Answer:
28.3°C
Explanation:
Using
T(t) = (T(0) - 20)*(e^(-k*t)) + 20
for some positive number k, and some initial temperature T(0).
Boundary conditions:
T(4) = T(0) - 5 _______ (i)
T(8) = T(0) - 7 _______ (ii)
==> solving for T(0) and k :
(i):
(T(0) - 20)*(e^(-k*4)) + 20 = T(0) - 5 ==>
(T(0) - 20)*(e^(-k*4)) = T(0) - 20 - 5
(T(0) - 20)*(e^(-k*4)) = (T(0) - 20) - 5
5 = (T(0) - 20) - (T(0) - 20)*(e^(-k*4))
5 = (T(0) - 20) * ( 1 - e^(-k*4) )
(ii):
(T(0) - 20)*(e^(-k*8)) + 20 = T(0) - 7
(T(0) - 20)*(e^(-k*8)) = (T(0) - 20) - 7
7 = (T(0) - 20) - (T(0) - 20)*(e^(-k*8))
7 = (T(0) - 20) * (1 - e^(-k*8))
In both results, subsitute x = e^(-4k) and C = (T(0) - 20)
(i): 5 = C * (1 - x)
(ii): 7 = C * (1 - x^2) = C * (1-x)*(1+x)
Substitute C*(1-x) from (i) into (ii):
(ii): 7 = 5*(1+x) ==> (1+x) = 7/5 ==> x = 2/5
back into (i):
(i): 5 = C * (1 - 2/5) ==> 5 = C * 3/5 ==> C = 25/3
C = T(0) - 20 ==>
T(0) = C + 20 = 25/3 + 20 = 25/3 + 60/3 = 85/3
= 28.3°C
A bus carrying 10 people has over turned on a remote hillside during an intense thunderstorm. What three factors could contribute to creating a delay in advanced care
Answer:
The three factors that can contribute to creating a delay in advanced care for the passengers in the overturned bus include:
1. Lack of communication: Since the accident happened on the remote hillside, there is a possibility that, there would be no communication network which could have afforded them the opportunity to call medical or technical team.
2. Steep Nature of the Hill: This is another factor which will affect the care which they could have received. Steeply area tends to be difficult for climbing in or out from.
3. Thunderstorm: This factor is another reason which could contribute to delay in receiving advance care. Thunderstorm create barriers for location f the area where the bus overturned or in other situation complicate the rescue efforts of the team sent out to rescue.
Explanation:
At the pizza party you and two friends decide to go to Mexico City from El Paso, TX where y'all live. You volunteer your car if everyone chips in for gas. Someone asks how much the gas will cost per person on a round trip. Your first step is to call your smarter brother to see if he'll figure it out for you. Naturally he's too busy to bother, but he does tell you that it is 2015 km to Mexico City, there's 11 cents to the peso, and gas costs 5.8 pesos per liter in Mexico. You know your car gets 21 miles to the gallon, but we still don't have a clue as to how much the trip is going to cost (in dollars) each person in gas ($/person).
Answer:
cost_cost = $ 96
Explanation:
In this exercise we have units in the groin system and the SI system, to avoid problems let's reduce everything to the SI system
performance = 21 miles / gallon (1,609 km / 1 mile) (1 gallon / 3,785 l)
perfomance= 8,927 km / l
now let's use a direct rule of proportions (rule of three). If a liter travels 8,927 km, how many liters are needed to travel the 2015 km
#_gasoline = 2015 km (1l / 8.927 km) = 225.72 liters
Now let's find the total cost of fuel. Ns indicates that $ 0.11 = 1 peso and the liter of fuel costs 5.8 pesos
cost_litre = 5.8 peso ($ 0.11 / 1 peso) = $ 0.638
cost_gasoline = #_gasoline cost_litro
cost_gasoline = 225.72 0.638
cost_gasoline = $ 144
This cost is for the one way trip, the total round trip cost is
cost_total = 2 cost_gasoline
cost_total = $ 288
Now let's look for the cost in the vehicle, you and two people will go, for which a total of 3 people will go, so the cost per person is
cost_person = total_cost / #_people
cost_person = 288/3
cost_cost = $ 96
When the atmosphere is not quite clear, one may sometimes see colored circles concentric with the Sun or the Moon. These are generally not more than a few diameters of the Sun or Moon and invariably the innermost ring is blue. The explanation for these phenomena involves:_________
A) reflection
B) refraction
C) interference
D) diffraction
E) Doppler effect
Answer:
D) diffraction
Explanation:
Corona is an optical phenomenon produced by the diffraction of sunlight or moonlight, as light moves through water droplets in the atmosphere.
