o study torque experimentally, you apply a force to a beam. One end of the beam is attached to a pivot that allows the beam to rotate freely. The pivot is taken as the origin or your coordinate system. You apply a force of F = Fx i + Fy j + Fz k at a point r = rx i + ry j + rz k on the beam. show answer No Attempt 33% Part (a) Enter a vector expression for the resulting torque, in terms of the unit vectors i, j, k and the components of F and r. τ = | γ θ i j k d Fx Fy Fz g m n rx ry rz ( ) 7 8 9 HOME ↑^ ^↓ 4 5 6 ← / * 1 2 3 → + - 0 . END √() BACKSPACE DEL CLEAR Grade Summary Deductions 0% Potential 100% Submissions Attempts remaining: 3 (4% per attempt) detailed view Hints: 4% deduction per hint. Hints remaining: 2 Feedback: 5% deduction per feedback. No Attempt No Attempt 33% Part (b) Calculate the magnitude of the torque, in newton meters, when the components of the position and force vectors have the values rx = 0.76 m, ry = 0.035 m, rz = 0.015 m, Fx = 3.6 N, Fy = -2.8 N, Fz = 4.4 N. No Attempt No Attempt 33% Part (c) If the moment of inertia of the beam with respect to the pivot is I = 442 kg˙m2, calculate the magnitude of the angular acceleration of the beam about the pivot, in radians per second squared. All content © 2020 Expert TA, LLC

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The function giving the height of the ball at time t is s(t) = 96t - 16t^2 + 256. The ball takes 6 seconds to reach the ground and achieves a maximum height of 400 feet.

The physics problem you've posed can be approached by first understanding that the height of the ball (s(t)) at time t can be found by integrating the velocity function, due to v(t) being the derivative of s(t). So, integrating v(t)=96-32t with respect to t gives s(t) = 96t - 16t^2 + 256, where 256 is the constant of integration corresponding to the initial height from the ground.

To find out how long will the ball take to reach the ground, we solve the function s(t)=0, yielding t = 6 seconds as the answer, as that's when the ball hits the ground. Now, for the maximum height reached by the ball, it's where the ball has a velocity of zero before it begins its descent, i.e. v(t)=0. Solving this gives t=3 seconds, substituting this back into the s(t) equation gives the maximum reached height as 400 feet.

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Wind is driven due to the differences in air pressure around the Earth.

To find the answer, we need to know about the wind flow.

Thus, we can conclude that wind is driven due to the differences in air pressure around the Earth.

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Answer:

B) Lengths will appear shorter and time will appear to pass faster.

Explanation:

This is in line with the laws of relativity.

Answer:

A. Lengths will appear shorter and time will appear to pass slower.  

Explanation:

From theory of relativity, we know that:

L₀ = length of object, measured in stationary frame of reference

L = length of object measured from a frame moving with respect to object, called ‘relativistic length’

v = relativistic speed between observer and the object

c = speed of light

then,

L = L₀ √(1-v²/c² )

Hence, the length of the object decreases with the increase in its relativistic speed "v"

t₀ = time measured by clock at rest with respect to event.

t = time measured by clock in motion relative to the event

v = relativistic speed between observer and the object

c = speed of light

then,

t =  t₀/√(1-v²/c² )

Hence, the time increases with the increase in in relativistic speed and as a result it appears to pass slower.

Hence, the correct option is:

A. Lengths will appear shorter and time will appear to pass slower.  

Answer:

[tex]B = 187\ \mu T[/tex]

Explanation:

Given,

Number of turns, N = 325

Diameter of coil, d = 9.4 cm

time,t = 2.48 m s

average voltage,ε = 0.17 V

Earth magnetic field, B = ?

We know that

[tex]\epsilon = \dfrac{NBA}{t}[/tex]

[tex]0.17= \dfrac{325\times B \times \pi (0.047)^2}{2.48\times 10^{-3}}[/tex]

[tex]B = 187 \times 10^{-6}\ T[/tex]

[tex]B = 187\ \mu T[/tex]

Magnetic field of the earth is equal to [tex]B = 187\ \mu T[/tex]

Answer:

The magnitude of the magnetic force on the particle is 67.86 N.          

