Calculate the first three natural frequencies of torsional vibration of a shaft of Figure 6.7 clamped at x = 0, if a disk of inertia J0 = 10 kg m2 /rad is attached to the end of the shaft at x = l. Assume that l = 0.5 m, J = 5 m4 , G = 2.5 x 109 Pa, rho = 2700 kg/m3 .

The maximum energy stored in the inductor at any time is 18J.

(a) The formula for the angular frequency of oscillation (W) for an electromagnetic oscillator (LC circuit) is given by:

\(W = 1 / sqrt(LC)\)

Given L = 1 and C = 4F,

we have:

W = 1 / sqrt(1 x 4)

W = 1 / 2rad/s

(b) The formula for the charge on a capacitor in an electromagnetic oscillator (LC circuit) at any time t is given by:

q(t) = Q0 cos(Wt)

and the formula for the voltage across the capacitor in an electromagnetic oscillator (LC circuit) at any time t is given by:

\(v(t) = V0 sin(Wt)\)

At the point when the capacitor is fully discharged for the second time, the voltage across the capacitor will be zero (V0 sin(Wt) = 0).

Thus, sin(Wt) = 0, and Wt = nπ.

Since we are interested in the second time the capacitor is fully discharged, n = 2.

Therefore, Wt = 2π, and t = 2π / W

= 2π x 2 = 4s.

(c) The formula for the energy stored in an inductor in an electromagnetic oscillator (LC circuit) at any time t is given by: \(U(t) = (1/2)Li²(t)\)

Since the capacitor is fully charged to 3V, we can calculate the initial charge on the capacitor as:

Q0 = CV0

= 4 x 3

= 12CAt

t = 0, the charge on the capacitor is Q0 cos(0) = Q0 = 12C, and the current in the inductor is zero.

Thus, the energy stored in the inductor at t = 0 is zero.

Since energy is conserved in an electromagnetic oscillator (LC circuit), the total energy stored in the circuit must remain constant.

Thus, the maximum energy stored in the inductor at any time is equal to the initial energy stored in the capacitor, which is given by:

(1/2)CV0²

= (1/2)(4)(3²)

= 18J

Therefore, the maximum energy stored in the inductor at any time is 18J.

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Answer:

Explanation:

Let the angle required be θ with direction opposite to current .

cos θ = 3 / 5

θ = 53° .

Resultant velocity towards the opposite side

= √ ( 5 ² - 3²)

= 4 km /h

distance covered = 1.2 km

time taken = 1.2 / 4 = .3 h

= 18 min .

The information given on the X-axis of the graph attached is the years from 1920-2005 (option B).

A graph in mathematics or statistics is a data chart (graphical representation of data) intended to illustrate the relationship between a set (or sets) of numbers (quantities, measurements or indicative numbers) and a reference set.

A graph consists of two axes namely; X-axis and Y-axis. The x-axis on a graph is usually drawn left to right and usually shows the range of values of an independent variable.

On the other hand, the Y-axis is the axis on a graph that is usually drawn from bottom to top and usually shows the range of values of variable dependent on one other variable.

Therefore, according to the graph illustrated above, the x-axis shows the years from 1920-2005.

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The possible algebraic signs of the charges are both a- positive (+0.139 C) or both negative (-0.139 C)

b- magnitude of the charges is approximately 0.139 C, which is equivalent to 19.5 μC.

The calculation to determine the possible algebraic signs and magnitude of the charges:

Spring constant (k) = 190 N/m

Displacement of the spring (x) = 0.039 m

Using Hooke's Law, we can calculate the force exerted by the spring:

Force (F) = k * x

F = 190 N/m * 0.039 m

F ≈ 7.41 N

Now, using Coulomb's Law, we can determine the magnitude of the charges:

q₁ * q₂ = F * r² / k

Since the charges have equal magnitudes, we can write q₁ = q₂ = q.

q * q = 7.41 N * (0.31 m)² / 190 N/m

q² = 0.0192 C²

Taking the square root of both sides, we find:

q ≈ ± √(0.0192 C²)

q ≈ ± 0.139 C

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The true azimuth of the AB alignment is 91º 52' (east of north), the magnetic azimuth is 100º 22' (east of north), and the grid azimuth is 108º 52' (east of north).

