2\)

K' = m'v'²

Since both kinetic energies are the same, since the drop from the same height,

K = K'

\(\dfrac{3mv^2}{4 }= m'v'^2\)

\(\dfrac{v^2}{v'^2} =\dfrac{ 4m}{3m'}\)

\(\dfrac{v^2}{v'^2} = \dfrac{4}{3}(\dfrac{m}{m'})\)

\(\dfrac{v}{v'} = \sqrt{[\dfrac{4}{3}(\dfrac{m}{m'})]\)

Since the hoop weighs more than the cylinder m/m' < 1 and 4/3(m/m') < 4/3 ⇒ √ [4/3(m/m')] < √4/3 ⇒ v/v' < 1.16 ⇒ v'/v > 1/1.16 ⇒ v'/v > 0.866. Since 0.866 < 1, it implies v' < v.

Since v' = speed of steel hoop < v = speed of wooden cylinder, the wooden cylinder reaches the bottom first.

(b) Since the kinetic energy, K = translational + rotational

We find the translational kinetic energy of each object.

For the wooden cylinder,

\(K = K_o + \dfrac{1}{2}Iw^2\)

where

K₀ = translational kinetic energy of wooden cylinder

\(K - \dfrac{1}{2}Iw^2 = K_o\)

\(\dfrac{3}{4}mv^2 - \dfrac{1}{2}(\dfrac{mr^2}{2})(\dfrac{v}{r})^2 = K_a\)

\(\dfrac{3}{4}mv^2 - \dfrac{1}{4}mv^2 = K_o\)

\(K_o = \dfrac{1}{2}mv^2\)

For the steel hoop,

\(K' = K_1 + \dfrac{1}{2}I'w'^2\)

where

K₁ = translational kinetic energy of steel hoop

\(K' - \dfrac{1}{2}I'w'^2 = K_1\)

\(m'v'^2 - \dfrac{1}{2}(m'r'^2)(\dfrac{v'}{r'})^2 = K_1\)

\(m'v'^2 - \dfrac{1}{2}m'v'^2 = K_1\)

\(K_1= \dfrac{1}{2}m'v'^2\)

So, K₀/K₁ =  1/2mv²÷1/2m'v'² = mv²/m'v'² = (m/m')(v²/v'²) = (m/m')4/3(m/m') = 4/3(m/m')².

Since (m/m') < 1 ⇒  (m/m')² < 1 ⇒ 4/3(m/m')² < 4/3 ⇒ K₀/K₁  < 1.33 ⇒ K₀ > K₁

So, the kinetic energy of the wooden cylinder is greater than that of the steel hoop.

So, the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.

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Answer:

strongest are at the points of the north pole and the south pole, specifically between the red box and the letter of each pole.

Explanation:

The lines of magnetic force are drawn so that the density of lines is proportional to the intensity of the magnetic field.

Therefore, the sections where the magnetic field is strongest are at the points of the north pole and the south pole, specifically between the red box and the letter of each pole.

Answer:

A, Passive Solar.

Explanation:

The potential energy of the roller coaster is 176,400 J (joules).

The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.

In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).

Using the formula, we can calculate the potential energy:

PE = mgh

= (900 kg)(9.8 \(m/s^2\))(20 m)

= 176,400 J

Therefore, the potential energy of the roller coaster is 176,400 J (joules).

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Answer:

Explanation:

In the microscopic world of quantum mechanics, particles don't behave like familiar everyday objects. They can exist in multiple states simultaneously and behave as both particles and waves. When we try to measure or observe a particle, we typically use light or other particles to interact with it. However, this interaction can disturb the particle's state. Imagine trying to measure the position of an electron using light. Light consists of photons, and when photons interact with the electron, they transfer energy to it. This energy exchange causes the electron's position and momentum to become uncertain. The more precisely we try to measure its position, the more uncertain its momentum becomes, and vice versa. This is known as the Heisenberg uncertainty principle.

