A 20 kg child is on a swing that hangs from 2.6-m-long chains. What is her maximum speed if she swings out to a 46 angle?

Answer:

The speed at which the magnet falls through the copper block will be reduced dramatically.

Explanation:

Eddy's current are loops of electrical current induced within conductors by a changing magnetic field in the conductor. Eddy's current is proportional to the the magnetic field strength, the rate of change of flux, the area of the loop, and is inversely proportional to the resistivity of the material. Eddy currents flows perpendicularly to the magnetic field, and in closed loops within conductors.

Reducing the resistivity of the copper will increase the Eddy current on the copper, which will in turn increase the opposition to the action producing the flux change (the falling magnet through the copper block). The result is that the speed at which the magnet falls through the copper block will be reduced dramatically.

Answer:

The answer is 40 N for APX

Explanation:

Answer:

ω = 3.61 rad/sec

Explanation:

Firstly, we should know that the bug will not slip if friction can provide sufficient opposing force.

μmg = mv^2/r = mω^2r

Thus;

μg = ω^2r

ω^2 = μg/r

ω = √(μg/r)

ω = √(0.321 * 9.8)/0.241

ω = √(13.05)

= 3.61 rad/sec

Explanation:

It is given that,

Angle of incidence from air to another medium, i = 26°

The angle of reflection, r = 32°

We need to find the refractive index of the medium. The ratio of sine of angle of incidence to the sine of angle of reflection is called refractive index. It can be given by :

[tex]n=\dfrac{\sin i}{\sin r}\\\\n=\dfrac{\sin (26)}{\sin (32)}\\\\n=0.82[/tex]

So, the index of refraction is 0.82. Hence, the correct option is C.

Answer:

A) 1.76U×10⁻³N

B) 2.716×10⁻³N

C) 264.5⁰

Explanation:

See detailed workings for (a), (b), (c) attached.

Answer:

a) The speed of the electron as it reaches the inner conductor is closest to:

v = 1.45 × 10⁷m/s

b) The electric field magnitude between the cylinders is

E = 10,000V/m

Explanation:

given

inner radius of the cylinder r₁ = 20mm = 0.02m

outter radius of the cylinder r₂ = 80mm = 0.08m

potential difference V= 600V

mass of electron = 9.1×10⁻³¹kg

charge on electron = 1.6×10⁻¹⁹C

calculating the work done in bringing electron at inner conductor is

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

note:

[tex]V = \frac{W}{q}[/tex]

∴W = (ΔV)q

(ΔV)q = [tex]\frac{1}{2}mv^{2}[/tex]

(600)1.6×10⁻¹⁹ = ¹/₂ × 9.1×10⁻³¹ × v²

v² ≈ 2.11 × 10¹⁴

v = 1.45 × 10⁷m/s

According to the energy conservation law, the total energy of an isolated system is always constant.  

The energy of an isolated system can neither be created nor be destroyed, it can only convert one form to another form.

∴ the maximum electric field

E = ΔV/d

E = 600/d

where d is the distance between the two points

where d = 0.06m

E = 600/0.06

E = 10,000V/m

Note: the electric field due to the potential difference between to points depends upon the potential difference V and the distance between both points d.

a) The speed of the electron as it reaches the inner conductor is closest to: v = 1.45 × 10⁷m/s

b) The electric field magnitude between the cylinders is, E = 10,000V/m

Given:

Inner radius of the cylinder r₁ = 20mm = 0.02m

Outer radius of the cylinder r₂ = 80mm = 0.08m

Potential difference V= 600V

Mass of electron = [tex]9.1*10^{-31}kg[/tex]

Charge on electron = 1.6×10⁻¹⁹C

A)

Calculation for Work Done:

[tex]W=1/2mv^2[/tex]............(1)

Also.

[tex]V=\frac{W}{q}[/tex]

Thus, [tex]W=\triangle V*q[/tex]...........(2)

On equating 1 and 2:

[tex]\triangle V*q=1/2mv^2\\\\(600)1.6*10^{-19} = 1/2 * 9.1*10^{-31}* v^2\\\\v^2 =2.11 * 10^{14}\\\\v = 1.45 * 1067m/s[/tex]

B)

The energy of an isolated system can neither be created nor be destroyed, it can only convert one form to another form.