To find the true azimuth, magnetic azimuth, and grid azimuth of the AB alignment, we need to consider the magnetic declination. The magnetic declination indicates the angle between true north and magnetic north at a specific location. In this case, the magnetic declination is 8º 30' E, which means that the magnetic north is 8º 30' east of the true north.

To calculate the true azimuth, we subtract the magnetic declination from the grid azimuth. The grid azimuth is given as 100º 22', so subtracting the magnetic declination of 8º 30' E gives us a true azimuth of 91º 52' (east of north).

The magnetic azimuth remains the same as the grid azimuth, which is 100º 22' (east of north).

The grid azimuth is calculated by adding the magnetic declination to the true azimuth. Since the magnetic declination is east, we add it to the true azimuth. Adding 8º 30' E to the true azimuth of 91º 52' gives us a grid azimuth of 108º 52' (east of north).

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Answer:

F = Q V X B

V X B = south X downard = East - deflection is West

Since Q is negative the deflection = West

a = F / m = Q V B / m

a = 1.6E-19 * 5*E6 * 3.5E-5 / 9.1E-31

a = 1.6 * 5 * 3.5 / 9.1 * 10^13 m/s^2 = 3.1 * 10^13 m/s^2

Answer:

C

Explanation:

Answer:

D. All of the above

Explanation:

To calculate the torque required to accelerate the plastic disk from 0 to 1800 rpm in 4.8 seconds, we need to use the rotational kinematic equation.

First, let's convert the final angular velocity from rpm to rad/s. Since 1 revolution is equal to 2π radians,The angular acceleration (α) is given in radians per second squared (rad/s²). Therefore, we can proceed with the calculations using the values.

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Answer:

heres some ways i personally think might help!

Explanation:

Have a Compelling Vision. Your vision must be larger than yourself and larger than the moment, says world-famous business guru Tony Robbins. ...

Build Collaboration.

Be Focused.

Innovate.

Use Emotional Intelligence.

Pass Your Leadership On.

Leadership. Greatness in leaders is expressed though a positive attitude. ...

Service. To be of real service in this world, we must add something to other people's lives that cannot be bought. ...

Results. Getting the results we desire comes from how hard we work and how optimistic our outlook is.

Efficiency.

Quality.

Reliability.

Catch People Doing Something Right. ...

Recognize Effort and Hard Work, not Intelligence. ...

Be Better at Noticing. ...

Say, Thank You More Often. ...

Make More Positive Emotional Connections. ...

Think about Who Blessed My Life Today.

Answer:

Pascal's law states that a change in pressure at any point in an enclosed fluid is transmitted equally throughout the fluid.

Explanation:

Applications of Pascal's law include

>The hidden standard of the water powered jack and pressure driven press.  

>Power intensification in the slowing mechanism of most engine vehicles.  

>Utilized in artesian wells, water pinnacles, and dams.  

>Scuba jumpers must comprehend this rule. At a profundity of 10 meters submerged, pressure is double the environmental weight adrift level, and increments by around 100 kPa for each expansion of 10 m depth.[5]  

>Generally Pascal's standard is applied to bound space (static flow), however because of the consistent flow process, Pascal's rule can be applied to the lift oil instrument (which can be represented as a U tube with pistons on either end).

Without Pascal's law, none of the above could be possible.

Answer:

200 (m) for 20 seconds

10 times 20 is 200

Answer:

200

Explanation:

Jill is running at 10 meters per second

20 * 10 = 200

Answer:

24.25m/s

Explanation:

m = 0.5kg

u ( initial velocity) = 0m/s

v ( final velocity) =?

a = 9.8m/s^2

d (displacement) = 30m

Since u don't have time, u only have the choice to use this formula

V^2 = u^2 + 2ad

V^2 = 0 + 2 x 9.8 x 30

V^2 = 588

V = 24.25 m/s

Answer:

power= work done /time.

Answer:

W = Force  * distance

Power = W/ time

Explanation:

Answer:

The bird and the arrow are 84.621 meters far from the hunter.

Explanation:

The arrow experiments of a parabolic motion, which is the combination of horizontal motion at constant velocity and vertical uniform accelerated motion. The arrow strikes the bird when it reaches its maximum height. First, we determined the time taken by the arrow before striking the bird:

\(v = v_{o}\cdot \sin \theta + g\cdot t\) (1)

Where:

\(v_{o}\) - Initial speed of the arrow, in meters per second.

\(v\) - Final speed of the arrow, in meters per second.

\(\theta\) - Launch angle, in sexagesimal degrees.

