a certain engine has a second-law efficiency of 85%. During each cycle, it absorbs 480J of heat form a reservoir at 300C and dumps 300J of heat to a cold termperature reservoir.What is the temperature of the cold reservoir?

Answer:

Vx =  10.9 m/s ,  Vy = 15.6 m/s

Explanation:

Given velocity V= 19 m/s

the angle 35 ° is taken from Y-axis so the angle with x-axis will be 90°-35° = 55°

θ = 55°

to Find Vx = ? and Vy= ?

Vx = V cos θ

Vx = 19 m/s  × cos 55°

Vx =  10.9 m/s

Vx = V sin θ

Vy = 19 m/s  × sin 55°

Vy = 15.6 m/s

15.56m/s and 10.90m/s respectively

The vertical and horizontal components of a given vector, say A, are given by

[tex]A_{Y}[/tex] = A sin θ                  ----------------(i)

[tex]A_{X}[/tex] = A cos θ                 ----------------(ii)

Where;

[tex]A_{Y}[/tex] is the vertical component of the vector A

[tex]A_{X}[/tex] is the horizontal component of the vector A

A is the magnitude of the vector A

θ is the angle the vector makes with the positive x-axis (horizontal direction).

Now, from the question;

The vector is the velocity of the 1-kg discus. Lets call it vector V

The magnitude of the velocity vector V = V = 19m/s

The angle that the vector makes with the positive x-axis = θ

To calculate θ;

Notice that the velocity vector makes an angle of 35° from the vertical direction rather than the horizontal direction.

Therefore, to get the horizontal direction of the velocity vector, we subtract 35° from 90° as follows;

θ = 90° - 35° = 55°

Now, the vertical and horizontal components of the velocity vector, V, are given by

[tex]V_{Y}[/tex] = V sin θ              --------------------(iii)

[tex]V_{X}[/tex] = V cos θ             ------------------------(iv)

Substitute all the necessary values into equations(iii) and (iv) as follows;

[tex]V_{Y}[/tex] = 19 sin 55° = 19m/s x 0.8192 = 15.56m/s

[tex]V_{X}[/tex] = 19 cos 55° = 19m/s x 0.5736 = 10.90m/s

Therefore, the vertical and horizontal velocity components are respectively 15.56m/s and 10.90m/s.

Answer:

The  force that the wire exerts on the electron is [tex]-4.128\times10^{-20}i-6.88\times10^{-20}j+0k[/tex]

Explanation:

Given that,

Current = 8.60 A

Velocity of electron [tex]v= (5.00\times10^{4})i-(3.00\times10^{4})j\ m/s[/tex]

Position of electron = (0,0.200,0)

We need to calculate the magnetic field

Using formula of magnetic field

[tex]B=\dfrac{\mu I}{2\pi d}(-k)[/tex]

Put the value into the formula

[tex]B=\dfrac{4\pi\times10^{-7}\times8.60}{2\pi\times0.200}[/tex]

[tex]B=0.0000086\ T[/tex]

[tex]B=-8.6\times10^{-6}k\ T[/tex]

We need to calculate the force that the wire exerts on the electron

Using formula of force

[tex]F=q(\vec{v}\times\vec{B}[/tex]

[tex]F=1.6\times10^{-6}((5.00\times10^{4})i-(3.00\times10^{4})j\times(-8.6\times10^{-6}) )[/tex]

[tex]F=(1.6\times10^{-19}\times3.00\times10^{4}\times(-8.6\times10^{-6}))i+(1.6\times10^{-19}\times5.00\times10^{4}\times(-8.6\times10^{-6}))j+0k[/tex]

[tex]F=-4.128\times10^{-20}i-6.88\times10^{-20}j+0k[/tex]

Hence, The  force that the wire exerts on the electron is [tex]-4.128\times10^{-20}i-6.88\times10^{-20}j+0k[/tex]

Part A) Components of the Force The force components on the electron are: [tex]\[F_x = -8.26 \times 10^{-20} \, \text{N}, \quad F_y = -1.38 \times 10^{-19} \, \text{N}, \quad F_z = 0 \, \text{N}\][/tex]

Part B) Magnitude of the Force The magnitude of the force is:[tex]\[F \approx 1.60 \times 10^{-19} \, \text{N}\][/tex]

Part A: Calculate the force components

The force on a moving charge in a magnetic field is given by the Lorentz force equation:

[tex]\[\vec{F} = q \vec{v} \times \vec{B}\][/tex]

First, we need to find the magnetic field [tex]\(\vec{B}\)[/tex] produced by the wire at the position of the electron. The magnetic field due to a long, straight current-carrying wire is given by:

[tex]\[B = \frac{\mu_0 I}{2 \pi r}\][/tex]

where:

- [tex]\(\mu_0 = 4 \pi \times 10^{-7} \, \text{T} \cdot \text{m/A}\)[/tex] (the permeability of free space)

