What do thermal energy and electrical energy have in common

Answer:

The equation of motion is [tex]x(t)=-[/tex][tex]\frac{1}{3} cos4\sqrt{6t}[/tex]

Explanation:

Lets calculate

The weight attached to the spring is 24 pounds

Acceleration due to gravity is [tex]32ft/s^2[/tex]

Assume x , is spring stretched length is ,4 inches

Converting the length inches into feet [tex]x=\frac{4}{12} =\frac{1}{3}feet[/tex]

The weight (W=mg) is balanced by restoring force ks at equilibrium position

mg=kx

[tex]W=kx[/tex] ⇒ [tex]k=\frac{W}{x}[/tex]

The spring constant , [tex]k=\frac{24}{1/3}[/tex]

                            = 72

If the mass is displaced from its equilibrium position by an amount x, then the differential equation is

    [tex]m\frac{d^2x}{dt} +kx=0[/tex]

    [tex]\frac{3}{4} \frac{d^2x}{dt} +72x=0[/tex]

  [tex]\frac{d^2x}{dt} +96x=0[/tex]

Auxiliary equation is, [tex]m^2+96=0[/tex]

                                 [tex]m=\sqrt{-96}[/tex]

                               =[tex]\frac{+}{} i4\sqrt{6}[/tex]

Thus , the solution is [tex]x(t)=c_1cos4\sqrt{6t}+c_2sin4\sqrt{6t}[/tex]

                                 [tex]x'(t)=-4\sqrt{6c_1} sin4\sqrt{6t}+c_2[/tex]  [tex]4\sqrt{6}[/tex] [tex]cos4\sqrt{6t}[/tex]

The mass is released from the rest x'(0) = 0

                    [tex]=-4\sqrt{6c_1} sin4\sqrt{6(0)}+c_2[/tex] [tex]4\sqrt{6}[/tex] [tex]cos4\sqrt{6(0)}[/tex] =0

                                                    [tex]c_2[/tex] [tex]4\sqrt{6} =0[/tex]

                                     [tex]c_2=0[/tex]

Therefore , [tex]x(t)=c_1[/tex] [tex]cos 4\sqrt{6t}[/tex]

Since , the mass is released from the rest from 4 inches

                    [tex]x(0)= -4[/tex] inches

[tex]c_1 cos 4\sqrt{6(0)} =-\frac{4}{12}[/tex] feet

   [tex]c_1=-\frac{1}{3}[/tex] feet

Therefore , the equation of motion is  [tex]-\frac{1}{3} cos4\sqrt{6t}[/tex]

Answer:

harmful effects

1. that will cause air pollution

2. that will destroy our earth

Answer:

useful effects of volcano are :-

harmful effects of volcano are:-

hope it is helpful to you ☺️

At 30°C, the rms speed of a sample of oxygen with a molar mass of 16 g/mol is approximately 482.34 m/s.

The root mean square (rms) speed of a gas molecule is a measure of the average speed of the gas particles in a sample. It can be calculated using the formula:

vrms = √(3kT/m)

Where:

vrms is the rms speed

k is the Boltzmann constant (1.38 x 10^-23 J/K)

T is the temperature in Kelvin

m is the molar mass of the gas in kilograms

To calculate the rms speed of oxygen at 30°C (303 Kelvin) with a molar mass of 16 g/mol, we need to convert the molar mass to kilograms by dividing it by 1000:

m = 16 g/mol = 0.016 kg/mol

Substituting the values into the formula, we have:

vrms = √((3 * 1.38 x 10^-23 J/K * 303 K) / (0.016 kg/mol))

Calculating this expression yields the rms speed of the oxygen sample:

vrms ≈ 482.34 m/s

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Wavelength = speed / frequency.

Wavelength = 3x10^8 m/s / 30 hz

Wavelength = 10 million meters

1/2 wavelength = 5 million meters

(that's about 3,100 miles)

I'm pretty sure the frequency is wrong in the question.

I think it's actually 30 kHz, not 30 Hz.

That makes the antenna about 3.1 miles long.

Answer: Kinectic Energy (KE) is equal to half of an object's mass (1/2*m) multiplied by the velocity.

Explanation: If an object with a mass of 10 kg (m=10 kg) is moving at a velocity of 5 meters per second (v=5 m/s), the kinetic energy is equal to 125 Joules, or (1/2* 10 kg) * 5 m/s^2.

Answer:

Wait lang po sandali po wait lang

Answer:

  k y -b [tex]\frac{dy}{dt}[/tex]dy / dt = m [tex]\frac{d^2y}{dt^2}[/tex]

give us some initial conditions

1) friction force fr = 1N when v = 4m / s

2) an initial displacement of x = 0.08 m for t=0 s

Explanation:

In this exercise, you are asked to state the problem you are posing. We are going to find the equation of motion for this exercise. Let's start with Newton's second law

Let's set a reference system with the y-axis in a vertical and positive direction upwards.

