A 1.70 mm string of weight 0.0135 NN is tied to the ceiling at its upper end, and the lower end supports a weight WW. Ignore the very small variation in tension along the length of the string that is produced by the weight of the string. When you pluck the string slightly, the waves traveling up the string obey the equation
y(x,t) = (8.50mm)cos(172rad?m?1x?2730rad?s?1t)
Assume that the tension of the string is constant and equal to W.
1) How much time does it take a pulse to travel the full length of the string?
2) What is the weight W?
3) How many wavelengths are on the string at any instant of time?
4) What is the equation for waves traveling down the string?
a) y(x,t) = (8.50 mm)cos(172rad?m?1 x ?2730rad?s?1t)
b) y(x,t) = (8.50 mm)cos(172rad?m?1 x +2730rad?s?1t)
c) y(x,t) = (10.5 mm)cos(172rad?m?1 x +2730rad?s?1t)
d) y(x,t) = (10.5 mm)cos(172rad?m?1 x ?2730rad?s?1t)

Answer:

a) 0.22 m/s

b) 531.67 N

c) 508.81 J

d) 38.72 J

Explanation:

the mass of the astronaut = 121 kg

astronaut's push of speed = 2.9 m/s

mass of the space capsule = 1600 kg

a) according to the conservation of momentum, the summation of the total momentum in a system must be equal to zero.

let us take the direction of the astronaut as positive.

Astronaut's momentum p = mv

where

m is the mass

v is the velocity

momentum p = 121 x 2.9 = 350.9 kg-m/s

The space capsules momentum = mv

==> 1600 x (-v) = -1600v    this is because the space capsule moves in the opposite direction to the astronaut.

according to conservation of momentum

350.9 + (-1600v) = 0

350.9 = 1600v

v = 350.9/1600 = 0.22 m/s

b) magnitude of the force F is the rate of change of momentum.

The astronaut and the space capsule both change momentum from 0 to 350.9 kg-m/s. In 0.66 seconds, the force will be

F = [tex]\frac{m(v - u)}{t}[/tex]

where

u is their initial velocity = 0 m/s

where v = 2.9

t = 0.66

substituting, we have

F = [tex]\frac{121(2.9 - 0)}{0.66}[/tex] = 350.9/0.66 = 531.67 N  this same force is experienced by the space capsule

c) Kinetic energy of the astronaut = [tex]\frac{1}{2} mv^{2}[/tex]

m is the mass = 121 kg

v is the velocity = 2.9 m/s

KE = [tex]\frac{1}{2}*121*2.9^{2}[/tex] = 508.81 J

d) Kinetic energy of the space capsule = [tex]\frac{1}{2} mv^{2}[/tex]

KE = [tex]\frac{1}{2}* 1600* 0.22^{2}[/tex] = 38.72 J

Answer:

The  work function is  [tex]\phi = 2.46 \ eV[/tex]

Explanation:

From the question we are told that

    The light energy is  [tex]E = 3.56 eV[/tex]

     The  stopping voltage is  [tex]V = 1.10 \ V[/tex]

Generally work function is mathematically represented as

      [tex]\phi = E - KE[/tex]

Where KE is the kinetic energy of the ejected electron and it is mathematically represented as

         [tex]KE = V * e[/tex]

Where  e is the charge on the electron

So  

        [tex]KE = 1.10eV[/tex]

Thus  

        [tex]\phi = 3.56eV - 1.10 eV[/tex]

=>      [tex]\phi = 2.46 \ eV[/tex]

Answer:

[tex] \boxed{\sf Kinetic \ energy \ (KE) = 48 \ J} [/tex]

Given:

Mass (m) = 6 kg

Speed (v) = 4 m/s

To Find:

Kinetic energy (KE)

Explanation:

Formula:

[tex] \boxed{ \bold{\sf KE = \frac{1}{2} m {v}^{2} }}[/tex]

Substituting values of m & v in the equation:

[tex] \sf \implies KE = \frac{1}{2} \times 6 \times {4}^{2} [/tex]

[tex] \sf \implies KE = \frac{1}{ \cancel{2}} \times \cancel{2} \times 3 \times 16[/tex]