Thus, the maximum electric field

[tex]E = \triangle V/d\\\\E = 600/d[/tex]

where d is the distance between the two points

d = 0.06m

[tex]E = 600/0.06\\\\E = 10,000V/m[/tex]

Thus, the maximum electric field is 10,000V/m.

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Answer:

Increase

Explanation:

Because For a given focal length, a lens with a larger front element will generally be faster. That is, it'll have a larger maximum aperture, allowing a shorter exposure time, But a larger aperture requires larger elements to maintain the same angle of view

The velocity and force are required.

The speed of the racket is 8.7 m/s

The required force is 471.43 N.

[tex]m_1[/tex] = Mass of racket = 1000 g

[tex]m_2[/tex] = Mass of ball = 60 g

[tex]u_1[/tex] = Initial velocity of racket = 12 m/s

[tex]u_2[/tex] = Initial velocity of ball = -15 m/s

[tex]v_1[/tex] = Final velocity of racket

[tex]v_2[/tex] = Final velocity of ball = 40 m/s

[tex]\Delta t[/tex] = Time = 7 ms

The equation of the momentum will be

[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\Rightarrow v_1=\dfrac{m_1u_1+m_2u_2-m_2v_2}{m_1}\\\Rightarrow v_1=\dfrac{1\times 12+0.06\times (-15)-0.06\times 40}{1}\\\Rightarrow v_1=8.7\ \text{m/s}[/tex]

Force is given by

[tex]F=m_2\dfrac{v_2-u_2}{\Delta t}\\\Rightarrow F=0.06\times \dfrac{40-(-15)}{7\times 10^{-3}}\\\Rightarrow F=471.43\ \text{N}[/tex]

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Answer:

A.) 909 cm/s

B.) 33075 N

Explanation:

A.) Given that the

Mass M = 43 g

Height h = 4.05 R

Radius r = R

At the top of the loop, the maximum potential energy P.E = mgh

Substitutes m and h into the formula where g = 9.8 m/s^2 = 9610.517 cm/s^2

P.E = 43 × 9610.517 × 4.05R

P.E = 1673671.536R J

According to conservative of energy

The maximum P.E = maximum K.E

But K.E = 1/2mv^2

1673671.536R = 1/2mv^2

Substitutes for mass m into the formula

1673671.536R = 1/2× 4.05R × v^2

The R will cancel out

Cross multiply

4.05 v^2 = 3347343.072

V^2 = 3347343.072 / 4.05

V^2 = 826504.4622

V = sqrt( 826504.4622)

V = 909 cm/s

B.) At the top of the loop, the centripetal force = the sum of the normal force N and the weight W of the car. That is,

MV^2/R = N + W

Make N the subject of formula

N = mv^2/ R - W

Where W = mg

Substitute all the parameters into the formula

N = (4.05R × 909^2) /R - 4.05R × 9610.517

N = 3346438.05 - 38922.59

N = 3307515 N

Answer:

gₓ = 6.52 m/s²

Explanation:

The value of acceleration due to gravity on the surface of earth is given as:

g = GM/R²   -------------------- equation 1

where,

g = acceleration due to gravity on surface of earth

G = Universal Gravitational Constant

M = Mass of Earth

R = Radius of Earth

Now, for the alien planet:

gₓ = GMₓ/Rₓ²

where,

gₓ = acceleration due to gravity at the surface of alien planet

Mₓ = Mass of Alien Planet = 2.4 M

Rₓ = Radius of Alien Planet = 1.9 R

Therefore,

gₓ = G(2.4 M)/(1.9 R)²

gₓ = 0.66 GM/R²

using equation 1

gₓ = 0.66 g

gₓ = (0.66)(9.81 m/s²)

gₓ = 6.52 m/s²

Answer:

Option D is the correct option.

Explanation:

Given,

Mass ( m ) = 3 kg

Acceleration due to gravity ( g ) = 9.8 m/s²

Weight ( w ) = ?