This phenomenon produces one or more diffuse concentric rings of light around the Sun or Moon, usually seen as colored circles.
Therefore, the explanation for these phenomena of colored concentric circles, sometimes seen with the Sun or the Moon involves diffraction.
Light passes from a material with index of refraction 1.3 into one with index of refraction 1.2. Compared to the incident ray, what happens to the refracted ray?
Answer:
It bends away from the normal
Explanation:
From Snell's law of Refraction, when a ray passes from a medium of lower Refractive index to a medium with higher Refractive index, the Refractive ray will bend towards the normal. However, when the ray passes from a medium of higher Refractive index to a medium of lower Refractive index, the Refractive ray will bend away from the normal.
Now, from the question we are told that Light passes from a material with index of refraction 1.3 into one with index of refraction 1.2.
This means from a higher Refractive index to a lower one and from Snell's law as earlier said, the refracted ray will bend away from the normal
The refracted ray is seen to bend away from the normal.
Let us recall that an optically denser medium will have a higher refractive index. This means that the medium with a refractive index of 1.3 is the denser medium and the medium with a refractive index of 1.2 is the less dense medium.
From the statement in the question, we can boldly say that light is travelling from a denser to less dense medium given the values of the refractive index given. When light is travelling from a denser to a less dense medium, the refracted ray bends away from the normal.
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A plane monochromatic light wave is incident on a double slit as illustrated in Figure 37.1.
(i) As the viewing screen is moved away from the double slit, what happens to the separation between the interference fringes on the screen?
(a) It increases,
(b) It decreases,
(c) It remains the same,
(d) It may increase or decrease, depending on the wavelength of the light.
(e) More information is required,
(ii) As the slit separation increases, what happens to the separation between the interference fringes on the screen? Select from the same choices.
Explanation:
The separation between the interference fringes on the screen increases because the distance of the screen from the slit is increased. Therefore option (a) is correct.
The separation between the interference fringes on the screen increases because the distance of the screen from the slit is increased, which is contradictory. Therefore option (b) is incorrect.
The separation between the interference fringes on the screen increases because the distance of the screen from the slit is increased, which is contradictory. Therefore option (c) is incorrect.
The separation between the interference fringes on the screen increases because the distance of the screen from the slit is increased, which is contradictory. Therefore option (d) is incorrect.
The separation between the interference fringes on the screen increases because the distance of the screen from the slit is increased, which is contradictory. Therefore option (e) is incorrect.
Which of
of
these
following material is
used as fuse material?
carbon,
silver
Copper
Aluminium
The provided question is not correct as, there is more than one options are correct, however the explaining every correct option -
Answer:
The correct answer are - silver, copper and aluminium all three used as fuse material.
Explanation:
A safety device in any electric circuit of that prevents the electric system in case of short circuit by breaking the connection of electric system or circuit termed as the Fuse or fuse element. Normally the fuse are made up of wire or element of material that are low in melting point and high in resistance.
Zinc, lead, tin, silver, copper, aluminium, and alloy of tin and alloy are used as fuse element or material for their low melting point and high resistance these are easily breaks the electric path in case of short circuit.
Find the rms current delivered by the power supply when the frequency is very large. Answer in units of A.
Answer:
The rms current is 0.3112 A.
Explanation:
Given that,
Suppose, The capacitance is 170 μF and the inductance is 2.94 mH. The resistance in the top branch is 278 Ohms, and in the bottom branch is 151 Ohms. The potential of the power supply is 47 V .
We know that,
When the frequency is very large then the capacitance can be treated as a short circuit and inductance as open circuit.
So,
We need to calculate the rms current
Using formula of current
[tex]I=\dfrac{V}{R}[/tex]
Where, V = voltage
R = resistance
Put the value into the formula
[tex]I=\dfrac{47}{151}[/tex]
[tex]I= 0.3112 \ A[/tex]
Hence, The rms current is 0.3112 A.
What did the results of photoelectric-effect experiments establish?