We have four forces: an external downward force, negative in sign, the but that goes down and is negative, the Hook force that goes up and is positive and the friction force that opposes the movement, in this case it goes down being negative

let's write Newton's second law

          F_e -F -fr - W = m a

where

          F_e = -kDy = - k y

          fr = - b v = -b dy / dt

          W = mg

we substitute for the specific case, that is, using the signs

          k y  -b [tex]\frac{dy}{dt}[/tex] - m g - F = m [tex]\frac{d^2y}{dt^2}[/tex]

In the initial condition of the problem, before starting the movement, the friction force is zero and the acceleration is also zero

         k y - m g - F = 0

from this equation you can find the spring constant, y= 9m and F=2 N

It is not clear if when the movement starts this external force becomes zero, but since it balances the weight we can eliminate the two forces that have the same magnitude and opposite direction, so the equation remains

              k y - b [tex]\frac{dy}{dt}[/tex]dy / dt = m [tex]\frac{d^2y}{dt^2}[/tex]

give us some initial conditions

1) friction force fr = 1N when v = 4m / s

2) an initial displacement of x = 0.08 m for t=0 s

therefore, to initiate the movement, a small external force F 'is applied that moves the system to a new equilibrium position and this small force F' is made zero, thus initiating an oscillatory movement, described by the equation.

             k y -b [tex]\frac{dy}{dt}[/tex]dy / dt = m [tex]\frac{d^2y}{dt^2}[/tex]

This is a differential equation of the second degree, therefore it needs two initial conditions for its complete solution

The initial amount of displacement corresponds to the amplitude of movement A = 0.08 m

Answer:

Explanation:

Moment of inertia I = M k² , where M is mass and k is radius of gyration .

Putting the given values in the equation

5000 = 200 x k²

k² = 25

k = 5 cm .

Radius of gyration is 5 cm .

Answer:

sorry I am not confident you the answer

Answer:

8 kV

Explanation:

Here is the complete question

Assume a device is designed to obtain a large potential difference by first charging a bank of capacitors connected in parallel and then activating a switch arrangement that in effect disconnects the capacitors from the charging source and from each other and reconnects them all in a series arrangement. The group of charged capacitors is then discharged in series. What is the maximum potential difference that can be obtained in this manner by using ten 500 μF capacitors and an 800−V charging source?

Solution

Since the capacitors are initially connected in parallel, the same voltage of 800 V is applied to each capacitor. The charge on each capacitor Q = CV where C = capacitance = 500 μF and V = voltage = 800 V

So, Q = CV

= 500 × 10⁻⁶ F × 800 V

= 400000 × 10⁻⁶ C

= 0.4 C

Now, when the capacitors are connected in series and the voltage disconnected, the voltage across is capacitor is gotten from Q = CV

V = Q/C

= 0.4 C/500 × 10⁻⁶ F

= 0.0008 × 10⁶ V

= 800 V

The total voltage obtained across the ten capacitors is thus V' = 10V (the voltages are summed up since the capacitors are in series)

= 10 × 800 V

= 8000 V

= 8 kV

Answer:

velocity = 37.01 m/s

Explanation:

momentum = mass * velocity

61250 = 1655 * x

x = 61250 / 1655

x = 37.0090634441

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

[tex]K = \dfrac{1}{2}mv^2 + \dfrac{1}{2}Iw^2[/tex]

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,

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

[tex]K = \dfrac{3mv^2}{4}[/tex]

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,

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

[tex]K' = \dfrac{1}{2}m'v'^2 + \dfrac{1}{2}m'v'^2[/tex]

K' = m'v'²

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

K = K'

[tex]\dfrac{3mv^2}{4 }= m'v'^2[/tex]

[tex]\dfrac{v^2}{v'^2} =\dfrac{ 4m}{3m'}[/tex]

[tex]\dfrac{v^2}{v'^2} = \dfrac{4}{3}(\dfrac{m}{m'})[/tex]

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

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,

[tex]K = K_o + \dfrac{1}{2}Iw^2[/tex]

where

K₀ = translational kinetic energy of wooden cylinder

[tex]K - \dfrac{1}{2}Iw^2 = K_o[/tex]

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

[tex]\dfrac{3}{4}mv^2 - \dfrac{1}{4}mv^2 = K_o[/tex]

[tex]K_o = \dfrac{1}{2}mv^2[/tex]

For the steel hoop,

[tex]K' = K_1 + \dfrac{1}{2}I'w'^2[/tex]

where

K₁ = translational kinetic energy of steel hoop

[tex]K' - \dfrac{1}{2}I'w'^2 = K_1[/tex]

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

[tex]m'v'^2 - \dfrac{1}{2}m'v'^2 = K_1[/tex]

[tex]K_1= \dfrac{1}{2}m'v'^2[/tex]

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: 550 cm

Explanation:

Original equation: 1/f= 1/do + 1/di.

