34. JAnswer this: Pure (24 carat) gold has a density of 19 g/mL. If you bought"gold" ring and found it had a volume of 0.3 ml and that it weighed 5.7 grams, is it pure gold? Show your work to support your answer.​

Answers

Answer 1

Explanation:

Density = mass / volume

ρ = 5.7 g / 0.3 mL

ρ = 19 g/mL

Yes, it's pure gold.

Answer 2

Yes, it's pure gold.

How do you calculate gold density?The mass of an object divided by its volume is the formula for determining density. This is expressed mathematically as d = m/v, where d denotes density, m denotes mass, and v denotes object volume. The common measurements are kg/m³.

What is the formula of volume?The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape.

What is the volume of pure gold?Gold has a specific gravity of 19.3. In light of this, 19.3 grams take up 1 cubic centimeter. 31.1 grams make up a Troy ounce. As a result, we need 31.1/19.3 = 1.61 cubic centimeters to equal 1 Troy Oz.

According to the question:

Density = mass / volume.

ρ = 5.7 g / 0.3 mL.

ρ = 19 g/mL.

Hence, Yes it's pure gold.

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Related Questions

explain the different methods that can be used to model the motion of an object.

Answers

Answer:Even things that appear to be at rest move.

When we describe the motion of one object with

respect to another, we say that the object is moving

relative to the other object.

• A book that is at rest, relative to the table it lies

on, is moving at about 30 kilometers per second

relative to the sun.

• The book moves even faster relative to the center

of our galaxy.

Explanation:

In a particular wire in a circuit, conventional current flows in the z direction. What is the direction of electron current in the wire

Answers

Answer:

Electron current will flow in the negative z axis

Explanation:

This is because flow of conventional current is opposite that if electron current so since conventional is in +z axis electron will be -z axis

A car travels in a straight line with an average velocity of 80 km/h for 2.5 h and then with an average velocity of 40 km/h for 1.Sh. What is the total displacement for the 4h trip and what is the average velocity for the total trip

Answers

Answer:

260 km

65 km/hr

Explanation:

The displacement of an object is the distance moved by that object in a particular direction.

velocity = displacement / time, therefore,

Displacement = velocity * time.

Total displacement for the 4 HR trip = displacement for 2.5 hr + displacement for 1.5 hr

total displacement = (80 * 2.5) + (40 * 1.5)

Total displacement = 200 + 60

Total displacement = 260 Km

average velocity for the total trip = total displacement / total time taken

average velocity = 260 km/ 4 hr

average velocity = 65 km/hr

"If we increase the amplitude of transverse waves on a string, what happens to the speed of a wave along the string?"

Answers

Answer:

It is increased

Explanation:

If the amplitude of a transverse wave in a string is increased, then also, the speed of that wave along the string also increases.

In transverse waves, the particles of the medium does move vertically, m either up or down and also moves at right angles to the direction of the wave. It should be noted also, that the wave amplitude of a transverse wave is defined as the difference in height between the crest(high) and the resting position(low).

The highest point particles of the medium reach is often tagged as the crest, while the lowest point is tagged as the resting position. The higher the height of the crests are, the greater the amplitude of the wave will be.

Help me please !!!!!

Answers

Answer:

confounding cause they had exposure to many programmes

Answer:

Confounding should be your answer please mark brainliest

A bus took 8 hours to travel 639 km. For the first 5 hours, it
travelled at an average speed of 72 km/h. What was the
average speed for the remaining time of the journey?

Answers

Answer:

93

Explanation:

Two students measure the speed of light. One obtains (3.001 0.001)10^8 m/s; the other obtains (2.999 0.006)10^8 m/s.Required:Which is more precise?

Answers

Answer:

(30010001) 10^8 m/s

Explanation:

Approximately how long will it take light to travel to 1.7 AU in minutes? Use 3 × 108 m/s for the speed of light. unanswered

Answers

Answer:

14.1mins

Explanation:

We know that

Time =Distance/Speed

So

= 1.7 au/ (3 E8 m /s )

= 1.7 x 1.496 x 10^11 m /(3 x 10^8 m /s

Converting Au to meters (1.7 x 1.496 x 10^11 m)

= 847.7 s

=14.1 mins

Answer:

Time = 847.73 s = 14.12 min

Explanation:

The distance traveled by an object travelling at a constant speed is given by the following formula:

Distance = (Speed)(Time)

Time = Distance/Speed

where,

Distance = 1.7 AU

converting it into meters:

Distance = (1.7 AU)(1.496 x 10¹¹ m/1 AU) = 2.543 x 10¹¹ m

Speed = 3 x 10⁸ m/s

Therefore, using these values in the equation we get:

Time = (2.543 x 10¹¹ m)/(3 x 10⁸ m/s)

Time = 847.73 s = 14.12 min

Two long wires hang vertically. Wire 1 carries an upward current of 1.20 A. Wire 2, 20.0 cm to the right of wire 1, carries a downward current of 4.20 A. A third wire, wire 3, is to be hung vertically and located such that when it carries a certain current, each wire experiences no net force.
(a) Is this situation possible?
A. Yes
B. No
Is it possible in more than one way?
A. Yes
B. No
(b) Describe the position of wire 3.
distance ________ cm
direction: left of wire 1
(c) Describe the magnitude and direction of the current in wire 3.
magnitude
direction
down

Answers

Answer:

Explanation:

A, yes

b,

The force(per unit length) on wire 1 by 2 is to the left and

= μo*I1*I2/2πr

= 2*10^-7 * 1.2 * 4.2/0.20

= 5.04*10^-6N/m

From third law we have the force on wire2 by wire 1 is 5.04*10^-6N/m and to the right

So the magnitude of the force on each wire by wire 3 must be 4.2*10^-6N/m

Since the current in wire 2 is > wire 1 then wire 3 must be closer to wire 1 than 2

and wire 3 must be to the left of wire 1

Let x be the distance from wire 3 to wire 1 so x + 0.20 = distance from wire 3 to wire 2

Now μo*I1*I3/2πx = μo*I3*I2/2π(x + 0.20)

so solving for x we get

I1/x = I2/(x+0.20)

or x +0.20 = 4x

so x = 0.20/3 = 0.0667m

Now μo*I1*I3/2πx = 4.2*10^-6

so I3 = 4.2x10^-6 * 0.0667/(2.0x10^-7 * 1.2) = 1.167 A and its direction is down

A billiard ball moves with 3 kg⋅m/s of momentum and strikes three other billiard balls. What is the total momentum of the balls after the collision? A. less than 3 kg⋅m/s B. It depends on the mass of each ball. C. 3 kg⋅m/s D. more than 3 kg⋅m/s

Answers

Answer:

It should be C

Explanation:

It depends on the mass of each ball

Remember the formula for momentum, mass X velocity

Momentum depends on the mass of the object

The momentum of the billiard balls after the collision is 3 Kgm/s.

Let the billiard ball be B.

Given the following data:

Momentum B = 3 Kgm/s

To find the momentum of the balls after the collision:

Momentum is simply a multiplication (product) of the mass of an object with its velocity.  Also, momentum is a vector quantity because it has both magnitude and direction.

Mathematically, momentum is given by the formula;

[tex]Momentum = Mass[/tex] × [tex]Velocity[/tex]

[tex]Total \; momentum = Momentum \; B + Momentum \;of \;the \;other\; balls.[/tex]

Since the other billiard balls were at rest (not experience any motion), there velocities would be zero (0) m/s.

Substituting the values, we have:

[tex]Total \; Momentum = 3 + 0[/tex]

Total momentum = 3 Kgm/s.

Therefore, the momentum of the billiard balls after the collision is 3 Kgm/s.

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A spaceship is traveling through deep space to a space station and needs to make a course correction to go around a nebula. The captain orders the ship to travel 2.3 106 kilometers before turning 70° and traveling 1.5 106 kilometers to reach the space station. If the captain had not ordered a course correction, what would have been the magnitude and direction of the path of the spaceship if it had traveled to the space station through the nebula?

Answers

Answer:

Explanation:

Using the given values

Let

Px= 2.3 x 10^6, Py=0, Qx=1.5x10^6cos(70),

Qy= 1.5x10^6sin(70)

So let

Hx= Px+Qx=2.813 x 10^6, Hy=Py+Qy=1.401 x 10^6

Magnitude = √ ((2.813 x 10^6)^2+(1.401 x 10^6)^2)= 3.14 x 10^6

To find direction

tan စ = Hy/Hx = 1.401/2.813= 0.4980

စ = 26.5°

The magnitude and direction of the path of the spaceship if it had traveled to the space station through the nebula are 3.14 x 10⁶ m and 26.5°.

What is nebula?

A nebula is a huge cloud consisting of dust and gas in space. Some nebula come from the gas and dust thrown out by the explosion of a dying star known as a supernova.

The captain orders the ship to travel in horizontal direction, Px= 2.3 x 10⁶ m, Py=0,

After turning 70° and it travels to reach the space station, Qx = 1.5x10⁶ x cos70° in horizontal direction.

and Qy= 1.5x10⁶sin70°

So, total horizontal distance moved is

Hx= Px+Qx = 2.813 x 10⁶

Total vertical distance moved is
Hy=Py+Qy  = 1.401 x10⁶

Magnitude of the path = sq rt [(2.813 x 10⁶)²+(1.401 x 10⁶)²]

Path = 3.14 x 10⁶ m

Direction of the path,

tan α = Hy/Hx

tan α = 1.401/2.813

tan α = 0.4980

α = 26.5°

Thus, the magnitude and direction of the path of spaceship is 3.14 x 10⁶ m and 26.5°.

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To conduct a study on depression, you ask people to rate their depression on
a scale of 1 to 10. Their responses are a(n) ___ in your study.
A. discrete variable
B. hidden variable
C. variable
D. observation

Answers

Answer:

The answer is C variable. Just took the quiz.

Explanation:

Answer:

C. variable

Explanation:

The horizontal and vertical components of the initial velocity of a projectile are 50 m/s and 120 m/s respectively. What is the magnitude of the initial velocity

Answers

Answer:

50 m/s

Explanation:

In a projectile motion, acceleration is only on the vertical plane, that is, the vertical velocity is the only velocity component that undergoes acceleration under gravitational force. The horizontal component of velocity dos not change with time, and hence is the same as the initial velocity of the projectile.

Why are experimental investigations the best type of scientific investigation o demonstrat cause-and-effect relationships?

Answers

Answer:

Isolation of Variables.

Explanation:

I am just taking a guess but Experimental investigations allow you to isolate variables (making most variables constant, allowing only the independent variable to have an impact on the dependent variable). With other scientific investigations, if they don't isolate the variables it is very possible that an unknown third variable could be skewing the results (which will result in correlation but not causation).

Answer:

Experimental investigations are the best type of scientific investigation to demonstrate cause-and-effect relationships because they allow the investigator to actively manipulate variables and control conditions. The independent variable can be isolated and manipulated, producing a change (or no change) in the dependent variable. This change can be measured to gather evidence to support or refute the cause-and-effect relationship. Experimental investigations also use a control group (a group that does not receive the factor being tested) for comparison.

Explanation:

Automated-response....it's right

What are the magnitude and direction of the net force on the third spider (S3) when it is resting at the origin

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

The  magnitude is  [tex]F_3 =0.62\ N[/tex]

Explanation:

From the question we are told that

    The distance between the spiders is  [tex]a =0.59\ m[/tex]

    The  charge on the [tex]S_1\ and\ S_3[/tex] is  [tex]q_{1}=q_{3}=q =+4.9\mu \ C[/tex]

     The  charge on [tex]S_2[/tex] is  [tex]q_2 = 4.9\mu \ C[/tex]

Given that the charge are arranged in an equilateral triangle, it implies that the angle at each vertices of the triangle is  60°

Generally the magnitude of net force on [tex]S_3[/tex] is mathematically represented as

   [tex]F_3= F_{13} cos(60)+ F_{21} cos(60)[/tex]

So

  [tex]F_{13} =\frac{k* q^2 }{a^2}[/tex]

Here k is the columns constant with value   [tex]k =  9*10^9 \ kg\cdot m^3\cdot s^{-4} \cdot A^{-2}.[/tex]

So

    [tex]F_{13}=\frac{9*10^9*((4.9*10^{-6})^2)}{0.59^2}[/tex]

=>  [tex]F_{13} =  0.62 \  N[/tex]

From the diagram we see that [tex]F_{13}= F_{23} =  0.62\  N[/tex]

So

    [tex]F_3=0.62cos(60)+0.62cos(60)[/tex]

     [tex]F_3 =0.62\ N[/tex]

Now from the diagram the ls [tex]270^o[\tex] counterclockwise from x-axis

     

If a proton and an electron are released when they are 7.00×10−10 m apart (typical atomic distances), find the initial acceleration of each of them. aelectron = nothing m/s2

Answers

Answer:

The acceleration of the proton is 2.823 x 10¹⁷ m/s²

The acceleration of the electron is 5.175 x 10²⁰ m/s²

Explanation:

Given;

distance between the electron and proton, r = 7 x 10⁻¹⁰ m

mass of proton, [tex]m_p[/tex] = 1.67 x 10⁻²⁷ kg

mass of electron, [tex]m_e[/tex] = 9.11 x 10⁻³¹ kg

The attractive force between the two charges is given by Coulomb's law;

[tex]F = \frac{k(q_p)(q_e)}{r^2}[/tex]

where;

k is Coulomb's constant = 9 x 10⁹ Nm²/c²

[tex]F = \frac{k(q_p)(q_e)}{r^2} \\\\F = \frac{(9*10^9)(1.602*10^{-19})(1.602*10^{-19})}{(7*10^{-10})^2} \\\\F = 4.714 *10^{-10} \ N[/tex]

Acceleration of proton is given by;

F = ma

[tex]F = m_pa_p\\\\a_p = \frac{F}{m_p}\\\\a_p = \frac{4.714*10^{-10}}{1.67*10^{-27}}\\\\a_p = 2.823 *10^{17} \ m/s^2[/tex]

Acceleration of the electron is given by;

[tex]F = m_ea_e\\\\a_e = \frac{F}{m_e}\\\\a_e = \frac{4.714*10^{-10}}{9.11*10^{-31}}\\\\a_e = 5.175 *10^{20} \ m/s^2[/tex]

The acceleration of proton and electron will be "[tex]2.823\times 10^{17} \ m/s^2[/tex]" and "[tex]5.175\times 10^{20} \ m/s^2[/tex]".

Given:

Mass of proton, [tex]m_p = 1.67\times 10^{-27} \ kg[/tex]Mass of electron, [tex]m_e = 9.11\times 10^{-31 } \ kg[/tex]Distance between electron & proton, [tex]r = 7\times 10^{-10} \ m[/tex]

By using Coulomb's law, the attractive force will be:

→ [tex]F = \frac{k(q_p) (q_e)}{r^2}[/tex]

By substituting the values, we get

        [tex]= \frac{(9\times 10^9)(1.602\times 10^{-19}) (1.602\times 10^{-19})}{(7\times 10^{-10})^2}[/tex]

        [tex]= 4.714\times 10^{-10} \ N[/tex]

Now,

The acceleration of proton will be:

→ [tex]F = ma[/tex]

       [tex]= m_p a_p[/tex]

or,

→ [tex]a_p = \frac{F}{m_p}[/tex]

        [tex]= \frac{4.714\times 10^{-10}}{1.67\times 10^{-27}}[/tex]

        [tex]= 2.823\times 10^{17} \ m/s^2[/tex]  

and,

The acceleration of electron will be:

→ [tex]F = m_c a_c[/tex]

or,

→ [tex]a_e = \frac{F}{m_e}[/tex]

        [tex]= \frac{4.714\times 10^{-10}}{9.11\times 10^{-31}}[/tex]

        [tex]= 5.175\times 10^{20} \ m/s^2[/tex]

Thus the above answer is correct.

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The gravitational pull of the sun on Earth keeps Earth orbiting around the sun. Which statement is correct about the force that Earth exerts on the sun?


A. Earth pulls the sun away from itself with a force equal to the ratio of the mass of the sun to the mass of Earth.

B. Earth pulls the sun toward itself with a force equal to the ratio of the mass of the sun to the mass of Earth.

C. Earth pulls the sun away from itself with an equal force.

D. Earth pulls the sun toward itself with an equal force,​

Answers

Answer:

Earth pulls the sun towards itself with a force equal to the ratio of the mass of the sun to the mass of Earth

The Earth pulls the sun toward itself with an equal force. (Option D)

According to the 3rd Newton's Law, forces existing in the universe are shown in pairs, that is to say, for all action force, there is a corresponding reaction force of equal magnitude and opposite direction. By the Newton's Law of Gravitation we understand that gravitation between the Sun and the Earth is done because of a gravitational field created by mutual interaction, in terms of their masses and distance among them. The pair of forces is not based on direct contact.

Hence, we conclude that the Earth pulls the sun toward itself with an equal force.

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To whom does the vha provide care for today ?

Answers

Answer:

The Veterans Health Administration (VHA) is the largest integrated health

care system in the United States, providing care at 1,255 health care

facilities, including 170 VA Medical Centers and 1,074 outpatient sites of care

of varying complexity ( VHA outpatient clinics) to over 9 million Veterans

enrolled in the VA .

What is the power in D of the eyes of a woman who can see an object clearly at a distance of only 9.5 cm

Answers

Answer:

Explanation:

It is the far point an myopic person . For it she uses concave lens . For her ,

object distance u = infinity

image v = - 9.5 cm

f = ?

form the lens formula

[tex]\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\[/tex]

[tex]\frac{1}{f} = \frac{1}{-9.5} - 0 \\[/tex]

f = - 9.5 cm  = - 9.5 / 100 m

P = 1 /f = - 100 / 9.5 =  - 10.52 D .

Calculate the kinetic energy of an 88-kg scooter moving at 12 m/s .

Answers

Answer:

kinetic energy = 1/2 X m(v)^2

= 1/2 X 88 X 12

= 528 j

Your question has been heard loud and clear.

Kinetic energy formula= 1/2mv^2

Mass = 88kg (convert to grams because velocity is in m/s)

Mass in grams = 88000g or 88*10^3 g

Velocity= 12m/s

Now kinetic energy = 1/2 * 88000*12*12= 6336 joules

Kinetic energy = 6336 Joules or 6.336 Kilo joules

Thank you.

Light of wavelength 3500Å is incident on two metals A and B whose work functions are 3.2 eV and 1.9 eV respectively. Which metal will emit photoelectrons?
(a) A
(b) B
(c) Both A and B
(d) Neither A nor B

Answers

Answer:

(c) Both A and B

Explanation:

Given;

wavelength of the incident light, λ = 3500 Å = 3500 x 10⁻¹⁰ m

The energy of the incident light is given by;

E = hf

where;

h is Planck's constant = 6.626 x 10⁻³⁴ J/s

f is frequency =  c / λ

[tex]E = \frac{hc}{\lambda} \\\\E = \frac{(6.626*10^{-34})(3*10^8)}{3500*10^{-10}}\\\\E = 5.68 *10^{-19} \ J\\\\E = 5.68 \ eV[/tex]

Work function is the minimum amount of energy required to liberate electrons from a metal surface.

The work function of metal A is 3.2 eV and

Th e work function of metal B is 1.9 eV

Both work functions are less than the incident energy of the light calculated as 5.68eV.

Thus, both metals will emit photoelectrons.

(c) Both A and B

What will be the force if the particle's charge is tripled and the electric field strength is halved? Give your answer in terms of F

Answers

Answer:

1.5F

Explanation:

Using

E= F/q

Where F= force

E= electric field

q=charge

F= Eq

So if qis tripled and E is halved we have

F= (E/2)3q

F= 1.5Eq=>> 1.5F

URGENT!!!!!! Assume that a wire has 1.5 ohms of resistance. If the wire is connected to two batteries with a total voltage of 3.0 V, how much current will flow through the wire? 3.0 amps 2.3 amps 2.0 amps 1.0 amps

Answers

Answer:

  2.0 amps

Explanation:

Current is the ratio of voltage to resistance:

  I = V/R = (3.0)/(1.5) = 2.0

The current in the wire is 2.0 amps.

According to Newton's Third Law, if someone jumps off a skateboard, the
skateboard will roll backwards because

Answers

Answer:

every action has a same an equal reaction

If someone jumps off a skateboard, the  skateboard will roll backwards because action and reaction are equal and opposite.

Newton's third law states that action and reaction are equal and opposite. That is, for every action there is a resulting reaction equal in magnitude to the action but opposite in direction.

If someone jumps off a skateboard, he will exert an action force downwards while the skate board exerts a reaction force upwards on him. This causes the skateboard to move backwards while he moves upwards.

Thus,  if someone jumps off a skateboard, the  skateboard will roll backwards because action and reaction are equal and opposite.

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what do u mean by the activity series of metals ??

Answers

Answer:

An activity series is a list of substances ranked in order of relative reactivity. For example, magnesium metal can knock hydrogen ions out of solution, so it is considered more reactive than elemental hydrogen. The activity series is a useful guide for predicting the products of metal displacement reactions.

The electric flux through a spherical surface is 1.4 ✕ 105 N · m2/C. What is the net charge (in C) enclosed by the surface?

Answers

Answer:

The  value is   [tex]Q_{net} =  1.239 *10^{-6} \  C[/tex]

Explanation:

From the question we are told that

   The electric flux is [tex]\Phi =  1.4*10^{5} \  N\cdot m^2/C[/tex]

     

Generally the net charge is mathematically represented as

    [tex]Q_{net} =  \Phi *  \epsilon_o[/tex]

Here [tex]\epsilon_o[/tex] is the permetivity of free space with value  

       [tex]\epsilon_o =  8.85*10^{-12}  \  \  m^{-3} \cdot kg^{-1}\cdot  s^4 \cdot A^2[/tex]

So

   [tex]Q_{net} =  1.4*10^5 *  8.85*10^{-12}[/tex]

=>   [tex]Q_{net} =  1.239 *10^{-6} \  C[/tex]


State two precautions each that you will take while performing refractive index of a glass box experiment​

Answers

Answer:

light should be direct

glass should not be cracked

pins should be pointed carefully

Explanation:

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.200 rev/s . The magnitude of the angular acceleration is 0.883 rev/s2 . Both the the angular velocity and angular accleration are directed counterclockwise. The electric ceiling fan blades form a circle of diameter 0.760 m .A. Compute the fan's angular velocity magnitude after time 0.204 s has passed.Express your answer numerically in revolutions per second.B. Through how many revolutions has the blade turned in the time interval 0.204 s from Part A?Express the number of revolutions numerically.C. What is the tangential speed vt of a point on the tip of the blade at time t = 0.204 s?Express your answer numerically in meters per second.D. Calculate the magnitude atat of the tangential acceleration of a point on the tip of the blade at time t = 0.204 s.Express the acceleration numerically in meters per second squared.

Answers

Answer:

(A). the angular velocity of fan is 0.380 rev/s.

(B). The number of revolution is 0.059 rad.

(C). The tangential speed of the blade is 0.907 m/s.

(D). The tangential acceleration of the blade is 2.10 m/s²

Explanation:

Given that,

Initial angular velocity = 0.200 rev/s

Angular acceleration = 0.883 rev/s²

Diameter = 0.760 m

Time = 0.204 s

(A). We need to calculate the angular velocity of fan

Using equation of angular motion

[tex]\omega_{f}=\omega_{i}+\alpha t[/tex]

Put the value into the formula

[tex]\omega_{f}=0.200+0.883\times0.204[/tex]

[tex]\omega_{f}=0.380\ rev/s[/tex]

(B). We need to calculate the number of revolution

Using formula of angular displacement

[tex]\theta=\omega_{i}t+\dfrac{1}{2}\alpha t^2[/tex]

Put the value into the formula

[tex]\theta=0.200\times0.204+\dfrac{1}{2}\times0.883\times(0.204)^2[/tex]

[tex]\theta=0.059\ rad[/tex]

(C). We need to calculate the tangential speed of the blade

Using formula of speed

[tex]v=\dfrac{d}{2}\omega_{f}[/tex]

Put the value into the formula

[tex]v=\dfrac{0.760}{2}\times0.380\times2\pi[/tex]

[tex]v=0.907\ m/s[/tex]

(D). We need to calculate the tangential acceleration of the blade

Using formula of tangential acceleration

[tex]a_{t}=\alpha r[/tex]

Put the value into the formula

[tex]a_{t}=0.883\times0.38\times2\pi[/tex]

[tex]a_{t}=2.10\ m/s^2[/tex]

Hence, (A). the angular velocity of fan is 0.380 rev/s.

(B). The number of revolution is 0.059 rad.

(C). The tangential speed of the blade is 0.907 m/s.

(D). The tangential acceleration of the blade is 2.10 m/s²

A stretched string is 2.11 m long and has a mass of 19.5 g. When the string oscillates at 440 Hz , which is the frequency of the standard A pitch, transverse waves with a wavelength of 15.3 cm travel along the string. Calculate the tension T in the string.

Answers

Answer:

The tension of the string is 41.876 N

Explanation:

Given;

length of the string, L = 2.11 m

mass of the string, m = 19.5 g = 0.0195 kg

frequency of the wave, f = 440 Hz

wavelength, λ = 15.3 cm = 0.153 m

The velocity of the wave is given by;

v = fλ

v = 440 x 0.153

v = 67.32 m/s

Also the velocity of the wave is given by

[tex]v = \sqrt{\frac{T}{\mu} }[/tex]

where;

μ is mass per unit length = 0.0195 / 2.11 = 0.00924 kg/m

T is the tension of the string

T = v²μ

T = (67.32)²(0.00924)

T = 41.876 N

Therefore, the tension of the string is 41.876 N

If one has twice the length of the other, what is the ratio of the diameter of the longer wire to the diameter of the shorter wire

Answers

Explanation:

The resistance of a wire is given by the formula as follows :

[tex]R=\rho \dfrac{l}{A}[/tex]

l is length of wire

A is area of cross section, [tex]A=\pi r^2[/tex]

Since, r=d/2, d = diameter

[tex]A=\pi \dfrac{d^2}{4}[/tex]

It is given in the problem that the resistance of two aluminum wires is same.

[tex]R_1=R_2\\\\\rho\dfrac{L_1}{\pi d_1^2/4}=\rho\dfrac{L_2}{\pi d_2^2/4}\\\\\dfrac{L_1}{L_2}=\dfrac{d_1^2}{d_2^2}[/tex]

We have, L₁=2L₂

So,

[tex]\dfrac{2L_2}{L_2}=\dfrac{d_1^2}{d_2^2}\\\\\dfrac{d_1^2}{d_2^2}=2\\\\\dfrac{d_1}{d_2}=\sqrt{2}[/tex]

So, the ratio of the diameter of the longer wire to the diameter of the shorter wire is [tex]\sqrt2:1[/tex]

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