Consider a double Atwood machine constructed as follows: A mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. The other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. Using two suitable generalized coordinates, set up the Lagrangian and use the Lagrange equations to find the acceleration of the mass 4m when the system is released. Explain why the top pulley rotates even though it carries equal weights on each side.

The answer is letter C vro

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Answer:

8.29m/s

Explanation:

Given

Height of hill H = 3.50m

Initial velocity u = 0m/s

Required

Final velocity v

Using the equation of motion

v² = u²+2gH

v² = 0²+2(9.81)(3.5)

v² = 0+7(9.81)

v² = 68.67

v = √68.67

v = 8.29m/s

Hence the final velocity of the hoop is 8.29m/s

Answer: P1V1 = P2V2

Explanation:

when the lava erupted from the volcano basalt was the rock that cooled quickly or basalt was the only one rock that cooled quickly after the lava erupted from the volcano

Explanation:

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Answer:

Time = 1000 h

Power = 0.05 W = 50 mW

Explanation:

First we will find the current consumed by the lamp. For this purpose we can use the Ohm's Law. The equation of Ohm's Law is written as follows:

V = IR

I = V/R

where,

I = Current = ?

V = Voltage = 5 V

R = Resistance = 500 Ω

Therefore,

I = 5 V/500 Ω

I = 0.01 A = 10 mA

Now the time duration of the operation f lamp can be found by:

Time = Rating/Current

Time = 10000 mAh/ 10 mA

Time = 1000 h

The power consumption of lamp is given as follows:

Power = IV

Power = (0.01 A)(5 V)

Power = 0.05 W = 50 mW

Statements 1,2,3 and 4 match statements B, C, A, and D respectively.A wind turbine converts rotational energy into electrical energy.

According to the Law of conservation of energy. Energy can not be created nor be destroyed, it can transfer from one to another form.

1.A wind turbine converts rotational energy into electrical energy.

2.A roller coaster going downhill converts gravitational energy into mechanical energy

3. Toaster converts electrical energy into thermal energy

4.A car converts rotational energy into mechanical energy.

Hence,statements 1,2,3 and 4 match statements B, C, A, and D respectively.

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Answer:

The magnitude is [tex]B = \frac{450}{7.9* 10^5}[/tex]

The direction is  the positive x axis

Explanation:

From the question we are told that

   The  electric field is  E = 450 V/m in the negative y ‑direction

   The speed of the proton is  [tex]v= 7.9* 10^5\  m/s[/tex] in the positive z direction

Generally the overall force acting on  the proton is mathematical represented as

              [tex]F_E =  q(\vec E + \vec v  * \vec B)[/tex]

Now for the beam of protons to continue un-deflected along its straight-line trajectory then  [tex]F_E =0[/tex]

So

          [tex] 0  =  q( E (-y) + v(z)  * \vec B)[/tex]

=>      [tex]E\^y = v \^ z  * \vec B[/tex]

Generally from unit vector cross product vector multiplication

         [tex]\^ z  \ *  \  \^ x  =  \^  y[/tex]

So the direction of  B (magnetic field must be in the positive x -axis )

So

       [tex]E\^y = v \^ z  *  B\^ x [/tex]

=>     [tex]E\^y = vB ( \^ z  *  \^ x) [/tex]

=>     [tex]E\^y = vB ( \^y) [/tex]        

=>      [tex]E = vB [/tex]  

=>      [tex]B = \frac{450}{7.9* 10^5}[/tex]

=>      [tex]B =  0.0005696 \ T [/tex]  

Answer:

vₓ = 6.73 m/s

Explanation:

       [tex]v_{x} = \frac{\Delta x}{\Delta t} (1)[/tex]

       [tex]\Delta h = \frac{1}{2} * g * t^{2} (2)[/tex]

       [tex]t = \sqrt{\frac{2*\Delta h}{g} } =\sqrt{\frac{2*37.0m}{9.8m/s2}} = 2.75 s (3)[/tex]    

       [tex]v_{x} = \frac{\Delta x}{\Delta t} = \frac{x}{t} = \frac{18.5m}{2.75s} = 6.73 m/s[/tex]

The correct arrangement of the question is;

If a projectile hits a stationary target, and the projectile continues to travel in the same direction,

A) the mass of the projectile is less than the mass of the target.