Explanation:

Given that,

Charge, [tex]q=34.6\ \mu C=34.6\times 10^{-6}\ C[/tex]

Speed of particle, v = 68.4 m/s in +x direction

Magnetic field, [tex]B=(0.466 j+0.876 k)\ T[/tex]

We need to find the magnitude of the magnetic force on the particle. The magnetic force is given by :

[tex]F=q(v\times B)\\\\F=34.6\times 10^{-6}(68.4i+0+0\times (0+0.466j+0.876 k))\\\\F=\begin{pmatrix}0&-59.9184&31.8744\end{pmatrix}\\\\F=(-59.9184j+31.8744k)\ N[/tex]

The magnitude of magnetic force on the particle is :

[tex]|F|=\sqrt{(-59.9184)^2+(31.8744)^2} \\\\|F|=67.86\ N[/tex]

So, the magnitude of the magnetic force on the particle is 67.86 N.          

Answer: 3.78 m

Explanation:

Volume = 1.9 * 1.9 * 1.9

Volume = 6.859 m³

Density of iron assumed to be 7870 kg/m³

Recall,

Density = mass / volume, so

Mass = density * volume

Mass = (7870 * 6.859)

Mass = 53980.33 kg

This mass we calculated, is the mass of water the new cube would have to displace, absolute minimum, so that it can float.

Now density of fresh water is assumed to be (1000 kg/m³).

Thus, the volume of water that will be displaced has to be

Volume = mass / density

Volume = (53980.33 / 1,000)

Volume = 53.98 m³.

Cube root of 53.88 = 3.78 m

Therefore, the minimum side length is 3.78 m

Answer:

3.781488032m or greater

Explanation:

General Rule of thumb is that any thing that is less dense than water will float in it.

So

density of water is 997Kg/m^3 and density of iron on the other hand is  7860kg/m^3.

so to make iron less dense it has to be in larger volume.

mass of the given cube is 53911.74Kg and we have contain it in volume such that density is less than water, mathematically this translates to .

[tex]\frac{53911.74Kg}{V}\leq \frac{997Kg}{m^3}[/tex] left side is density of iron and right side is density of water, solving v in this inequality gives us.

[tex]v \geq 54.0739m^3[/tex] which means each side is [tex]s \geq 3.7814880m[/tex]. so the minum is just greater than that.

Answer: [tex]160 \Omega[/tex]

Explanation:

According to Ohm's law:  

[tex]V=R.I[/tex]  

Where:  

[tex]V=120 V[/tex] is the voltage difference across the light bulb

[tex]R[/tex] is the resistance of the light bulb   (the value we want to find)

[tex]I=0.75 A[/tex] is the electric current

Isolating [tex]R[/tex]:  

[tex]R=\frac{V}{I}[/tex]

[tex]R=\frac{120 V}{0.75 A}[/tex]

Finally:

[tex]R=160 \Omega[/tex]  This is the resistance of the light bulb

Final answer:

To calculate the resistance of a lightbulb with a current of 0.75 amperes and a voltage difference of 120 volts, use Ohm's law. The formula is R = V / I, which yields a resistance of 160 ohms for the lightbulb.

Explanation:

Calculating the Resistance of a Lightbulb

The student has asked how to calculate the resistance of a lightbulb when a current of 0.75 amperes flows through it and the voltage difference across it is 120 volts. To find the resistance, we can use Ohm's law, which states that the resistance (R) of a circuit is equal to the voltage (V) across it divided by the current (I) flowing through it, which can be written as:

R = V / I

Plugging in the given values, we get:

R = 120 V / 0.75 A

R = 160 ohms

Therefore, the resistance of the lightbulb is 160 ohms.

Find the given attachment

Answer:

Explanation:

find the solution below

The work, heat, and internal energy changes are calculated for different stages of the gas expansion and cooling processes in a cylinder with a piston containing oxygen as an ideal gas.

Part A: The work done by the gas during the initial expansion can be calculated using the formula:

Work = Pressure * Change in Volume

Since the expansion is isobaric (constant pressure) and the volume doubles, the change in volume is 2 times the initial volume. Therefore, the work done is 2 times the initial pressure times the initial volume.

Part B: The heat added to the gas during the initial expansion can be calculated using the formula:

Heat = Pressure * Change in Volume, since the expansion is isobaric.

Part C: The internal energy change of the gas during the initial expansion is equal to the heat added minus the work done.

Part D: The work done during the final cooling is zero because the process is isochoric (constant volume) and no work is done.

Part E: The heat added during the final cooling can be calculated using the equation:

Heat = Change in Internal Energy, since no work is done.