- [tex]\(I = 8.60 \, \text{A}\)[/tex] (the current through the wire)

- [tex]\(r = 0.200 \, \text{m}\)[/tex] (the distance from the wire to the electron)

Calculating [tex]\(B\)[/tex]:

[tex]\[B = \frac{4 \pi \times 10^{-7} \times 8.60}{2 \pi \times 0.200} = \frac{4 \times 10^{-7} \times 8.60}{0.200} = \frac{3.44 \times 10^{-6}}{0.200} = 1.72 \times 10^{-5} \, \text{T}\][/tex]

The direction of [tex]\(\vec{B}\)[/tex] follows the right-hand rule. Since the current flows in the [tex]\(-x\)[/tex]-direction, at the point [tex]\((0, 0.200, 0)\)[/tex], the magnetic field [tex]\(\vec{B}\)[/tex] is directed into the page (negative [tex]\(z\)[/tex]-direction):

[tex]\[\vec{B} = -1.72 \times 10^{-5} \hat{k} \, \text{T}\][/tex]

Now we use the Lorentz force equation with:

[tex]\[q = -1.60 \times 10^{-19} \, \text{C} \quad (\text{charge of an electron})\][/tex]

[tex]\[\vec{v} = (5.00 \times 10^4 \hat{i} - 3.00 \times 10^4 \hat{j}) \, \text{m/s}\][/tex]

[tex]\[\vec{B} = -1.72 \times 10^{-5} \hat{k} \, \text{T}\][/tex]

The cross product [tex]\(\vec{v} \times \vec{B}\)[/tex]:

[tex]\[\vec{v} \times \vec{B} = \begin{vmatrix}\hat{i} & \hat{j} & \hat{k} \\5.00 \times 10^4 & -3.00 \times 10^4 & 0 \\0 & 0 & -1.72 \times 10^{-5}\end{vmatrix}= \hat{i}( (-3.00 \times 10^4)(-1.72 \times 10^{-5}) - 0) - \hat{j}( (5.00 \times 10^4)(-1.72 \times 10^{-5}) - 0)\][/tex]

[tex]\[= \hat{i}( 5.16 \times 10^{-1}) - \hat{j}( -8.60 \times 10^{-1})\][/tex]

[tex]\[= 0.516 \hat{i} + 0.860 \hat{j} \, \text{N/C}\][/tex]

Now, multiply by the charge of the electron:

[tex]\[\vec{F} = q \vec{v} \times \vec{B} = -1.60 \times 10^{-19} (0.516 \hat{i} + 0.860 \hat{j})\][/tex]

[tex]\[\vec{F} = -0.516 \times 1.60 \times 10^{-19} \hat{i} - 0.860 \times 1.60 \times 10^{-19} \hat{j}\][/tex]

[tex]\[\vec{F} = -8.26 \times 10^{-20} \hat{i} - 1.376 \times 10^{-19} \hat{j} \, \text{N}\][/tex]

So, the components of the force are:

[tex]\[F_x = -8.26 \times 10^{-20} \, \text{N}, \quad F_y = -1.376 \times 10^{-19} \, \text{N}, \quad F_z = 0 \, \text{N}\][/tex]

Part B: Calculate the magnitude of the force

The magnitude of the force is given by:

[tex]\[F = \sqrt{F_x^2 + F_y^2 + F_z^2}\][/tex]

[tex]\[F = \sqrt{(-8.26 \times 10^{-20})^2 + (-1.376 \times 10^{-19})^2}\][/tex]

[tex]\[F = \sqrt{(6.82 \times 10^{-39}) + (1.89 \times 10^{-38})}\][/tex]

[tex]\[F = \sqrt{2.57 \times 10^{-38}}\][/tex]

[tex]\[F \approx 1.60 \times 10^{-19} \, \text{N}\][/tex]

So, the magnitude of the force is approximately [tex]\(1.60 \times 10^{-19} \, \text{N}\).[/tex]

The complete question is attached here:

An electron is moving in the vicinity of a long, straight wire that lies along the z-axis. The wire has a constant current of 8.60 A in the -z-direction. At an instant when the electron is at point (0, 0.200 m, 0) and the electron's velocity is  (5.00 x 104 m/s) -(3.00 x 104 m/s).

Part A:What is the force that the wire exerts on the electron?

Part B:Calculate the magnitude of this force.

Answer:

It's converted into heat.

Explanation:

Most of the rest of the energy is converted into heat, as can be verified by touching an incandescent lamp that has been turned on for a while. This happens because the light itself is generated by heating the filament with an electric current (Joule heating) until it glows.