B) the mass of the projectile is equal to the mass of the target.

C) the mass of the projectile is greater than the mass of the target.

D) nothing can be said about the masses of the projectile and target without further information.

E) this is an unphysical situation and will not actually happen.

Answer:

Option C: The mass of the projectile is greater than the mass of the target.

Explanation:

We want to find what will happen when a projectile continues in motion after it hits a target.

Now, for the projectile to keep moving in that direction after it hits the target, it means it had a force bigger than the force of the target to overpower it and force it to move with it.

Now, from law of inertia, Force = ma.

But in this case acceleration is 0 because the speed of the projectile is constant.

Thus, the force depends on the mass. So for a higher force, the mass of the projectile has to be more than that of the stationary object.

Thus, option C is correct

Answer:

Objects want to keep doing the same thing is a way of stating Newtons First Law.

The correct option is (a) inertia. "Objects want to keep doing the same thing" it implies a connection to the principle of inertia in physics. Inertia is the property of matter that resists changes in its state of motion or rest.

According to Newton's first law of motion, an object will remain at rest or continue moving in a straight line at a constant velocity unless acted upon by an external force. This property is commonly known as "the law of inertia." In other words, objects tend to maintain their current state of motion (whether at rest or in motion) unless influenced by an external force.

When we say "Objects want to keep doing the same thing," we're drawing an analogy between this scientific principle and human behavior. It suggests that objects, like humans, have a natural inclination to resist change and continue their current course of action. This analogy helps convey the idea that objects exhibit a tendency to persist in their existing state.

"Objects want to keep doing the same thing" to inertia emphasizes the notion that objects, like humans, tend to maintain their current state of motion or rest unless influenced by an external force.

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The correct question is:

Objects want to keep doing the same thing is a way of stating ......

a) inertia

b) force

c) power

d) moment

Answer:

The answer is below

Explanation:

An LR series circuit has a differential equation in the form of:

[tex]L\frac{di}{dt}+iR=E(t)\\ \\Given\ that\ 50H,R=5\ ohms,E(t)=200,for\ 0 \leq t \leq\ 50. Hence:\\\\50\frac{di}{dt}+5i =200\\\\\frac{di}{dt}+0.1i =4\\\\Solving\ the\ differential\ equation:\\\\The\ integrating\ factor(I)=e^{\int\limits {0.1} \, dt }=e^{0.1t}. The\ DE\ becomes:\\\\e^{0.1t}\frac{di}{dt}+e^{0.1t}(0.1i) =4e^{0.1t}\\\\e^{0.1t}i=\int\limits {4e^{0.1t}} \, dt \\\\e^{0.1t}i=40e^{0.1t}+A\\\\i(t)=40+Ae^{-0.1t}\\\\but\ i(0)=0\\\\0=40+Ae^{-0.1(0)}\\\\A=-40\\\\i(t)=40-40e^{-0.1t}\\\\[/tex]

At 50 seconds:

[tex]i(50)=40-40e^{-0.1*50}\\\\i(50)=40-40e^{-5}[/tex]

[tex]L\frac{di}{dt}+iR=E(t)\\ \\Given\ that\ 50H,R=5\ ohms,E(t)=0,for\ t> 50. Hence:\\\\50\frac{di}{dt}+5i =0\\\\\frac{di}{dt}+0.1i =0\\\\\frac{di}{dt}=-0.1i\\\\\frac{di}{i}=-0.1dt\\\\\int\limits {\frac{di}{i}} =\int\limits {-0.1} \, dt\\ \\ln(i)=-0.1t+A\\\\taking\ exponential:\\\\i=e^{-0.1t+A}\\\\i=e^{-0.1t}e^A\\\\i(t)=Ce^{-0.1t}\\\\i(50)=40-40e^{-5}=Ce^{-5}\\\\C=40(e^5-1)\\\\i(t)=40(e^5-1)e^{-0.1t}\\\\[/tex]

[tex]i(t)=\left \{ {{40-40e^{-0.1t}\ \ \ \ 0 \leq t \leq 50 } \atop {40(e^5-1)e^{-0.1t}\ \ \ \ t>50}} \right.[/tex]

Answer:

C. mixture

Explanation:

A mixture is an impure substance. It has the following properties;

Granite is a rock. A rock is usually formed by a combination of different minerals.

