g If this combination of resistors were to be replaced by a single resistor with an equivalent resistance, what should that resistance be

Answer:

The answer is 40 N for APX

Explanation:

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:

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:

(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 average induced emf in the loop is 0.3 V

Explanation:

Given:

d = 22 cm

Magnetic field  is  B = 1.5 T

Change in time  Δt = 0.20 sec.

Radius of loop  = r = d/2 = 11 x [tex]10^{-2}[/tex] m

According to the faraday's law,  Induced emf is given by   e = - (ΔФ / Δt)

where Ф = magnetic flux

Ф = BAcos0   (in this occasion, Ф=0)

where area A = pi * r²

note that we have to neglect negative sign due to its lenz law...so

       B * pi * r

e = ----------------

          Δt

       1.5 ( 3.1416) 11 x [tex]10^{-2}[/tex] )²

e =  ------------------------------------

                        0.20

e = 0.3 V

Therefore, the average induced emf in the loop is 0.3 V

Answer: W.D = 1/2mv^2

Explanation:

If an external force or a single force is acting on a body. Just like the first law of thermodynamics, the force acting on the body will cause work done on the system.

Work done = force × distance

And the work done on the body will cause the molecules of the body to experience motion and thereby producing kinetic energy.

The work done will be converted to kinetic energy.

W.D = 1/2mv^2

Answer:

Explanation:

Using equations of motion:

(a)

v=u+at

∴0=19.4−8.57t

∴t=19.4/8.57

=2.3s

B. Using s= ut + 1/2 at²

19.4(2.3)-1/28.57(2.3)²

= 21.92rad

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:

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]

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:

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

Answer:

Explanation:

When the path difference is half the wave length or λ /2 , destructive interference takes place which results in reduced or zero intensity in case equal intensity waves interfere as in Young's double slit experiment

Hence dark fringe is formed at that place where intensity is zero .

Hence the right option is D

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

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:

Explanation:

Let the velocity of astronaut be u and the velocity of flat sheet of metal plate be v . They will move in opposite direction ,  so their relative velocity

= u + v = 2.3 m /s ( given )

We shall apply conservation of momentum law for the movement of astronaut and metal plate

mu  = M v where m is mass of astronaut , M is mass of metal plate

71 u = 230 x v

71 ( 2.3 - v ) = 230 v

163.3 = 301 v

v = .54 m / s

u = 1.76 m / s

honeycomb will be at rest  because honeycomb surface  is frictionless . Plate will slip over it . Over plate astronaut is walking .

a ) velocity of metal sheet relative to honeycomb will be - 1.76 m /s

b ) velocity of astronaut relative to honeycomb will be + .54 m /s

Here + ve direction is assumed to be the direction of astronaut .  

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:

a) 320N (if you take gravity as 10ms^-2) or 313.6N (if you take gravity as 9.8ms^-2

b) 41.6N

c) 6.25ms^-2

d) 1707.317 kg

Explanation:

a) W=mg

    W= 32 x 10 or 9.8

    W = 320N or 313.6N

b) F=ma

   F= 32 x 1.3

   F= 41.6N

c) F=ma

   200 = 32 x a

   a= 6.25ms^-2

d) F=ma

    7000= m x 4.1

     m= 1707.317 kg

I am not completely sure about the d) part because I dont whether you will be taking Friction and Normal Reaction too. As per my knowledge, I think no, as no angles nor the gradient of the floor/road is mentioned here.                  

a) The weight of your shopping cart is 313.6N .

b) The required force is  41.6N

c) The acceleration of the car is 6.25ms^-2

d) The mass of the car is 1707.317 kg.

Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).

a) The weight of the shopping cart:  W=mg

  W= 32 x  9.8 N

 W = 313.6N

b) The required force is to be applied: F=ma

F= 32 x 1.3 N.

F= 41.6N.

c) Let the acceleration of the cart is a.

Then, force:  F=ma

200 = 32 x a

a= 6.25ms^-2

Hence,  the acceleration of the cart is  6.25ms^-2.

d) Let the mass of the car is m.

Force applied on the car: F=ma

7000= m x 4.1

m= 1707.317 kg

The mass of the car is 1707.317 kg.

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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

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:

the three possible movements by the change in electric potential energy (Ue) of the object are NORTH EAST SOUTH

Explanation:

This is because When the object moves south, the force is in the direction of the displacement, and positive work is done with decreasing electric potential energy.

The opposite is true if the particle moves north—that is, negative work is done with increasing electric potential energy.

No work is done and the electric potential energy is constant if the motion is perpendicular to the electric field.

Answer:

A) 1.76U×10⁻³N

B) 2.716×10⁻³N

C) 264.5⁰

Explanation:

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

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:

The  total energy is  [tex]T = 169.02 \ J[/tex]

Explanation:

From the question we are told that

    The  Poynting vector (energy flux ) is  [tex]k = 0.939 \ W/m^2[/tex]

    The length of the rectangle is  [tex]l = 1.5 \ m[/tex]

    The  width of the rectangle is  [tex]w = 2.0 \ m[/tex]

    The time taken is [tex]t = 1 \ minute = 60 \ s[/tex]

The total electromagnetic energy falls on the area is mathematically represented as

      [tex]T = k * A * t[/tex]

Where A  is the area of the rectangle which is mathematically represented as

           [tex]A= l * w[/tex]

 substituting values

         [tex]A= 2 * 1.5[/tex]

        [tex]A= 3 \ m^2[/tex]

substituting values

        [tex]T = 0.939 * 3 * 60[/tex]

        [tex]T = 169.02 \ J[/tex]

Answer:

The magnitude of the net field located at the center of the square is the same in every of arrangement of the charges.

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:

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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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) before immersion

C = εA/d = (8.85e-12)(25e-4)/(1.31e-2) = 1.68e-12 F

q = CV = (1.68e-12)(255) = 4.28e-10 C

b) after immersion

q = 4.28e-10 C

Because the capacitor was disconnected before it was immersed, the charge remains the same.

c)*at 20° C

C = κεA/d = (80.4*)(8.85e-12)(25e-4)/(1.31e-2) = 5.62e-10 F

V = q/C = 4.28e-10 C/5.62e-10 C = 0.76 V

e)

U(i) = (1/2)CV^2 = (1/2)(1.68e-12)(255)^2 = 5.46e-8 J

U(f) = (1/2)(5.62e-10)(0.76)^2 = 1.62e-10 J

ΔU = 1.62e-10 J - 5.46e-8 J = -3.84e-8 J