Answer:

Answer explained below

Explanation:

magnetic force of charged particle placed in uniform magnetic field is given by

F = iLB sin theta

where i is current

L is length

B = magnetic field

theta is the angle between L and B

so we can design an experiment with the given apparatus

as we have device for measuring length ( meter stick and scale)

magnitude of magnetic field from bar magnetic using magnetic moments principle

Finally from conducting wires and power, we can measure current i using Ammeter

Answer:

Explanation:

The explanation or solution is given in the attach document

Final answer:

To find the voltage and current as functions of time in a circuit, replace current I(t) with C*dV(t)/dt, and substitute this into Ohm's law V(t)=I(t)R to obtain a differential equation V(t) = (C*dV(t)/dt)*R.

Explanation:

To rewrite the relation V(t)=I(t)R by replacing I(t) with an expression involving the time derivative of the voltage, first understand that the current I(t) is the rate of change of charge Q with respect to time, that is I(t) = dQ/dt. However, since Q is related to the voltage across a capacitor by the equation Q=CV(t), where C is the capacitance, the current can also be expressed in terms of the voltage as I(t) = C*(dV(t)/dt). Replacing this into the original equation gives us V(t) = (C * dV(t)/dt) * R, which is a first-order differential equation relating the voltage to its time derivative.

Answer:

[tex]\mu_k=\frac{a}{g}[/tex]

Explanation:

The force of kinetic friction on the block is defined as:

[tex]F_k=\mu_kN[/tex]

Where [tex]\mu_k[/tex] is the coefficient of kinetic friction between the block and the surface and N is the normal force, which is always perpendicular to the surface that the object contacts. So, according to the free body diagram of the block, we have:

[tex]N=mg\\F_k=F=ma[/tex]

Replacing this in the first equation and solving for [tex]\mu_k[/tex]:

[tex]ma=\mu_k(mg)\\\mu_k=\frac{a}{g}[/tex]

Answer: The charge on the particle is positive

While the magnitude = 0.00028C

Explanation:

Please find the attached file for the solution

Answer:(2) July

Explanation:

We all know the sun rises in the east and sets in the west.

No matter where you are on Earth excluding the North and South Poles, you have a due east and due west point on your horizon. That point marks the intersection of your horizon with the celestial equator, the imaginary great circle above the true equator of the Earth.

This is to say that the sun rises close to due east and sets close to due west, for everyone at the equinox. The equinox sun is on the celestial equator. The celestial equator intersects your horizon at due east and due west irrespective of where you are on earth.

The sun rises due east and sets due west during the spring and fall equinoxes. Other times, the sun rises either north or south due east. There are slight changes in the rising and setting of the sun each day. At summer solstice, the sun rises far to the north east and set to the north west. Everyday, the sun rises a bit in furtherance to the south.

Therefore in Newyork state, during summer in July, the sun rise north of due east.

"The correct answer is (2) July.  To understand why the sun rises north of due east in New York State during the month of July, we need to consider the concept of the solar path and the tilt of the Earth's axis.

The Earth orbits the Sun with an axial tilt of approximately 23.5 degrees. This tilt is the reason we experience seasons. As the Earth orbits the Sun, the direction of sunrise and sunset changes throughout the year for any given location north or south of the tropics.

In the Northern Hemisphere, the sun rises exactly due east on two days of the year: the spring (vernal) equinox and the autumnal equinox. These occur around March 20th and September 22nd, respectively. On these days, the sunrise location is at its southernmost point along the horizon for the year.

After the spring equinox, the sunrise location begins to move northward along the horizon each day, reaching its northernmost point on the summer solstice, which occurs around June 21st. After the summer solstice, the sunrise location starts to move southward again, but it continues to rise north of due east until several weeks after the solstice.

For New York State, which is located in the Northern Hemisphere at a latitude of approximately 43 degrees north, the sun rises north of due east from late March until late September. July is well within this period, confirming that the sun rises north of due east during this month.

By contrast, in February, the sun is still moving northward towards the due east position, and by October, it has already passed its northernmost rising point and is moving back towards due east. In December, the sun rises well south of due east.

Therefore, the correct answer to the question is July, when the sun rises north of due east in New York State."

Answer:

     v’= 9.74 m / s

Explanation:

The Doppler effect is due to the relative movement of the sound source and the receiver of the sound, in this case we must perform the exercise in two steps, the first to find the frequency that the bat hears and then the frequency that the audience hears that also It is sitting.

Frequency shift heard by the murciela, in case the source is still and the observer (bat) moves closer

        f₁ ’= f₀ (v + v₀)/v

Frequency shift emitted by the speaker in the bat, in this case the source is moving away from the observer (public sitting) that is at rest

         f₂’= f₁’ v/(v - vs)

Note that in this case the bat is observant in one case and emitter in the other, called its velocity v’

            v’= vo = vs

Let's replace

           f₂’= f₀   (v + v’)/v   v/(v -v ’)

           f₂’= f₀   (v + v’) / (v -v ’)

           (v –v’ ) f₂’ / f₀ = v + v ’

           v’ (1+ f₂’ /f₀) = v (f₂’/fo - 1)

           v’ (1 + 1.059) = 340 (1.059 - 1)

           v’= 20.06 / 2.059

           v’= 9.74 m / s

Coefficient of volume expansion is 8.1 ×10⁻⁴ C⁻¹.