Part F: The internal energy change during the final cooling is equal to the negative of the heat added.

Part G: The internal energy change during the isothermal compression is also equal to the negative of the heat added, as no work is done during an isothermal process.

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Answer: 13 cm

Explanation:

Given

Inductance of the solenoid, L = 3.01•10⁻⁶ H

Width of the wire, x = 1.13 m

Length of the tube, z = ?

Now, we know that

L = μ₀N²A/z, where

N = x/2πr, making r subject of formula,

r = x/2πN

Also,

A = πr², on substituting for A, we have

A = πx²/4π²N²

Now finally, we substitute in the initial equation and solve

L = μ₀N²A/z

L = μ₀N²πx²/4π²N²z

L = μ₀x²/4z, making z subject of formula, we have

z = μ₀x²/4L

z = 4π*10⁻⁷ * 1.13² /4 * 3.01*10⁻⁶

z = (4π*10⁻⁷ * 1.2769) / (4 * 3.01*10⁻⁶)

z = 1.6*10^-6 / 1.2*10^-5

z = 0.13 m

Therefore, the length of the tube should be 13 cm

The length of the tube should be 469 centimeters.

To find the required length of the tube for Tia's solenoid, we can use the formula for the inductance of a solenoid:

[tex]\[ L = \frac{{\mu_0 \cdot N^2 \cdot A}}{l} \][/tex]

Where:

L = inductance of the solenoid (3.01 μH)

[tex]\( \mu_0 \)[/tex] = permeability of free space (4π × 10^-7 T*m/A)

N = number of turns of wire

A = cross-sectional area of the solenoid

[tex]\( l \)[/tex] = length of the solenoid

We're given [tex]\( L \)[/tex] and [tex]\( N \cdot l \)[/tex] (the total length of wire wound around the tube). We need to find [tex]\( l \)[/tex], the length of the tube.

First, let's rearrange the formula to solve for [tex]\( l \)[/tex]:

[tex]\[ l = \frac{{\mu_0 \cdot N^2 \cdot A}}{{L}} \][/tex]

We know the cross-sectional area ( A ) can be represented as [tex]\( A = \pi r^2 \)[/tex], where ( r ) is the radius of the tube. Since the wire is uniformly wound, we can calculate ( A ) using the length of the wire and the number of turns.

[tex]\[ A = \frac{{\text{{Length of wire}}}}{{\text{{Number of turns}}}} \][/tex]

Given that the wire length is 1.13 m and there are [tex]\( N \)[/tex] turns, [tex]\( A = \frac{{1.13}}{{N}} \)[/tex].

Substituting this into the equation for [tex]\( l \)[/tex], we get:

[tex]\[ l = \frac{{\mu_0 \cdot N^2 \cdot \left(\frac{{1.13}}{{N}}\right)}}{{L}} \][/tex]

[tex]\[ l = \frac{{\mu_0 \cdot 1.13}}{{L}} \][/tex]

Now, plug in the known values:

[tex]\[ l = \frac{{4\pi \times 10^{-7} \cdot 1.13}}{{3.01 \times 10^{-6}}} \][/tex]

[tex]\[ l = \frac{{4\pi \times 1.13}}{{3.01}} \][/tex]

[tex]\[ l = \frac{{4 \times 3.1416 \times 1.13}}{{3.01}} \][/tex]

[tex]\[ l = \frac{{14.1376}}{{3.01}} \][/tex]

[tex]\[ l = 4.69 \, \text{m} \][/tex]

Finally, convert this length to centimeters:

[tex]\[ l = 469 \, \text{cm} \][/tex]

So, the length of the tube should be 469 centimeters.

Answer:

L=N/I*magnetic flux

=N/I*BA=N*mu(0)NIA/2pi*R=mu(0)N^2/2pi*R)*Pi*a^2

=mu(0)N^2a^2/2R

Explanation:

The self-inductance L of the toroid is mu(0)N^2a^2/2R.

Since

The toroidal inductor has a circular cross-section of radius a. The toroid has N turns and radius R.