Granite is made up of many compounds and so it is a mixture.

Answer:

[tex]K=4\times 10^4\ J[/tex]

Explanation:

Given that,

Mass of cannon is,M =  2000 kg

Mass of projectile, m = 2 kg

Velocity of the projectile, v = 200 m/s

We need to find the kinetic energy of the projectile. We know that the formula for the kinetic energy of an object is given by :

[tex]K=\dfrac{1}{2}mv^2\\\\\text{Putting all the values, we get}\\\\K=\dfrac{1}{2}\times 2\times (200)^2\\\\K=40000\ J[/tex]

or

[tex]K=4\times 10^4\ J[/tex]

So, the kinetic energy of the projectile will be [tex]4\times 10^4\ J[/tex].

The two balls have the same acceleration because they are in free fall.

The two balls projected downwards from the top of the build are influenced by gravity. Both ball experience free fall due to gravity.

The equation of motion of the two ball is given as;

v² = u² + 2gh

where;

Thus, we can conclude that the two balls have the same acceleration because they are in free fall.

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Answer:

Where

Explanation:

Answer:

a)  + Q charge is inducce that compensates for the internal charge

b) There is no excess charge on the external face q_net = 0

c) E=0

Explanation:

Let's analyze the situation when a negative charge is placed inside the cavity, it repels the other negative charges, leaving the necessary positive charges to compensate for the -Q charge. The electrons that migrated to the outer part of the sphere, as it is connected to the ground, can pass to the earth and remain on the planet; therefore on the outside of the sphere the net charge remains zero.

With this analysis we can answer the specific questions

a)  + Q charge is inducce that compensates for the internal charge

b) There is no excess charge on the external face q_net = 0

c) If we create a Gaussian surface on the outside of the sphere the net charge on the inside of this sphere is zero, therefore there is no electric field, on the outside

d) If it is very reasonable and this system configuration is called a Faraday Cage

e) We cannot apply this principle to gravity since there are no particles that repel, in all cases the attractive forces.

Answer:

D

Explanation:

Because first phase thr it will follow the law of thermodynamics as it will reach the equilibrium point then decrrases afterwards

Answer:

Option A: a_c = a_t

Explanation:

Let's denote the force acting on the car due to the truck as F_ct

Similarly, the force acting on the truck due to the car is denoted as F_tc.

Now, F_ct = m_c × a_c

Where;

m_c is mass of car

a_c is acceleration of car

Also, F_tc = m_t × a_t

Where;

m_c is mass of truck

a_c is acceleration of truck

Now, since the car is the one pushing the truck, from Newton's laws, we can say that they stick together and move in the same direction at the same acceleration.

Thus, the truck will move with an acceleration equal to that of the car pushing it.

Thus; a_c = a_t

Answer:

 m = 2,759 kg

Explanation:

For this exercise we use the torque relationship

           τ = I α

the moment is

          τ= F r sin θ

since the force is tangential to the ring, the angle is 90º sin 90 = 1

          τ = F r

the moment of inertia of a ring is given by

         I = m r²

let's substitute

           F r = m r²α

            m = F / r α

let's calculate

          m = 40 / (0.10 145)

          m = 2,759 kg

Answer:

hello your question is incomplete attached below is the complete question

and solution to the question

Explanation:

To write The equation of the motion in Matrix form

i)First we write the net torque equation for left mass

ii)Next we write the net torque equation for right mass

iii) represent the equation of motion in Matrix form

Answer:

(a) Wavelength = 3.21 m (b) Time = [tex]1.07\times 10^{-4}\ s[/tex]

Explanation:

Given that,

The frequency of FM radio station, f = 93.4 MHz

(a) We need to find the wavelength of the radio wave associated with this signal. The relation between wavelength and frequency is given by :

[tex]c=f\lambda\\\\\lambda=\dfrac{c}{f}\\\\\lambda=\dfrac{3\times 10^8}{93.4\times 10^6}\\\\\lambda=3.21\ m[/tex]

(b) It is given that, an FM radio station, 20 miles away. Let t is time taken for signal to reach your radio from the station. So,

[tex]t=\dfrac{d}{c}\\\\t=\dfrac{20\times 1609.34}{3\times 10^8}\\\\t=1.07\times 10^{-4}\ s[/tex]

Hence, this is the required solution.

In  Medicine, "etiology" means the origin or cause of a disease.

Similar to Hippocrates, modern scientists who study etiology believe that   diseases come from natural causes such as bites from infected insects.

Answer:diseases come from natural causes such as bites from infected insects

Explanation: just took test

Answer:

2 x 10^10 years.

Explanation:

Given that the sun produces energy via nuclear fusion at the rate of 4×1026 J/s . Based on the proposed overall fusion equation, how long will the sun shine in years before it exhausts its hydrogen fuel? (Assume that there are 365 days in the average year.)

Let us first calculate energy from hydrogen gas.

4(1.007825) + 2(0.00549) - 4.002603 = 0.029795 amu

Since 4.0313 amu H+ > 0.029795 amu =  ratio of 1 to 0.00739

dE = ((2*10^30 kg) x 0.8 x 0.25)(3.00x10^8 m/s)^2 = 3.6x10^46 kg x m^2/s^2  

3.6x10^46 kg x m^2/s^2 x 0.00739 = 2.6604 x 60^44 kg x m^2/s^2

4x10^26 J/s x s = 2.6604x10^44 kg x m^2/s^2  solve for s.

s = 6.651x10^17 seconds

6.651x10^17 seconds x 1 min/60 s x 1 hr/ 60 min x 1 day/ 24 hr x 1 yr / 365 days = 2.1x10^10 years

 Based on the proposed overall fusion equation, it will therefore take the sun shine 2 x 10^10 years before it exhausts its hydrogen fuel.

Answer:

T = 1.4696 10⁴ years

Explanation:

For this exercise we must use Kepler's laws, specifically the third law which is the application of the universal law of gravitation to Newton's second law

               F = ma

               G m M / r² = m a_c = m v² / r

                G M / r = v²

the speed of the circular orbit is

               v = 2π r / T

we substitute

               G M / r = 4π² r² / T²

               T² = (4π² / G M)  r³

Kepler proved that this expression is the same if the radius is changed by the semi-major axis of an ellipse

               T² = (4π² /GM)  a³

the constant is worth

                (4π² / GM) = 2.97 10⁻¹⁹    s² / m³

let's reduce the distance to SI units

AU is the distance from the Earth to the Sun

               a = 600 AU = 600 AU (1.496 10¹¹ m / 1 AU)

               a = 8.976 10¹³ m

               T² = 2.97 10⁻¹⁹ (8.976 10¹³)³

               T² = 21.4786 10²²

               T = 4.63 10¹¹ s

Let's reduce to years

               T = 4.63 10¹¹s (1 h / 3600s) (1 day / 24 h) (1 year / 365 days)

               T = 1.4696 10⁴ years

Answer:

The value is  [tex]v = 1.309*10^{5}\ m/s[/tex]

Explanation:

The radius is [tex]r = 7.40 *10^{20} \  m[/tex]

The mass of the ordinary matter is [tex]M_{rod} =  1.90 *10^{41}\  kg[/tex]

Generally the speed of the star is mathematically represented as

         [tex]v = \sqrt{\frac{G * M}{r} }[/tex]

Here G is the gravitational constant with a value

        [tex]G = 6.67384 * 10^{-11}[/tex]

So

      [tex]v = \sqrt{\frac{6.67384 * 10^{-11} * 1.90 *10^{41}}{7.40 *10^{20}} }[/tex]

=>    [tex]v = 1.309*10^{5}\ m/s[/tex]

Answer:

La aceleración necesaria para detener el avión es - 10.42 m/s².