\(g\) - Gravitational acceleration, in meters per square second.

\(t\) - Time, in seconds.

If we know that \(v_{o} = 40\,\frac{m}{s}\), \(\theta = 30^{\circ}\), \(g = -9.807\,\frac{m}{s^{2}}\), \(v = 0\,\frac{m}{s}\), then the time taken by the arrow is:

\(t = \frac{v-v_{o}\cdot \sin \theta}{g}\)

\(t = \frac{0\,\frac{m}{s}-\left(40\,\frac{m}{s}\right)\cdot \sin 30^{\circ} }{-9.807\,\frac{m}{s^{2}} }\)

\(t = 2.039\,s\)

And the initial horizontal distance of the arrow (\(x_{i}\)) is determined by this kinematic formula:

\(x_{i} = (v_{o}\cdot \cos \theta)\cdot t\) (2)

If we know that \(v_{o} = 40\,\frac{m}{s}\), \(\theta = 30^{\circ}\) and \(t = 2.039\,s\), then the initial horizontal distance is:

\(x_{i} = \left[\left(40\,\frac{m}{s} \right)\cdot \cos 30^{\circ}\right]\cdot (2.039\,s)\)

\(x_{i} = 70.633\,m\)

There is an inelastic collision between the arrow and the bird, the initial velocity of the bird-arrow system is:

\(v = \frac{m_{A}\cdot v_{o}\cdot \cos \theta}{m_{A}+m_{B}}\) (3)

Where:

\(v\) - Initial velocity of the bird-arrow system, in meters per second.

\(m_{A}\) - Mass of the arrow, in kilograms.

\(m_{B}\) - Mass of the bird, in kilograms.

If we know that \(m_{A} = 0.5\,kg\), \(m_{B} = 2\,kg\), \(v_{o} = 40\,\frac{m}{s}\) and \(\theta = 30^{\circ}\), then the initial velocity of the bird-arrow system is:

\(v = \frac{(0.5\,kg)\cdot \left(40\,\frac{m}{s} \right)\cdot \cos 30^{\circ}}{0.5\,kg + 2\,kg}\)

\(v = 6.928\,\frac{m}{s}\)

And the maximum height reached by the arrow (\(y\)), in meters, is:

\(y = y_{o} + (v_{o}\cdot \sin \theta)\cdot t +\frac{1}{2}\cdot g\cdot t^{2}\) (4)

Where \(y_{o}\) is the initial height of the arrow, in meters.

If we know that \(y_{o} = 0\,m\), \(v_{o} = 40\,\frac{m}{s}\), \(\theta = 30^{\circ}\),  \(g = -9.807\,\frac{m}{s^{2}}\) and \(t = 2.039\,s\), then the maximum height reached by the arrow is:

\(y = 0\,m + \left(40\,\frac{m}{s} \right)\cdot (2.039\,s)\cdot \sin 30^{\circ} +\frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}}\right)\cdot (2.039\,s)^{2}\)

\(y = 20.394\,m\)

Time needed by the bird-arrow system to land is determined by this expression based on (4):

\(y = y_{o} + (v_{o,y})\cdot t +\frac{1}{2}\cdot g\cdot t^{2}\)

If we know that \(y_{o} = 20.394\,m\), \(y = 0\,m\), \(v_{o,y} = 0\,\frac{m}{s}\) and \(g = -9.807\,\frac{m}{s^{2}}\), then the time needed to land is:

\(0\,m = 20\,m + \left(0\,\frac{m}{s} \right)\cdot t + \frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right)\cdot t^{2}\)

\(t = 2.019\,s\)

And the horizontal distance travelled by the bird-arrow system (\(x_{ii}\)), in meters, is calculated from a formula based on (2):

\(x_{ii} = v_{o, x}\cdot t\)

If we know that \(v_{o,x} = 6.928\,\frac{m}{s}\) and \(t = 2.019\,s\), then the distance travelled by the bird-arrow system is:

\(x_{ii} = \left(6.928\,\frac{m}{s} \right)\cdot (2.019\,s)\)

\(x_{ii} = 13.988\,m\)

The final distance of the bird-arrow system from the hunter is:

\(x = x_{i} + x_{ii}\)

\(x = 70.633\,m + 13.988\,m\)

\(x = 84.621\,m\)

The bird and the arrow are 84.621 meters far from the hunter.

