The current through an inductor of inductance L is given by I(t) = Imax sin(ωt).
(a) Derive an expression for the induced emf in the inductor as a function of time.
(b) At t = 0, is the current through the inductor increasing or decreasing?
(c) At t = 0, is the induced emf opposing or aiding the flow of the charge carriers? (Remember that the direction of a positive induced emf is the same as the current direction and the direction of a negative induced emf is opposite the current direction.)
(d) How are the answers to parts b and c consistent with the behavior of inductors discussed in the text?

Answer:

A13 mm is about 1/4 A5 mm

Explanation:

Find the attachment

Answer:

i) angle of incidence;i = 29.43°

ii) δm = 38.92°

Explanation:

Prism is equilateral so angle of prism (A) = 60°

Refractive index of glass; n_glass = 1.52

A) Let's assume the incident angle = i and Critical angle = θc

We know that, sin θc = 1/n

Thus;

sin θc = 1/n_glass

θc = sin^(-1) (1/n_glass)

θc = sin^(-1) (1/1.52)

θc = 41.14°

Now, the angle of prism will be the sum of external angle that is critical angle and reflected angle.

Thus;

A = r + θc

r = A - θc

So;

r = 60° - 41. 14°

r = 18.86°

From, Snell's law. If we apply it to this question, we will have;

(sin i)/(sin r) = n_glass

Where;

i is angle of incidence and r is angle of reflection.

Let's make i the subject;

i = sin^(-1) (n_glass × sin r)

i = sin^(-1) (1.52 × sin 18.86)

i = sin^(-1) 0.4914

i = 29.43°

B) The formula to calculate minimum deviation would be from;

μ = [sin ((A + δm)/2)]/(sin A/2)

Where;

μ is Refractive index

δm is minimum angle of deviation

A is angle of prism

Now Refractive index is given by a formula; μ = (sin i)/(sin r)

So; μ = (sin 29.43)/(sin 18.86)

μ = 1.52

Thus;

1.52 = [sin ((60 + δm)/2)]/(sin 60/2)

1.52 * sin 30 = sin ((60 + δm)/2)

0.76 = sin ((60 + δm)/2)

sin^(-1) 0.76 = ((60 + δm)/2)

49.46 × 2 = (60 + δm)

98.92 - 60 = δm

δm = 38.92°

Answer:

a. TRUTH

b. FALSE

c. TRUTH

d. FALSE

Explanation:

The emf (electromagnetic force) is generated in a loop or solenoid by the change in the magnetic flux in a closed conductor path (for example, a wire).

This can be noted in the following formula, which is known as the Lenz's law:

[tex]emf=-N\frac{d\Phi_B}{dt}=-N\frac{d(AB)}{dt}[/tex]   (1)

Then, the change, in time, of the area of the conductor, or the change in the magnitude of the magnetic field, the induced emf acquires different values. Furthermore, the loops have a resistance, then, a current can be measured when an emf is induced.

Based on this information you have:

a. an induced emf is caused by a changing magnetic flux. TRUTH

b. an emf can only be induced in a conducting loop by moving the loop through an area that has a constant magnetic field. FALSE

c. an induced emf can be observed by measuring the current that is created. TRUTH

d. an induced emf and conventional induced current are in opposite directions. TRUTH (the minus sing in the equation (1) )

Answer:

(a) 0.0885 Hz

(b) 0.21 m/s

Explanation:

(a) Frequency: This can  be defined as the number of cycle completed in one seconds.

From the question,

Note: 2 crest = one cycle,

If four crest = 22.6 s,

Then two crest = (22.6/2) s

= 11.3 s.

T = 11.3 s

But,

F = 1/T

F = 1/11.3

F = 0.0885 Hz.

(b)

Using,

V = λF...................... Equation 1

Where V = speed of wave, F = Frequency of wave, λ = wave length.

Given: F = 0.0885 Hz, λ = 2.37 m.

Substitute these values into equation 1

V = 2.37(0.0885)

V = 0.21 m/s.

Answer:

Air masses move with the global pattern of winds. In most of the United States, air masses generally move from west to east. They may move along with the jet stream in more complex and changing patterns. 

Answer:

The correct answer is C 1, 4, and 5 tie, then 2 and 3 tie

Explanation:

Solution

The electric field due to sheets E₁ positive =б/2E₀

E₂ is negative = б/2E₀

Now,

At the point 1, 4, 5 the electric field due to the sheets are in the opposite direction

At the point 1, the net field = -E₁ + E₂ =0

At the point A, the net field = -E₁ - E₂ = 0

Now,

At nay point inside between them, the electric field is seen to be at the same direction.

