.
1. How does the arrangement of a pulley system affect its ideal mechanical advantage​

Answers

Answer 1

Answer: In a pulley, the ideal mechanical advantage is equal to the number of rope segments pulling up on the object. The more rope segments that are supporting to do the lifting work, the less pressure that is needed for the job.

Explanation:


Related Questions

According to Newton, when the distance between two interacting objects doubles, the gravitational force is

Answers

Answer:

1/4 of its original value

Explanation:

Newton's law of universal gravitation states that when two bodies of masses M₁ and M₂ interact, the force of attraction (F) between these bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between these bodies. i.e

F ∝ [tex]\frac{M_1 M_2}{r^2}[/tex]       ------------(i)

From the equation above, it can be deduced that;

F ∝ [tex]\frac{1}{r^2}[/tex]

=> F = G [tex]\frac{1}{r^2}[/tex]       -----------(ii)

Where;

G = constant of proportionality called the gravitational constant

Equation (ii) can be re-written as

Fr² =  G

=> F₁r₁² = F₂r₂²              -----------(iii)

Where;

F₁ and r₁ are the initial values of the force and distance respectively

F₂ and r₂ are the final values of the force and distance respectively

From the question, if the distance doubles i.e;

r₂ = 2r₁,

Then the final value of the gravitational force F₂ is calculated as follows;

Substitute the value of r₂ = 2r₁ into equation (iii) as follows;

F₁r₁² = F₂(2r₁)²

F₁r₁² = 4F₂r₁²          [Divide through by r₁²]

F₁ = 4F₂                 [Make F₂ subject of the formula]

F₂ = F₁ / 4              [Re-write this]

F₂ = [tex]\frac{1}{4} F_1[/tex]

Therefore the gravitational force will be 1/4 of its original value when the distance between the bodies doubles.

Two children are balanced on a seesaw, but one child weighs twice as much as the other child. The heavier child is sitting half as far from the pivot as is the lighter child. Since the seesaw is balanced, the heavier child is exerting on the seesaw:_______.
a. a force that is less than the force the lighter child is exerting.
b. a force that is equal in amount but oppositely directed to the force the lighter child is exerting.

Answers

Answer:

B. A force that is equal in amount but oppositely directed to the force the lighter child is exerting.

Explanation:

If they are sitting at the same distance away from the pivot yet the seesaw is balanced, the only conclusion is the heavier child is exerting a lower force. This causes the pivot exertion and balances to be equal. The equilibrium of the pivot-seesaw is not affected by the weight because of force exertion.

A 240 m long segment of wire is hanging between 2 transmission lines. What is the total magnetic force only (ignore gravitational force) on this segment of wire if the current in the wire is 500 A and the field strength is 3e-5 T

Answers

Answer:

7.2 N

Explanation:

length of wire L  = 240 m

current I = 500 A

field strength B = 3 x 10^-5 T

magnetic force on a current carrying conductor F is given as

F = BILsin∅

The wires are perpendicular with field therefore sin∅ = sin 90° = 1

therefore,

F = BIL = 3 x 10^-5 X 500 X 240 = 3.6 N

If the wire exists between this two transmission lines, then total magnetic force on the wire = 2 x 3.6 = 7.2 N

What is the change in internal energy of an engine if you put 15 gallon of gasoline into its tank? The energy content of gasoline is 1.5 x 106 J/gallon. All other factors, such as the engine’s temperature, are constant. How many hours the engine can work if the power of the engine’s motor is 600 W? (8 marks)

Answers

Answer:

ΔU = 2.25 x 10⁸ J

t = 104.17 s

Explanation:

The change in internal energy of the engine can be given by the following formula:

ΔU = (Mass of Gasoline)(Energy Content of Gasoline)

ΔU = (1.5 x 10⁶ J/gallon)(15 gallon)

ΔU = 2.25 x 10⁸ J

Now, for the time of operation, we use the following formula of power.

P = W/t = ΔU/t

t = ΔU/P

where,

t = time of operation = ?

ΔU = Change in internal energy = 2.25 x 10⁸ J

P = Power of motor = 600 W

Therefore,

t = (2.25 x 10⁸ J)/(600 W)

t = (375000 s)(1 h/3600 s)

t = 104.17 s

This questic concerns a tablet that

has remained in storage for 2 years
since manufacture. From the drug
monograph the decomposition
rate constant (k) was found to be 6
x 10-2 year-1. The degradation
reaction is known to proceed via
first-order kinetics. Which one of
the following is the remaining
percentage of the original drug
? concentration​

Answers

Answer:

The remaining percentage of drug concentration is about 88.7% 2 years after manufacture.

Explanation:

Recall the formula for the decay of a substance at an initial [tex]N_0[/tex] concentration at manufacture:

[tex]N(t)=N_0\,e^{-k\,\,t}[/tex]

where k is the decay rate (in our case 0.06/year), and t is the elapsed time in years. Therefore, after 2 years since manufacture we have:

[tex]N=N_0\,e^{-0.06\,\,(2)}\\N=N_0\,e^{-0.12}\\N/N_0=e^{-0.12}\\N/N_0=0.8869[/tex]

This in percent form is 88.7 %. That is, the remaining percentage of drug concentration is about 88.7% 2 years after manufacture.

which statement did Ernest Rutherford make about atoms?

Answers

Answer:

Option A

Explanation:

Ernest Rutherford concluded that the atom has a small, dense center which constitutes the mass of the whole atom. He called it a "Nucleus". He also said that most of the space in the atom is empty.

Consider a sound wave modeled with the equation s(x, t) = 3.00 nm cos(3.50 m−1x − 1,800 s−1t). What is the maximum displacement (in nm), the wavelength (in m), the frequency (in Hz), and the speed (in m/s) of the sound wave?

Answers

Answer:

-   maximum displacement = 3.00nm

-   λ = 1.79m

-  f = 286.47 s^-1

Explanation:

You have the following equation for a sound wave:

[tex]s(x,t)=3.00nm\ cos(3.50m^{-1}x- 1,800s^{-1} t)[/tex]              (1)

The general form of the equation of a sound wave can be expressed as the following formula:

[tex]s(x,t)=Acos(kx-\omega t)[/tex]            (2)

A: amplitude of the wave = 3.00nm

k: wave number = 3.50m^-1

w: angular frequency = 1,800s^-1

- The maximum displacement of the wave is given by the amplitude of the wave, then you have:

maximum displacement = A = 3.00nm

- The wavelength is given by :

[tex]\lambda=\frac{2\pi}{k}=\frac{2\pi}{3.50m^{-1}}=1.79m[/tex]

The values for the wavelength is 1.79m

- The frequency is:

[tex]f=\frac{\omega}{2\pi}=\frac{1,800s^{-1}}{2\pi}=286.47s^{-1}[/tex]

The frequency is 286.47s-1

A particle is released as part of an experiment. Its speed t seconds after release is given by v (t )equalsnegative 0.4 t squared plus 2 t​, where v (t )is in meters per second. ​a) How far does the particle travel during the first 2 ​sec? ​b) How far does it travel during the second 2 ​sec?

Answers

Answer:

a) 2.933 m

b) 4.534 m

Explanation:

We're given the equation

v(t) = -0.4t² + 2t

If we're to find the distance, then we'd have to integrate the velocity, since integration of velocity gives distance, just as differentiation of distance gives velocity.

See attachment for the calculations

The conclusion of the attachment will be

7.467 - 2.933 and that is 4.534 m

Thus, The distance it travels in the second 2 sec is 4.534 m

A soccer ball is kicked straight upwards with an initial vertical speed of 8.0\,\dfrac{\text m}{\text s}8.0 s m ​ 8, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction. We can ignore air resistance. How long does it take the ball to have a downwards speed of 4.0\,\dfrac{\text m}{\text s}4.0 s m ​ 4, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction?

Answers

Answer:

1.2 s

Explanation:

Given:

v₀ = 8.0 m/s

v = -4.0 m/s

a = -10 m/s²

Find: t

v = at + v₀

(-4.0 m/s) = (-10 m/s²) t + (8.0 m/s)

t = 1.2 s

An object is launched at a velocity of 20 m/s in a direction making an angle of 25° upward with the horizontal.
a) What is the maximum height reached by the object?
b) What is the total flight time (between launch and touching the ground) of the object?
c) What is the horizontal range (maximum x above ground) of the object?
d) What is the magnitude of the velocity of the object just before it hits the ground?

Answers

Answer:

(a) max. height = 3.641 m

(b) flight time = 1.723 s

(c) horizontal range = 31.235 m

(d) impact velocity = 20 m/s

Above values have been given to third decimal.  Adjust significant figures to suit accuracy required.

Explanation:

This problem requires the use of kinematics equations

v1^2-v0^2=2aS .............(1)

v1.t + at^2/2 = S ............(2)

where

v0=initial velocity

v1=final velocity

a=acceleration

S=distance travelled

SI units and degrees will be used throughout

Let

theta = angle of elevation = 25 degrees above horizontal

v=initial velocity at 25 degrees elevation in m/s

a = g = -9.81 = acceleration due to gravity (downwards)

(a) Maximum height

Consider vertical direction,

v0 = v sin(theta) = 8.452 m/s

To find maximum height, we find the distance travelled when vertical velocity = 0, i.e. v1=0,

solve for S in equation (1)

v1^2 - v0^2 = 2aS

S = (v1^2-v0^2)/2g = (0-8.452^2)/(2*(-9.81)) = 3.641 m/s

(b) total flight time

We solve for the time t when the vertical height of the object is AGAIN = 0.

Using equation (2) for vertical direction,

v0*t + at^2/2 = S    substitute values

8.452*t + (-9.81)t^2 = 3.641

Solve for t in the above quadratic equation to get t=0, or t=1.723 s.

So time for the flight = 1.723 s

(c) Horiontal range

We know the horizontal velocity is constant (neglect air resistance) at

vh = v*cos(theta) = 25*cos(25) = 18.126 m/s

Time of flight = 1.723 s

Horizontal range = 18.126 m/s * 1.723 s = 31.235 m

(d) Magnitude of object on hitting ground, Vfinal

By symmetry of the trajectory, Vfinal = v = 20, or

Vfinal = sqrt(v0^2+vh^2) = sqrt(8.452^2+18.126^2) = 20 m/s

(9) A dancer spins at 72rpm about an axis through the center with arms outstretched. The dancer mass=90kg, model the head as a uniform sphere r=8.0cm Model the trunk and legs as uniform solid cylinder r=12.0cm, arms as slender rods L=60.0cm. On the average the head=7%, both arms together=13% and trunk and legs=80% of body mass. Find the K.E. of the dancer note: arms are I around an axis for slender rod: 1/3ML^2 each arm note2: Moments of Inertia are summable, i.e. I total = I1 + I2 + I 3 +...

Answers

Answer:

Explanation:

ω = angular velocity = 2π n = 2π x 72 / 60

= 7.536 rad /s

mass of head = 90 x .07 = 6.3 kg

moment of inertia of head = 2 /5 m R²

= .4 x 6.3 x .08²

= .016128 kg m²

moment of inertia of trunk + legs

= 1/2 m R²

= .5 x .8 x 90 x .12²

= .5184 kg m²

moment of inertia of arms

= 1/3 m L²

= 1 / 3 x .13 x 90 x .60²

= 1.404 kg m²

Total moment of inertia

I = 1.938 kg m²

kinetic energy = 1/ 2 I ω ²

where I is moment of inertia and ω is angular velocity

= .5 x 1.9338 x  7.536²

=55 J approx .

The definition of kinetic energy and moment of inertia allows finding the result for the kinetic energy of the dancer with arms extended is:

The kinetic energy  is:    KE = 56.3J

Given parameters

Frequency is: f = 72 rad / min (1 min / 60s) = 1.2 rad / s The mass is m = 90 k Head radius is r₁ = 8.0 cm = 0.08 m The leg and trunk are cylinders of radius r₂ = 12.0 cm = 0.12 m The length of the arms, approximated as rods L = 60.0 cm = 0.600 m The dancer spins with outstretched arms The percentage of the mass is:

       *    Head 7%

       *    Arms 13%

       *   Trunk and legs 80%

To find.

Kinetic energy

The kinetic energy is the energy due to the movement, in this case the movement is rotational, therefore the expression is:

             KE = ½ I w²

The angular velocity is related to the frequency.

            w = 2π f

            w = 2π 1.2

            w = 7.540 s

The moment of inertia is a scalar, therefore it is a quantity that can be added, the total moment of inertia of the dancer is the sum of the moments of inertia of each part with respect to the axis of rotation of the person.

          [tex]I_{toal}= I_{head}+ I_{trunk}+I_{arms}[/tex]

The moments of inertia with respect to the centers of mass are tabulated.

Sphere        I = 2/5 mr²

Cylinder      I = ½ m r²

Rod             I = ⅓ m r²

The axis of rotation of the head and the trunk are in the axis of rotation of the person, therefore their moment of inertia is those corresponding to the center of mass.

At the end of the arms it is at a distance of D = [tex]\frac{r_2}{2}[/tex]  from the axis of rotation of the dancer, therefore to find the moment of inertia we must use the theorem of parallel axes, see attached.                  

              [tex]I_{arms} = I_{cm} + M D^2[/tex]

             [tex]I_{arms}[/tex]  = ⅓ m L² + m D²

            [tex]I_{arms} = m_{arms} ( \frac{L^2}{3} + D^2)[/tex]            

                           

The masses of each part of the body are:

            [tex]m_{head}[/tex] = m 0.07

            [tex]m_{trunk}[/tex] = m 0.80  

            [tex]m_{arms}[/tex]  = m 0.13

Let's find the total  moment of inertia.  

            [tex]I_{total} = \frac{2}{5} \ 0.07m \ r_1^2 + 0.13m\ ( \frac{L^2}{3} + D^2) + \frac{1}{2} \ 0.80m \ r_2^2[/tex]  

            [tex]I_{total} = m ( 0.028 \ r_1^2 + 0.13 (\frac{L^2}{3} + D^2) + 0.40 \ r_2^2}[/tex]  

           

Let's calculate.  

           [tex]I_{total} = 90\ ( 0.028 \ 0.08^2 + 0.13\ ( \frac{0.6^2}{3} + 0.06^2) + 0.40 \ 0.12^2 )[/tex]

           

           [tex]I_{total}= 90 \ 0.0220 \\ \\I_{total} = 1.9806 \ Kg m^2[/tex]

             

we substitute in the kinetic energy

           KE = ½ 1.9806  7,540²

           KE = 56.3  J

In conclusion using the definition of kinetic energy and moment of inertia we can find the result for the kinetic energy of the dancer with the extended arms is:

The kinetic energy is:   KE = 56.3 J

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Consider a skateboarder who starts from rest at the top of ramp that is inclined at an angle of 18.0 ∘ to the horizontal.
Assuming that the skateboarder's acceleration is gsin 18.0 ∘, find his speed when he reaches the bottom of the ramp in 3.50 s .

Answers

Answer:

Explanation:

v= u + at

v is final velocity , u is initial velocity . a is acceleration and t is time

Initial velocity u = 0 . Putting the given values in the equation

v = 0 + g sin 18 x 3.5

= 10.6 m /s

For a skateboarder who starts from the rest, the speed when he reaches the bottom of the ramp will be 10.6 m/s.

What are Velocity and Acceleration?

The term "velocity" refers to a vector measurement of the rate and direction of motion. Velocity is the rate of movement in a single direction, to put it simply. Velocity can be used to determine how fast a rocket is heading into space and how fast a car is moving north on a congested motorway.

There are several types of velocity :

Instantaneous velocityAverage VelocityUniform VelocityNon-Uniform Velocity

The pace at which a person's velocity changes is known as acceleration. This implies that an object is accelerating if its velocity is rising or falling. An object that is accelerating won't have a steady change in location every second like an item moving at a constant speed does.

According to the question, the given values are :

Time, t = 3.50 sec

Initial Velocity, u = 0 m/s

Use equation of motion :

v = u+at

v = 0+ g sin 18 × 3.5

v = 10.6 m/s.

So, the final velocity will be 10.6 m/s.

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What force is required so that a particle of mass m has the position function r(t) = t3 i + 7t2 j + t3 k?

Answers

Answer:

[tex]F(t)=m\,\,a(t)=6\,m\,t\,\hat i+14\,m\,\hat j+6\,m\,t\,\hat k\\F(t)=\,(6\,m\,t,14\,m,6\,m\,t)[/tex]

Explanation:

Recall that force is defined as mass times acceleration, and acceleration is the second derivative with respect to time of the position. Since the position comes in terms of time, and with separate functions for each component in the three dimensional space, we first calculate the velocity (with the first derivative, and then the acceleration as the second derivative:

[tex]r(t)=t^3\,\hat i+7\,t^2\,\hat j+t^3\,\hat k\\v(t)=3\,t^2\,\hat i+14\,t\,\hat j+3\,t^2\,\hat k\\a(t)=6\,t\,\hat i+14\,\hat j+6\,t\,\hat k[/tex]

Therefore, the force will be given by the product of this acceleration times the mass "m":

[tex]F(t)=m\,\,a(t)=6\,m\,t\,\hat i+14\,m\,\hat j+6\,m\,t\,\hat k[/tex]

In an experiment different wavelengths of light, all able to eject photoelectrons, shine on a freshly prepared (oxide-free) zinc surface. Which statement is true

Answers

Answer:

the energy of the photons is greater than the work function of the zinc oxide.

                     h f> = Ф

Explanation:

In this experiment on the photoelectric effect, it is explained by the Einstein relation that considers the light beam formed by discrete energy packages.

                    K_max = h f - Ф

in the exercise phase, they indicate that different wavelengths can inject electrons, so the energy of the photons is greater than the work function of the zinc oxide.

                     h f > = Ф

A bicycle tire pump has a piston with area 0.43 In2. If a person exerts a force of 16 lb on the piston while Inflating a tire, what pressure does this produce on the air in the pump?

Answers

Answer:

The pressure produced on the air in the pump is 37.209 pounds per square inch.

Explanation:

By definition, the pressure is the force exerted on the piston divided by its area. Given that, force is distributed uniformly on the piston area, the formula to determine the pressure is:

[tex]p = \frac{F}{A}[/tex]

Where:

[tex]p[/tex] - Pressure, measured in pounds per square inch.

[tex]F[/tex] - Force exerted on the piston, measured in pounds.

[tex]A[/tex] - Piston area, measured in square inches.

If [tex]F = 16\,lb[/tex] and [tex]A = 0.43\,in^{2}[/tex], the pressure produced on the air in the pump is:

[tex]p = \frac{16\,lb}{0.43\,in^{2}}[/tex]

[tex]p = 37.209\,psi[/tex]

The pressure produced on the air in the pump is 37.209 pounds per square inch.

How fast is the spaceship traveling towards the Sun? The radius of the orbit of Jupiter is 43.2 light-minutes, and that of the orbit of Mars is 12.6 light-minutes.

Answers

Question:

A spaceship enters the solar system moving toward the Sun at a constant speed relative to the Sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 35.0 minutes

How fast is the spaceship traveling towards the Sun? The radius of the orbit of Jupiter is 43.2 light-minutes, and that of the orbit of Mars is 12.6 light-minutes.

Answer:

S = 5.508 × 10¹¹m

V = 2.62 × 10⁸ m/s

Explanation:

The radius of the orbit of Jupiter, Rj is 43.2 light-minutes

radius of the orbit of Mars, Rm is 12.6 light-minutes

Distance travelled S = (Rj - Rm)

= 43.2 - 12.6 = 30.6 light- minutes

= 30.6 × (3 ×10⁸m/s) × 60 s

= 5.508 × 10¹¹m

time = 35mins = (35 × 60 secs)

= 2100 secs

speed = distance/time

V = 5.508 × 10¹¹m / 2100 s

V = 2.62 × 10⁸ m/s

What is the potential difference across one wire of a 70 m extension cord made of 16 gauge copper wire carrying a current of 4 A at room temperature (20degrees Celsius)

Answers

Answer:

V = 3.6 volts

Explanation:

From Ohm's Law, we know that:

V = IR

but,

R = ρL/A

Therefore,

V = IρL/A

where,

V = Potential Difference = ?

I = Current = 4 A

ρ = resistivity of copper = 1.68 x 10⁻⁸ Ω.m

L = Length = 70 m

A = Cross-sectional Area = πd²/4 = π(1.29 x 10⁻³ m)²/4     [16 gauge wire has a diameter of 1.29 mm]

A = 1.31 x 10⁻⁶ m²

V = (4 A)(1.68 x 10⁻⁸ Ω.m)(70 m)/(1.31 x 10⁻⁶ m²)

V = 3.6 volts

The potential difference across the given length of copper wire is obtained to be 3.6 V.

Ohm's Law

The resistance of the wire depends on the length, area of cross-section of the wire and resistivity of the material.

Given the length of the wire, [tex]L = 70\,m[/tex].

The diameter of a 16 gauge copper wire is given by, [tex]d = 1.29\times 10^{-3}\,m[/tex].

Therefore, the radius of the cross-section is;

[tex]r=\frac{d}{2} = \frac{1.29\times 10^{-3}\,m}{2} =6.45\times 10^{-4}\,m[/tex]

So, the resistance of the given length of wire can be written as,

[tex]R= \rho\, \frac{L}{A} =(1.68 \times 10^{-8} \, \Omega .m)\times \frac{70\,m}{\pi \times (6.45\times 10^{-4}m)^2} = 0.9\, \Omega[/tex]

According to Ohm's Law, we can write;

[tex]V=IR[/tex]

Substituting the known values, we get the voltage drop is;

[tex]V = 4A \times 0.9\Omega = 3.6\,V[/tex]

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A farmer with 600 ft of available fencing wants to enclose a rectangular are located adjacent to a farmhouse (with no fencing required along the farmhouse) and then divide it into four sections with fencing perpendicular to the side of the farmhouse. Show that the largest possible area of the four sections will be 18,000 square feet, and state the corresponding dimensions of the rectangular area.

Answers

Answer:

The corresponding dimensions will be "x = 300 & y = 60".

Explanation:

Available fencing = 600 ft

Fencing,

⇒  [tex]5y+x=600[/tex]

⇒  [tex]x=600-5y[/tex]

As we know,

⇒  [tex]Area =xy[/tex]

On substituting the given values, we get

             [tex]=(600-5y)y[/tex]

             [tex]=600y-5y^2[/tex] ...(equation 1)

On differentiating with respect to y, we get

⇒  [tex]\frac{dA}{dy} =600-10y[/tex]

       [tex]0 = 600-10y[/tex]

    [tex]600=10y[/tex]

       [tex]y=\frac{600}{10}[/tex]

       [tex]y=60[/tex]

On putting the values of y in equation 1, we get

⇒  [tex]600(60)-5(60)^2[/tex]

⇒  [tex]600(60)-5(3600)[/tex]

⇒  [tex]36000 - 18000[/tex]

⇒  [tex]18000[/tex]

Dimensions of the rectangular area:

x = 300

y = 60

An electron, moving south, enters a magnetic field of certain strength. Because of this field the electron curves upward. What is the direction of the magnetic field

Answers

Answer: The magnetic field points to the west.

Explanation:

If we take the plane as:

North = positive y-axis

East = positive x-axis.

We have that the electron is moving south, so the velocity of the electron can be written in vector form as:

V = (0, -v, 0)

Now, when the electron interacts with the magnetic field, the electron moves upwards.

We know that the interaction between an electron and a magnetic field is:

F = q*VxB

So we have that this force acts on the z-direction.

Now, to solve this we can use the righ hand rule.

First, we point wit our hand to the direction of the velocity (negative y-axis) now, we want that our thumb points up (the direction of the force) so the side where our palm faces is the direction of the field B.

But, remember that an electron has a negative charge, so the actual equation is:

F = -q*VxB

So the magnetic field actually points in the opposite direction of our palm, to the west.

Now, we can also solve it mathematically as:

F = (0, 0, f) = -q*(0, -v,0)x(a, b, c)

where B = (a, b, c) is the vector of the magnetic field.

     (0, 0, f) = -q*(-v*b -0, -0 + 0, 0 -(- a*v)) = -q*(-v*b, 0, a*v)

then we have that b must be equal to zero, and that:

f = -q*a*v

and f is positive, then we have:

a = -(f/q*v)

then the vector of the magnetic field is:

B = (-(f/q*v), 0, 0)

so it points in the negative x-axis, that is the West, as we found earlier.

Suppose the current in a conductor decreases exponentially with time according to the equation I(t) = I0e-t/τ, where I0 is the initial current (at t = 0), and τ is a constant having dimensions of time. Consider a fixed observation point within the conductor.

Required:
a. How much charge passes this point between t = 0 and t = τ?
b. How much charge passes this point between t = 0 and t = 10 τ?
c. What If ? How much charge passes this point between t = 0 and t = [infinity]?

Answers

Answer:

Pls see attached file

Explanation:

A particle with kinetic energy equal to 282 J has a momentum of magnitude 26.4 kg · m/s. Calculate the speed (in m/s) and the mass (in kg) of the particle.

Answers

Answer:

[tex]v=21.36\,\,\frac{m}{s}\\[/tex]

[tex]m=1.2357\,\,kg[/tex]

Explanation:

Recall the formula for linear momentum (p):

[tex]p = m\,v[/tex]  which in our case equals 26.4 kg m/s

and notice that the kinetic energy can be written in terms of the linear momentum (p) as shown below:

[tex]K=\frac{1}{2} m\,v^2=\frac{1}{2} \frac{m^2\,v^2}{m} =\frac{1}{2}\frac{(m\,v)^2}{m} =\frac{p^2}{2\,m}[/tex]

Then, we can solve for the mass (m) given the information we have on the kinetic energy and momentum of the particle:

[tex]K=\frac{p^2}{2\,m}\\282=\frac{26.4^2}{2\,m}\\m=\frac{26.4^2}{2\,(282)}\,kg\\m=1.2357\,\,kg[/tex]

Now by knowing the particle's mass, we use the momentum formula to find its speed:

[tex]p=m\,v\\26.4=1.2357\,v\\v=\frac{26.4}{1.2357} \,\frac{m}{s} \\v=21.36\,\,\frac{m}{s}[/tex]

A 12.5-µF capacitor is connected to a power supply that keeps a constant potential difference of 24.0 V across the plates. A piece of material having a dielectric constant of 3.75 is placed between the plates, completely filling the space between them.
(a) How much energy is stored in the capacitor before and after the dielectric is inserted?
(b) By how much did the energy change during the insertion? Did it increase or decrease?

Answers

Answer:

a) 0.0036 J & 0.0135 J

b) 0.0099 J

Explanation:

Given that

Capacitance of a capacitor, C(i) = 12.5*10^-6 F

Potential difference across the capacitor, V = 24 V

Dielectric constant, k = 3.75

Energy in a capacitor is given by the formula

U = ½ CV²

Now, applying this to our solution, we have.

a, the energy stored before the dielectric was inserted is 0.0036. After inserting the dielectric, we then take cognizance into it, essentially multiplying by the constant of the dielectric, we got 0.0135 J

b) Now, Change in energy is gotten by subtracting the two energies, and we have

ΔU = U - U(1)

ΔU = 0.0036 - 0.0135

ΔU = 00099 J

See attachment for calculation

What is Dark Matter?

Answers

Explanation:

dark matter is a form of matter thought to account for approximately 85% of the matter in the universe and about a quarter of its total mass–energy density or about 2.241×10⁻²⁷ kg/m³. Its presence is implied in a variety of astrophysical observations, including gravitational effects that cannot be explained by accepted theories of gravity unless more matter is present than can be seen. For this reason, most experts think that dark matter is abundant in the universe and that it has had a strong influence on its structure and evolution. Dark matter is called dark because it does not appear to interact with the electromagnetic field, which means it doesn't absorb, reflect or emit electromagnetic radiation, and is therefore difficult to detect.

A length of organ pipe is closed at one end. If the speed of sound is 344 m/s, what length of pipe (in cm) is needed to obtain a fundamental frequency of 50 Hz

Answers

Answer:

The length = 27.52m

Explanation:

v=f x wavelength

A 5000 kg railcar hits a bumper (a spring) at 1 m/s, and the spring compresses 0.1 meters. Assume no damping. a) Find the spring constant k.

Answers

Answer:

k = 0.5 MN/m

Explanation:

Mass of the railcar, m = 5000 kg

Speed of the rail car, v = 1 m/s

The Kinetic energy(KE) of the railcar is given by the equation:

KE = 0.5 mv²

KE = 0.5 * 5000 * 1²

KE = 2500 J

The spring's compression, x = 0.1 m

The potential energy(PE) stored in the spring is given by the equation:

PE = 0.5kx²

PE = 0.5 * k * 0.1²

PE = 0.005k

According to the principle of energy conservation, Kinetic energy of the railcar equals the potential energy stored in the spring

KE = PE

2500 = 0.005k

k = 2500/0.005

k = 500000 N/m

k = 0.5 MN/m

A thin spherical shell of radius 7.6 cm carries a uniform surface charge density of 6.7 times 10-9 C/m2. The magnitude of the electric field (in N/C) at r = 7.8 cm is approximately:___________.

Answers

Answer:

 E= 1.968 10¹¹  N/C

Explanation:

To calculate the electric field of a sphere we can use Gaussian law

        Ф = ∫ E. dA = [tex]q_{int}[/tex]/ ε₀

In this case we must use a Gaussian surface of spherical shape, since the radii of the sphere and the electric field line have been parallel, consequently the scalar product is reduced to an algebraic product.

         The error of a sphere is

          A = 4π π r²

         E (4π r³) = [tex]q_{int}[/tex] / εo                           (1)

to find the charge inside the sera we use the concept of density

         ρ = quint / V

         qint = rho V

the volume of a sphere is

          V = 4/3 pi r³

we substitute in 1

    E 4π r² = ρ 4/3 π r³

     E = ρ / 3ε₀

now let's change the charge density to the charge

      E = Q 3 / 4π r³    r / 3ε₀

       E = (1 / 4πε₀) Q / r²

       E = k Q /r²

calculate

        E = ρr / 3ε₀

       E = 6.7 10⁻⁹  7.8  10⁻² / 3 8.85 10⁻¹²

         E= 1.968 10¹¹  N/C

Gravitational potential energy is greatest at the highest point of a roller coaster and least at the lowest point.

Answers

Answer:

because gravitational potential enegry is directly proportional to the height so more the height more the gravitational potential enegry. therefore gravitational potential enegry is greatest at high point than lower points.

Water flowing through a garden hose of diameter 2.76 cm fills a 20.0-L bucket in 1.45 min. (a) What is the speed of the water leaving the end of the hose

Answers

Answer:

v = 31.84 cm/s or 0.318 m/s

the speed of the water leaving the end of the hose is 31.84 cm/s or 0.318 m/s

Explanation:

Given;

Diameter of hose d = 2.76 cm

Volume filled V = 20.0 L = 20,000 cm^3

Time t = 1.45 min = 105 seconds

The volumetric flow rate of water is;

F = V/t = 20,000cm^3 ÷ 105 seconds

F = 190.48 cm^3/s

The volumetric flow rate is equal the cross sectional area of pipe multiply by the speed of flow.

F = Av

v = F/A

Area A = πd^2/4

Speed v = F/(πd^2/4)

v = 4F/πd^2 ......1

Substituting the given values;

v = (4×190.48)/(π×2.76^2)

v = 31.83767439628 cm/s

v = 31.84 cm/s or 0.318 m/s

the speed of the water leaving the end of the hose is 31.84 cm/s or 0.318 m/s

a heat engine with an efficiency of 30.0% performs 2500 j of work. how much heat is discharged to the lower temperature reservoir

Answers

Answer:

Q₂ = 5833.33 J

Explanation:

First we need to find the energy supplied to the heat engine. The formula for the efficiency of the heat engine is given as:

η = W/Q₁

where,

η = efficiency of engine = 30% = 0.3

W = Work done by engine = 2500 J

Q₁ = Heat supplied to the engine = ?

Therefore,

0.3 = 2500 J/Q₁

Q₁ = 2500 J/0.3

Q₁ = 8333.33 J

Now, we find the heat discharged to lower temperature reservoir by using the formula of work:

W = Q₁ - Q₂

Q₂ = Q₁ - W

where,

Q₂ = Heat discharged to the lower temperature reservoir = ?

Therefore,

Q₂ = 8333.33 J - 2500 J

Q₂ = 5833.33 J

How much electricity is in human body?​

Answers

Answer:

100 on average

Explanation:

The human body is a physical substance from where a human can breathe, drink, eat, walk, etc, and consists of various cells. A human being cannot live with their functions and when functions stop working that means a human being is dead.

Therefore, in the human body, there is also electricity that contains 100 watts on average.

So, According to the given situation, the correct answer is 100 on average.

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