So, the act of observing a particle disturbs its state because the interaction between the observer and the particle affects its properties. The very act of measurement or observation introduces a level of uncertainty and alters the particle's behavior. It's important to note that this behavior is specific to the quantum world and doesn't directly translate to the macroscopic world we experience in our daily lives. Quantum mechanics operates at extremely small scales and involves probabilities and uncertainties that are not typically noticeable in our macroscopic observations.

Answer:

a high density i believe

Explanation:

Answer:

it may have a higher density

Answer:

Researchers use a wide range of technologies today to help gather data, depending on the field of study and the type of data they need to collect. Here are some examples:

   Sensors: Sensors are devices that can detect and measure physical quantities such as temperature, pressure, and motion. Researchers use sensors to collect data on the environment, human behavior, and other phenomena.

   Drones: Drones or unmanned aerial vehicles (UAVs) are aircraft that are remotely controlled or can fly autonomously. Researchers use drones to collect data from hard-to-reach or dangerous areas, such as remote forests, volcanoes, or disaster zones.

   Satellites: Satellites are spacecraft that orbit the Earth and can collect data on a wide range of environmental and climatic factors, such as temperature, rainfall, and ocean currents. Researchers use satellite data to study climate change, natural disasters, and other global phenomena.

   Imaging technologies: Imaging technologies such as magnetic resonance imaging (MRI) and computed tomography (CT) scans are used to collect detailed images of the body's internal structures. Researchers use these images to study the human brain, diagnose diseases, and develop new medical treatments.

   Social media and online platforms: Social media and online platforms provide researchers with access to large amounts of data on human behavior, opinions, and attitudes. Researchers use this data to study social trends, political movements, and public opinion.

   Wearable technology: Wearable technology such as fitness trackers and smartwatches collect data on physical activity, heart rate, and other health metrics. Researchers use this data to study human health and behavior.

These are just a few examples of the many technologies researchers use today to help gather data. The use of advanced technology has revolutionized the way researchers collect and analyze data, allowing them to make new discoveries and gain a deeper understanding of the world around us.

Answer:

Therefore, the force required to accelerate a 500 kg object at a rate of 10 m/s^2 is 5000 Newtons (N).

Explanation:

The force required to accelerate an object can be calculated using the formula:

force = mass x acceleration

where "mass" is the mass of the object being accelerated, and "acceleration" is the rate at which the object's velocity is changing.

In this case, the mass of the object is 500 kg, and the acceleration is 10 m/s^2. Plugging these values into the formula gives:

force = mass x acceleration

force = 500 kg x 10 m/s^2

force = 5000 N

Therefore, the force required to accelerate a 500 kg object at a rate of 10 m/s^2 is 5000 Newtons (N).

Answer:

ask in the English then I can help you

Explanation:

please mark me as brain list

To determine whether the batter will hit a home run, we need to analyze the ball's trajectory and determine if it will clear the 11.34m high Green Monster wall.

Let's break down the problem into steps:

Step 1: Calculate the time of flight (t) for the ball's horizontal motion.

We can use the horizontal distance and the average exit velocity to find the time it takes for the ball to reach the Green Monster wall. The horizontal distance (range) can be determined using the formula:

range = horizontal velocity * time

In this case, the range is given as 94.5m, and the average exit velocity is 41.0m/s. Let's solve for time:

94.5m = (41.0m/s) * t

Simplifying the equation, we have:

t = 94.5m / 41.0m/s

t ≈ 2.31s

Step 2: Find the initial vertical velocity (Viy) at the peak of the trajectory.

Since the ball brushes against the top of the Green Monster, we can assume it reaches its peak at half of the total time of flight (t/2). The vertical motion is influenced by gravity, so the equation to determine the initial vertical velocity is:

Viy = (displacement) / (time)

In this case, the displacement is half the height of the Green Monster, which is 11.34m/2 = 5.67m. The time is half of the total time of flight:

Viy = (5.67m) / (t/2)

Viy = (5.67m) / (2.31s/2)

Viy ≈ 2.46m/s

Step 3: Calculate the horizontal velocity (Vix).