At the 2, 3 points the field is seen at the right

Thus,

E net = E₁ + E₂

= б/2E₀ + σ/2E₀

=б/E₀

Note: Kindly find an attached copy of the complete question to the solution

The correct answer is option C

The rank of the points according to the magnitude of the electric field is 1, 4, and 5 tie, then 2 and 3 tie

Let sheet 1 has positive surface charge density and sheet 2 has a negative surface charge density

The electric field (without direction) due to sheets will be

E₁ =σ/2E₀

E₂= σ/2E₀

Now,

At the point 1, 4, 5 the electric field due to the sheets is given by:

E = E₁ - E₂

E = σ/2E₀ - σ/2E₀

since the positive charge plate will have electric field lines away from the sheet and the negative charge plate will have electric field lines towards the sheet

E = 0

Now,

At points 2, 3 which are between the plates,

The net electric field is:

E = E₁ + E₂

since the electric field due to both the plates will be from positive to negative ( towards the negatively charged plate)

E = σ/2E₀ + σ/2E₀

E = σ/E₀

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Answer:

Energy is stored by a 50 ampere-minute 12

volt battery is approximately = 36,000 J = 36 kJ

Explanation:

Power in electrical circuits is given as

Power = IV

But power generally is defined as energy expended per unit time

Power = (Energy/time)

Energy = Power × Time

Energy = IV × Time

Energy = (I.t × V)

I.t = 50 Ampere-minute = 50 × 60 = 3000 Ampere-seconds

V = 12 V

Energy = 3,000 × 12 = 36,000 J = 36 kJ

Hope this Helps!!!

Answer:

The apparent weight of the person as she pass the highest point is  [tex]N = 458.8 \ N[/tex]

Explanation:

From the question we are told that

   The radius of the Ferris wheel is [tex]r = 5.0 \ m[/tex]

    The period of revolution is [tex]T = 8.0 \ s[/tex]

     The weight of the person is  [tex]W = 670 \ N[/tex]

Generally the speed of the wheel is mathematically represented as

      [tex]v = \frac{2 \pi r}{T }[/tex]

substituting values

      [tex]v = \frac{2 * 3.142 * 5}{8 }[/tex]

       [tex]v = 3.9 3 \ m/s[/tex]

The apparent weight (the normal force exerted on her by the bench) at the highest point is mathematically evaluated as

          [tex]N = mg - \frac{mv^2}{r}[/tex]

Where m is the mass of the person which is mathematically evaluated as

     [tex]m = \frac{W}{g}[/tex]

substituting values

    [tex]m = \frac{670}{9.8}[/tex]

    [tex]m = 68.37 \ kg[/tex]

So

    [tex]N = 68.37 * 9.8 - \frac{68.37 * {3.93}^2}{5}[/tex]

    [tex]N = 458.8 \ N[/tex]

Answer:idk

Explanation:idk

Answer:

shortage of 50 water bottles

$2

30

Explanation:

Explanation:

2.  No, not always.  Normal force is equal to force of gravity only when there's no acceleration in the vertical direction.

For example, when you stand in an elevator that's not moving, or moving at constant speed, then the normal force equals your weight.  But when the elevator accelerates upward, the normal force increases (making you feel heavier).  And when the elevator slows down, the normal force decreases (making you feel lighter).

3.  Yes, it is possible for an object to be moving eastward and experience a net force westward.  An example is a car applying the brakes.

4.  Friction force allows you to walk.  When you push against the floor, the floor's friction pushes back, as Newton's third law says.

If you try to walk on a slippery surface like ice, you won't be able to push against the ice, and the ice won't push back.

Answer:

20 Yards

Explanation:

|---20----|

|            |

| 50       |50

|---D--->|

Start      End

Total displacement(D)  20 yards (East).

Answer:

130.528779365 degrees

Explanation:

The angle of incidence is 30 degrees. From this, we can use Snell's Law to calculate the angle of refraction.

n1/n2 = sin(theta2)/sin(theta1)

let theta1 be 30 degrees, and n1 be the refractive index of air = 1

1/1.5 = sin(theta2)/sin(30deg)

solve:

sin(theta2) = 2/3 sin(30deg) = 1/3

theta2 = arcsin (1/3) = 19.4712206345 degrees

The angle of reflection will always be equal to the angle of incidence, in this case, 30 degrees.

Because these angles are measured relative to the normal, the angle formed between the two rays is the difference between the normal line (180 degrees) and the sum of the two angle measures.

Angle between = 180-30-19.4712206345 = 130.528779365 degrees

The angle between the reflected and transmitted rays 130.5287 degrees

The angle of incidence is 30 degrees. From this, we can use Snell's Law to calculate the angle of refraction.