Explanation:

The volume expansion of a liquid is given by ΔV,

ΔV = α V₀ ΔT

ΔT = change in temperature  = 48.5° C

α =  coefficient of volume expansion =?

V₀ = initial volume = 2.35 m³

We need to find α , by plugin the given values in the equation and by rearranging the equation as,

[tex]\alpha=\frac{\Delta \mathrm{V}}{\mathrm{V}_{0} \Delta \mathrm{T}}=\frac{0.0920}{2.35 \times 48.5}=0.00081[/tex]

  = 8.1 ×10⁻⁴ C⁻¹.

Answer:

8.1

Explanation:

Answer:

X = 15.88 m

Explanation:

Given:

Initial Velocity V₀ = 13.4 m/s

θ = 30.1 °

g = 9.8 m/s²

To Find horizontal distance let "X" we have to time t first.

so from motion 2nd equation at Height h = 0

h = V₀y t + 1/2 (-g) t ²                                (ay = -g)

0 = 13.4 sin 30.1° t - 0.5 x 9.81 x t²           (V₀y = V₀ Sin θ)

⇒  t = 1.37 s

Now For Horizontal distance  X, ax =0m/s²

X = V₀x t + 1/2 (ax) t ²

X = 13.4 m × cos 30.1° x 1.37 s + 0

X = 15.88 m

To find the distance between the points where the stones strike the ground, analyze the motion of each stone separately and find the horizontal displacements.

To find the distance between the points where the stones strike the ground, we can analyze the motion of each stone separately. For the stone thrown below the horizontal, we can use the equations of motion in the x and y directions to find the time of flight and the horizontal displacement. For the stone thrown above the horizontal, we can use the same approach. Finally, we can subtract the two horizontal displacements to find the distance between the points where the stones strike the ground.

https://brainly.com/question/35866733

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Answer:

d. The spring force and gravity.

Explanation:

The forces that can be associated with a potential energy function are only the conservative forces. These are the forces whose work done on an object by the force does not depend on the path taken, but only on the initial and final position of the object.

The only two conservative forces in this problem are:

- Gravity

- The spring force

While the air resistance is a non-conservative force.

The potential energy associated with the gravitational force is:

[tex]U=mgh[/tex]

where

m is the mass of the object

g is the acceleration due to gravity

h is the position of the object with respect to a reference level (e.g. the ground)

The potential energy associated to the spring force is

[tex]U=\frac{1}{2}kx^2[/tex]

where:

k is the spring constant

x is the elongation of the spring with respect to the equilibrium position

Answer:

power developed by the turbine = 18342 kW  

Explanation:

given data

pressure = 4 MPa

specific enthalpy h1 = 3015.4 kJ/kg

velocity v1 = 10 m/s

pressure = 0.07 MPa

specific enthalpy h2 =   2400 kJ/kg

velocity v2 = 90 m/s

mass flow rate = 30 kg/s

solution

first we apply here  thermodynamic equation that is express as energy equation is  

[tex]h1 + \frac{v1}{2} + q = h2 + \frac{v2}{2} + w[/tex]      .......................1

we know turbine is insulated so q is  0

put here value we get

[tex]3015.4 \times 1000 + \frac{10^2}{2} = 2400 \times 1000 + \frac{90^2}{2} + w[/tex]    

w =  611400 J/kg = 611.4 kJ/kg  

and  now we get power developed by the turbine W is

W = mass flow rate × w     ................2

put here value

W = 30 × 611.4

W = 18342 kW  

power developed by the turbine = 18342 kW  

Answer:

Explanation:

Answer:

Explanation:

The intensity and the temperature of metal is constant so the number of photo electrons remains constant. As the number of photo electrons remains same so the photo electric remains constant.

As the frequency is increased, the kinetic energy of the photo electrons increases and thus, the speed of photo electrons increases.

When the frequency of the incident light is increased above a certain threshold, electrons will start being ejected from the metal's surface, with their maximum velocity increasing linearly with the frequency.

As the frequency of the incident light is increased beyond a certain threshold frequency, electrons will begin to be ejected from the surface of the metal. However, their kinetic energy will not increase proportionally with the frequency, rather the maximum velocity of the ejected electrons will increase linearly with the frequency of the incident light.

Answer:

K= 1226.25 N/m

Explanation:

Given:  mass m = 10 kg, Distance x= 8 cm = 0.08 m, g= 9.81 m/s²

By Hook's Law

F=K x

F=W=mg = 10 kg x 9.8 m/s² = 98.1 N

to Find Spring constant k = F/x  = 98 N /0.08 m

K= 1226.25 N/m

Answer:

The no. of electron in the beam = [tex]1.64\times10^{12}[/tex]

Explanation:

Given :

The diameter of circular ring = 68 m.

The current flowing in the beam = 0.37 A

Speed of light = [tex]3\times10^{8} ms^{-1}[/tex]

We know that the current is equal to the charge per unit time.

⇒    [tex]I = \frac{Q}{t}[/tex]

∴    [tex]Q=It[/tex]

Here given in the question, electron revolving in a circle with the diameter

[tex]d = 68[/tex]m

⇒ Time take to complete one round [tex](t) =[/tex] [tex]\frac{\pi d }{v}[/tex]

∴    [tex]Q = \frac{I\pi d }{v}[/tex]

     [tex]Q = \frac{0.37 \times 3.14 \times 68}{3 \times 10^{8} }[/tex]

     [tex]Q = 26.33 \times 10^{-8}[/tex]

Now, for finding the no. of electron we have to divide [tex]Q[/tex] to the charge of the electron  [tex]q = 1.6 \times 10^{-19}[/tex]

∴     [tex]n[/tex] =  [tex]\frac{26.33 \times 10^{-8} }{1.6 \times 10^{-19} }[/tex]

      [tex]n = 1.64 \times 10^{12}[/tex]

Thus, the no. of electron in the beam is [tex]1.64 \times 10^{12}[/tex].

Final answer:

To calculate the number of electrons in the beam, first determine the total charge passing a point in one second using the current, then divide by the charge of one electron. Using the given current of 0.37 A, this method reveals the total number of electrons in the beam.

Explanation:

To determine the number of electrons in a beam with a current of 0.37 A, the given data of the SPEAR storage ring can be used. First, recall that the charge of one electron is approximately ‑1.602 × 10⁻¹⁹ C (coulombs).

Current (I) is defined as the rate of charge (Q) flow through a given point, over time (t), expressed as I = Q/t. Therefore, the total charge in the beam can be calculated for one second as the product of the current and time.

To find the number of electrons (N), the total charge is divided by the charge of one electron, mathematically represented as N = Q / e. Substituting the given value of 0.37 A for I and using 1 second for t, the calculation would be N = (0.37 C/s) / (1.602 × 10⁻¹⁹ C/electron). This gives the total number of electrons circulating in the beam.

Answer: The car makes a sudden stop.

Explanation:

Manuel is coasting on his bike. Because he is not pedaling, his bike will come to a stop. Which of these will cause Manuel's bike to stop? - the force of friction.

Hope this helps! enjoy your day.

Answer:

v = 196 - 186*e^( - 0.05*t )      

v-terminal = 196 m/s

Explanation:

Given:

- The differential equation for falling object velocity v in gravity with air resistance is given by:

                                m*dv/dt = m*g - b*v

- The initial conditions and constants are as follows:

                 v(0) = 10 , m = 100 kg , b = 5 kg/s , g = 9.8 m/s^2  

Find:

- Find a formula for the velocity of the object at time t. Further, find the terminal (or limiting) velocity of the object. Circle your velocity formula and the terminal velocity.

Solution:

- Rewrite the differential equation in te form:

                                 dv/dt + (b/m)*v = g

- The integration factor function P(t) = b/m. The integrating factor u(t) is:

                                 u(t) = e^∫P(t).dt

                                 u(t) = e^∫(b/m).dt

                                 u(t) = e^[(b/m).t]

- Solve the differential equation after expressing in form:

                                 v.u(t) = ∫u(t).g.dt    

                                 v.e^[(b/m).t] = g*∫e^[(b/m).t].dt    

                                 v.e^[(b/m).t] = g*m*e^[(b/m).t] / b + C

                                  v = g*m/b + C*e^[-(b/m).t]                

- Apply the initial conditions v(0) = 10 m/s and evaluate C:

                                  10 = 9.8*100/5 + C*e^[-(b/m).0]

                                  10 = 9.8*100/5 + C

                                  C = -186

- The final ODE solution is:

                                  v = 196 - 186*e^( - 0.05*t )

- The Terminal velocity vt can be expressed by a limiting value for v(t), where t ->∞.        

                                  vt = Lim t ->∞ ( v(t) )

                                  vt = Lim t ->∞ ( 196 - 186*e^( - 0.05*t ) )

                                  vt = 196 - 0 = 196 m/s

Answer:

a) When the current is from west to east and the magnetic field is from south to north the magnitude of the force is 2.1x10⁻⁴N and the direction is upwards.

b) The current is moving vertically upward, the magnitude of the force is 2.1x10⁻⁴N and the direction is west.

c) The force is 0 because the magnetic field and the direction of the current are in parallel.

d) No, the force is less.