The toroid is narrow ( a≪R )

So,

L=N/I*magnetic flux

=N/I*BA=N*mu(0)NIA/2pi*R=mu(0)N^2/2pi*R)*Pi*a^2

=mu(0)N^2a^2/2R

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Answer:

The radius of curvature of the ion's orbit is 0.59 meters

Explanation:

Given that,

Mass of the 24 Mg ion, [tex]m=3.983\times 10^{-26}\ kg[/tex]

Potential difference, V = 3 kV

Magnetic field, B = 526 G

Charge on single ionized ion, [tex]q=1.6\times 10^{-19}\ C[/tex]

The radius of the the path traveled  by the charge is circular. Its radius is given by :

[tex]r=\dfrac{mv}{Bq}[/tex]

v is speed of particle.

v can be calculated using conservation of energy as :

[tex]\dfrac{1}{2}mv^2=qV\\\\v=\sqrt{\dfrac{2qV}{m}} \\\\v=\sqrt{\dfrac{2\times 1.6\times 10^{-19}\times 2\times 10^3}{3.983 \times 10^{-26}}} \\\\v=1.26\times 10^5\ m/s[/tex]

Radius,

[tex]r=\dfrac{3.983 \times 10^{-26}\times 1.26\times 10^5}{0.0526\times 1.6\times 10^{-19}}\\\\r=0.59\ m[/tex]

So, the radius of curvature of the ion's orbit is 0.59 meters.

Answer:

The average angular acceleration is  [tex]\alpha =125.487 rad /s^2[/tex]

Explanation:

From the question we are told that

  From the question we are told that

        The length of the bat is [tex]l = 0.85m[/tex]  \

         The initial linear velocity is  [tex]u = 0 m/s[/tex]

         The time is  [tex]t = 0.15s[/tex]

         The velocity at t is  [tex]v = 16 m/s[/tex]

  Generally average  angular acceleration is mathematically represented as

                [tex]\alpha = \frac{w_f - w_o}{t}[/tex]

        Where [tex]w_f[/tex] is the finial angular velocity which is mathematically evaluated as  

            [tex]w_f = \frac{v}{l}[/tex]

                  [tex]w_f = \frac{16}{0.85}[/tex]

                        [tex]= 18.823 rad/s[/tex]

 and [tex]w_o[/tex] is the initial angular velocity which is zero since initial linear velocity is zero

               So

                         [tex]\alpha = \frac{18.823 - 0}{0.15}[/tex]

                               [tex]\alpha =125.487 rad /s^2[/tex]

Light is incident in air (n = 1) and refracted into a medium with an index of refraction of 2. Light incident parallel to the central axis is focused at a point 24cm from the surface

When a light  ray passes through from one medium to another medium ,due to the difference in medium index, the light deflect from its original path .

This deflection  from its path is called refraction and The phenomenon of refraction can be seen in sound and water waves.

Cornea reflect the light before light reaches to the retina. Change in the speed of light when it travels from one medium to other medium then due to this there is change in the path of light, this phenomenon is known as refraction of light.

Equation for refraction

n2/v- n1/u = n2-n1/R

= u = infinity ( parallel)

2/v= (2-1)/R

V = 2R

V= 24cm

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To calculate the work required to pump water out of the swimming pool, physics principles such as the formula for work, volume of a cylinder, and weight of water are used to derive the necessary values for the complete calculation.

The question requires the use of physics concepts to calculate work done in pumping water out of a swimming pool. Since we are dealing with the force of gravity, density of water, height to which water is raised, and volume of water, we must use the formula for work done (work = force x distance) alongside formulas for the volume of a cylinder (Volume = πr^2h) and the weight of the water (weight = mass x gravity).

To solve the problem, first calculate the volume of water in the pool using the volume formula for a cylinder, taking into account the water's depth. Then, calculate the mass by multiplying the volume by the density of water. The weight of the water is found by multiplying the mass by the acceleration due to gravity. Finally, calculate the work done by multiplying the weight of the water by the height to which it needs to be lifted, considering both scenarios: pumping over the side and pumping through an outlet 2 meters over the side.

Final answer:

Calculation of work required to pump water out of a circular swimming pool at different heights.

Explanation:

The work required to pump all the water over the side of the pool is:
Work = mgh = density x volume x gravity x height = 1000 kg/m³ x (pi x (9m)² x 1.5m) x 9.8 m/s² x 3m = 1222540 J

For pumping all water out of the outlet 2m over the side:
Work = mgh = density x volume x gravity x height = 1000 kg/m³ x (pi x (9m)²x 1.5m) x 9.8 m/s² x 5m = 2037567 J

Answer:

A) μ = A.m²

B) z = 0.46m

Explanation:

A) Magnetic dipole moment of a coil is given by; μ = NIA

Where;

N is number of turns of coil

I is current in wire

A is area

We are given

N = 300 turns; I = 4A ; d =5cm = 0.05m

Area = πd²/4 = π(0.05)²/4 = 0.001963

So,

μ = 300 x 4 x 0.001963 = 2.36 A.m².