[tex]\dfrac{n_1}{n_2} = \dfrac{sin(\theta_2)}{sin(\theta_1)}[/tex]

let [tex]\theta_1[/tex] be 30 degrees, and n1 be the refractive index of air = 1

[tex]\dfrac{1}{1.5} = \dfrac{sin(\theta_2)}{sin(30)}[/tex]

solve:

[tex]sin(\theta_2) = \dfrac{2}{3} sin(30) = \dfrac{1}{3}[/tex]

[tex]\theta_2 = sin ^{-1}\dfrac{1}{3} = 19.4712 \ degrees[/tex]

The angle of reflection will always be equal to the angle of incidence, in this case, 30 degrees.

Because these angles are measured relative to the normal, the angle formed between the two rays is the difference between the normal line (180 degrees) and the sum of the two angle measures.

Angle between = 180-30-19.4712206345 = 130.528779365 degrees

Hence the angle between the reflected and transmitted rays 130.5287 degrees

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Answer:

Since you would have to do work on the charge to bring it back to its original position, the charge moves to a position of lower potential and lower potential energy.

The positive charge is released from a point such that it will move along an uniform electric field to the position of lower potential and lower potential energy. Therefore, option (A) is correct,

When a positive charge (say +Q) is released from a point (say A) and moves in an uniform electric field to reach the point (say B), then some work is done on the charge. This work done is given as,

[tex]W=+Q(V_{A}-V_{B})[/tex]

Here, [tex]V_{A}[/tex] and [tex]V_{B}[/tex] are the potential differences between the points A and B respectively..

This means the charge is moving from higher potential to lower potential. And since it is moving along the uniform electric field, therefore the electric potential energy of charged system is decreased.

Thus, we conclude that on releasing the positive charge from a point, it starts moving along the electric field towards the direction of lower electric potential and lower electric potential energy. Hence, option (A) is correct.

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Answer: A chemical change results from a chemical reaction, while a physical change is when matter changes forms but not chemical identity. Examples of chemical changes are burning, cooking, rusting, and rotting. Examples of physical changes are boiling, melting, freezing, and shredding. Often, physical changes can be undone, if energy is input.

Explanation: hope this helps have a good day

Answer:

If the reaction is a chemical change, new substances with different properties and identities are formed. This may be indicated by the production of an odor, a change in color or energy, or the formation of a solid.

Answer:

a) 463.29 K

b) 8065.65 Pa

c) 0 J

Explanation:

The parameters given are;

Volume of the tank, V = 3.72 m³

Number of moles of gas present in the tank, n = 22.1 moles

Temperature of the gas before heating, T₁ = 300 k

Heat added to the gas, ΔQ = 4.5 × 10⁴ J

Specific heat capacity at constant volume, [tex]c_v[/tex], for monatomic gas = 12.47 J/K/mole

Avogadro's number = 6.022 × 10²³ particles per mole

a) ΔQ = n × [tex]c_v[/tex] × ΔT

Where:

ΔT = T₂ - T₁

T₂ = Final temperature of the gas

Hence, by plugging in the values, we have;

4.5 × 10⁴ = 22.1 × 12.47 × (T₂ - 300)

[tex]T_{2} - 300 = \frac{4.5\times 10^{4}}{22.1\times 12.47}[/tex]

T₂ = 300 + 163.29 = 463.29 K

b) The pressure of the gas is found from the relation;

P×V = n×R×T

[tex]P = \dfrac{n \times R \times T}{V}[/tex]

Where:

P = Pressure of the gas

R = Universal gas constant = 8.3145 J/(mol·K)

T = Temperature of the gas

V = Volume of the gas = 3.72 ³ (constant)

n = Number of moles of gas present = 22.1 moles (constant)

Hence the change in pressure is given by the relation;

[tex]\Delta P = \dfrac{n \times R \times (T_2 - T_1)}{V} = \dfrac{n \times R \times \Delta T}{V}[/tex]

Plugging in the values, we have;

[tex]\Delta P = \dfrac{22.1 \times 8.3145 \times 163.29}{3.72} = 8065.65 \, Pa[/tex]

c) Work done, W, by the gas is given by the area under the pressure to volume graph which gives;

W = f(P) × ΔV

The volume given in the question is constant

∴ ΔV = 0

Hence, W =  f(P) × 0 = 0 J

No work done by the gas during the process.

Answer:

B. At the instant when the block is at the highest point, directed at the block.

Explanation:

Motion of an object is the change in the position of the object with respect to time. On the earth, gravity has a great influence on the motion of an object (especially in a vertical direction).