F=50.0 cm, and do=55.0.

Since we don't have di, we'll have to subtract do to the other side, making the equation: 1/f - 1/do= 1/di.

Doing the math, 1/f - 1/do is 0.0018181818

Then to get di by itself, you multiply both sides by di. Then you divide by 0.0018181818 to get di by itself. You then get: di= 1/0.0018181818

At that point, you just divide 1 by 0.0018181818, which will give you 550 cm

There could be simpler way, but that is just what I did to get the answer. Answer was right on Acellus

Answer:

The cart mark (a) has the most potential energy and the cart marked (b) has the most kinetic energy

Answer:

increasing the masses of the objects and decreasing the distance between the objects

Explanation:

Answer:

well in the pot there is conventional heat, the pot itself is giving off conductable heat, and the radiational heat is coming from the stove.

Answer:

Wind deposits sand into a small mound. So the answer is Deposition

Answer:

just search it up you'll get ur answer

Chris used a non-plane mirror to check out a box resting on a shelf, the focal length of the mirror is mathematically given as

f=8.38cm

Question Parameter(s):

The image of the box was located 15 cm behind the mirror

and the box was placed 19 cm from the mirror.

Generally, the equation for the focal length is mathematically given as

1/f=1/u+1/v

Therefore

1/f=1/15+1/19

f=8.3823529cm

In conclusion,  the focal length of the mirror

f=8.3823529cm

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Answer:

12 min

Explanation:every 4 minutes is 1 mile

Answer:18 watts

Explanation:i just got this question trust me

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Answer:

Conservation of Energy: Like all things, Stirling Engines follow the conservation of energy principle (all the energy input is accounted for in the output in one form or another). ... The hot one supplies all of the energy QH, while the cold one removes energy QC (a necessary part of the cycle).

Explanation:

Answer: Yes

Explanation: All the energy input is accounted for in the output in one form or another

Answer:

[tex]24.9\ \text{m/s}[/tex]

[tex]206.7\ \text{m}[/tex]

Explanation:

m = Mass of skydiver = 80 kg

[tex]x_1[/tex] = Height for which the parachute is closed = 1000-200 = 800 m

[tex]x_2[/tex] = Height for which the parachute is open = 200 m

[tex]f_1[/tex] = Resistive force when parachute is closed = 50 N

[tex]f_2[/tex] = Resistive force when parachute is open = 3600 N

v = Velocity of skydiver on the ground

g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]

h = Height from which the skydiver jumps = 1000 m

The energy balance of the system will be

[tex]mgh-f_1x_1-f_2x_2=\dfrac{1}{2}mv^2\\\Rightarrow 80\times 9.81\times 1000-50\times 800-3600\times 200=\dfrac{1}{2}\times 80\times v^2\\\Rightarrow v=\sqrt{\dfrac{2(80\times 9.81\times 1000-50\times 800-3600\times 200)}{80}}\\\Rightarrow v=24.9\ \text{m/s}[/tex]

The velocity fo the skydiver when he lands will be [tex]24.9\ \text{m/s}[/tex]

x = Height where the person opens the parachute

v = 5 m/s

[tex]mgh-f_1x_1-f_2x_2=\dfrac{1}{2}mv^2\\\Rightarrow 80\times 9.81\times 1000-50\times (1000-x)-3600\times x=\dfrac{1}{2}\times 80\times 5^2\\\Rightarrow 80\times 9.81\times 1000-50000+50x-3600x=\dfrac{1}{2}\times 80\times 5^2\\\Rightarrow x=\dfrac{80\times 9.81\times 1000-50000-\dfrac{1}{2}\times 80\times 5^2}{3550}\\\Rightarrow x=206.7\ \text{m}[/tex]

The height at which the parachute is to be opened is [tex]206.7\ \text{m}[/tex]

1: Ming

2: Chloe

3: 40m

Answer:

The answer is "0.92 c"

Explanation:

[tex]v_1\ (earth) = 0.62 \ c \\\\v_2\ ( enterprise ) = -0.30[/tex]

so,

[tex]v_2 \ (earth) = 0.62 \ c - (-0.30 \ c) \\\\[/tex]

               [tex]= 0.62 \ c +0.30 \ c\\\\= 0.92 \ c[/tex]