Since the horizontal motion is unaffected by gravity, the horizontal velocity remains constant throughout the ball's trajectory. We can use the horizontal distance and time of flight calculated earlier to find the horizontal velocity:

Vix = (horizontal distance) / (time)

Vix = 94.5m / 2.31s

Vix ≈ 40.95m/s

Step 4: Determine the total initial velocity (Vi) using the Pythagorean theorem.

The total initial velocity of the ball can be calculated using the horizontal and vertical velocities:

Vi = √(Vix^2 + Viy^2)

Vi = √((40.95m/s)^2 + (2.46m/s)^2)

Vi ≈ √(1676.9025m^2/s^2 + 6.0516m^2/s^2)

Vi ≈ √(1682.9541m^2/s^2)

Vi ≈ 41.02m/s

Now we have found the total initial velocity of the ball, which is approximately 41.02m/s.

To determine whether it's a home run, we need to consider the ball's trajectory and the height of the Green Monster. Since the height of the wall is 11.34m and the ball's vertical velocity is 2.46m/s, the ball will not clear the Green Monster and will not result in a home run.

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(a) The magnitude of the angular momentum of the system is 5,252 kg m²/s.

(b) The rotational energy of the system is 2,826 J.

(c) The new moment of inertia is 31.25 Kgm².

(d) The new speed of each astronaut is 420.15 m/s.

(e) The new rotational energy of the system is 65.82 kJ.

(f) The work is done by the astronauts in shortening the rope -45,317,098 KJ.

(a) To calculate the magnitude of the angular momentum of the system, we can use the following equation:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. Since we are treating the astronauts as particles, we can assume they are point masses and use the formula for the moment of inertia of a point mass:

I = mr²

where m is the mass of each astronaut and r is the distance between them. The angular velocity can be found from the linear velocity and the distance between the astronauts:

ω = v/r

Putting in the given values, we get:

r = 5.00 m

m = 90.5 kg

v = 5.80 m/s

I = 2(mr²) = 2(90.5 kg)(5.00 m)²

              = 4,525 kg m²

ω = v/r = 5.80 m/s / 5.00 m

           = 1.16 rad/s

L = Iω = (4,525 kg m²)(1.16 rad/s)

          = 5,252 kg m²/s

Therefore, the magnitude of the angular momentum of the system is 5,252 kg m²/s.

(b) To calculate the rotational energy of the system, we can use the following equation:

E = (1/2)Iω²

Putting in the values for I and ω that we found in part (a), we get:

E = (1/2)(4,525 kg m²)(1.16 rad/s)²

  = 2,826 J

Therefore, the rotational energy of the system is 2,826 J.

(c) When the distance between the astronauts is shortened to 5.00 m, the moment of inertia of the system changes. We can calculate the new moment of inertia using the parallel axis theorem:

I = Icm + md²

where Icm is the moment of inertia about the center of mass (which remains the same), m is the mass of each astronaut, and d is the distance between each astronaut and the center of mass (which is half the original distance, or 2.50 m).

The new moment of inertia is:

I = Icm + 2md²

 = 2(m(2.50 m)²)

 = 31.25 kg m²

Therefore the new moment of inertia is 31.25 Kgm².

(d) To find the new speeds of the astronauts, we can use the conservation of angular momentum:

L = Iω = L'

where L is the initial angular momentum (which we found in part (a)) and L' is the new angular momentum (which we can find using the new moment of inertia and the new distance between the astronauts, which is 5.00 m).

Solving for ω', we get:

ω' = L' / I = L / I'

Putting in the values, we get:

L' = L = 5,252 kg m²/s

I' = 31.25 kg m²

ω' = 5,252 kg m²/s / 31.25 kg m² = 168.06 rad/s

The new speed of each astronaut is the tangential velocity at a distance of 2.50 m from the center of mass, which can be found using the formula:

v = ω'r

where r is the distance from the center of mass. Putting in the values, we get:

v = 168.06 rad/s * 2.50 m = 420.15 m/s

Therefore, the new speed of each astronaut is 420.15 m/s.

(e) To find the new rotational energy of the system after the astronauts have shortened the rope to 5.00 m, we can use the conservation of angular momentum:

L = Iω

where L is the angular momentum of the system, I is the moment of inertia of the system, and ω is the angular speed of the system. Since the rope is assumed to have negligible mass, we can treat the system as two point masses moving in a circle around their center of mass. The moment of inertia of this system can be calculated as:

I = 2mr²/5

where m is the mass of each astronaut and r is the distance between them. Initially, the moment of inertia of the system is:

I = 2 * 90.5 kg * (10.0 m / 2)² / 5

= 3638 kg m²

The initial angular momentum of the system is:

L = Iω = 3638 kg m² * (5.80 m/s) / (10.0 m / 2)

          = 4213.6 kg m²/s

After the astronauts have shortened the rope to 5.00 m, the moment of inertia of the system is:

I' = 2 * 90.5 kg * (5.00 m / 2)² / 5

  = 1352.5 kg m²

Since the angular momentum of the system is conserved, the new angular speed of the system is:

ω' = L/I' = 4213.6 kg m²/s / 1352.5 kg m² = 3.115 rad/s

E' = (1/2)I'ω'² = (1/2) * 1352.5 kg m² * (3.115 rad/s)²

                    = 65,817.6 J

                    = 65.82 kJ

Therefore, the new rotational energy of the system is 65.82 kJ.

(f) The work done by the astronauts in shortening the rope is:

W = ∫F dl = (F' - F) ∫dl

   = (6,043,064.25 N - 630.56 N) * (-7.50 m)

   = -45,317,098 KJ

Therefore, the work is done by the astronauts in shortening the rope -45,317,098 KJ.

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Answer:

\(\theta=34 \textdegree\)

Explanation:

From the question we are told that:

Mass \(m=55kg\)

Angle \(\theta =28.0\)

Coefficient of static friction \(\alpha =0.680\)

Generally, the equation for Newtons second Law is mathematically given by

For

\(\sum_y=0\)

\(N=mgcos \theta\)

for

\(\sum_x=0\)

\(F_{s}=mgsin\theta\)

Where

\(F_{s}=\alpha*N\\\\F_{s}=\alpha*m*gcos \theta\)

\(F_{s}=0.68*55*9.8*cos 28\)

\(F_{s}=323.62N\)

Therefore

\(\alpha mgcos \theta=mg sin \theta\)

\(\theta=tan^{-1}(0.68)\)

\(\theta=34 \textdegree\)

(a) The static frictional force which holds the box in place is 323.62 N.

(b) The maximum angle that the incline can make with the horizontal is 34.2⁰.

The net force applied to keep the box at rest must be zero in order for the box to remain in equilibrium position. Apply Newton's second law of motion to determine the net force.

∑F = 0

The static frictional force is calculated as follows;

Fs = μFncosθ

Fs = 0.68 x (55 x 9.8) x cos28

Fs = 323.62 N

Fn(sinθ) - μFn(cosθ) = 0

mg(sinθ) - μmg(cosθ) = 0

μmg(cosθ) = mg(sinθ)

μ(cosθ) = (sinθ)

μ = sinθ/cosθ

μ = tanθ

θ = tan⁻¹(μ)

θ = tan⁻¹(0.68)

θ = 34.2⁰

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The equivalent resistance of the circuit is approximately 60Ω.

According to the question

1. The resistors are connected in parallel.
2. The resistances of the resistors are: R1 = 120Ω, R2 = 300Ω, and R3 = 200Ω.
3. The voltage across the parallel connection is 12V.

To find the equivalent resistance (Req) of the parallel circuit, we can use the formula:

1/Req = 1/R1 + 1/R2 + 1/R3

Now, let's plug in the values of the resistances:

1/Req = 1/120Ω + 1/300Ω + 1/200Ω

To solve for Req, you can follow these steps:

Step 1: Calculate the reciprocals of the resistances:
1/120Ω ≈ 0.00833, 1/300Ω ≈ 0.00333, 1/200Ω ≈ 0.005

Step 2: Add the reciprocals:
0.00833 + 0.00333 + 0.005 = 0.01667

Step 3: Find the reciprocal of the sum:
Req = 1/0.01667 ≈ 60Ω
So, the equivalent resistance of the circuit is approximately 60Ω.

