2. A constant voltage is applied to a series RL circuit by closing a switch. The voltage across L is 30 volts at t = 0 and drops to 6 volts at t = .0025 sec. If L = 0.2 H, what must be the value of R?

Answer:

Explanation:

thickness of oil t = 200 nm

index of refraction μ = 1.5

For transmitted light :---

path difference = 2μ t

For constructive interference

path difference = n λ , λ is wavelength  of light

2μ t = n λ

λ = 2μ t /  n

For longest λ , n = 1

λ = 2μ t

= 2 x 1.5 x 200 nm

= 600 nm

Wavelength in water

= 600 / refractive index of water

= 600 / 1.33

= 451.1 nm Ans

Answer:

Explanation:

Given

Force=18lb

extension=8in

Using Hooke's law to get the spring constant(k)

F=ke

Then,

K=f/e

K=18/8

K=2.25lb/in

Work done by spring is given by

W=1/2Fe

Or W=1/2ke²

Then,

Work done in stretching the spring to 14in

W=1/2ke²

W=0.5×2.25×14²

W=220.5lbin

1 Inch-pounds Force to Joules = 0.113J

Then, to joules

W=0.133×220.5

W=29.33J

Answer:

λ = 22.667 m

Explanation:

The range of frequency (f) of sound wave = 15 Hz to 50 KHz

Temperature (T) = 20 °C

Speed (v) of sound = 344 m/s

Lets assume, wavelength corresponding to the lower cut-off point of the sounds= λ

We know that, the speed (v), frequency (f) and wavelength (λ) are related as

So,

λ = 22.667 m

Answer:

Explanation:

Given that

F=ax^3/2. a is a constant

The force does a work of

W=2.01KJ from x=0 to x=15.2m

We need to find a

Work is give as,

W=∫F.ds

But this is in x direction only then,

W=∫Fdx. from x=0 to x=15.2m

W=∫ax^3/2dx from x=0 to x=15.2m

W=ax^(3/2+1)/(3/2+1).

W=ax^(5/2)/5/2

W=ax^(2/5)/2.5 from x=0 to x=15.2m

Cross multiply

2.5W=ax^2.5. from x=0 to x=15.2m

2.5W= a (15.2^2.5-0)

W=2.01KJ=2010J

2.5×2010=a×900.76

Therefore,

a=5.56

The given question is incomplete. The complete question is as follows.

A river has a steady speed of 0.360 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point.

(a) If the student can swim at a speed of 1.29 m/s in still water, how long does the trip take?

(b) How much time is required in still water for the same length swim?

(c) Intuitively, why does the swim take longer when there is a current?

Explanation:

(a)  Relative velocity of the student while going upstream is as follows.

          (1.29 - 0.360) m/s

         = 0.93 m/s

Now, relative velocity of the student while coming downstream is as follows.

          (1.29 + 0.360) m/s

        = 1.65 m/s

When the student is going upstream then time taken to cover 1 km distance is calculated as follows.

         = 1075.26 sec

When the student is going downstream then time taken by it to cover 1 km distance is as follows.

         = 606.06 sec

Hence, total trip time will be calculated as follows.

     Total trip time = (1075.26 sec + 606.06 sec)

                             = 1681.32 sec

(b)  Time taken in still water is calculated as follows.

             = 1550.38 sec

(c)  When there will be current then there will occur a decrease in relative velocity of the swimmer. Therefore, he will take more time.

Answer:

They will attract.

Explanation:

We know, in conductors electrons are free to move> in the case given both metal ball and rod are conductor.

Now, when conductor are brought to a charge all the opposite charges moves through the point of conductor which is close to the charge and attraction takes place.

In this case too, when metal ball is bought near rod, rod also develop opposite charge and attraction takes place.  

Hence, this is the required solution.

Answer:

-0.234 N

Explanation:

Electrostatic force is:

Substitute the values:

Negative sign indicates that the force is attractive in nature which is also true as the charges are opposite in nature.