Explanation:

Un movimiento uniformemente acelerado (M.U.A) es aquél cuya aceleración es constante y la velocidad de un objeto cambia a medida que el movimiento evoluciona.

Siendo la aceleración "a" el cambio de velocidad al tiempo transcurrido en un punto A a B, la velocidad inicial la velocidad que tiene un cuerpo al iniciar su movimiento en un período de tiempo y la velocidad final la velocidad que tiene un cuerpo al finalizar su movimiento en un período de tiempo, entonces en  M.U.A se cumple:

Vf² - Vo² = 2*a*d

donde:

En este  caso:

Reemplazando:

(0 m/s)² - (50 m/s)² = 2*a*120 m

Resolviendo:

[tex]a=\frac{(0 m/s)^{2} -(50 m/s)^{2} }{2*120 m}[/tex]

a= - 10.42 m/s²

La aceleración necesaria para detener el avión es - 10.42 m/s².

Answer:

throw them away............

Answer:

1. frequency (f) = 4.194 × 10^14Hz

2. Energy of photon (E) = 2.779 × 10^-19 J

3. Color is RED

Explanation:

1. Based on the information in this question, a visible light has a wavelength of 715.3 nm.

λ = v/f

Where; λ = wavelength (nm)

v = speed of light (3 × 10^8m/s)

f = frequency (Hz)

f = v/λ

f = 3 × 10^8/715.3 × 10^-9

f = 0.004194 × 10^(8+9)

f = 0.004194 × 10^17

f = 4.194 × 10^14Hz

2. Energy per photon is calculated thus;

E = hf

Where; E = energy of photon (J)

h = Planck's constant (6.626 × 10^-34 J/s)

f = frequency (Hz)

E = 6.626 × 10^-34 × 4.194 × 10^14

E = 27.789 × 10^(-34+14)

E = 27.789 × 10^-20

E = 2.779 × 10^-19 J

3. Based on the wavelength range of the visible spectrum, wavelength of 715.3nm falls between 625-740nm, which is RED color of light. Hence, the color of the visible light is RED.

The frequency is "[tex]419.5\times 10^{12} \ s^{-1}[/tex]", energy per photon is "[tex]2.780\times 10^{-19} \ J[/tex]" and the color is "red".

Given:

Wavelength,

or,

           [tex]= 715.1 \ nm\times (10^-9 \ m/nm)[/tex]

As we know the formula,

→ [tex]Frequency = \frac{Speed \ of \ light}{wavelength}[/tex]

By substituting the values, we get

                    [tex]= \frac{(3\times 10^8) }{715.1\times 10^{-9} }[/tex]

                    [tex]= 419.5\times 10^{12} \ s^{-1}[/tex]  

Now,

The energy per photon will be:

→ [tex]E = Planck's \ constant\times Frequency[/tex]

      [tex]= 6.626\times 10^{-34}\times 419.5\times 10^{12}[/tex]

      [tex]= 2.780\times 10^{-19} \ J[/tex]

Thus the above answer is correct.

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Answer:

The current density in the sphere is 0.32 A/m²

Explanation:

Given that,

Current = 1.0 A

Diameter = 1.0 mm

Radius of sphere = 1.0 m

We need to calculate the current density in the sphere

Using formula of current density

[tex]J=\dfrac{I}{A}[/tex]

Where, I = total current

A = area of sphere

Put the value into the formula

[tex]J=\dfrac{1.0}{\pi\times(1.0)^2}[/tex]

[tex]J=0.32\ A/m^2[/tex]

Hence, The current density in the sphere is 0.32 A/m²

Answer: The correct answer is A) The track was not level and was tilted slightly downward.

Explanation: This is because of the two values: 0.4 kg and 0.5 kg. I won't go into much detail but due to this difference of mass, we know that the track was not level.

"The track was not level and was tilted slightly downward" could explain the difference in the mass.

Thus Option A is appropriate.

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