The total resistance of the resistors in the circuit from the diagram is 20  Ω.

Resistance is a measure of the opposition to current flow in an electrical circuit.

To calculate the total resistance of the resistors in parallel, we use the formula below.

Note: Both resistors are connected in series.

Formula:

For series connection

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the total resistance is 20 Ω.

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Answer:

B; a path through a town with uprooted trees

Explanation:

took the quiz and got it right on edge2020!

The effect of tornadoes on the environment is a path through a town with uprooted trees. This, option B is correct.

It is the typical weather event that contains strong winds and leaves a path of destruction up to 50 miles long. It is also defined as the violently rotating column of air that touches the ground and is usually attached to a thunderstorm.

It is developed from a severe thunderstorm in warm, moist, and unstable air and extended up to 300 miles. The thunderstorms also generate heavy damage and devastate the environment in seconds and cause more fatalities.

A swirling, funnel-shaped, whirling wind is called a tornado and it is accompanied by hurricanes and storms. Strong tornadoes last for twenty minutes and the winds are between 200 mph to 300mph. The United States and Canada are mostly tornado-affecting countries.

The effect of tornadoes is a path through a town with uprooted trees and hence, the ideal solution is option B.

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Answer:

The ball exerts a force of 400 N on the bat.

Explanation:

Given that,

A baseball player hits a ball with 400 N of force.

We need to find the force the ball exert on the bat.

We know that,

According to Newton's third law, when object 1 exerts a force on an object 2, then object 2 will exert a force on object 1 but in opposite direction.

So, the ball exerts a force of 400 N on the bat.

Answer:

what is the problem that i need to solve?

Explanation:

The work required is greater for accelerating the car from 20 to 30 m/s than from 10 to 20 m/s.

The effort is greater when the car is accelerated from 20 to 30 m/s than from 10 to 20 m/s due to the change in kinetic energy. This is due to the fact that an object's kinetic energy grows as a function of velocity, hence as velocity rises, so does the amount of work needed to produce a given increase in kinetic energy.

The kinetic energy of an object determines how much labour is necessary to accelerate it from one velocity to another.

The equation: gives the kinetic energy of an item

K = (1/2)mv^2

where

m is the mass of the object

v is its velocity.

We have to find the at which velocity a car required more work to accelerate a car from 10 to 20 m/s or from 20 to 30 m/s we can find it by comparison,

To determine the change in kinetic energy, we may compute the car's kinetic energy at each velocity and then subtract the beginning kinetic energy from the final kinetic energy.

Let's take mass of that the car is 1000 kg.

Case1:  accelerating the car from 10 m/s to 20 m/s:

Initial kinetic energy \(= (1/2)mv^2\)

Initial kinetic energy \(= (1/2)(1000 kg)(10 m/s)^2\)

Initial kinetic energy \(= 50,000 J\)

Final kinetic energy \(= (1/2)mv^2\)

Final kinetic energy  \(= (1/2)(1000 kg)(20 m/s)^2\)

Final kinetic energy  \(= 200,000 J\)

Change in kinetic energy = 200,000  - 50,000

Change in kinetic energy = 150,000 J

Case2: accelerating the car from 20 m/s to 30 m/s:

Initial kinetic energy \(= (1/2)mv^2\)

Initial kinetic energy \(= (1/2)(1000 kg)(20 m/s)^2\)

Initial kinetic energy \(= 200,000 J\)

Final kinetic energy \(= (1/2)mv^2\)

Final kinetic energy \(= (1/2)(1000 kg)(30 m/s)^2\)

Final kinetic energy \(= 450,000 J\)

Change in kinetic energy = 450,000  - 200,000

Change in kinetic energy = 250,000 J

We can see that accelerating the automobile from 10 to 20 m/s results in less effort than accelerating it from 20 to 30 m/s due to the change in kinetic energy.

The automobile must thus put in more effort to accelerate from a greater velocity than from a lower one.

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Answer

v= 1/R mark me brainliest pls

Answer:

I believe it's B.

Explanation:

The force that a magnet exerts on certain materials, including other magnets, is called magnetic force. The force is exerted over a distance and includes forces of attraction and repulsion. North and south poles of two magnets attract each other, while two north poles or two south poles repel each other.

Answer:

see attachment for the answer.

Explanation:

Answer:

Average velocity, V = 2.5m/s

Explanation:

Given the following data

Displacement = 10m

Time = 4secs

Average velocity can be defined as the rate of change in displacement with time. Velocity is a vector quantity and as such it has both magnitude and direction.