Explanation:

Given:

L = length of the wire = 2.5 m

i = current in wire = 1.5 A

B = magnetic field = 0.55x10⁻⁴T

a) The magnitude of magnetic force is equal to:

[tex]F=BiL=0.55x10^{-5} *1.5*2.5=2.1x10^{-4} N[/tex]

b) The same way to a):

F = 2.1x10⁻⁴N

c) F = 0

The magnetic field and the direction of the current are in parallel.

d) The answer is no, the force is less

Answer:

Explanation:

Acceleration of cylinder

a = g sin 30 / 1+ k² / r² where k is radius of gyration and r is radius of cylinder.

For cylinder k²  = (1 / 2)  r²

acceleration

= gsin30 / 1.5

= g / 3

= 3.27

v² = u² + 2as

= 2 x 3.27 x 6

v = 6.26 m /s

v = angular velocity x radius

6.26 = angular velocity x .10

angular velocity  = 62.6 rad / s

b ) vertical component of velocity

= 6.26 sin 30

= 3.13 m /s

h = ut + 1/2 g t²

5 = 3.13 t + .5 t²

.5 t²+ 3.13 t- 5 = 0

t = 1.32 s

horizontal distance covered

= 6.26 cos 30 x 1.32

= 7.15  m

The conservation of energy and kinematics allows to find the results for the questions about the movement of the cylinder on the ceiling and when falling are:  

          a) The angular velocity is w = 6.26 rad / s

          b) the distance to the ground is: x = 7,476 m

Given parameters

To find

a) The angular velocity.

b) Horizontal distance.

Mechanical energy is the sum of kinetic energy and potential energies. If there is no friction, it remains constant at all points.

Linear and rotational kinematics study the motion of bodies with linear and rotational motions.

a) Let's write the mechanical energy at the points of interest.

Starting point. When it comes out of the top

          Em₀ = U = m g h

Final point. On the edge of the roof.

          [tex]Em_f[/tex]  = K = ½ mv² + ½ I w²

Since the cylinder does not slide, friction is zero and energy is conserved.

         Em₀ = [tex]Em_f[/tex]  

         mg h = ½ m v² + ½ I w²

The moment of inertia of the cylinder is;

        I = ½ m r²

Linear and angular variables are related.

        v = w r

let's substitute.

         m g h = ½ m (wr) ² + ½ (½ m r²) w²

        gh = ½ w² r² (1 + ½) = ½ w² r² [tex]\frac{3}{2}[/tex]  

        w² = [tex]\frac{4}{3 } \ \frac{gh}{r^2}[/tex]  

Let's use trigonometry to find the height of the ceiling.

        sin θ = h / L

        h = L sin θ

We substitute.

       w=    [tex]\sqrt{ \frac{4}{3} \ \frac{g \ L sin \theta }{r^2} }[/tex]

Let's calculate.

       w = [tex]\sqrt{\frac{4}{3} \frac{9.8 \ 6.0 sin 30}{0.10^2} }[/tex]

Let's calculate

        w = Ra 4/3 9.8 6.0 sin 30 / 0.10²

        w = 62.6 rad / s

b) For this part we can use the projectile launch expressions.

Let's find the time it takes to get to the floor.

         y = y₀ + go t - ½ g t²

The initial height is y₀ = H, when it reaches the ground its height is y = 0 and let's use trigonometry for the vertical initial velocity.

        sin  30 = [tex]\frac{v_{oy}}{v_o}[/tex]I go / v

      [tex]v_{oy}[/tex]  = v sin 30 = wr sin 30

       [tex]v_{oy}[/tex]  = 62.6 0.1 sin 30

       [tex]v_{oy}[/tex] = 3.13 m / s

       0 = H + voy t - ½ g t²

       0 = 5 + 3.13 t - ½ 9.8 t³

        t² - 0.6387 t - 1.02 = 0

We solve the quadratic equation.

         t =[tex]\frac{0.6387 \pm \sqrt{0.6387^2 - 4 \ 1.02} }{2}[/tex]  

         t = [tex]\frac{0.6378 \pm 2.118}{2}[/tex]

         t₁ = 1.379 s

         t₂ = -0, 7 s

The time o must be a positive quantity, therefore the correct answer is:

           t = 1.379 s

We look for the horizontal distance.

          x = v₀ₓ t

          vₓ = v cos θ

          v = wr

Let's substitute.

          x = wr cos t

Let's calculate.

          x = 62.6 0.1  cos 30   1.379

          x = 7.476 m

In conclusion using the conservation of energy and kinematics we can find the results for the questions about the movement of the cylinder on the ceiling and when falling are:  

         a) The angular velocity is w = 6.26 rad / s

         b) the distance to the ground is: x = 7,476 m

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Back emf is 85.9 V.

Explanation:

Given-

Resistance, R = 3.75Ω

Current, I = 9.1 A

Supply Voltage, V = 120 V

Back emf = ?