[tex] \sf \implies KE =3 \times 16[/tex]

[tex] \sf \implies KE = 48 \: J[/tex]

Answer:

The  value is  [tex]\mu_k = 0.102 0[/tex]

Explanation:

From the question we are told that

    The initial speed is  [tex]u = 10 \ m/s[/tex]

    The  distance traveled is  [tex]d = 50 \ m[/tex]

Generally we can obtain the acceleration using the kinetic equation as follows

     [tex]v^2 = u^2 + 2as[/tex]

=>   [tex]a = \frac{v^2 - u^2 }{ 2s}[/tex]

=>   [tex]a = \frac{0^2 - 10^2 }{ 2 * 50 }[/tex]

=>   [tex]a = -1 m/s^2[/tex]

The  negative sign shows that the pluck is decelerating

  The force driving the pluck is mathematically evaluated as

       [tex]F = ma[/tex]

 This force is also equivalent to the frictional force acting on the pluck

So  

      [tex]ma = m * g* \mu_k[/tex]

=>  [tex]\mu_k = \frac{a}{g}[/tex]

=>   [tex]\mu_k = \frac{1}{9.8 }[/tex]

=>   [tex]\mu_k = 0.102 0[/tex]

Answer:

a. 14,400 Watts

Explanation:

Power is current times voltage.

P = IV

Voltage is current times resistance.

V = IR

Substitute:

P = I²R

P = (12 A)² (100 Ω)

P = 14,400 W

Answer:

0.2871 kg m/s

Explanation:

p = mv

convert 33g into kg (0.033)

mulitply byt 8.7 to get 0.2871

Answer:

The pressure on the wall is 9416.25 N/m²

Explanation:

Please see the attachments below

Answer:

A. The fan does work on the air in the room leading to an increase in its thermal energy and temperature.

Explanation:

Fans move fluid, typically a gas, such as air, through a room or an enclosure. A fan consists of a rotating arrangement of vanes or blades (impeller), which acts on the air. The action of the impeller does work on the fan by compressing and moving the air forward, doing work on it in the process. The work done on the fan leads to an increase in the thermal energy of the air.

Explanation:

The total displacement is 3 miles

What is displacement?

Simply put it is the sum total of the changes in position of an object from it initial position to it final position, It is a vector quantity and has a direction and magnitude.

In our example the displacement the total points of movement can be annotated as

From A to B to C

From A to B= 1 mile

From B to C= 1 miles

Displacement is 1 + 2= 3 miles

Answer:

D

Explanation:

pressure change have nothing to do with the spontaneity.

Entropy change , enthalpy change , temperature have roles in deciding spontaneity.

Answer:

a) the size of the sport DECREASES  , b)the spot size is increased

c)  it has no effect  and d) spot size DECREASES

Explanation:

The expression for constructive interference in diffraction is

         a sin θ = m λ

the chaff of the spot is given by the minimum interference m = 1

           a sin θ = λ

let's use trigonometry to find the angle

         tan λ= y / L

         tan θ = sin θ / cos t = sin θ

         sin θ = y / L

          a y / L = lam

in the case of materials with circular dome, the problem must result in polar coordinates, with which a numerical constant is introduced

          y = 1.22 L / a lam

let's analyze each electrode action in this equation

a) Decrease lam

         y ’= 1.22 L / a lm2

          lam2 <lamo

          y '<y

therefore the size of the sport DECREASES

b) decreases the lens diameter

       a '<a

         y ’= 1.22 L / a’ lam

         y '> y

the spot size is increased

c) Decrease the focal length

The expression does not depend on the focal length, so it has no effect

d) decrease in L

         y ’= 1.22 L’ / a lam

spot size DECREASES

Answer:

λ = 2.7608 x 10⁻⁷ m = 276.08 nm

Explanation:

The work function of a metallic surface is the minimum amount of photon energy required to release the photo-electrons from the surface of metal. The work function is given by the following formula:

Work Function = hc/λ

where,

Work Function = (4.5 eV)(1.6 x 10⁻¹⁹ J/1 eV) = 7.2 x 10⁻¹⁹ J

h = Plank's Constant = 6.626 x 10⁻³⁴ J.s

c = speed of light = 3 x 10⁸ m/s

λ = longest wavelength capable of releasing electron.