Mathematically, average velocity is given by the equation;

\(Velocity = \frac{displacement}{time}\)

\(V = \frac{d}{t}\)

Substituting into the above equation;

\(V = \frac{10}{4}\)

Average velocity, V = 2.5m/s

Answer:

The correct option is;

Computer, Sensor Machines

Explanation:

In order to detect the exact location of the landing of a tennis ball, a device known as Hawk-Eye is used

Hawk-Eye tracks the balls trajectory using visual sensors and computing technology combined as computerize vision that monitors the path of the  ball path and by statistical computation, graphically presents the most probable path in which the ball travels which can then be viewed onscreen as what is known as a Shot Spot.

The Hawk-Eye system is applied in ball playing games such as tennis, volley ball, association football, hurling, rugby union, Garlic football, badminton, and cricket.

To calculate the de Broglie wavelength (λ) for a proton moving with a speed of 1.1 x 10^6 m/s, we can use the de Broglie wavelength equation:

λ = h / p,

where λ is the de Broglie wavelength, h is the Planck's constant (approximately 6.626 x 10^(-34) J·s), and p is the momentum of the proton.

The momentum (p) of a proton can be calculated using the equation:

p = m * v,

where m is the mass of the proton and v is its velocity.

The mass of a proton (m) is approximately 1.67 x 10^(-27) kg.

Substituting the given values into the equations, we have:

p = (1.67 x 10^(-27) kg) * (1.1 x 10^6 m/s),

p ≈ 1.837 x 10^(-21) kg·m/s.

Now, we can calculate the de Broglie wavelength:

λ = (6.626 x 10^(-34) J·s) / (1.837 x 10^(-21) kg·m/s),

λ ≈ 3.602 x 10^(-13) meters.

Therefore, the de Broglie wavelength for a proton moving with a speed of 1.1 x 10^6 m/s is approximately 3.602 x 10^(-13) meters.

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The appropriate unit of measurement would depend on the distance, precision required, and standard unit used in the country.

The best unit of estimation to use for Dianna's estimation would rely upon a few factors, for example, the distance, the accuracy required, and the standard unit utilized in her country.

In the event that the distance is generally short, utilizing a more modest unit of estimation like meters or feet would be fitting. In any case, in the event that the distance is longer, utilizing a bigger unit of estimation like kilometers or miles would be more suitable.

Furthermore, the accuracy required would likewise assume a part in deciding the proper unit of estimation. In the event that a serious level of accuracy is required, utilizing more modest units of estimation like centimeters or inches would be more proper.

In any case, in the event that a best guess is adequate, utilizing bigger units like miles or kilometers would do the trick.Finally, the standard unit of estimation utilized in Dianna's nation would likewise impact the decision of the unit of estimation.

For instance, assuming Dianna is in the US, utilizing miles would be the most proper unit of estimation. In any case, on the off chance that she is in Europe, utilizing kilometers would be the standard unit of estimation.

Generally speaking, it is critical to consider the distance, accuracy required, and the standard unit of estimation utilized in the nation while deciding the suitable unit of estimation for Dianna's estimation.

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The complete question is:

What is the most appropriate unit of measurement for Dianna to use when measuring the distance from her house in Johns Creek to the airport, and why would this unit be the best choice? Can you provide some context or additional information to help determine the ideal unit of measurement for Dianna's measurement task?

Approximately 10-20 hp of added power is required when using a cartop carrier and driving at 100 km/h in a 25 km/h headwind, compared to not using the carrier in the same conditions.

The added power required when using a cartop carrier and driving at 100 km/h in a 25 km/h headwind is due to the increased drag on the car caused by the carrier and the wind. The exact amount of added power required will depend on the size and shape of the carrier, as well as the specific car and engine being used. However, estimates suggest that this added power could be in the range of 10-20 hp. It is important to note that using a cartop carrier can also impact the handling and stability of the car, so it is important to follow the manufacturer's instructions and drive with caution.

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Answer:

Eliminate D as there is no nonconservative force, then look at each energies before and after. The speed of the book will increase, so kinetic energy is increasing. The height of the book is increasing, so gravitational potential energy is increasing. However, since the spring is becoming decompressed, the elastic potential energy is decreasing.

Explanation:

Answer:

it is A

Explanation: