Given that the voltage from a wall outlet is AC if you were to correctly use your digital multimeter to measure the wall outlet voltage to be 120 V, what is the maximum voltage level provided by the wall outlet

Answer:

Explanation:

This exercise we will work using energy conservation, let's use two points

 lower. Ramp starting point

        Em₀ = K = ½ m v² + ½ I w²

more height. Point where e stops

        [tex]Em_{f}[/tex] = m g h

at the starting point the sphere is spinning let's look for the relationship between the angular and linear variables

        v = w r

the moment of inertia of a sphere is tabulated

         I = 2/5 M R2

let's use that energy is conserved

        Em₀ = Em_{f}

        ½ m v² + ½ (2/5 m r²) (v / r)² = m g h

        ½ v² + 1/5 v2 = g h

        h= 7/10 v² / g

Answer:

ac = 3.92 m/s²

Explanation:

In this case the frictional force must balance the centripetal force for the car not to skid. Therefore,

Frictional Force = Centripetal Force

where,

Frictional Force = μ(Normal Force) = μ(weight) = μmg

Centripetal Force = (m)(ac)

Therefore,

μmg = (m)(ac)

ac = μg

where,

ac = magnitude of centripetal acceleration of car = ?

μ = coefficient of friction of tires (kinetic) = 0.4

g = 9.8 m/s²

Therefore,

ac = (0.4)(9.8 m/s²)

ac = 3.92 m/s²

Based on the data provided, the centripetal acceleration is 3.92 m/s²

Centripetal acceleration is the acceleration of a body moving in a circular path which is directed toward the center of the circle.

In the given question, the frictional force must balance the centripetal force for the car not to skid.

where,

Frictional Force = μR

R = mg

F = μmg

Centripetal Force = m

Then

μmg = ma

a = μg

ac = 0.4 * 9.8 m/s²

ac = 3.92 m/s²

Therefore, the centripetal acceleration is 3.92 m/s².

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Answer:

The hydrostatic force on one end of the trough is 54994.464 N

Explanation:

Given;

liquid density, ρ = 810 kg/m³

side of the equilateral triangle, L = 8m

acceleration due to gravity, g =  9.8 m/s²

Hydrostatic force is given as;

H = ρgh

where;

h is the vertical height of the equilateral triangle

Draw a line to bisect upper end of the trough, to the vertex at the bottom, this line is the height of the equilateral triangle.

let the half side of the triangle = x

x = ⁸/₂ = 4m

The half section of the triangle forms a right angled triangle

h² = 8² - 4²

h² = 48

h = √48

h = 6.928m

F = ρgh

F = 810 x 9.8 x 6.928

F = 54994.464 N

Therefore, the hydrostatic force on one end of the trough is 54994.464 N

Answer:

b

Explanation:

determine the rotational kinetic energy about it's center of mass

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

The power created  is  [tex]P_{avg} = F * v_{avg}[/tex]

Explanation:

From the question we are told that

    The that the average power is  mathematically represented as

            [tex]P_{avg} = \frac{W }{\Delta t }[/tex]

Where W is  is the Workdone which is  mathematically represented as

         [tex]W = F * s[/tex]

      Where F is  the applies force and  s  is the displacement  due to the force  

        So  

                [tex]P_{avg} = \frac{F *s }{\Delta t }[/tex]

Now this  displacement can be represented mathematically as  

            [tex]s = v_{avg} * \Delta t[/tex]

Where [tex]v_{avg }[/tex] is the average  velocity and [tex]\Delta t[/tex] is the time  taken  

So  

            [tex]P_{avg} = \frac{F *v_{avg} * \Delta t }{\Delta t }[/tex]

=>         [tex]P_{avg} = F * v_{avg}[/tex]

Answer:

Pavg =  Fvavg

Explanation:

Since the P (power) done by the F (force) is:

P = Fs/t

and we are looking for the velocity, so then it would be:

P = Fv

with the average velocity the answer is:

Pavg =  Favg

If an object is moving at a constant speed, and the force F is also constant, this formula can be used to find the average power. If v  is changing, the formula can be used to find the instantaneous power at any given moment (with the quantity v in this case meaning the instantaneous velocity, of course).

Answer:

depending on how high it goes at 100m it has taken 2 secondes

Explanation:

At the highest point, the arrow is changing from moving up to moving down. At that exact point, its speed AND its velocity are both ZERO.

And air resistance actually makes no difference.

Answer:

the lines become more narrow

Explanation: Two nearly equal wavelengths of light are incident on an N slit grating. The two wavelengths are not resolvable. When N is increased they become resolvable. This is because:

The lines become more narrow.

Answer:

20J

Explanation:

In a collision, whether elastic or inelastic, momentum is always conserved. Therefore, using the principle of conservation of momentum we can first get the final velocity of the two bodies after collision. This is given by;

m₁u₁ + m₂u₂ = (m₁ + m₂)v          ---------------(i)

Where;

m₁ and m₂ are the masses of first and second objects respectively

u₁ and u₂ are the initial velocities of the first and second objects respectively

v  is the final velocity of the two objects after collision;

From the question;

m₁ = 2.0kg

m₂ = 8.0kg

u₁ = 5.0m/s

u₂ = 0        (since the object is initially at rest)

Substitute these values into equation (i) as follows;

(2.0 x 5.0) + (8.0 x 0) = (2.0 + 8.0)v

(10.0) + (0) = (10.0)v

10.0 = 10.0v

v = 1m/s

The two bodies stick together and move off with a velocity of 1m/s after collision.

The kinetic energy(KE₁) of the objects before collision is given by

KE₁ = [tex]\frac{1}{2}[/tex]m₁u₁² +  [tex]\frac{1}{2}[/tex]m₂u₂²       ---------------(ii)

Substitute the appropriate values into equation (ii)

KE₁ = ([tex]\frac{1}{2}[/tex] x 2.0 x 5.0²) +  ([tex]\frac{1}{2}[/tex] x 8.0 x 0²)

KE₁ = 25.0J

Also, the kinetic energy(KE₂) of the objects after collision is given by

KE₂ = [tex]\frac{1}{2}[/tex](m₁ + m₂)v²      ---------------(iii)

Substitute the appropriate values into equation (iii)

KE₂ = [tex]\frac{1}{2}[/tex] ( 2.0 + 8.0) x 1²

KE₂ = 5J

The kinetic energy lost (K) by the system is therefore the difference between the kinetic energy before collision and kinetic energy after collision

K = KE₂ - KE₁

K = 5 - 25

K = -20J

The negative sign shows that energy was lost. The kinetic energy lost by the system is 20J

Answer:

344.8 x10^-8J/m³

Explanation:

Using=> energy intensity/ speed oflight

= 1000/2.9x10^8

= 344.8 x10^-8J/m³

The electromagnetic energy is 344.8 x10⁻⁸J/m³

We have to use the formula which says

Electromagnetic energy = energy intensity/ speed of light

We are given intensity as 1000 W/m²

Electromagnetic energy    = 1000/2.9 x 10⁸

                                             = 344.8 x 10⁻⁸J/m³

Therefore the electromagnetic energy is contained in each cubic meter will be  344.8 x 10⁻⁸J/m³

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Answer:

The moment of inertia of the merry-go round is 453.125 kg.m²

Explanation:

Given;'

angular velocity of the merry-go round, ω = 1.6 rad/s

rotational kinetic energy, K =  580 J

Rotational kinetic energy is given as;

K = ¹/₂Iω²

Where;

I is the moment of inertia of the merry-go round

[tex]I = \frac{2K}{\omega^2} \\\\I = \frac{2*580}{1.6^2} \\\\I = 453.125 \ kg.m^2[/tex]