Therefore,

7.2 x 10⁻¹⁹ J = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/λ

λ = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(7.2 x 10⁻¹⁹ J)

λ = 2.7608 x 10⁻⁷ m = 276.08 nm

Answer:

C) three

Explanation:

Let gram of gold required be m . Let temperature change in both be Δ t .

heat absorbed = mass x specific heat x change in temperature

for copper

heat absorbed = 1 x .385 x Δt

for gold

heat absorbed = m x .129 x Δt

So

m x .129 x Δt = 1 x .385 x Δt

m = 2.98

= 3 g approximately .

Answer:

"You can create an electromagnet by wrapping an insulated wire around a metal with ferromagnetic properties and applying an electric current."

Explanation:

An electromagnet is created by coiling a ferromagnetic material with the help of an insulated wire around it and applying a  current . Insulated wire carrying current produces magnetic field around it . This field produces magnetic flux in the magnetic material and makes it magnet . When we switch of current , magnetic field ceases to exist and therefore , magnetic material ceases to be a magnet .

Explanation:

Answer:

The pressure is [tex]P_2 = 1.84 \ a.t.m[/tex]

Explanation:

From the question we are told that

   The first  volume of  is  [tex]v_1 = 3.5 \ L[/tex]

   The first  pressure is  [tex]P_1 = 2.7 \ a.t.m[/tex]

   The first  temperature is  [tex]T_1 = 350 \ K[/tex]

    The  new temperature is  [tex]T_2 = 620 \ K[/tex]

     The  new volume is  [tex]V_2 = 9.1 \ a.t.m[/tex]

Generally according to the combined gas law we have that

      [tex]\frac{P_1 V_1 }{T_1 } = \frac{P_2 V_2 }{T_2 }[/tex]

=>  [tex]P_2 = \frac{P_1 * V_1 * T_2 }{T_1 * V_2 }[/tex]

=>    [tex]P_2 = \frac{ 2.7 * 3.5 * 620 }{ 350 * 9.1 }[/tex]

=>  [tex]P_2 = 1.84 \ a.t.m[/tex]

Answer:

The  value is  [tex]l = 8.58 \ m[/tex]

Explanation:

From the question we are told that

  The  frequencies of two successive harmonics  is  [tex]f_ a = 220 \ Hz[/tex] , [tex]f_b = 240 \ Hz[/tex]

   The  speed of sound in the air is  [tex]v = 343 \ m/s[/tex]

Generally a harmonic frequency is mathematically represented as

        [tex]f_n = \frac{n * v }{2l}[/tex]

here l is the length of the pipe

n is the order of position of the harmonics

 Now since we do not know the order of the given harmonic frequencies but we are told that they are successive then the frequencies can be mathematically represented as

     [tex]220 = \frac{n * v}{ 2 l }[/tex]

and

     [tex]240 = \frac{ (n+1 ) v }{2l}[/tex]

So  

    [tex]240 - 220 = \frac{ (n+1 ) v }{2l} - \frac{n * v}{ 2 l }[/tex]

   [tex]20 = \frac{v}{2l}[/tex]

=>   [tex]l = 8.58 \ m[/tex]

Answer:

  y/y₀ = 1/2 + v₀²/(2 g y₀)

Explanation:

         This in a kinematics exercise in a mention  

ball A.  

Since the ball is dropped, its velocity starts at zero, at the meeting point the equation is  

[tex]v_{A}^2[/tex]= - 2 g (y₀-y)  

ball B  

v_{B}^2 = v₀² - 2 g y

we substitute  

               2v_{B}^2 = -2 g (y₀ -y)  

               v_{B}^2 = - g y₀ + 2g y  

              v_{B}^2 = v₀² - 2gy

we have a system of two equations with two unknowns, therefore it can be solved. Let's multiply-by -1 and add  

       0 = g y₀ + v₀² -2gy  

we clear the height  

      y = (g yo + v₀²) / 2g  

     y = yo / 2 + v₀² / 2g

In this exercise we assume that the height of the building is known and the initial velocity of ball B  