Answer:

0.0026 m/s²    

Explanation:

Centripetal acceleration is given as follows:

Substitute the values:

Answer:

-9446.22 J

Explanation:

Parameters given:

Mass of climber and harness = 56kg

Mass of cable = 0.7kg

Distance between climber and top of rock face = 17m

The work done in pulling the climber is given as:

W = F * d

F is the force applied on the rope. It is opposite the force of gravity pulling the climber, hence, it is given as:

F = -Fg

Fg = force of gravity

Fg = m * g

g = acceleration due to gravity.

The mass of the climber, harness and cable = 56 + 0.7 = 56.7kg

=> Fg = 56.7 * 9.8

Fg = 555.66 N

Therefore, the work done will be:

W = - 555.66 * 17

W = -9446.22 J

The negative value of work means that the work done is opposite the value of the force acting on the climber.

Answer:

6.85C

Explanation:

the charge and the current are related by

Q= I×t

where Q = charge  in columbs

v = 10.8

P = IV

I = P/V = 74/10.8

I =6.85 A

the battery will supply a charge of (6.85×1) C

6.85C

in 1 hour

Answer:

3 Minutes 2 seconds to 22 minutes 16 seconds

Explanation:

Lets assume the Mars to be at the closest distance to Earth. This distance (D) = 54.6 Million km

The signal travels at the speed of light, so speed of the signal (V) = 300000 km/s

So, the time (T) taken by the radio wave to reach Earth from Mars will be,

Thus, T = 182 Sec = 3 Minutes 2 seconds.

The radio wave will take minimum 03 Minutes 02 seconds to reach Earth. Here is should be noted that the distance between the two planets keep on changing as they revolve around the Sun. There will come a point when Mars is farthest from Earth and the distance (D) will be 401 Million km. Then, the time will change to ,

T = 1336.67 sec = 22.27 Minutes.

So the maximum time will be 22 minutes 16 seconds.

Answer:

The minimum quantity of steam required per pound of ice is -22.5 BTU/lbm

Explanation:

Q = mCT

Q/m = CT

Q/m is the quantity of steam required per pound of ice

C is the heat capacity of ice = 0.45 BTU/lbm°F

T is the temperature of ice = -50 °F

Q/m = 0.45 BTU/lbm°F × -50 °F = -22.5 BTU/lbm

Answer:

the output power of the hearing aid in two significant figures is 3.2 × 10⁻⁸ W

Explanation:

Output power of sound is given as;

P = I*A

where;

I is the sound intensity = 90dB = 1 × 10⁻³ W/m²

A is the area through which the transmits;

since the canal is circular in shape.

Given;

D as diameter = 6.4mm = 0.0064 m

Output power of the hearing aid = (1 × 10⁻³ W/m²)*(3.217 × 10⁻⁵ m²)

                                                      = 3.2 × 10⁻⁸ W

Therefore, the output power of the hearing aid in two significant figures is 3.2 × 10⁻⁸ W.

Explanation:

A) x-component of forces is 7.297 N

For x-component FX;

FX = F1 cos 65 + F2 cos 53.9

FX = 9.20 cos 65 + 5.8 cos 53.9

NB both forces are positive if resolved along the x-axis.

FX = 3.88 + 3.417 = 7.297 N

B) 6-component of forces is -3.654 N

For y-component FY

FY = -F1 sin 65 + F2 sin 53. 9

FY = - 9.2 sin 65 + 5.8 sin 53.9

NB F1 is negative along y-axis

FY = - 8.34 + 4.686 = - 3.654 N

C) The magnitude of the resultant force is 8.16 N

Magnitude = (FX^2 + FY^2)^0.5

(7.297^2 + (-3.654)^2)^0.5 = 8.16N

D) Angle made with negative x-axis is 26.56°

Tan^ -1 of FY/FX gives the angle of the resultant force.

= tan^-1 of -3.654/7.297

=tan^-1 of -0.5

= -26.56°

I.e 26.55° from the negative x-axis in a clockwise direction.

