A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to 2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g

Answer:

E = 0.1472  J

Explanation:

Given that,

The number of turns in the solenoid, N = 2100

Area of the solenoid, A = 10 cm² = 0.001 m²

The length of the solenoid, l = 30 cm = 0.3 m

Current in the solenoid, I = 4 A

We need to find the magnetic energy stored in the solenoid. The expression for the stored energy is :

[tex]E=\dfrac{1}{2}LI^2[/tex]

Where

L is self inductance of the solenoid,

[tex]L=\dfrac{\mu_oN^2A}{l}\\\\L=\dfrac{4\pi \times 10^{-7}\times 2100^2\times 0.001}{0.3}\\\\L=0.0184\ H[/tex]

So,

[tex]E=\dfrac{1}{2}\times 0.0184\times 4^2\\\\E=0.1472\ J[/tex]

So, 0.1472  J of energy is stored in the solenoid.

Answer:

V = 0.0723 volts = 72.3 milivolts

Explanation:

The emf induced in the rod is the motional emf due to the magnetic field. This motional emf can be calculated by the following formula:

[tex]EMF = V = vBl Sin\theta[/tex]

where,

V = Motional EMF = ?

v = speed of rod = 12.5 m/s

B = Magnetic Field = 6.23 mT = 0.00623 T

l = Length of rod = 92.9 cm = 0.929 m

θ = angle between v and B = 90°

Therefore,

[tex]V = (12.5\ m/s)(0.00623\ T)(0.929\ m)Sin\ 90^o\\[/tex]

V = 0.0723 volts = 72.3 milivolts

Answer: [tex]240\ rad/s^2[/tex]

Explanation:

Given

Length of beam [tex]l=2\ m[/tex]

mass of beam [tex]m=5\ kg[/tex]

Two forces of equal intensity acted in the opposite direction, therefore, they create a torque of magnitude

[tex]\tau =F\times l=200\times 2=400\ N.m[/tex]

Also, the beam starts rotating about its center

So, the moment of inertia of the beam is

[tex]I=\dfrac{ml^2}{12}=\dfrac{5\times 2^2}{12}\\\\I=\dfrac{5}{3}\ kg.m^2[/tex]

Torque is the product of moment of inertia and angular acceleration

[tex]\Rightarrow \tau=I\alpha\\\\\Rightarrow 400=\dfrac{5}{3}\times \alpha\\\\\Rightarrow \alpha =240\ rad/s^2[/tex]

Answer:

The example of the center of the gravity is the middle of a seesaw

Explanation:

I hope this will help you and plz mark me brainlist

Answer:

you may get bullied or teased for being a differrent race, ethnic.

Answer:

Workload

Explanation:

You may feel stressed about a heavier workload or more too do. You will also be paid as an employee unlike, a student.

The correct statement about the wind is:

Wind is the movement of air currents in relation to the Earth's surface, which is caused by pressure differences and air movement.

Therefore, we can conclude that the wind is the current of air that occurs in the atmosphere due to natural causes, from high pressure areas to low pressure areas.

Learn more about Characteristics of the wind here: https://brainly.com/question/11463167

Answer:

speed: 35m/s

direction: left

Explanation:

Assuming the right side is the positive direction:

before explosion:

P = mv = 0

after explosion:

P' = 15P + 5P

(Set the velocity of the 15kg piece after explosion as v1' and the velocity of the 5kg piece after explosion as v2')

P' = 0.75mv1' + 0.25mv2'

P' = (15kg)v' + (5kg)(105m/s)

P' = 525kg/m/s + (15kg)v1'

P = P'

525kg/m/s + (15kg)v1' = 0

(15kg)v1' = -525kg/m/s

v1' = -35m/s

speed = |-35| = 35m/s

direction is to the left since the right side is the positive direction.

Answer:

B) a 1200 kg car driving 25 m/s

Explanation:

Momentum can be defined as the multiplication (product) of the mass possessed by an object and its velocity. Momentum is considered to be a vector quantity because it has both magnitude and direction.

Mathematically, momentum is given by the formula;

[tex] Momentum = mass * velocity [/tex]

This ultimately implies that, the mass of an object or body is directly proportional to its momentum. Thus, the higher the mass of an object or body, the greater would be its momentum and vice-versa.

By mere inspection of the data given, we can see that the object with the greatest amount of mass and velocity is the car weighing 1200 kilograms and moving at 25 meters per seconds.

Substituting into the formula, we have;

[tex] Momentum = 1200 * 25 [/tex]

Momentum = 30,000 Kgm/s

Answer:

Explanation:

angle of incidence.

Answer:

When the glass rod is rubbed with silk, the silk strips electrons from the rod, leaving it a positive charge. When the hard rubber rod is rubbed with wool, it gains electrons from the wool, gaining a negative charge.