Assumption - There is no effects of inductance.

A motor will have a back emf that opposes the supply voltage, as the motor speeds up the back emf increases and has the effect that the difference between the supply voltage and the back emf is what causes the current to flow through the armature resistance.

So if 9.1 A flows through the resistance of 3.75Ω then by Ohms law,

The voltage across the resistance would be

v = I x R

  = 9.1 x 3.75

  = 34.125 volts

We know,

supply voltage = back emf + voltage across the resistance

By plugging in the values,

120 V = back emf + 34.125 V

Back emf = 120 - 34.125

                = 85.9 Volts

Therefore, back emf is 85.9 V.

To solve this problem we will apply the concepts related to Orbital Speed as a function of the universal gravitational constant, the mass of the planet and the orbital distance of the satellite. From finding the velocity it will be possible to calculate the period of the body and finally the gravitational force acting on the satellite.

PART A)

[tex]V_{orbital} = \sqrt{\frac{GM_E}{R}}[/tex]

Here,

M = Mass of Earth

R = Distance from center to the satellite

Replacing with our values we have,

[tex]V_{orbital} = \sqrt{\frac{(6.67*10^{-11})(5.972*10^{24})}{(6370*10^3)+(6370*10^3)}}[/tex]

[tex]V_{orbital} = 5591.62m/s[/tex]

[tex]V_{orbital} = 5.591*10^3m/s[/tex]

PART B) The period of satellite is given as,

[tex]T = 2\pi \sqrt{\frac{r^3}{Gm_E}}[/tex]

[tex]T = \frac{2\pi r}{V_{orbital}}[/tex]

[tex]T = \frac{2\pi (2*6370*10^3)}{5.591*10^3}[/tex]

[tex]T = 238.61min[/tex]

PART C) The gravitational force on the satellite is given by,

[tex]F = ma[/tex]

[tex]F = \frac{1}{4} mg[/tex]

[tex]F = \frac{270*9.8}{4}[/tex]

[tex]F = 661.5N[/tex]

(a) The orbital speed of the satellite is 5591.62 m/s.

(b) The period of revolution is 238.47 minutes.

(c) The gravitational force on satellite 661.5 N.

(a) The orbital velocity is given by;

[tex]v_{o}=\sqrt{\frac{GM}{r} }[/tex]

Here, 'M' is the mass of the earth and 'r' is the distance is from the centre of the earth to the satellite.

[tex]v_o = \sqrt{\frac{(6.67 \times 10^{-11})\times (5.972\times 10^{24})}{2\times 6370\times 10^{3}} } =5591.62\,m/s[/tex]

(b) The period of revolution is given by;

[tex]T=\frac{2\pi r}{V_o}=\frac{2\times 3.14\times 2\times 6370\times 10^3}{5591.62} =14308.411\,s = 238.47\,min[/tex]

(c) The gravitational force on the satellite is given by;

[tex]F_g = mg_s[/tex]

Where [tex]g_s[/tex] is the acceleration due to gravity at the satellite's height.

Given that, [tex]g_s = \frac{g}{4}[/tex]

[tex]F_g = \frac{270\times 9.8}{4} =661.5\,N[/tex]

Learn more about orbital motion here:

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Answer:2.01 s

Explanation:

Given

Applied voltage [tex]V=8\ V[/tex]

Inductance [tex]L=2.3\ H[/tex]

Change in Current [tex]\Delta i=8-1=7\ A[/tex]

Induced EMF is given by

[tex]V=L\times \dfrac{\Delta A}{\Delta t}[/tex]

[tex]8=2.3\times \dfrac{7}{\Delta t}[/tex]

[tex]\Delta t=\dfrac{2.3\times 7}{8}[/tex]

[tex]\Delta t=2.0125\ s[/tex]

Answer:

d.  The ideal diode acts as a short circuit for forward currents and as an open circuit with reverse voltage applied.

Explanation:

Ideal diode acts like an ideal conductor. In case of forward voltage it acts like an ideal conductor. However when it is reverse biased then it behaves like an ideal insulator. You can understand it bu considering a switch. When the voltage is forward then ideal diode acts like a closed switch. When the voltage is reverse biased then ideal diode behaves like an open switch.

        That is why we can say that the ideal diode acts as a short circuit (higher conduction) for forward currents and as an open circuit ( zero conduction) with reverse voltage applied.

Answer:

0.36s, 2.3s

Explanation:

Let gravitational acceleration g = 9.81 m/s2. And let the throwing point as the ground 0 for the upward motion. The equation of motion for the rock leaving your hand can be written as the following:

[tex]s = v_0t + gt^2/2[/tex]

where s = 4 m is the position at 4m above your hand. [tex]v_0 = 13 m/s[/tex] is the initial speed of the rock when it leaves your hand. g = -9.81m/s2 is the deceleration because it's in the downward direction. And t it the time(s) it take to get to 4m, which we are looking for

[tex]4 = 13t - 9.81t^2/2[/tex]

[tex]4.905 t^2 - 13t + 4 = 0[/tex]

[tex]t= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]t= \frac{13\pm \sqrt{(-13)^2 - 4*(4.905)*(4)}}{2*(4.905)}[/tex]

[tex]t= \frac{13\pm9.51}{9.81}[/tex]

t = 2.3 or t = 0.36

Explanation:

Below is an attachment containing the solution.

Answer:

[tex]\sigma_i=1.06*10^{-6}C[/tex]

Explanation:

When the space is filled with dielectric, an induced opposite sign charge appears on each surface of the dielectric. This induced charge has a charge density related to the charge density on the electrodes as follows:

[tex]\sigma_i=\sigma(1-\frac{E}{E_0})[/tex]

Where E is the eletric field with dielectric and [tex]E_0[/tex] is the electric filed without it. Recall that [tex]\sigma[/tex] is given by:

[tex]\sigma=\epsilon_0E_0[/tex]

Replacing this and solving:

[tex]\sigma_i=\epsilon_0E_0(1-\frac{E}{E_0})\\\sigma_i=8.85*10^{-12}\frac{C^2}{N\cdot m^2}*3.40*10^5\frac{V}{m}*(1-\frac{2.20*10^5\frac{V}{m}}{3.40*10^5\frac{V}{m}})\\\sigma_i=1.06*10^{-6}C[/tex]

Answer:

This is the property of metals like W (Tungsten) to produce a continuous spectrum.

Explanation:

The molecules of a gas are highly differentiated and single atoms absorb photons instead of bulk like metals and only give line spectrum for example line spectrum given by hydrogen etc. On the other hand, metals like Tungsten gets very hot and emission of every possible wavelength of light is observed. This emission is continuous because the wavelengths of light in the spectrum has no breakages.

Answer:

(A) three times as large as the initial value.

Explanation:

Boyle law states that the pressure is inversely proportional to volume if we kept the temperature constant.

[tex]P_{1} V_{1} = P_{2} V_{2}[/tex]        (1)

here [tex]P_{1}[/tex] and [tex]V_{1}[/tex] are the initial pressure and volume.

[tex]P_{2}[/tex] and [tex]V_{2}[/tex] are the final pressure and volume respectively.

now

[tex]P_{1} = p\\V_{1} = v\\P_{2} = ?\\V_{2} = \frac{v}{3}[/tex]

by putting these values in equation 1.

hence it is proved that " if the volume is decreased to one third of its original value then the pressure will be three times larger then its initial value".

Answer:

the case is the one  with the greatest current, L=15 cm ,   i = 2.19 10⁸  A

Explanation:

Ohm's law is

          V = i R

Resistance is

         R = ρ L / A

Where L is the length of the electrons pass and A the area perpendicular to the current

      i = V / R

      i = V (A / ρ L)

      i = V / ρ  (A / L)

We can calculate the relationship between the area and the length to know in which direction the maximum currents

Case 1

      L = 0.15 m

      A = 0.26 0.43 = 0.1118 m2

      A / L = 0.1118 / 0.15

      A / L = 0.7453 m

Case 2

        L = 0.26 m

        A = 0.15 0.43 = 0.0645 m2

        A / L = 0.248 m

Case 3

       L = 0.43 m

       A = 0.15 0.26 = 0.039 m2

        A / L = 0.0907 m

We can see that the case is the one  with the greatest current, L=15 cm

Let's calculate the current

     i = 5 / 1.7 10⁻⁸ (0.7453)

      i = 2.19 10⁸  A

Answer:

It's only 1.11 m/s2 weaker at 400 km above surface of Earth

Explanation:

Let Earth radius be 6371 km, or 6371000 m. At 400km above the Earth surface would be 6371 + 400 = 6771 km, or 6771000 m

We can use Newton's gravitational law to calculate difference in gravitational acceleration between point A (Earth surface) and point B (400km above Earth surface):

[tex]g = G\frac{M}{r^2}[/tex]

where G is the gravitational constant, M is the mass of Earth and r is the distance form the center of Earth to the object

[tex]\frac{g_B}{g_A} = \frac{GM/r^2_B}{GM/r^2_A}[/tex]

[tex]\frac{g_B}{g_A} = \left(\frac{r_A}{r_B}\right)^2 [/tex]

[tex]\frac{g_B}{g_A} = \left(\frac{6371000}{6771000}\right)^2 [/tex]

[tex]\frac{g_B}{g_A} = 0.94^2 = 0.885[/tex]

[tex]g_B = 0.885 g_A[/tex]

So the gravitational acceleration at 400km above surface is only 0.885 the gravitational energy at the surface, or 0.885*9.81 = 8.7 m/s2, a difference of (9.81 - 8.7) = 1.11 m/s2.