Answer:

F₁ / F₂ = exp (-Q_{v} / k)  exp [(T₂-T₁) / T₁T₂]

Q_{v} = -k ΔT / T₁T₂  ln (F₁ / F₂)

Explanation:

The Boltzmann equation for vacancies is

           n = n₀ exp (-Eₙ /kT)

Where n and n₀ are  the number of current and maximum vacancies, respectively, Eₙ is the activation energy (), K the Boltzmann constant and T the absolute temperature

The fraction is

         F = n / n₀ = exp (- Q_{v} / kT)

Let's apply this equation to our case

For temperature T = T₁

       F₁ = exp (-Qv / k T₁)

For temperature T = T₂

      F₂ = exp (-Qv / kT₂)

The ratio of the vacancy fraction is

     F₁ / F₂ = exp (-Q_{v} / k T₁) / exp (- Q_{v} / k T₂)

     F₁ / F₂ = exp (-Q_{v} / k)  exp [(T₂-T₁) / T₁T₂]

In general, the activation energy is sought by clearing this equation

     Q_{v} = -k ΔT / T₁T₂  ln (F₁ / F₂)

Answer:Both ions have the same kinetic energy.

Explanation:

The kinetic energy of the ions depends on the accelerating potential. The greater the accelerating potential, the greater the kinetic energy of the ions and vice versa. Ions are usually accelerated in such a way that they all have the same kinetic energy. Since the accelerating potential of the He+ and Ar+ are the same, they will both possess the same kinetic energy.

Answer:

A.

Explanation:

• According to the work energy theorem, the work done by external forces on a mass, must equal to the change in kinetic energy.
• When thrown upward, the change in kinetic energy is negative, due to it must have some initial velocity, which it will diminishing while going upward, as gravity is slowing down it.
• So, in this part of the trajectory, work done by gravity (only force acting on the ball if we neglect air resistance) must be negative.
• In the downward part of the trajectory, as the change in kinetic energy is positive (the ball is speeding up when falling), the work done by gravity must be positive too.
• So, the option A is the one that is true.

Answer:

5183 sec.

Explanation:

• The power dissipated in the resistance, will be used to raise the temperature of the water completely.
• This power can be found applying Joule's law, which states the following:

• If the resistance of the heating coil can be assumed as constant with the temperature, we can find the current I applying Ohm's Law, as follows:

• Now, from (1) we can find P, as follows:

• The energy supplied by this power, is just the product of the power times the time during which the energy was delivered:

• This energy, will be supplied as heat to the mass of water, as stated by the following equation (assuming no heat losses out of the heater):

• where c= specific heat of water = 4186 J/ºC*kg, m= 115 kg, and ΔT= 57ºC.
• From (2) and (3), if left sides are equal each other, so do right sides:

• Replacing by the values, we can solve for  Δt, as follows:

• The time required to raise the temperature of  115 kg of  water, from 18ºC, to 75ºC, is 5183 sec (approximately 1hr 26').

Answer:

(a) 12210  Ω

(b) 9.92 Ω

Explanation:

From Electricity,

(a)

When resistors are connected in series, the total resistance is the sum of the individual resistance.

From the question,

Rt = R1 + R2 + R3................................. R37 ....................... Equation 1

Where Rt = Total resistance of combined resistance, R1 = resistance of the first resistor, R2 = Resistance of the second resistor .......... and so on up to the 37th resistor.

Note: Since The resistor are identical.

Rt = n(R) ..................... Equation 2

Where n = number of resistor, R = resistance of each resistor.

Given: n = 37, R = 330 Ω

Substitute into equation 2

Rt = 37(330)

Rt = 12210 Ω

(b)

For parallel connection,

Rt = R/n...................... Equation 2

Given: R = 330 Ω, n = 37

Substitute into equation 2

Rt = 330/37

Rt = 8.92 Ω

Hence the resistance when connected in parallel = 9.92 Ω

Answer:

7.55 * 10^(-5) m

Explanation:

Parameters given:

Wavelength of light, λ = 381 nm = 3.81 * 10^(-7) m

Distance between screen and slit, L = 85 cm = 0.85 m

Distance of the first-order dark band from the center of the pattern, x = 0.43cm = 0.0043 m

The relationship between λ, L, x and the width of the slit, w is given as:

λ/w = x/L

=> w = λL/x

w = (3.81 * 10^(-7) * 0.85)/(0.0043)

w = 7.55 * 10^(-5) m