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The statement that is NOT true is "the spaces between the particles increased.

option D.

If we consider the solids and liquids, when the temperature increases the molecules gain energy and start moving in all directions. This expands the substance and the volume of the substance increases.

Similar, when the ball is heated, the volume of the ball increases due to thermal expansion.

As the temperature increases, the average kinetic energy of the particles within the ball also increases, causing them to move faster.

However, the spaces between the particles do not necessarily increase. In fact, the expansion of the ball occurs due to the particles themselves moving farther apart, but the intermolecular spacing within the ball remains relatively constant.

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The velocity of the bus after 6.8 secs later will be ; 16.7 m/s

Given data:

Initial speed = 8 m/s

Increment speed = 1.5 m/s

Total time travelled = 6.8 s

Determine the final velocity after 6.8 secs

After 1 sec : speed = 8 m/s

After 2 secs : speed = 8 + 1.5

After 3 secs :  speed = 8 + 1.5 + 1.5

After 4 secs : speed = 8 + 1.5 + 1.5 + 1.5

After 5 secs : speed = 8 + 1.5 + 1.5 + 1.5 + 1.5

After 6 secs : speed = 8 + 1.5 + 1.5 + 1.5 + 1.5 + 1.5 =  15.5 m/s

∴ After 6.8 secs : speed = 15.5 + [ ( 1.5 / 10 ) * 8 ] = 16.7 m/s

Hence we can conclude that the velocity of the bus after 6.8 secs is 16.7m/s

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Answer:

Explanation:

"fuse wire" typically refers to a thin, single-use wire that is used to protect an electrical circuit from overloading or short circuiting. The wire is designed to melt and break the circuit if the current flowing through it exceeds a certain level, which helps to prevent damage to the electrical equipment or a potential fire hazard. Once the fuse wire has melted, it must be replaced with a new one.

an "MCB" (miniature circuit breaker) is a type of switch that automatically trips and breaks the circuit when there is an overcurrent or short circuit.

Unlike a fuse wire, an MCB can be reset after it has tripped, making it more convenient for protecting electrical circuits. MCBs are typically more expensive than fuse wires, but they offer greater protection and are often used in modern electrical systems.

Answer:

kilogram

Explanation:

Answer:

kilogram!

Explanation:

Answer:

.66354 T

Explanation:

Use F=ILB

B =  \(\frac{F}{IL}\)

B = Magnetic field

F= force due to magnetic

I= current

L= length in meters

F = mg

Final formula:

B=\(\frac{mg}{IL}\)

B=\(\frac{(.13)(9.8)}{(6)(.32)}\)

B= .66354

ayo btw ion know how to find direction, my b G

The minimum magnetic field required to move the wire is 66354 T.

The direction of magnetic field is normal to the page outwards.

The region surrounding a magnet that experiences the effects of magnetism is known as the magnetic field. When describing the distribution of the magnetic force within and around a magnetic object in nature, the magnetic field is a useful tool.

Given parameter:

Current passing through the wire, I = 6.0 A.

Length of the wire ,L = 32 cm = 0.32 m.

Mass of the wire, m = 0.13 Kg.

Acceleration due to the gravity, g = 9.8 m/s².

We know that, force acting on a current caring wire due to magnetic field is,  F=ILB

Where,

B = Required magnetic field.

To find the minimum magnetic field that is required to move the

wire, force acting on a current caring wire due to magnetic field is equal to weight the wire, that is, mg.

Hence, we can write,

mg = ILB

⇒ B = mg/IL

= (0.13 * 9.8)/(6.0 * 0.32)

=0.66354 Tesla

Hence, the minimum magnetic field is 0.66354 Tesla.

b) By using Maxwell's right hand thumb Rule along current flow, the direction of magnetic field is  determined as normal to the page pointing outwards.

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