Now, let's find the weight :

[tex]w \: = \: m \times g[/tex]

plug the values

[tex] = 3 \times 9.8[/tex]

Multiply the numbers

[tex] = 29.4 \: [/tex] Newton

Hope this helps!!

best regards!!

Answer:

27°

Explanation:

The force is proportional to the sine of the angle between the wire and the magnetic field. (See the ref.)

So theta = arcsin(0.45)

=27°

The angle between the wire and the magnetic field is 27°.

Since The magnetic force per meter on a wire is measured to be only 45 %

So here we know that The force should be proportional to the sine of the angle between the wire and the magnetic field

Therefore,

theta = arcsin(0.45)

=27°

Hence, The angle between the wire and the magnetic field is 27°.

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Answer:

D

Explanation:

Gravity is the force of attraction between two objects.

Each object creates a gravitational field in wich every other object is affected by it.

Answer:

Explanation:

Kinetic frictional force acting on the block = μ mg

where μ is coefficient of friction , m is mass of block.

.3 x 1.5 x 9.8 = 4.41 N .

Let v be the velocity of bullet + block after collision

kinetic energy of composite mass after the strike

= 1 /2 x 1.52 x v²

this will be equal to work done by friction .

.76 v² = 4.41 x 7

v² = 40.62

v = 6.37 m /s

Now we can obtain muzzle speed of bullet by applying conservation of momentum .

Let this speed be u

initial momentum of bullet

= .02 x u

final momentum of composite mass

= 1.52 x 6.37

.02 u = 1.52 x 6.37

u = 484.12 m /s .

= 480 m /s ( in two significant figures )

Answer:

Explanation:

E= −L ΔI / Δt.

L = E Δt / ΔI

Hence the unit of inductance may be V s A⁻¹

or volt s per ampere .

In the given case

change in current ΔI = - 2.5 A

change in time = .015 s

L = .56 H

E = − L ΔI / Δt.

= .56 x 2.5 / .015

= 93.33 V .

Answer:

Velocity of bear (v) = 20 m/s

Explanation:

Given:

Mass of bear (m) = 500 kg

Mechanical kinetic energy (K.E) = 100,000 J

Find:

Velocity of bear (v) = ?

Computation:

Mechanical kinetic energy (K.E) = 1/2(m)(v)²

100,000 = 1/2(500)(v)²

200,000 = 500(v)²

400 = (v)²

Velocity of bear (v) = 20 m/s

Answer:

The answer is B. When the magnet is placed on a globe to correctly align with Earth’s magnetic field, it is considered to be suspended freely. The Earth has geographical poles as well with North and South poles. Since unlike poles attract, the South Pole of the magnet will be attracted to the geographical North.

Explanation:

B)Place the magnet vertically on the equator, with the south end facing the North pole.

A bar magnet is a square piece of an item, made from iron, metal, or every other ferromagnetic substance or ferromagnetic composite, that indicates everlasting magnetic homes. It has two poles, a north and a south pole such that when suspended freely, the magnet aligns itself so that the northern pole factors towards the magnetic north pole of the earth.

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Answer:

The longer the cord, the lower the illumination

Explanation:

The illumination provided by the light bulb will be reduced as the length of the extension cord increases. This is because the resistance provided by the wire increases with its length.

Long wires have more electrical resistance than shorter ones.

Let us consider this formula:

Resistance =[tex]\frac{\rho L}{A}[/tex]

From this formula, we can see that as the length increases, the resistance to current flow offered by the wire increases also provided the resistivity and cross-sectional area of the wire remain constant. As a result of this, the illumination will drop.

Answer:

The expected year is 2017.

Explanation:

Total years that the millionaire to live = 15 years

Travel away from the earth at  = 0.8 c

This is a time dilation problem so if she travels at 0.8 c then her time will pass at slower. Below is the following calculation:

[tex]T = \frac{T_o}{ \sqrt{1-\frac{V^2}{c^2}}} \\T = \frac{15}{ \sqrt{1-\frac{0.8^2}{c^2}}} \\T = 25 years[/tex]

Thus the doctors are expecting to celebrate in the year, 1992 + 25 = 2017

Answer:

Explanation:

A nearsightedness is an eye defect that occurs when someone is only able to see close ranged object but not far distance object. According to the question, if the length of my eye decreases slightly as I age, this means there is a possibility that I will find it difficult to view a far distance object as I age.