The fraction is

y/yo = 1/2 + v₀²/(2gyo)

Answer:

2.42631E-13m

Explanation:

First we find the mass defect

Which is m= 0-2(9.10939E-33kg)

= - 1.82188E-30kg

Now find the energy

S

E= mc²=( -18.82188E-30)(2.999792E8)²

= 1.63742E-13J

Thus energy per photon will be

1.63742E-13J/2= 8.18710E-14J

So wavelength is given as

Lambda= hc/E

= (6.62608E-34)(2.997E8)/8.18710J

= 2.42631E-13m

The wavelength of radiation used to annihilate a positron and an electron is required.

The wavelength of the electromagnetic radiation used is 2.42 pm.

The mass of positron and electron are equal

m = Mass = [tex]\dfrac{0.000549}{6.022\times 10^{26}}=9.11\times 10^{-31}\ \text{kg}[/tex]

c = Speed of light = [tex]3\times 10^{8}\ \text{m/s}[/tex]

h = Planck's constant = [tex]6.626\times 10^{-34}\ \text{Js}[/tex]

Total energy in the collision is

[tex]E_T=mc^2+mc_2\\\Rightarrow E_T=2mc^2\\\Rightarrow E_T=2\times 9.11\times 10^{-31}\times (3\times 10^{8})^2\ \text{J}[/tex]

Energy released per photon is

[tex]E=\dfrac{E_T}{2}\\\Rightarrow E=\dfrac{2\times 9.11\times 10^{-31}\times (3\times 10^{8})^2}{2}\\\Rightarrow E=9.11\times 10^{-31}\times (3\times 10^{8})^2\ \text{J}[/tex]

Energy is given by

[tex]E=\dfrac{hc}{\lambda}\\\Rightarrow \lambda=\dfrac{hc}{E}\\\Rightarrow \lambda=\dfrac{6.626\times 10^{-34}\times 3\times 10^8}{9.11\times 10^{-31}\times (3\times 10^{8})^2}\\\Rightarrow \lambda=2.42\times 10^{-12}\ \text{m}=2.42\ \text{pm}[/tex]

The wavelength of the electromagnetic radiation used is 2.42 pm.

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Answer:

Explanation:

Displacement of train = 60 - 25 = 35 mile

= 35 x 1.6 = 56 km

duration of time = 45 - 15 = 30 minutes

= 30 x 60 = 1800 s

velocity of train = displacement / time

= 56 / 1800 = .03111 km /s

= 31.111 m / s

Answer:

The height of the object is 50 feet

Explanation:

Given that:

The path of an object projected at a 45 degree angle with initial velocity of 80 feet per second is given by the  function  [tex]h (x) =\dfrac{-32}{(80)^2}x^2+x[/tex]

where;

x  is the horizontal distance traveled and  h(x) is the height in feet.

The objective is to use the TRACE feature of your calculator to determine the height of the object when it has traveled 100 feet away horizontally.

Before then;

If the function [tex]h (x) =\dfrac{-32}{(80)^2}x^2+x[/tex]

and x = 100

then :

[tex]h (x) =\dfrac{-32}{(80)^2}(100)^2+100[/tex]

[tex]h (x) =\dfrac{-32}{6400} \times 10000+100[/tex]

[tex]h (x) =- 0.005 \times 10000+100[/tex]

[tex]h (x) =- 50+100[/tex]

h(x) = 50 feet

Using the TRACE CALCULATOR,

In your Trace calculator;

input Y = X - 32 X^2/(80)        this  because in the calculator Y denotes h(x)

Now over to the WINDOW

set the window as follows:

Xmin = 0

Xmax = 200

Xsc1 =1

Ymin = 0

Ymax = 50

Ysc = 1

Xres = 1

After that, click on the graph key and an output will display as seen in the image below.

Therefore, the show the value of Y which we earlier said it denotes the h(x) = 50 feet

Answer:

Therefore, the brick appears to have an additional force pushing it upward.