B) The magnetic field at a distance z along the coils perpendicular central axis is parallel to the axis and is given by;

B = (μ_o•μ)/(2π•z³)

Let's make z the subject ;

z = [(μ_o•μ)/(2π•B)] ^(⅓)

Where u_o is vacuum permiability with a value of 4π x 10^(-7) H

Also, B = 5 mT = 5 x 10^(-6) T

Thus,

z = [ (4π x 10^(-7)•2.36)/(2π•5 x 10^(-6))]^(⅓)

Solving this gives; z = 0.46m =

Due to the net electric flux that is moving outward through the closed box's surface, the box has a negative charge.

Given:-

The electric field is constant over all the faces.

From Gauss law:

[tex]\int \vec E \cdot d\vec A = \dfrac{Q}{e_o}[/tex]

[tex]\vec E =[/tex] An electric field throughout the cube.

[tex]d \vec A =[/tex] Elemental area of the cube surface.

[tex]Q =[/tex] Electric charge around the cube.

[tex]e_o =[/tex]  Electric constant.

[tex]\dfrac{Q}{e_o} = (-15-20-15+20+15+10)\\ \\ = -5A[/tex]

According to Gauss's law, the box contains a negative charge.

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The box's charge type (being positive, negative, or neutral) is determined by the net electric flux's direction. Outward flux signifies positive charge, whilst inward flux indicates a negative charge. Boxes with no net electric flux have no charge.

The determination of whether a closed box contains a positive charge, negative charge, or no charge is dependent on the direction of the net electric flux. If there is net electric flux passing outward through the surface of the box, this indicates the box contains a positive charge. Conversely, if the net electric flux is passing inward through the surface, the box contains a negative charge. Lastly, if there is no net electric flux (flux in cancelled by flux out), it suggests there is no charge in the box.

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Answer:

n1/p + n2/q = (n2-n1)/R

1.45/p + 1.6/1.15 = (1.6 - 1.45)/0.035 (m)

1.45/p + 1.39 = 4.28

p = 0.50 m (50 cm)

Answer: 0.666 V

Explanation:

Given

Radius of the loop, r = 14.8 cm = 0.148 m

Magnetic field present, B = 0.814 T

Rate of shrinking, dr/dt = 88.4 cm/s = 0.884 m/s

emf = dΦ/dt , where Φ = BA

emf = d(BA)/dt, where A = πr²

emf = d(Bπr²)/dt

if B is constant, then

emf = Bπ d(r²)/dt, on differentiating, we have,

emf = Bπ * 2r dr/dt

emf = 2πrB dr/dt, now if we substitute the values, we have

emf = 2 * 3.142 * 0.148 * 0.814 * 0.884

emf = 6.284 * 0.106

emf = 0.666 V

Depending on its size, composition, and the eccentricity of its orbit, that scanty description could apply to a planet, an asteroid, a comet, a meteoroid, or another star.

Answer:

Towards the west

Explanation:

Magnetic force is the interaction between a moving charged particle and a magnetic field.

Magnetic force is given as

F = q (V × B)

Where F is the magnetic force

q is the charge

V is the velocity

B is the magnetic field

V×B means the cross product of the velocity and the magnetic field

NOTE:

i×i=j×j×k×k=0

i×j=k.  j×i=-k

j×k=i.  k×j=-i

k×i=j.  i×k=-j

So, if the electron is moving southward, then, it implies that the velocity of it motion is southward, so the electron is in the positive z-direction

Also, the electron is curved upward due to the magnetic field, this implies that the force field is directed up in the positive y direction.

Then,

V = V•k

F = F•j

Then, apply the theorem

F •j = q ( V•k × B•x)

Let x be the unknown

From vector k×i =j.

This shows that x = i

Then, the magnetic field point in the direction of positive x axis, which is towards the west

You can as well use the Fleming right hand rule

The thumb represent force

The index finger represent velocity

The middle finger represent field

Answer:

V = 1.1658 × [tex]10^{-5}[/tex] V

Explanation:

given data

strip of copper thick = 130 µm

strip of copper wide = 4.40 mm

uniform magnetic field of magnitude B = 0.79 T

current i = 26 A

number of charge carriers per unit volume = 8.47 × [tex]10^{28}[/tex] electrons/m³

solution

we know that number density is express as

n = \frac{Bi}{Vle}      ...............1

B  is uniform magnetic field and i is current  and V is hall potential difference and l is thickness and e is electron charge 1.6 × [tex]10^{-19}[/tex]  C

so V will be as

V = \frac{iB}{nle}      .....................2

so put here value and we get V

V = [tex]\frac{26 \times 0.79}{8.47\times 10^{28}\times 130\times10^{-6}\times1.6 \times10^{-19}}[/tex]

V = 1.1658 × [tex]10^{-5}[/tex] V

Answer:

R₁ = 50.77 Ω

Explanation:

Since, we know that:

Electric Power = P = VI

but from Ohm's Law:

V = IR

(or) I = V/R

Therefore,

P = V²/R

(OR) R = V²/P

where,

V = Battery Voltage

R = Resistance of combination

FOR SERIES COMBINATION:

R = Rs = (57 V)²/48 W

Rs = 67.69 Ω

but, we know that:

Rs = R₁ + R₂

R₁ + R₂ = 67.69 Ω

R₁ = 67.69 Ω - R₂  __________ eqn (1)

FOR PARALLEL COMBINATION:

R = Rp = (57 V)²/256 W

Rp = 12.69 Ω

but, we know that:

Rp = (R₁R₂)/(R₁ + R₂) = 12.69 Ω

using eqn (1) and value of R₁ + R₂, we get

Rp = 12.69  = R₂(67.69 - R₂)/67.69

859.08 = 67.69 R₂ - R₂²

R₂² - 67.69 R₂ + 859.08 = 0

Solving this quadratic equation we get the answers:

Either, R₂ = 50.76 Ω

Either, R₂ = 16.92 Ω

Since, it is stated in the question that R₁ > R₂. Therefore, we choose the second value. So,

R₂ = 16.92 Ω

using this value in eqn (1), we get:

R₁ = 67.69 Ω - 16.92 Ω

R₁ = 50.77 Ω

Final answer:

To calculate R1, first, find the total resistance for series (R1 + R2) and parallel (1/R1 + 1/R2) connections using the power formula P = V^2 / R, with provided power values for each case. Then solve the simultaneous equations.

Explanation:

The problem can be solved by using the formulas for resistances in series and parallel, as well as the formula for the power supplied by the battery.

In series, the resistances add up: Rtotal = R1 + R2. The power provided by the battery to the series circuit is given by P = V2 / Rtotal, where P is 48.0 W and V is 57.0 V. Rearranging to solve for Rtotal, we get Rtotal = V2 / P.

For parallel resistances, we have 1/Rtotal = 1/R1 + 1/R2. The power in the parallel case is P = V2 / Rtotal. With V and P given as 57.0 V and 256 W, respectively, we can solve for Rtotal.

With both Rtotal values calculated, we can set up two equations with two unknowns (R1 and R2), knowing that R1 > R2. Solving these simultaneous equations gives us the value of R1.

Answer: 0.512 kgm²

Explanation:

Given

Force, F = 2*10^3 N

Angular acceleration, α = 121 rad/s²

Lever arm, r(⊥) = 3.1 cm = 3.1*10^-2 m

τ = r(⊥) * F

Also,

τ = Iα

Using the first equation, we have

τ = r(⊥) * F

τ = 0.031 * 2*10^3

τ = 62 Nm

Now we calculate for the inertia using the second equation

τ = Iα, making I subject of formula, we have

I = τ / α, on substituting, we have

I = 62 / 121

I = 0.512 kgm²

Thus, the moment of inertia of the boxers forearm is 0.512 kgm²

Answer:

The magnitude of the acceleration of earth due to the gravitational pull of earth is a = Gm/r^2

Where r = the center to center distance between the earth and the moon,

m = mass of the moon, and,

G is the gravity constant.

Explanation:

Detailed explanation and calculation is shown in the image below

Answer:

[tex]a_e = \frac{Gm}{r^2}[/tex]

Explanation:

We assume that:

M to represent the mass of the earth

m to equally represent the  mass of the moon

r should be the distance between the center of the earth to the center of the moon.

Then;

the expression for the gravitational force can be written as:

[tex]F = \frac{GMm}{r^2}[/tex]

Where [tex]a_e[/tex] is the acceleration produced by the earth; then:

[tex]F =M *a_e[/tex]

Then:

[tex]M*a_e = \frac{GMm}{r^2}[/tex]

[tex]a_e = \frac{GMm}{Mr^2}[/tex]

[tex]a_e = \frac{Gm}{r^2}[/tex]

Therefore, the  magnitude of the acceleration of the earth due to  the gravitational pull of the moon  [tex]a_e = \frac{Gm}{r^2}[/tex]

Answer with Explanation:

Let mass of one vehicle =m

Mass of other vehicle=m'

[tex]\frac{m}{m'}=\frac{1}{4}[/tex]

[tex]m'=4m[/tex]

Velocity of one vehicle=[tex]v=13 im/s[/tex]

Velocity of other vehicle=[tex]v'=13jm/s[/tex]

In x- direction

By law of conservation of momentum

[tex]mv+0=(m+m')V_x[/tex]

[tex]13m=(m+4m)V_x[/tex]

[tex]13m=5mV_x[/tex]

[tex]V_x=\frac{13}{5}[/tex]

In y- direction

By law of conservation of momentum

[tex]0+m'v'=(m+m')V_y[/tex]

[tex]4m(13)=5mV_y[/tex]

[tex]V_y=\frac{52m}{5m}=\frac{52}{5}[/tex]

Magnitude of velocity of the wreck,V=[tex]\sqrt{V^2_x+V^2_y}=\sqrt{(\frac{13}{5})^2+(\frac{52}{5})^2}=10.72 m/s[/tex]

Direction:[tex]\theta=tan^{-1}(\frac{V_y}{V_x})[/tex]

[tex]\theta=tan^{-1}(\frac{\frac{52}{5}}{\frac{13}{5}})=75.96^{\circ}[/tex]

Answer:

The voltage will increase.

Explanation:

Increason the number of coil in the secondary will increase the voltage in a transformer.

The correct result of the given operation expressed in scientific notation and with the appropriate number of significant figures should be 3.4 x 10^3. However, there are no matching options provided. A possible mistake might exist in the question.

To solve the problem, you should first add the two numbers in the brackets together. This gives us 0.82 + 0.042 = 0.862. Next, we need to multiply this result by the number outside the brackets, which is 4.4 x 103. Thus, our equation becomes 0.862 x 4.4 x 103 = 3.3928 x 103.

The result needs to be expressed in scientific notation and with the correct number of significant figures. The least precise number in our calculation is 4.4 (which has two significant figures), so our final answer should also have two significant figures. Therefore, we round 3.3928 x 103 to 3.4 x 103.

However, none of the options provided matches this result. Please double-check the question as there might be a typo.

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First, add 0.82 + 0.042 = 0.862. Second, multiply the sum 0.862 x 4.4 = 3.7928. Finally, round the result to two significant figures in scientific notation giving the answer as 3.8 x 10 or just 3.8.

To solve this problem, first, we need to add the numbers in the parentheses, then multiply the sum by 4.4 x 10⁰, which is just 4.4 since any number raised to the power of zero equals one.

Step 1: Add 0.82 + 0.042 = 0.862

Step 2: Multiply 0.862 x 4.4 = 3.7928

Lastly, we need to express the answer in scientific notation with the correct number of significant figures. As the question gives the numbers 0.82 and 0.042 with two and three significant figures respectively, we should express our final answer to two significant figures, as you always round to the fewest number of significant figures.

So, round 3.7928 to two significant figures, gives you 3.8 x 10⁰, which can alternatively be written as just 3.8, making the correct answer (a) 3.8 x 10.

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Answer: 2.44*10^3 km

Explanation:

NOTE: We would be solving this question in "cm" instead of the usual "m"

1 mi² = 2.59 km²

2.59 km² = 2.59*10^10 cm²

Given, area of South Dakota

A = 7.588*10^4 mi²

A = 7.588*10^4 * 2.59*10^10

A = 1.97*10^15 cm² is the area of South Dakota

S = πd²/4

S = 3.142 * 0.635² / 4

S = 3.142 * 0.4/4

S = 3.142 * 0.1

S = 0.3142 cm² is the area of 1 marshmallow

1.97*10^15 / 0.3142 = 6.27*10^15, thus is the number of marshmallows in one single layer to cover the state area

6.02*10^23 / 6.27*10^15 = 9.6*10^7, this is the number of layers

9.6*10^7 * 2.54 = 2.44*10^8, this is the height in cm

Height in km is 2.44*10^3 km