Explanation:

Answer:

B i think

Explanation:

...

Answer:

B

Explanation:

Answer:

6.26 m/s

Explanation:

Since we are neglecting viscous losses and surface tension effects in the liquid jet, by conservation of energy, the potential energy loss of the jet = kinetic energy gain of the jet

So, mgh = 1/2mv² where m = mass of water in jet, g = acceleration due to gravity = 9.8 m/s², h = height of outlet = 2.0 mand v = velocity of liquid jet

So, mgh = 1/2mv²

gh = 1/2v²

v² = 2gh

v = √(2gh)

v = √(2 × 9.8 m/s² × 2.0 m)

v = √(39.2 m²/s²)

v = 6.26 m/s

Answer:

t = 0.437 s

Explanation:

The speed of sound is a constant that is worth v = 343 m / s

           v = d / t

            t = d / v

the time it takes for the sound to reach Clark at d = 150 m is

           t = 150/343

           t = 0.437 s

This same sound takes much longer to reach you

          t₂ = 127 10³/343

          t₂ = 370 s

Answer:

The energy goes from the ground state to the excited states above it.

Answer:

3.54

Explanation:

some nerd thing I found it on Yahoo answers

Answer:

3.54º

Explanation:

Find the blue θ first

sin⁻¹(540x10⁻⁹/2.88x10⁻⁶)=8.99°

Then find the orange θ

sin⁻¹(625x10⁻⁹/2.88x10⁻⁶)=12.53°

Take the differences and subtract

12.53°－8.99°=3.54°

Answer:

500km per hour

Explanation:

if in 2 hours the airplane flies 1000 km then 1000 divided by 2 is 500km per hour.

Answer:

K E=( mv²)/2

=(60×3.5²)/2

=367.5J

Answer:

a.

Explanation:

there would be a new planet is our solar system which could cause different gravitation pull on all the planets also there could be possible be new life form or other valuable metals that haven't been discovered on this planet. hope this helps somewhat

Answer: B

Explanation:

Answers A and C are examples of physical weathering while B is chemical weathering when water and lime mix it creates a reaction

Answer:

como  ías

Explanation:

Answer:

The predicted height is 2.809 meters, writing this in centimeters we get (1m = 100cm):

h = 2.809 m = (2.809)*(100cm) = 280.9 cm

And the total energy is:

E = 6.696 J

Explanation:

First let's see the problem.

We have an object of mass m = 274g which is thrown upwards with an initial velocity v0 = 6.991 m/s, in a place with a gravitational acceleration of g = 8.7 m/s^2

When the object is on the air, the only force acting on it will be the gravitational force, then the acceleration of the object will be equal to the gravitational acceleration, then we can write:

a(t) = -8.7 m/s^2

Where the negative sign is because this acceleration points down.

Now to get the velocity of the object we can integrate over time to get:

v(t) = (-8.7 m/s^2)*t + v0

Where v0 is a constant of integration, which is the initial velocity, then we can write this as:

v(t) = (-8.7 m/s^2)*t + 6.991 m/s

Now we can integrate again over the time to get the position equation.

p(t) = (1/2)*(-8.7 m/s^2)*t^2 + (6.991 m/s)*t + p0

Where p0 is the initial position, because the ball is being thrown from the ground, the initial position is 0.

Then the position equation is:

p(t) = (1/2)*(-8.7 m/s^2)*t^2 + (6.991 m/s)*t

Ok, now we know all the movement equations for the object.

The first thing we want to know is the maximum height of the object.

We know that the object reaches its maximum height when the velocity is zero (this is, the velocity stops being positive, meaning that the object stops going up, then in that time we have the maximum height)

We need to solve:

v(t) = 0m/s = (-8.7 m/s^2)*t + 6.991 m/s

(8.7 m/s^2)*t =  6.991 m/s

t =  6.991 m/s/( (8.7 m/s^2)  = 0.804 seconds

The maximum height of the object is given by:

p(0.804s) = (1/2)*(-8.7 m/s^2)*(0.804)^2 + (6.991 m/s)*(0.804) = 2.809 m

The maximum height of the object is 2.809 meters.

Now let's find the maximum energy.

Remember that the energy of an object can be written as the sum of the potential energy U and the kinetic energy K.

E = K + U

Such that for an object of mass m and velocity v, the kinetic energy is:

K = (1/2)*m*v^2

And for an object of mass m, at a height h from the ground and with gravitational acceleration g, the potential energy is:

U = m*g*h

Now, when the object is at its maximum height, the velocity is zero.

Then K = 0

And for conservation of energy, the total energy of the object becomes potential energy.

E = 0 + U

E = U

So if we find the potential energy at the maximum height of the object's path, we can find the total energy of the object.

We know that:

mass = m = 274g = 0.274 kg  (here i used that 1kg = 1000g)

height = h = 2.809 meters.

gravitational acceleration = g = 8.7 m/s^2

Then the potential energy at this point is:

U =  0.274 kg*(2.809 meters)*(8.7 m/s^2) = 6.696 J

This means that the total energy of the object is:

E = 6.696 J

Answer:

Energy in carriage (Potential energy) = 4,116 J

Explanation:

Given:

Mass of baby = 20 kg

Height = 21 m

Find:

Energy in carriage (Potential energy)

Computation:

The energy accumulated in an object as a result of its location relative to a neutral level is known as potential energy.

In carriage accumulated energy is potential energy.

Energy in carriage (Potential energy) = mgh

Energy in carriage (Potential energy) = (20)(9.8)(21)

Energy in carriage (Potential energy) = 4,116 J

Answer:

[tex]4.47\ \text{km/h}[/tex]

Explanation:

[tex]\dfrac{da}{dt}[/tex] = Rate at which the distance between A and starting point of B is changing = -20 km/h

[tex]\dfrac{db}{dt}[/tex] = Rate at which the distance of B is changing = 15 km/h

[tex]\dfrac{dc}{dt}[/tex] = Rate at which the distance between A and B is changing

Time after which the rate at which the distance between A and B is changing is 4 hours

Distance covered by A in 4 hours = [tex]20\times 4=80\ \text{km}[/tex]

a = Distance remaining to the start point of B = [tex]110-80=30\ \text{km}[/tex]

b = Distance covered by B in 4 hours = [tex]15\times 4=60\ \text{km}[/tex]

Distance between A and B after 4 hours

[tex]c=\sqrt{a^2+b^2}\\\Rightarrow c=\sqrt{30^2+60^2}\\\Rightarrow c=67.08\ \text{km}[/tex]

[tex]c^2=a^2+b^2[/tex]

Differentiating with respect to time we get

[tex]c\dfrac{dc}{dt}=a\dfrac{da}{dt}+b\dfrac{db}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{a\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{30\times -20+60\times 15}{67.08}\\\Rightarrow \dfrac{dc}{dt}=4.47\ \text{km/h}[/tex]

The rate at which the distance between the ships is changing at 4 PM is [tex]4.47\ \text{km/h}[/tex].

Answer:

66.67 km/h

Explanation:

20 + 30 = 50

50/.75 = 66.67

Answer:

r₂ = 0.316 m

Explanation:

The sound level is expressed in decibels, therefore let's find the intensity for the new location

            β = 10 log [tex]\frac{I}{I_o}[/tex]

let's write this expression for our case

           β₁ = 10 log \frac{I_1}{I_o}

           β₂ = 10 log \frac{I_2}{I_o}

          β₂ -β₁ = 10 ( [tex]log \frac{I_2}{I_o} - log \frac{I_1}{I_o}[/tex])

          β₂ - β₁ = 10 [tex]log \frac{I_2}{I_1}[/tex]

          log \frac{I_2}{I_1} = [tex]\frac{60 - 20}{10}[/tex] = 3

           [tex]\frac{I_2}{I_1}[/tex] = 10³

           I₂ = 10³ I₁

having the relationship between the intensities, we can use the definition of intensity which is the power per unit area

           I = P / A

           P = I A

the area is of a sphere

          A = 4π r²

the power of the sound does not change, so we can write it for the two points

          P =  I₁ A₁ =  I₂ A₂

          I₁ r₁² = I₂ r₂²

we substitute the ratio of intensities

          I₁ r₁² = (10³ I₁ ) r₂²

         r₁² = 10³ r₂²

         r₂ = r₁ / √10³

we calculate

          r₂ = [tex]\frac{10.0}{\sqrt{10^3} }[/tex]

          r₂ = 0.316 m

Answer:

The induced current can be increased in the coil in the following ways: By increasing the strength of the magnet. By increasing the speed of the magnet through the coil.

Explanation:

Answer:

[tex]\theta=76\ rad[/tex]

Explanation:

Hoven that,

Initial angular velocity of the wheel = 24 rad/s

Final angular velocity = 14 m/s

Time, t = 4 s

We need to find how many radians does the wheel turn through during the 4 s interval. Let the displacement is [tex]\theta[/tex]. Using second equation of rotational kinematics to find it such that,

[tex]\theta=\omega_i t+\dfrac{1}{2}\alpha t^2[/tex]

Where

[tex]\alpha[/tex] is angular acceleration

[tex]\alpha =\dfrac{\omega_f-\omega_i}{t}\\\\\alpha =\dfrac{14-24}{4}\\\\\alpha =-2.5\ rad/s^2[/tex]

So,

[tex]\theta=24\times 4+\dfrac{1}{2}\times (-2.5)\times 4^2\\\\\theta=76\ rad[/tex]

So, it will turn 76 radian during the 4 s interval.