Explanation:

When a brick is submerged in the water, it has two forces acting upon it. One force is the gravitational force or the weight of the brick, that acts downward. The weight force also acts on the brick when it is not in water. But, in water an additional force acts on the brick. This additional force is named as Buoyant Force. This force is equal to the weight of the water displaced by the brick. And this Buoyant Force acts on the brick in the upward direction. The formula for this force is given as follows:

Buoyant Force = (Density of Water)(Volume of Water Displaced)(g)

Therefore, the brick appears to have an additional force pushing it upward.

Answer:

increase the tension on the hose and shake the end fewer times per second.

Explanation:

This is because Tension of the rope is directly proportional to wavelength and inversely proportional to the frequency ( shakes per second) so increasing tension increases wavelength and vice versa

Wavelength= Tension/ frequency

The most efficient way for her to increase the wavelength is to increase the rate of shaking the rope per second.

Wavelength measures the distance of wave that occur between one crest and another crest.

To increase the wavelength the rope end should be shaked in a number of time per second this will help build up tension in the rope.

Therefore, she should increase the rate of shaking the rope per second.

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Answer:

   I_FWHW = 3.2 μW / m²

Explanation:

In the analysis of optics and electricity a very useful magnitude is the width at half height (FWHW) and the intensity at this height, which is given by

               I_FWHW = I₀ / 2

corresponds to the width of the line for this intensity.

In this case they give the maximum intensity for which

               I_FWHW = 6.2 / 2

               I_FWHW = 3.2 μW / m²

You do not give more data in your exercise, but the most interesting calculation is to find the angle values ​​for which you have this intensity since it is this range is 50% of the energy of the system, have I write the equation for this calculation

             I = Io cos² x₁   (sin x / x)²

             x₁ = π d sin θ /λ

             x = π b sin θ /λ

where d is the separation of the slits and b the width of each slit

Answer

a)0.0495 J

b)0.01681 m

c)0.7218 m/s

Explanation:

Given

Mass of the.toy M = 0.190 kg

force constant k = 350 N/m

Displacement from equilibrium x = 0.0140 m

Speed v = 0.400 m/s

a)What is the toy's total energy at any point of its motion?

The total energy at any point of it's motion can be calculated by adding together both the potential and kinetic energy of the toy, since it's posses potential energy when at rest and kinetic energy at motion

Total energy E = kinetic energy + potential energy

E = ¹/₂mv² + ¹/₂kx²

E = ¹/₂ (0.190)(0.4)² + ¹/₂ (350)(0.0140)²

E = 0.0495 J

Hence,the total energy is 0.0495 J

b) the amplitude of the motion can be calculated using below formula

Let amplitude = A

E = ¹/₂KA²

if we make Amplitude A the subject of the formula we have

A=√(2E/k)

But we have calculated our E up there, our K was given in question then if we substitute we have

A= √(2×0.0495)/350

Ans: 0.01681 m

Hence, our Amplitude is 0.01681 m

c) the the toy's maximum speed during its motion can be calculated using the expression below

Let maximum speed = vmax

E = (1/2)M * vmax^2

If we make vmax the subject of the formula we have

vmax =√(2E/m)

vmax= √(2×0.0495)/0.190

vmax=0.7218 m/s

Hence our vmax is 0.7218 m/s

Explanation:

Assuming constant speed:

Distance = speed × time

17.8 m = (5.3 m/s) t

t = 3.36 s

Answer:

Energy will be reduced by 0.3

Explanation:

Given that E = 1/2 QV

So if V is increased by 6

=> V = E/ 3Q

So the energy will be divided by a factor 1/3 of be reduced by 0.3

Answer:

B

Explanation:

in graph B, you can see that the position increases and remains constant for a while before returning to 0

Answer:

T = 0

Explanation:

Given that,

Mass of the box, m = 55 kg

We need to find the tension in the rope if the box is at rest. When the object is at rest, its acceleration is equal to 0. It would mean that the net force equals 0. So, the tension in the rope is equal to 0.

Answer:

In this process, the pressure increases by a factor of 2.

Explanation:

For an isothermal process, the temperature remains constant throughout the process.

Also, PV = constant

It means that there is an inverse relationship between pressure and volume of the gas.

If the volume is decreased by a factor of 2, the pressure increases by a factor of 2. Hence, the correct option is (c).

Answer:A is the correct answer

Explanation: