Accurate radiometric dating typically requires that a rock contains a measurable amount of __________.

Answers

Answer 1

Answer:

Both daughter and parent atoms

Explanation:

Daughter atoms are an offshoot of daughter elements, and are formed when a radioactive element undergoes radioactive decay. The new element is the daughter element, while the initial, the former element is the parent element.

Same analogy goes for daughter atoms and parent atoms..

Radiometric dating is also called radioactive dating or even radioisotope dating. It is a technique that is used to date materials like carbon or even rocks, that has trace radioactive impurities selectively incorporated into it when they were formed.

Answer 2

Radiometric dating is defined as the technique, which is used to date rocks, carbon, or radioactive impurities. The rocks that consist of parent and daughter atoms are used for accurate radiometric dating.

The correct statement for the blank is:

Accurate radiometric dating typically requires that rock contains a measurable amount of parent and daughter atoms.

It can be defined as:

1. Daughter atoms are formed when the radioactive element undergoes radioactive decay. The element formed is the daughter element from which it is formed is known as the parent element.

2. A radioactive isotope is also called radioactive dating, which is used to date rocks and radioactive elements. These elements are incorporated into the elements when they are formed.

Thus, the correct answer is parent and daughter atoms.

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Related Questions

Many behavioral psychologists would disagree with the social cognitive theory because most believe that behavior is __________. A. affected by cognition B. not affected by cognition C. affected by conditioning D. not affected by conditioning (psychology)
Its B: not affected by cognition

Answers

The correct answer B. Not affected by cognition

Explanation:

In the Social Cognitive Theory, the most important aspects are social interaction and cognition that involves mental processes such as comprehension. Indeed, this theory proposes behaviors are the result of observing other people as part of social interaction, understanding this behavior, and then imitating it.

Despite this, many psychologists do not support this theory and the main reason is that they deny the learning of behavior is related to cognition or complex mental processes. Instead, some believe behavior is the result of certain impulses or that is regulated by conditioning such as behaving correctly to avoid negative consequences.

Answer:

B. is correct on Edge 2020

Explanation:

Peace and Love

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which force is a nonconact force?
a. raft floating on water
b. all normal forceses
c. a person pulling a wagon
d, magnetic attracting metal

Answers

D. Magnet attracting metal.
This is because magnetic forces are non contact forces; they pull or push on objects without touching them.

Answer:

d, magnetic attracting metal, because the force is still going on without the magnet touching metal, and you cant see the force

Explanation:

Hope this helps <33

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?A) the one of smallest diameter B) the one of greatest mass C) the disk D) the sphere E) They will reach the bottom at the same time.

Answers

Answer:

(D) the sphere

Explanation:

The bodies given are Disk and Solid sphere (uniform sphere)

Moment of inertia of the bodies are

I(disk) = [tex]\frac{MR^2}{2}[/tex]

I(sphere) = [tex]\frac{2MR^2}{5}[/tex]

Since the moment of inertia of sphere is less than that of disk, therefore sphere will reach the bottom first.

How do inkblots show your personality?

---

A. Inkblots rely on creativity.
B.Your description of an inkblot will give deeper meaning of your inner ideas.
C. Inkblot responses are a way to test if you're lying.
D. Inkblot tests were never reliable to use.

Answers

Answer:

B

Explanation:

Examples of ink blots would be Faceless women, Rocket or Tower, Roast chicken which gives more meaning of your personality and you yourself of the picture that is shown.

Please give an explanation.

Thank you.

Answers

Definitions and Equations

Isothermal means constant temperature.  On a P-V diagram, this appears as a curve.

Constant volume of course appears as a vertical line.

Work done BY an ideal gas at constant pressure is W = PΔV.

Work done BY an ideal gas at constant temperature is:

W = nRT ln(Vf / Vi)

W = nRT ln(Pi / Pf)

Heat added to an ideal gas at constant volume is Q = (Cᵥ/R) VΔP.

For a monotomic gas, Cᵥ = 3R/2.

For a diatomic gas, Cᵥ = 5R/2.

Change in internal energy equals heat added to the gas minus the work done BY the gas.

ΔE = Q − W

For an ideal gas, if the temperature is constant, ΔE = 0.

Process A

At state 1, the pressure is 94.0 kPa and the volume is 4.0 L.  From ideal gas law:

PV = nRT

(94.0 kPa) (4.0 L) = nRT

nRT = 376 J

At state 2, the volume triples to 12.0 L.  The work done is:

W = nRT ln(Vf / Vi)

W = (376 J) ln(12 / 4)

W = 413 J

The process is isothermal, so ΔE = 0 J.  Therefore, Q = 413 J.

The new pressure is:

P₁ V₁ = P₂ V₂

(94.0 kPa) (4.0 L) = P₂ (12.0 L)

P₂ = 31.3 kPa

Process B

At state 3, the volume is constant at 12.0 L, and the pressure rises back to 94.0 kPa.  Since there's no change in volume, W = 0 J.  The heat added is:

Q = (Cᵥ/R) VΔP

Q = (3/2) (12.0 L) (94.0 kPa − 31.3 kPa)

Q = 1130 J

So ΔE = Q − W = 1130 J.

Process C

From ideal gas law:

PV = nRT

(94.0 kPa) (12.0 L) = nRT

nRT = 1128 J

At state 4, the volume returns to 4.0 L.  The work done is:

W = nRT ln(Vf / Vi)

W = (1128 J) ln(4 / 12)

W = -1240 J

The process is isothermal, so ΔE = 0 J.  Therefore, Q = -1240 J.

The new pressure is:

P₃ V₃ = P₄ V₄

(94.0 kPa) (12.0 L) = P₄ (3.0 L)

P₄ = 376 kPa

Process D

Finally back to state 1, the volume is constant at 4.0 L, and the pressure drops back to 94.0 kPa.  Again, since there's no change in volume, W = 0 J.  The heat added is:

Q = (Cᵥ/R) VΔP

Q = (3/2) (4.0 L) (94.0 kPa − 376 kPa)

Q = -1690 J

So ΔE = Q − W = -1690 J.

Entire Cycle

For the entire cycle:

Q = 413 J + 1130 J − 1240 J − 1690 J = -1390 J

W = 413 J + 0 J − 1240 J + 0 J = -827 J

ΔE = 0 J + 1130 J + 0 J − 1690 J = -560 J

A force F is applied to a cylindrical steel cable of diameter 3.5 mm and length 10.0 m. Determine the value of F if the change in length of the cable is 7.8 mm.
Ysteel = 20 x 10^10 N/m2

Answers

Explanation:

Mathematicians seek and use patterns[8][9] to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements.[10] Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.[11]

Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences.

The value of force (F) if the change in length of the cable is 7.8 mm is 1500.89 N

The value of the force can be determined by using the young modulus equation that shows the relation between the tensile of the steel cable when the force is applied.

[tex]\mathbf{\gamma = \dfrac{F/A}{\Delta L/L}}[/tex]

[tex]\mathbf{\gamma = \dfrac{F} {A }\times \dfrac{L}{\Delta L} }[/tex]

Making the force the subject of the formula and replacing the values, we have:

[tex]\mathbf{F =\dfrac{A \times \gamma \times \Delta L }{L} }[/tex]

[tex]\mathbf{F =\dfrac{ \pi \times (3.5 \times 10^{-3}) \times ( 20 \times 10^{10} \ N/m^2 ) \times (7.8 \times 10^{-3}) }{4 \times 10} }[/tex]

[tex]\mathbf{F =1500.89 \ N }[/tex]

Therefore, we can conclude that the value of force (F) if the change in length of the cable is 7.8 mm is 1500.89 N

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The work function for a metal surface is 3.82 eV. What is the largest wavelength of light in nm that will produce photoelectrons from this surface?1 eV = 1.602 ? 10?19 J,
e = 1.602 ? 10?19 C,
c = 2.998 ? 108 m/s,
and
h = 6.626 ? 10?34 J

Answers

Answer:

The largest wavelength of light that will produce photoelectrons from this surface is 324.6 nm.

Explanation:

Given;

work function, Ф = 3.82 eV

The work function of the metal is minimum energy required to produce electron from the metal surface.

Ф = hf

where;

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

f is the frequency of the photon

f = c / λ

[tex]\phi = \frac{hc}{\lambda}[/tex]

where;

c is speed of light = 2.998 x 10⁸ m/s

λ is the wavelength = ?

[tex]\phi = \frac{hc}{\lambda}\\\\\lambda = \frac{hc}{\phi }\\\\\lambda = \frac{(6.626*10^{-34})(2.998*10^8)}{3.82*1.602*10^{-19}}\\\\\lambda = 3.246*10^{-7} \ m\\\\\lambda = 324.6 *10^{-9} \ m\\\\\lambda = 324.6 \ nm[/tex]

Therefore, the largest wavelength of light that will produce photoelectrons from this surface is 324.6 nm.

A conductor of uniform radius 1.20 cm carries a current of 3.00 A produced by an electric field of 120 V/m. What is the resistivity of the material?

Answers

Answer:

The value is  [tex]\rho = 0.0180 97 9 \ \Omega m^{-1}[/tex]

Explanation:

From the question we are told that

   The radius of the conductor is [tex]r = 1.20 \ cm = 0.012 \ m[/tex]

    The current it is carrying is  [tex]I = 3.00 \ A[/tex]

    The electric field is  [tex]E = 120 \ V/m[/tex]

Generally the resistivity of the material is mathematically represented as

        [tex]\rho = \frac{EA}{ I }[/tex]

Here A is the area of the conductor which is mathematically represented as

      [tex]A = \pi r^2[/tex]

=>  [tex]A =3.142 * (0.012)^2[/tex]

=>  [tex]A = 0.000452 \ m^2[/tex]

So

    [tex]\rho = \frac{120 * 0.000452}{ 3 }[/tex]

=> [tex]\rho = 0.0180 97 9 \ \Omega m^{-1}[/tex]

The resistivity of the material will be "0.0180979 Ωm⁻¹".

Given values,

Radius, r = 1.20 m or 0.012 mCurrent, I = 3.00 AElectric field, E = 120 V/m

Now,

The area of conductor,

→ [tex]A = \pi r^2[/tex]

      [tex]= 3.142\times (0.012)^2[/tex]

      [tex]= 0.000452 \ m^2[/tex]

hence,

The resistivity will be:

→ [tex]\rho = \frac{EA}{I}[/tex]

By substituting the values, we get

     [tex]= \frac{120\times 0.000452}{3}[/tex]

     [tex]= 0.0180979 \ \Omega m^{-1}[/tex]

Thus the above response is right.  

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What is the force required to accelerate 1 kilogram of mass at 1 meter per second per second.

1 Newton

1 pound

1 kilometer

1 gram

Answers

Answer:

it's answer is 1 newton

Zinc is electroplated from a ZnSO4 solution. How many grams of zinc will be deposited if a 1.6A current runs for 25 minutes?

Answers

Answer:

0.817g

Explanation:

Zn2+ + 2e -----> An

Amount of electricity used

Q = It

= 1.6A x 25 x 60 seconds

= 2400 coulomb's

Number of moles of electrons = Q/f

F = 96500 coulomb's

= 2400/96500

= 0.025mol

From the equation above,

We see that the number of Zn moles firmed is equal to half the number of electrons used.

Molecular weight of Zn = 65.38

0.025x65.38/2

= 0.817 grams of zinc

Thank you!

n LC circuit has an oscillation frequency of 105 Hz. If C = 0.1 F , then L must be about:

Answers

Answer:

L = 22.97 H

Explanation:

Given that,

Capacitance, [tex]C=0.1\ \mu F=0.1\times 10^{-6}\ F[/tex]

Oscillation frequency, f = 0.5 Hz

The frequency of an AC circuit is given by :

[tex]f=\dfrac{1}{2\pi \sqrt{LC} }[/tex]

Where

L is impedance

[tex]f^2=\dfrac{1}{4\pi ^2LC}\\\\L=\dfrac{1}{4\pi ^2 f^2 C}\\\\\text{Putting all the values}\\\\L=\dfrac{1}{4\pi^2 \times (105)^2\times 0.1\times 10^{-6}}\\\\L=22.97\ H[/tex]

So, the impedance of LC circuit 22.97 H.

ne student rubs a balloon against his hair several times. Another student passes a comb through her hair several times. The students place the comb near the balloon and observe that the comb repels the balloon. Which is the most likely reason the comb is able to repel the balloon?

A.The balloon has a positive charge and the comb is neutral.

B. The balloon and the comb have the same electrical charge.

C. The balloon has a negative charge and the comb is neutral.

D. The balloon and the comb have opposite electrical charges

Answers

Answer:the ballon and the comb have the same electrical charge

Explanation:because I got the answer right

The comb is able to repel the balloon is that the balloon and the comb possess the same electrical charge. Therefore, option (B) is correct.

What is the electrical charge?

Electric charge is the physical property of matter that offers it to experience a force when keep in an electric or magnetic field. An electric charge is related to an electric field, and the moving electric charge produced a magnetic field.

The interaction of the charges creates an electromagnetic force and the combination of an electric field and magnetic field is called an electromagnetic field.

When the students rub a balloon and comb against his hair several times static charges are built up on the balloon and the comb.  When the students place the comb near the balloon and the comb repels the balloon means that both the comb and the balloon possess the same type of electrical charges.

Therefore, the balloon and the comb acquired the same electrical charge.

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How much work is it to lift a 20. kg sack of potatoes vertically 6.5 m?

Answers

W=FD
W=20*6.5
W= 130 Joul

Consider a ball thrown at an angle of 200 above the horizontal and another ball thrown at 200 below the horizontal. Both balls thrown with the same initial speed of 20 m/s from the top of the Science Center. Draw the motion diagram for both cases indicating the velocity and acceleration vectors. Explain the physics of these two situations and calculate the time taken for the balls to reach the ground.

Answers

Only if you give brainliest

In a police ballistics test, 2.00-g bullet traveling at 700 m/s suddenly hits and becomes embedded in a stationary 5.00-kg wood block. Does the bullet gain or lose momentum?

Answers

Answer:

The bullet will lose momentum

Explanation:

mass of the bullet, m₁ = 2.0 g = 0.002 kg

initial velocity of the bullet, u₁ = 700 m/s

mass of the wood block, m₂ = 5 kg

initial velocity of the wood block, u₂ = 0

let the final velocity of the bullet-block system after collision = v

Apply the principle of conservation of linear momentum;

m₁u₁ + m₂u₂ = v(m₁ + m₂)

(0.002 x 700) + (5 x 0) = v(0.002 + 5)

1.4 = 5.002 v

v = 1.4 / 5.002

v = 0.28 m/s

Change in momentum of the bullet is given by;

ΔP = m₁v - m₁u₁

ΔP = m₁(v - u₁)

ΔP = 0.002( 0.28 - 700)

ΔP = -1.4 kg.m/s

Therefore, the bullet will lose momentum

What happens to a black body radiator as it increases in temperature?

A. it gives off a range of electromagnetic radiation of shorter wavelengths.
B. It gives off only one wavelength of electromagnetic radiation
C. It releases only ultraviolet waves of electromagnetic radiation
D. It becomes hotter but gives off less electromagnetic radiation

Answers

Answer: A

Explanation:

Answer is a hope this helps guys!

The black body radiator as it increases in temperature gives off a range of electromagnetic radiation of shorter wavelengths so, the option A is correct.

What is radiation?

Radiation is the movement of atomic and subatomic particles as well as waves, such as those that define X-rays, heat rays, and light rays. Radiation of both types, from cosmic and earthly sources, is constantly being thrown at all matter.

The characteristics and behavior of radiation, as well as the matter it interacts with, are outlined in this article, which also explains how energy is transferred from radiation to its surroundings.

The effects of such an energy transfer to living matter, including the typical effects on numerous biological processes, are given a great deal of attention (e.g., photosynthesis in plants and vision in animals).

Thus, the black body radiator gives off a range of electromagnetic radiation of shorter wavelengths.

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6kg of cold water at 10°c is added to 6kg of hot water of 100°c what is the value of temp after the water is mixed​

Answers

Explanation:

so sorry

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don't know but please mark me as brainliest please

A student makes the following claim:
The energy of electromagnetic waves increases with decreasing wavelength.
Which of the following statements support this claim?
O A. Dental patients need to wear lead aprons to protect themselves from X-rays but do not wear
protection from flashlights.
B. Both radio waves and gamma rays are invisible to human eyes.
C. Ultraviolet radiation causes sunburn but radio waves do not.
D. Microwaves are used for communication.
E. Gamma rays are used to kill cancer cells, but microwaves have no known effect on cancer
cells.

Answers

Answer:

A, C, E

Explanation:

I put this and got it right.

Calculate the volume of the metal required to make a hemisperical bowl with internal and external radii 8.4cm and 9.1cm respectively​

Answers

External = R
Internal = r
Volume of hemisperical = 2/3 π(R³-r³)
V= 2/3 π(9.1³ - 8.4³)
V= 336.9 cm³

If a dog runs 25m east and then turns around and runs
back 20 west, what is the total distance ran? How far is the
dog displacement from the starting line?

Answers

Answer:

The dog ran a total distance of 45m but he is only 5m away from the starting line

Explanation: When you add 25 to 20 you get 45 for the total distance and if he ran back in the same direction then you would subtract 20 from 25 and get 5m

This object was observed in 1997.

The object in the picture is ____ a/an .

Answers

Answer: Hale-Bopp was an unusually bright comet that flew by Earth, reaching its closest approach to the planet in 1997.

Explanation:

Hale-Bopp is the answer

Answer: This is Comet Hale--Bopp

Explanation:

The cation of sodium (Na) bonds to the anion of sulfur (S) to form an ionic compound
with the chemical formula Na S. What is the name of this compound?

Answers

The name of the compound NaS is sodium sulfide.

The name of the ionic compound NaS is sodium sulfide.

What is ionic compound?

Ionic compounds are defined as substances bound together by ionic bonding. In order to reach their closest arrangement as a noble gas, elements can either gain or lose electrons. For the completion of the octet, ions are formed (either by adding or losing electrons), which aids in their stabilisation.

Metals typically lose electrons to complete their octet in a reaction with non-metals, whereas non-metals typically acquire electrons to complete their octet. Ionic compounds are typically created when metals and non-metals react.

When sodium (Na) metal reacts with sulfur (S) non-metal, an ionic compound forms named sodium sulfide with chemical formula NaS.

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A parallel-plate capacitor has plates of area 0.40 m2 and plate separation of 0.20 mm. The capacitor is connected to a 9.0 V battery. (a) What is the electric field between the plates?(b) What is the capacitance of the capacitor?
(c) What is the magnitude of the charge on each plate of the capacitor?

Answers

Answer:

a) E = 4.5*10⁴ V/m

b) C= 17.7 nF

c) Q = 159. 3 nC  

Explanation:

a)

By definition, the electric field is the electrostatic force per unit charge, and since the potential difference between plates is just the work done by the field, divided by the charge, assuming a uniform electric field, if V is the potential difference between plates, and d is the separation between plates, the electric field can be expressed as follows:

       [tex]E = \frac{V}{d} = \frac{9.0V}{2*10-4m} =4.5 * 10e4 V/m (1)[/tex]

b)

For a parallel-plate capacitor, applying the definition of capacitance as the quotient between the charge on one of the plates and the potential difference between them, and assuming a uniform surface charge density σ, we get:

       [tex]Q = \sigma* A (2)[/tex]

        From (1), we know that V = E*d, but at the same time, applying Gauss'

        Law at a closed surface half within the plate, half outside it , it can be

        showed than E= σ/ε₀, so finally we get:

       [tex]C = \frac{Q}{V} =\frac{\sigma*A}{E*d} = \frac{\sigma*A}{\frac{\sigma}{\epsilon_{o} } d} =\frac{\epsilon_{0}*A}{d} = \frac{8.85e-12F/m*0.4m2}{2e-4m} = 17.7 nF (3)[/tex]

c)    

From (3) we can solve for Q as follows:

       [tex]Q = C* V = 17.7 nF * 9.0 V = 159.3 nC (4)[/tex]

a) Electric field between the plates, E = 4.5*10⁴ V/m

b) Capacitance of the capacitor, C= 17.7 nF

c) Magnitude of the charge, Q = 159. 3 nC  

a) Calculation of Electric field:

It is the electrostatic force per unit charge, and since the potential difference between plates is just the work done by the field, divided by the charge, assuming a uniform electric field, if V is the potential difference between plates, and d is the separation between plates, the electric field can be expressed as follows:

[tex]E=\frac{V}{d} \\\\E=\frac{90V}{2*10^{-4}m} \\\\E=4.5*10e4V/m[/tex]

b) Calculation for Capacitance:

For a parallel-plate capacitor, It is the quotient between the charge on one of the plates and the potential difference between them, and assuming a uniform surface charge density σ, we get:

[tex]Q=\sigma*A[/tex]

On comparing equation 1 and 2:

[tex]C=\frac{Q}{V}\\\\C=\frac{\sigma*A}{E*d}\\\\\\C=\frac{\sigma*A}{\frac{\sigma}{E_0}*d}\\\\C=\frac{8.85e^{-12}F/m-0.4m^2}{2e-4m}\\\\C=17.7nF\\\\[/tex]

c) Calculation for magnitude of the charge:

From equation 3:

[tex]Q=C*V\\\\Q=17.7*9.0\\\\Q=159.3nC\\[/tex]

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Which statement does NOT describe redesign?
A You would want to make major changes.

B Engineers retest multiple times.

C Engineers try to make items more efficient.

D It happens all the time.

Answers

D. It happens all the time

Why do you think that the inside and outside of electric wire are make from different material?​

Answers

Answer:

Explanation:

i think that the inside and outside of electric wire are make from different material because outdoor electrical wires are always exposed to the fluctuations of temperature and moisture, they are made with more durable insulation. If an indoor electrical wire is used outdoors, it is possible for sunlight to break down the protective layers. Electrical conductors are made up of metals such as, copper, aluminum, etc. These metals are used to make wires. Most wires are made out of copper because it conducts electricity with high flexibility and very little resistance. The first stage in the manufacturing process of a conductor is the wire-drawing

Dillan rolls a rubber band ball off a desk. If the desk is 0.9 m tall, and the ball lands 2.5 m away, what was the horizontal velocity of the rubber band ball as it went off the table?

Answers

Answer: 6.25 m/s

explanation: remember an easir way to solve problems like this is to have a horizontal side (x) and a vertical side (y) and on each side always set up for initial speed, average speed, final speed, distance, time, and acceleration.

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Which type of electromagnetic wave is used for nuclear power and medical treatment?
A. UV wave
B. Radio wave
C. Visible light wave
D. Gamma ray

Answers

Answer:

D. Gamma ray

Explanation:

You are welcome

Answer:

D) Gamma ray

Explanation:

Let me know if this is helpful.

A 4.0-kg object is supported by an aluminum wire of length 2.0 m and diameter 2.0 mm. How much will the wire stretch?

Answers

Answer:

The extension of the wire is 0.362 mm.

Explanation:

Given;

mass of the object, m = 4.0 kg

length of the aluminum wire, L = 2.0 m

diameter of the wire, d = 2.0 mm

radius of the wire, r = d/2 = 1.0 mm = 0.001 m

The area of the wire is given by;

A = πr²

A = π(0.001)² = 3.142 x 10⁻⁶ m²

The downward force of the object on the wire is given by;

F = mg

F = 4 x 9.8 = 39.2 N

The Young's modulus of aluminum is given by;

[tex]Y = \frac{stress}{strain}\\\\Y = \frac{F/A}{e/L}\\\\Y = \frac{FL}{Ae} \\\\e = \frac{FL}{AY}[/tex]

Where;

Young's modulus of elasticity of aluminum = 69 x 10⁹ N/m²

[tex]e = \frac{FL}{AY} \\\\e = \frac{(39.2)(2)}{(3.142*10^{-6})(69*10^9)} \\\\e = 0.000362 \ m\\\\e = 0.362 \ mm[/tex]

Therefore, the extension of the wire is 0.362 mm.

A heavy object and a light object are dropped from the same height. If we neglect air resistance, which will hit the ground first?

Answers

Answer:

None, both objects will hit ground at the same time.

Explanation:

Assuming no air resistance present, and that both objects start from rest, we can apply the following kinematic equation for the vertical displacement:

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

As the left side in (1) is the same for both objects, the right side will be the same also.Since g is constant close to the surface of the Earth, it's also the same for both objects.So, the time t must be the same for both objects also.

The engine of a model airplane must both spin a propeller and push air backward to propel the airplane forward. Model the propeller as three 0.30-m-long thin rods of mass 0.040 kg each, with the rotation axis at one end.
What is the moment of inertia of the propeller?
How much energy is required to rotate the propeller at 5800 rpm? Ignore the energy required to push the air.

Answers

Solution :

Given :

Length of the propeller rods, L =0.30 m

Mass of each, M = 0.040 kg

Moment of inertia of one propeller rod is given by  

[tex]$I=\frac{1}{3}\times M \times L^2$[/tex]

Therefore, total moment of inertia is

[tex]$I=3 \times \frac{1}{3}\times M \times L^2$[/tex]

[tex]$I=M\times L^2$[/tex]

[tex]$I=0.04\times (0.3)^2$[/tex]

  [tex]$0.0036 \ kg \ m^2$[/tex]

Now energy required is given by

[tex]$E=\frac{1}{2}\times I \times \omega^2 $[/tex]

where, angular speed, ω = 5800 rpm

[tex]$\omega = 5800 \times \frac{2 \pi}{60} $[/tex]

 = 607.4 rad/s

Therefore energy,

[tex]$E=\frac{1}{2}\times 0.0036 \times (607.4)^2 $[/tex]

   = 664.1 J

The moment of inertia of the propeller is 0.0036 kgm² and the energy required is 663.21 J

Energy required for propeller:

Given that the mass of the propellers is m = 0.040kg,

and their length is L = 0.30m

The moment of inertia of a rod with the rotation axis at one end is given by :

[tex]I = \frac{1}{3}m L^2[/tex]

so for 3 propellers:

[tex]I=3\times\frac{1}{3}\times(0.04)\times(0.3)^2[/tex]

I = 0.04 × 0.09

I = 0.0036 kgm²

Now, the frequency is given f = 5800 rpm

so anguar speed, ω = 5800×(2π/60)

ω = 607 rad/s

Energy required:

E = ¹/₂Iω²

E = 0.5 × 0.0036 × (607)² J

E = 663.21 J

Learn more about moment of inertia:

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