At 70, once my eyes had decreased slightly in length, this means I will only be able to see close ranged object but not far distant object, showing that I am now suffering from nearsightedness according to its definition above.

Answer:

The magnetic  flux is  [tex]\phi = 15 \ Nm^2 /C[/tex]

Explanation:

From the question we are told that

    The value of the charge is  [tex]q = 0.80 \ nC = 0.80 *10^{-9} \ C[/tex]

     The length of each side of  the cube is [tex]d = 4.0 \ m[/tex]

Generally the magnetic flux through a closed surface is  mathematically represented as

          [tex]\phi = \frac{q}{\epsilon_o} * D[/tex]

Where  D is the area enclosing the charge

  Now  a  cube is made up of six faces but in this question we are considering only one face which is mathematically represented as

      [tex]D = \frac{1}{6}[/tex]

So  the electric flux through one face of the cube  is  mathematically represented as

         [tex]\phi = \frac{q}{6 * \epsilon _o }[/tex]

where  [tex]\epsilon _o[/tex] is the permitivity of free space with value  

           [tex]\epsilon_o = 8.85 *10^{-12} F/m[/tex]

substituting value  

      [tex]\phi = \frac{0.80 *10^{-9}}{6 * 8.85 *10^{-12} }[/tex]

     [tex]\phi = 15 \ Nm^2 /C[/tex]

Answer:

The magnitude of the net gravitational force exerted by these objects on a 42.0-kg object is 1.818 x 10⁻⁷ N

Explanation:

Given;

first object with mass, m₁ = 285 kg

second object with mass, m₂ = 585 kg

distance between the two objects, r = 4.3 m

The midpoint between the two objects = r/₂ = 4.3 /2 = 2.15 m

Gravitational force between the first object and the 42 kg object;

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

where;

G = 6.67 x 10⁻¹¹ Nm²kg⁻²

[tex]F = \frac{6.67*10^{-11} *285*42}{2.15^2} \\\\F = 1.727*10^{-7} \ N[/tex]

Gravitational force between the second object and the 42 kg object

[tex]F = \frac{6.67*10^{-11} *585*42}{2.15^2} \\\\F = 3.545*10^{-7} \ N[/tex]

Magnitude of net gravitational force exerted on 42kg object;

F = 3.545x 10⁻⁷ N  -  1.727 x 10⁻⁷ N

F = 1.818 x 10⁻⁷ N

Therefore, the magnitude of the net gravitational force exerted by these objects on a 42.0-kg object is 1.818 x 10⁻⁷ N

Answer:

The  angular acceleration is [tex]\alpha = 0.4418 \ rad /s^2[/tex]

Explanation:

From the question we are told that

      The  angular speed is [tex]w_f = 45 \ rev / minutes = \frac{45 * 2 * \pi }{60 }= 4.713 \ rad/s[/tex]

       The  angular displacement is  [tex]\theta =4 \ rev = 4 * 2 * \pi = 25.14 \ rad[/tex]

From the first equation of motion we can define the movement of the record as

      [tex]w_f ^2 = w_o ^2 + 2 * \alpha * \theta[/tex]

Given that the record started from rest [tex]w_o = 0[/tex]

So

       [tex]4.713^2 = 2 * \alpha * 25.14[/tex]

        [tex]\alpha = 0.4418 \ rad /s^2[/tex]

Answer:

5.4x10^4km

Explanation:

See attached file

Answer:

Explanation:

The double slit interference phonemene is described for the case of constructive interference

          d sin θ= m λ                   (1)

let's use trigonometry to find the sinus

        tan θ = y / L

in general in interference phenomena the angles are small

       tan θ = sin θ / cos θ = sin θ

The double slit interference phonemene is described for the case of constructive interference

          d sin θ = m lam                    (1)

let's use trigonometry to find the sinus

        tan θ = y / L

in general in interference phenomena the angles are small

       tan θ = sin θ / cos θ = sin θ

we substitute

      sin θ = y / L

we substitute in equation 1

         d y / L = m λ

         λ = dy / L m

let's reduce the magnitudes to the SI system

  d = 0.44 mm = 0.44 10⁻³ m

  y = 5.5 mm = 5.5 10⁻³ m

  L = 4.2m

  m = 1

let's calculate

        λ = 0.44  10⁻³ 5.5 10⁻³ / (4.2 1)

        λ = 5.76190 10-7 m

let's reduce to num

  lam = 5.56190 10-7 m (109 nm / 1m)

  lam = 556,190 nmtea

we substitute

      without tea = y / L

we substitute in equation 1

         d y / L = m lam

         lam = dy / L m

let's reduce the magnitudes to the SI system

  d = 0.44 me = 0.44 10-3 m

  y = 5.5 mm = 5.5 10-3

  L = 4.2m

  m = 1

let's calculate

        lam = 0.44 10⁻³  5.5 10⁻³ / (4.2 1)

        lam = 5.76190 10⁻⁷ m

let's reduce to num

  lam = 5.56190 10⁻⁷ m (109 nm / 1m)

  lam = 556,190 nm

Answer:

The speed of the light signal as viewed from the observer is c.

Explanation:

Recall the basic postulate of the theory of relativity that the speed of light is the same in ALL inertial frames. Based on this, the speed of light is independent of the motion of the observer.

Answer:

Zack should direct his throw outward and toward the back of the car.

Explanation:

As the car is moving forward, the book will be thrown with a forward component. Therefore, throwing this book backwards at a constant speed would cancel the motion of the car, allowing the book to have a greater chance of ending on the driveway. I say a greater chance as Zack may not have the exact timings as to land the book in his driveway. That too he may not have thrown the book with the right momentum.

The solution is throw 3.

I say a greater chance as Zack may not have the exact timings as to land the book in his driveway. That too he may not have thrown the book with the right momentum as the skydivers.

The statement that best applies Newton’s laws of motion to explain the skydiver’s motion is that an upward force balances the downward force of gravity on the skydiver. Newton's 3rd law often applies to skydiving.

When gravity is not acting upon the skydivers they would continue moving in the direction the vehicle they jumped from was moving. If no air resistance takes place, then the skydivers would still accelerating at 9.8 m/s until they hit the ground.

The skydiver after leaving the aircraft will accelerates downwards due to the force of gravity usually as there is no air resistance acting in the upwards direction, and there is a resultant force acting downwards, the skydiver will accelerates towards the ground.

Therefore, I say a greater chance as Zack may not have the exact timings as to land the book in his driveway. That too he may not have thrown the book with the right momentum as the skydivers.

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Answer:

(a) f

(b) r

(c) s

Explanation:

There are two forces on the sphere: weight and buoyancy.

Sum of forces in the y direction:

∑F = ma

B − mg = 0

B = mg

Buoyancy is equal to the weight of the displaced fluid, or ρVg, where ρ is the density of the fluid and V is the displaced volume.

ρVg = mg

ρV = m

V = m/ρ

(a) The mass decreases, so the displaced volume decreases.

(b) The sphere's density is constant and its radius increases, which means its mass increases, so the displaced volume increases.

(c) The mass stays the same, so the displaced volume is the same.

Answer:

The weight of the rod is 32.87 N

Explanation:

Density of the rod = 7800 kg/m

length of the rod = 81.2 cm = 0.812 m

diameter of rod = 2.60 cm = 0.026 m

acceleration due to gravity = 9.80 m/s^2

The rod can be assumed to be a cylinder.

The volume of the rod can be calculated as that of a cylinder, and can be gotten as

V = [tex]\frac{\pi d^{2} l}{4}[/tex]

where d is the diameter of the rod

l is the length of the rod

V = [tex]\frac{3.142* 0.026^{2}* 0.812}{4}[/tex] = 4.3 x 10^-4 m^3

We know that the mass of a substance is the density times the volume i.e

mass m = ρV

where ρ is the density of the rod

V is the volume of the rod

m = 4.3 x 10^-4 x 7800 = 3.354 kg

The weight of a substance is the mass times the acceleration due to gravity

W = mg

where g is the acceleration due to gravity g = 9.80 m/s^2

The weight of the rod W = 3.354 x 9.80 = 32.87 N