When the block is projected up in the air, it moves with a varying velocity until the velocity becomes zero due to gravity. Which make the object to rest a little in the air (when velocity = gravity) and starts to fall freely.

To ensure hitting the block by the ball, it is thrown at the block when the block is at its highest point in the air. Since the block would be at rest at this instant before it start to fall at a constant acceleration under gravity.

Answer:

Make a hypothesis, conduct an experiment, Analyze the experimental data..

Answer:

The actual height is  [tex]A =3.158 \ m[/tex]

Explanation:

From the question we are told that

   The depth of the person is  [tex]d = 1.1 \ m[/tex]

    The apparent height  is  [tex]D = 4.2 \ m[/tex]

Generally

     The refractive index of water is  [tex]n_w = 1.33[/tex]

      The refractive index of the air is  [tex]n_a = 1[/tex]

The apparent depth is mathematically represented as

      [tex]D = A [\frac{n_w}{n_a} ][/tex]  

substituting values

     [tex]4.2 = A [\frac{1.33}{1} ][/tex]  

=>   [tex]A = \frac{4.2 }{1.33}[/tex]

      [tex]A =3.158 \ m[/tex]

The ball was dropped at the height of "3.158 m". To understand the calculation, check below.

According to the question,

Water's refractive index, [tex]n_w[/tex] = 1.33

Air's refractive index, [tex]n_a[/tex] = 1

Apparent height, D = 4.2 m

Person's depth, d = 1.1 m

We know the relation,

→ D = A[[tex]\frac{n_w}{n_a}[/tex]]

By substituting the values, we get

4.2 = A[[tex]\frac{1.33}{1}[/tex]]

By applying cross-multiplication,

  A = [tex]\frac{4.2}{1.33}[/tex]

      = 3.158 m

Thus the approach above is correct.

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Answer:

a. 42N

b. 11.8m/s

c. 1.69s

d. 160N

Explanation:

a)  The tension of the rope is 130.66 N.

b) The speed of the bucket while strike the water = 4.64 m/s.

c) The time of fall is  = 4.303 second.

d)  While the bucket is falling, what is the force exerted on the cylinder by the axle is  130.66 N.

Mass of the water bucket; M = 15.0 kg

Mass of the cylinder; m =  12.0 kg

Height of the bucket; h = 10.0 m.

They are connected by a rope and a pivots.

So, acceleration of them is same and let it be a.

So equation of motion of both of them be:

Mg - T = Ma

and, T - mg = ma

Hence, a = g(M-m)/(M+m)

= 9.8(15-12)/(15+12)

= 1.08 m/s²

And, T = m(g+a)

= 12.0(9.8+1.08)

= 130.66 N.

a) so tension of the rope is 130.66 N.

b) speed of the bucket while strike the water = √2ah =√(2×1.08×10.0) m/s = 4.64 m/s.

c) The time of fall is = √2h/a = √(2×10/1.08) second = 4.303 second.

d) While the bucket is falling, what is the force exerted on the cylinder by the axle is tension of the rope, that is, 130.66 N.

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Answer:

2C

Explanation:

The equivalent capacitance of a parallel combination of capacitors is the sum of their capacitance.

So, if the capacitance of each capacitor is half the previous one, we have a geometric series with first term = C and rate = 0.5.

Using the formula for the sum of the infinite terms of a geometric series, we have:

Sum = First term / (1 - rate)

Sum = C / (1 - 0.5)

Sum = C / 0.5 = 2C

So the equivalent capacitance of this parallel connection is 2C.

Answer:

e.) power you supply to the crate

Explanation:

According to given data, we have:

F = Force exerted on the crate

M = Mass of the crate

v = Speed of motion of the crate

d = Distance traveled by the crate across the floor

t = Time interval passed

Now, we try to analyze the given quantity:

=> F d/t

=> (Force)(Displacement)/(Time)

but, (Force)(Displacement) = Work Done

Therefore,

=> Work Done/Time

but, Work Done/Time = Power

Therefore,

=> Power

Hence, the quantity F d/t is:

e.) power you supply to the crate

Answer:

a) a = 3.09 m/s²

b) aₓ = 2.60 m/s²

Explanation:

a) The magnitude of her acceleration can be calculated using the following equation:

[tex] V_{f}^{2} = V_{0}^{2} + 2ad [/tex]

Where:

[tex]V_{f}[/tex]: is the final speed = 8.89 m/s

[tex]V_{0}[/tex]: is the initial speed = 0 (since she starts from rest)

a: is the acceleration

d: is the distance = 12.8 m    

[tex] a = \frac{V_{f}^{2}}{2d} = \frac{(8.89 m/s)^{2}}{2*12.8 m} = 3.09 m/s^{2} [/tex]

Therefore, the magnitude of her acceleration is 3.09 m/s².              

b) The component of her acceleration that is parallel to the ground is given by:

[tex] a_{x} = a*cos(\theta) [/tex]

Where:

θ: is the angle respect to the ground = 32.6 °

[tex] a_{x} = 3.09 m/s^{2}*cos(32.6) = 2.60 m/s^{2} [/tex]

Hence, the component of her acceleration that is parallel to the ground is 2.60 m/s².

I hope it helps you!

A skateboarder, starting from rest, rolls down a 12.8-m ramp the magnitude of the skateboarder's acceleration is approximately 3.07 [tex]m/s^2[/tex], the component of her acceleration that is parallel to the ground is approximately 1.66 [tex]m/s^2[/tex].

(a) The following kinematic equation can be used to calculate the skateboarder's acceleration:

[tex]v^2 = u^2 + 2as[/tex]

[tex](8.89)^2 = (0)^2 + 2a(12.8)[/tex]

78.72 = 25.6a

a = 78.72 / 25.6

a = 3.07 [tex]m/s^2[/tex]

(b) Trigonometry can be used to calculate the part of her acceleration that is parallel to the ground. We are aware that the ramp's angle with the ground is 32.6°.

[tex]a_{parallel }= a * sin(\theta)[/tex]

Plugging in the values:

[tex]a_{parallel[/tex] = 3.07  [tex]m/s^2[/tex]* sin(32.6°)

[tex]a_{parallel[/tex]≈ 1.66  [tex]m/s^2[/tex]

Therefore, the component of her acceleration that is parallel to the ground is approximately 1.66  [tex]m/s^2[/tex].

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Answer:

 v = 126 m / s

Explanation:

Let's analyze this exercise a little, they give us the thrust that is the applied force and the time that it lasts, and they ask us for the final speed, so we can use the Impulse ratio and the variation of the amount of movement

       I = F t = Dp

       F t = pf -p₀

      Now let's use Newton's second law to find the net thrust

        F = E - fr

the friction force has the formula

       fr = μ N

let's write Newton's second law on the y-axis

       N-W = 0

       N = W

we substitute

      fr = μ mg

we look for the net out

       F = 200 - μ mg

With the skater starting from rest, the initial speed is zero (vo = 0)

we substitute

      (200 - very m g) t = m v

       v = (200 µm - very g) t

let's calculate

     v = (200/75 - 0.10 9.8) 75

      v = 126 m / s

Answer:  If the woodpecker drums upon a tree 5 times in one second, then the frequency is 5 Hz; each drum must endure for one-fifth a second, so the period is 0.2 s.

Answer:

Mg or your weight.

Explanation:

When your velocity is constant, the net force acting on you is 0. That means the upwards force of air resistance must fully balance the downwards force of gravity on you, which is Mg.

Answer:

[tex]\tau = 1\ ms[/tex]

Explanation:

First we need to find the capacitance of the capacitor.

The capacitance is given by:

[tex]C = \epsilon_0 * area / distance[/tex]

Where [tex]\epsilon_0[/tex] is the air permittivity, which is approximately 8.85 * 10^(-12)

The radius is 12/2 = 6 mm = 0.006 m, so the area of the capacitor is:

[tex]Area = \pi * radius^{2}\\Area = \pi * 0.006^2\\Area = 113.1 * 10^{-6}\ m^2[/tex]

So the capacitance is:

[tex]C = \frac{8.85 * 10^{-12} * 113.1 * 10^{-6}}{0.001}[/tex]

[tex]C = 10^{-12}\ F = 1\ pF[/tex]

The time constant of a rc-circuit is given by:

[tex]\tau = RC[/tex]

So we have that:

[tex]\tau = 10^{9} * 10^{-12} = 10^{-3}\ s = 1\ ms[/tex]

Answer:

-2.24 m/s²

Explanation:

Given:

v₀ = 20 mi/hr = 8.94 m/s

v = 0 m/s

t = 4.0 s

Find: a

v = v₀ + at

0 m/s = 8.94 m/s + a (4.0 s)

a = -2.24 m/s²

Answer:

Coefficient of friction.

Explanation:

The amount of friction divided by the weight of an object is equal to the coefficient of friction. It is a dimensional less number. It can be given by :

[tex]F=\mu N[/tex]

N is normal force.

[tex]\mu[/tex] = coefficient of friction

[tex]\mu=\dfrac{F}{N}[/tex]