Therefore, the moment of inertia of the merry-go round is 453.125 kg.m²

Since the small merry-go round is spinning about its center in a clockwise direction, its moment of inertia is equal to 453.13 [tex]Kgm^2[/tex]

Given the following data:

To calculate the moment of inertia of the small merry-go round:

Mathematically, the rotational kinetic energy of an object is giving by the formula:

[tex]E_{rotational} = \frac{1}{2} Iw^2[/tex]

Where:

Making moment of inertia (I) the subject of formula, we have:

[tex]I = \frac{2E_{rotational}}{w^2}[/tex]

Substituting the given parameters into the formula, we have;

[tex]I = \frac{2(580)}{1.6^2}\\\\I = \frac{1160}{2.56}[/tex]

Moment of inertia (I) = 453.13 [tex]Kgm^2[/tex]

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Answer:

Higher voltages pose huge dangers to humans with changes in resistance however, the use of hand lotion and rubber gloves help to reduce the amount of current flowing through the human. Notwithstanding higher currents can lead to death by stopping blood flow to the heart causing a heart attack. Best way to survive voltages above 120 volts is to use a rubber glove and avoid touching bare wires.

Explanation:

Other classes of gloves that can be used include:  Class 1 gloves which can be used for current up to 7,500 volts of AC, Class 2 up to 17,000 volts AC, Class 3 up to 26,500 volts AC, and Class 4 up to 36,000 volts AC. However, cotton gloves can be used inside to absorb perspiration and to improve the comfort of the user.

Answer: c. expansion coefficients.

Explanation: Bimetallic strips used as adjustable switches in electric appliances consist of metallic strips that must have different expansion coefficients.

I found the answer on Quizlet. :)

Bimetallic strips used as adjustable switches in electric appliances consist of metallic strips that must have different expansion coefficients. The correct option is c.

The coefficient of thermal expansion (CTE) is the rate at which a material expands as its temperature rises. This coefficient is determined at constant pressure and without a phase change, i.e. the material is expected to remain solid or fluid.

Bimetallic strips, which are utilized as adjustable switches in electric appliances, are made up of metallic strips with differing expansion coefficients. The coefficient of thermal expansion indicates how the size of an object varies as temperature changes.

Therefore, the correct option is c. expansion coefficients.

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Answer:

3.6×10⁻⁶  Nm

Explanation:

From the question,

The expression for maximum torque is given as

τ = BANI.................Equation 1

where τ = maximum torque, B = magnetic field, A = Area of the coil, N = number of turns, I = current carried by the coil.

Given: B = 0.1 T, A = (5×12) = 60 cm² = 0.006 m², N = 600 turns, I = 10⁻⁵ A.

Substitute these values into equation 1

τ = 0.1(0.006)(600)(10⁻⁵)

τ = 3.6×10⁻⁶  Nm

Kinetic energy is the energy an object has due to its Motion.

Kinetic energy is a characteristic of a moving particle. It is a type of energy that a matter or particle possesses due to its motion.

It is expressed:

[tex]K_E = \frac{1}{2}mv^2[/tex]

Where m is the mass of the particle and v is velocity.

Hence, Kinetic energy is the energy an object has due to its Motion.

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Answer:

R = 1138.9 Ω

Explanation:

Hello,

In this case, for the given power (P) and current (I), we can compute the resistance (R) via:

R = P / I²

Thus, we obtain:

R = 1.64x10⁵ W / (12.0 A)²

R = 1138.9 Ω

Best regards.

Answer:

ML²/6

Explanation:

Pls see attached file

The total mass is M = CL²/2, and the moment of inertia is I = ML²/2,

The length of the rod is L. It has a non-uniform distribution of mass given by:

dm/dx = Cx

where C has units kg/m²

dm = Cxdx

the total mass M of the rod can be calculated by integrating the above relation over the length:

[tex]M =\int\limits^L_0 {} \, dm\\\\M=\int\limits^L_0 {Cx} \, dx\\\\M=C[x^2/2]^L_0\\\\M=C[L^2/2]\\\\[/tex]

Thus,

C = 2M/L²

Now, the moment of inertia of the small element dx of the rod is given by:

dI = dm.x²

dI = Cx.x²dx

[tex]dI = \frac{2M}{L^2}x^3dx\\\\I= \frac{2M}{L^2}\int\limits^L_0 {x^3} \, dx \\\\I= \frac{2M}{L^2}[\frac{L^4}{4}][/tex]

I = ML²/2

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Answer:

C) It is either ferromagnetic or paramagnetic

Explanation:

The complete question is given below

We observe that a small sample of material placed in a non-uniform magnetic field accelerates toward a region of stronger field. What can we say about the material?

A) It must be ferromagnetic.

B) It must be paramagnetic.

C) It is either ferromagnetic or paramagnetic.

D) It must be diamagnetic.

A ferromagnetic material will respond towards a magnetic field. They are those materials that are attracted to a magnet. Ferromagnetism is associated with our everyday magnets and is the strongest form of magnetism in nature. Iron and its alloys is very good example of a material that readily demonstrate ferromagnetism.

Paramagnetic materials are weakly attracted to an externally applied magnetic field. They usually accelerate towards an electric field, and form internal induced magnetic field in the direction of the external magnetic field.

The difference is that ferromagnetic materials can retain their magnetization when the externally applied magnetic field is removed, unlike paramagnetic materials that do not retain their magnetization.

In contrast, a diamagnetic material is repelled away from an externally applied magnetic field.

In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 8.00 cos (5t + π / 8) where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. cm (b) At t = 0, find velocity of the piston. cm/s (c) At t = 0, find acceleration of the piston. cm/s2 (d) Find the period and amplitude of the motion. period s amplitude cm

(a) 7.392cm

(b) -15.32 cm/s

(c) -184cm/s²

(d) 0.4πs and 8.00cm

The general equation of a simple harmonic motion (SHM) is given by;

x(t) = A cos (wt + Φ)        --------------(i)

Where;

x(t) = position of the body at a given time t

A =  amplitude or maximum displacement during oscillation

w = angular velocity

t = time

Φ = phase constant.

Given from question:

x(t) = 8.00 cos (5t + π / 8)         ---------------(ii)

(a) At time t = 0;

The position, x(t), of the body (piston) is given by substituting the value of t = 0 into equation (ii) as follows;

x(0) = 8.00 cos (5(0) + π / 8)

x(0) = 8.00 cos (π /8)

x(0) = 8.00 x 0.924

x(0) = 7.392 cm

Therefore, the position of the piston at time t = 0 is 7.392cm

(b) To get the velocity, v(t), of the piston at t = 0, first differentiate equation (ii) with respect to t as follows;

v(t) = [tex]\frac{dx(t)}{dt}[/tex]

v(t) = [tex]\frac{d(8.00cos(5t + \pi / 8 ))}{dt}[/tex]

v(t) = 8 (-5 sin (5t + π / 8))

v(t) = -40sin(5t + π / 8)     --------------------(iii)

Now, substitute t=0 into the equation as follows;

v(0) = -40 sin(5(0) + π / 8)

v(0) = -40 sin(π / 8)

v(0) = -40 x 0.383

v(0) = -15.32 cm/s

Therefore, the velocity of the piston at time t = 0 is -15.32 cm/s

(c) To find the acceleration a(t) of the piston at t = 0, first differentiate equation (iii), which is the velocity equation, with respect to t as follows;

a(t) = [tex]\frac{dv(t)}{dt}[/tex]

a(t) = [tex]\frac{d(-40sin (5t + \pi /8))}{dt}[/tex]

a(t) = -200 cos (5t + π / 8)

Now, substitute t = 0 into the equation as follows;

a(0) = -200 cos (5(0) + π / 8)

a(0) = -200 cos (π / 8)

a(0) = -200 x 0.924

a(0) = -184.8 cm/s²

Therefore, the acceleration of the piston at time t = 0 is -184cm/s²

(d) To find the period, T, first, let's compare equations (i) and (ii) as follows;

x(t) = A cos (wt + Φ)                   --------------(i)

x(t) = 8.00 cos (5t + π / 8)         ---------------(ii)

From these equations it can be deduced that;

Amplitude, A = 8.00cm

Angular velocity, w = 5 rads/s

But;

w = [tex]\frac{2\pi }{T}[/tex]           [Where T = period of oscillation]

=> T = [tex]\frac{2\pi }{w}[/tex]

=> T = [tex]\frac{2\pi }{5}[/tex]

=> T = 0.4π s

Therefore, the period and amplitude of the piston's motion are respectively 0.4πs and 8.00cm

Answer:

10.4 m/s

Explanation:

Given that

mass of the first snowball, m1 = 0.3 kg

mass of the second snowball, m2 = 0.7 kg

Magnitude of initial velocity for both masses, u = 10.4 m/s

To start with, we use the formula of conservation of linear momentum which states that

magnitude of initial momentum is equal to magnitude of final momentum.

m1u1 + m2u2 = V(m1 + m2)

0.3 * 10.4 + 0.7 * 10.4 = V(0.3 + 0.7)

3.12 + 7.28 = V(1)

10.4 = V

The 1 kg mass is an addition Of the 0.3 mass & 0.7 kg mass.

Thus, the speed of the 1 kg mass is 10.4 m/s

Answer:

The area  of the water stream will be 1.74 cm^2

Explanation:

initial velocity of water u = 33.2 cm/s

initial area = 6.4 cm^2

height of fall = 7.05 cm

final area before hitting the sink = ?

as the water falls down the height, it accelerates under gravity; causing the speed to increase, and the area to decrease.

first we find the velocity before hitting the sink

using

[tex]v^{2} = u^{2} + 2gh[/tex]  -----Newton's equation of motion

where  v is the velocity of the water stream at the sink

u is the initial speed of the water at the spout

h is the height of fall

g is acceleration due to gravity, and it is positive downwards.

g = 981 cm/s^2

imputing relevant values, we have

[tex]v^{2} = 33.2^{2} + (2 * 981 * 7.05)[/tex]

[tex]v^{2} = 1102.24 + 13832.1 = 14934.34[/tex]

[tex]v = \sqrt{14934.34}[/tex] = 122.206 cm/s

according to continuity equation,

A1v1 = A2v2

where A1 is the initial area

V1 = initial velocity

A2 = final area

V2 = final velocity

6.4 x 33.2 = 122.206 x A2

212.48 = 122.206 x A2

A2 = 212.48 ÷ 122.206 ≅ 1.74 cm^2

Answer:

Such limitations are given below.

Explanation:

Answer:

The centripetal acceleration changed by a factor of 0.5

Explanation:

Given;

first radius of the horizontal circle, r₁ = 500 m

speed of the airplane, v = 150 m/s

second radius of the airplane, r₂ = 1000 m

Centripetal acceleration is given as;

[tex]a = \frac{v^2}{r}[/tex]

At constant speed, we will have;

[tex]v^2 =ar\\\\v = \sqrt{ar}\\\\at \ constant\ v;\\\sqrt{a_1r_1} = \sqrt{a_2r_2}\\\\a_1r_1 = a_2r_2\\\\a_2 = \frac{a_1r_1}{r_2} \\\\a_2 = \frac{a_1*500}{1000}\\\\a_2 = \frac{a_1}{2} \\\\a_2 = \frac{1}{2} a_1[/tex]

a₂ = 0.5a₁

Therefore, the centripetal acceleration changed by a factor of 0.5

Answer:

The period is [tex]T = 0.700 \ s[/tex]

Explanation:

From the question we are told that  

    The mass is [tex]m = 0.350 \ kg[/tex]

     The extension of the spring is  [tex]x = 12.0 \ cm = 0.12 \ m[/tex]

The spring constant for this is mathematically represented as

       [tex]k = \frac{F}{x}[/tex]

Where F is the force on the spring which is mathematically evaluated as

       [tex]F = mg = 0.350 * 9.8[/tex]

       [tex]F =3.43 \ N[/tex]

So  

    [tex]k = \frac{3.43 }{ 0.12}[/tex]

    [tex]k = 28.583 \ N/m[/tex]

The period of oscillation is mathematically evaluated as

      [tex]T = 2 \pi \sqrt{\frac{m}{k} }[/tex]

substituting values

     [tex]T = 2 * 3.142* \sqrt{\frac{0.35 }{28.583} }[/tex]

     [tex]T = 0.700 \ s[/tex]

Answer:

The total work done by the person is given as = m g h

= 4.5kg x 9.8m/s²x1.2m

= 52.92J

This is the work done in moving the block in a vertical distance

However there is no work done when the block is moved in a horizontal direction since ko work is done against gravity.

Explanation:

Answer:

v = 8.5 m/s

Explanation:

In order for the passengers not to fall out of the loop circle, the centripetal force must be equal to the weight of the passenger. Therefore,

Weight = Centripetal Force

but,

Weight = mg

Centripetal Force = mv²/r

Therefore,

mg = mv²/r

g = v²/r

v² = gr

v = √gr

where,

v = minimum speed required = ?

g = 9.8 m/s²

r = radius = 7.4 m

Therefore,

v = √(9.8 m/s²)(7.4 m)

v = 8.5 m/s

Minimum speed for a roller coaster while travelling upside down  so that the person will not fall out = 8.5 m/s

For a roller coaster be traveling when upside down the Force balance equation can be written for a person of mass m.

In the given condition the weight of the person must be balanced by the centrifugal force.

and for the person not to fall out centrifugal force must be greater than or equal to the weight of the person

According to the Newton's Second Law of motion we can write force balance

[tex]\rm mv^2/r -mg =0 \\\\mg = mv^2 /r (Same\; mass) \\\\\\g = v^2/r\\\\v = \sqrt {gr}......(1)[/tex]

Given Radius of loop = r = 7.4 m

Putting the value  of r = 7.4 m  in equation (1) we get

[tex]\sqrt{9.8\times 7.4 } = \sqrt{72.594} = 8.5\; m/s[/tex]

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Complete Question

A 10 gauge copper wire carries a current of 20 A. Assuming one free electron per copper atom, calculate the drift velocity of the electrons. (The cross-sectional area of a 10-gauge wire is 5.261 mm2.) mm/s

Answer:

The drift velocity is [tex]v = 0.0002808 \ m/s[/tex]

Explanation:

From the question we are told that

    The current on the copper is  [tex]I = 20 \ A[/tex]

     The cross-sectional area is  [tex]A = 5.261 \ mm^2 = 5.261 *10^{-6} \ m^2[/tex]

The number of copper atom in the wire is  mathematically evaluated

      [tex]n = \frac{\rho * N_a}Z}[/tex]

Where [tex]\rho[/tex] is the density of copper with a value [tex]\rho = 8.93 \ g/m^3[/tex]

          [tex]N_a[/tex] is the Avogadro's number with a value [tex]N_a = 6.02 *10^{23}\ atom/mol[/tex]

         Z  is the molar mass of copper with a value  [tex]Z = 63.55 \ g/mol[/tex]

So

     [tex]n = \frac{8.93 * 6.02 *10^{23}}{63.55}[/tex]

     [tex]n = 8.46 * 10^{28} \ atoms /m^3[/tex]

Given the 1 atom is equivalent to 1 free electron then the number of free electron is  

         [tex]N = 8.46 * 10^{28} \ electrons[/tex]

The current through the wire is mathematically represented as

         [tex]I = N * e * v * A[/tex]

substituting values

        [tex]20 = 8.46 *10^{28} * (1.60*10^{-19}) * v * 5.261 *10^{-6}[/tex]

=>     [tex]v = 0.0002808 \ m/s[/tex]

Answer:

Explanation:

Magnetic field due to a solenoid

B = μ₀ nI  where n is no of turns per unit length and I is current

for outer  layer of turns

B = μ₀  x (250 / .3) x 3

= 4π x 10⁻⁷ x (250 / .3) x 3

= 3.14 x 10⁻³ T  

for inner layer of turns

B = μ₀  x (300 / .3) x 3

= 4π x 10⁻⁷ x (300 / .3) x 3

= 3.77 x 10⁻³ T

Total magnetic field

= (3.14 + 3.77 ) x 10⁻³ T  

= 6.91 x 10⁻³ T  .

Answer:

2404 MPa

Explanation:

See attachment for solution

The maximum stress that exists at the tip of the internal crack is 3,400 Mpa.

The given parameters;

The maximum stress that exists at the tip of the internal crack is calculated as follows;

[tex]\sigma _{max} = 2\sigma \times \sqrt{(\frac{l}{r} )} \\\\\sigma _{max} = 2 \times 170 \times 10^6 \times \sqrt{(\frac{2.5\times 10^{-2}}{2.5 \times 10^{-4}})} \\\\\sigma _{max} = 3.4 \times 10^{9} \ Pa\\\\\sigma _{max} = 3,400\ Mpa[/tex]

Thus, the maximum stress that exists at the tip of the internal crack is 3,400 Mpa.

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Answer:

Increasing the number of slits not only makes the diffraction maximum sharper, but also much more intense. If a 1 mm diameter laser beam strikes a 600 line/mm grating, then it covers 600 slits and the resulting line intensity is 90,000 x that of a double slit. Such a multiple-slit is called a diffraction grating.

Given that,

Outer diameter = 14 mm

Inner diameter = 11 mm

Length = 21 cm

Young's modulus = 68 GPa

Tensile strength = 7 Mpa

(a). We need to calculate the effective spring constant of the straw with respect to elongation

Using formula of effective spring constant

[tex]\dfrac{Y}{\Delta l}=\dfrac{YA}{l}[/tex]

[tex]k=\dfrac{YA}{l}[/tex]

Where, k = effective spring constant

Y= Young's modulus

A = area

l = length

Put the value into the formula

[tex]k=\dfrac{68\times10^{9}\times\dfrac{\pi}{4}(0.014^2-0.011^2)}{21\times10^{-2}}[/tex]

[tex]k=1.90\times10^{7}\ N/m[/tex]

(b). Force = 90 N

We need to calculate the stretch the straw

Using formula of stretch

[tex]\Delta l=\dfrac{F}{k}[/tex]

Where, F = force

k = effective spring constant

Put the value into the formula

[tex]\Delta l=\dfrac{90}{1.90\times10^{7}}[/tex]

[tex]\Delta l=0.0000047\ m[/tex]

[tex]\Delta l=4.7\times10^{-6}\ m[/tex]

(c). We need to calculate the extend the length of the straw before it breaks

Using formula of extend length

[tex]E_{max}=\dfrac{Y\Delta l}{l}[/tex]

[tex]\Delta l=\dfrac{E_{max}l}{Y}[/tex]

Put the value into the formula

[tex]\Delta l=\dfrac{7\times10^6\times21\times10^{-2}}{68\times10^{9}}[/tex]

[tex]\Delta l=0.0000216\ m[/tex]

[tex]\Delta l=0.0216\times10^{-3}\ m[/tex]

[tex]\Delta l=0.0216\ mm[/tex]

Hence, (a). The effective spring constant of the straw with respect to elongation is [tex]1.90\times10^{7}\ N/m[/tex]

(b). The stretch the straw is [tex]4.7\times10^{-6}\ m[/tex]

(c). The extend length of the straw before it breaks is 0.0216 mm.