Answer:
Option A
Electrons are emitted if low intensity, high-frequency light hits a metal surface.
Explanation:
From the experiments conducted to study the photoelectric effect, conclusions were made that the key factor that contributes to the emission of electrons from the surface of the metal is the frequency of the beam of light. This frequency has to be beyond a minimum threshold, if not, there will be no emission of electrons from the metal surface no matter the intensity of the beam of light or the length of time it is incident upon the metal surface.
This makes option A correct because it highlights the contributions made by the threshold frequency to the photoelectric effect.
The intensity of the waves from a point source at a distance d from the source is I. What is the intensity at a distance 2d from the source?
Answer:
The intensity at distance 2d from source is [tex]I_1 = \frac{1}{4} * I[/tex]
Explanation:
From the question we are told that
The distance of the wave from point source is d
The intensity is [tex]I[/tex]
The distance we are considering is 2d
Generally the intensity of a wave is mathematically represented as
[tex]I = \frac{ P }{\pi d^2 }[/tex]
Here P is power of point source
Now when d = 2d
[tex]I_1 = \frac{ P }{\pi (2d)^2 }[/tex]
[tex]I_1 = \frac{ 1 }{4 } * \frac{ P }{\pi d^2 }[/tex]
=> [tex]I_1 = \frac{1}{4} * I[/tex]
The intensity at a distance 2d from the source is equal to [tex]I'=\frac{I}{4}[/tex]
Given the following data:
Distance = dIntensity = ITo determine the intensity at a distance 2d from the source:
Mathematically, the intensity of a wave is given by the formula:
[tex]I=\frac{P}{\pi d^2}[/tex]
Where:
I is the intensity of a wave.P is the power.d is the distance.Since the distance is doubled (2d), we have:
Let the new intensity be [tex]I'[/tex][tex]I'=\frac{P}{\pi (2d)^2}\\\\I'=\frac{P}{4\pi (d)^2}\\\\I'=\frac{1}{4} \times \frac{P}{\pi (d)^2}\\\\I'=\frac{1}{4} \times I\\\\I'=\frac{I}{4}[/tex]
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An electric device delivers a current of 5.0 A to a circuit. How many electrons flow through this circuit in 5 s?
Answer:
1.6×10²⁰
Explanation:
An ampere is a Coulomb per second.
1 A = 1 C / s
The amount of charge after 5 seconds is:
5.0 A × 5 s = 25 C
The number of electrons is:
25 C × (1 electron / 1.6×10⁻¹⁹ C) = 1.6×10²⁰ electrons
A circuit consists of four 100W lamps
connected in parallel across a 230V supply.
Inadvertently, a voltmeter has been connected
in series with the lamps. The resistance of the
voltmeter is 15000 and that of the lamps
under the conditions stated is six times their
value when burning normally. What will be the
reading of the voltmeter?
Complete question is;
A circuit consists of four 100-W lamps connected in parallel across a 230-V supply. Inadvertently, a voltmeter has been connected in series with the lamps. The resistance of the voltmeter is 1500 Ω and that of the lamps under the conditions stated is six times their value then burning normally. What will be the reading of the voltmeter?
Answer:
150.42 V
Explanation:
We are told that the circuit consists of four 100W lamps.
We know that Power is given by the equation;
P = V²/R
Thus;
R = V²/P
Now, we are told that the four lamps are connected in parallel across a 230V supply.
Thus, V = 230 V
So resistance, R = 230²/100
R = 529 Ω
We are told that the resistance of the lamps under the conditions stated is six times their value when burning normally.
Thus, total resistance of each lamp under the conditions = 529 × 6 = 3174 Ω
So, since they are connected in parallel, equivalent resistance for each lamp = 3174/4 = 793.5 Ω
Now, since this resistance is connected in series with the voltmeter resistance of 1500 Ω
Therefore, total circuit resistance = 1500 + 793.5 = 2293.5 Ω
Thus;
circuit current = 230/2293.5 = 0.100283 A
Now, according to Ohm’s law, voltage drop across the voltmeter = 1500 × 0.100283 ≈ 150.42V
CHECK THE COMPLETE QUESTION BELOW
A circuit consists of four 100-W lamps connected in parallel across a 230-V supply. Inadvertently, a voltmeter has been connected in series with the lamps. The resistance of the voltmeter is 1500 Ω and that of the lamps under the conditions stated is six times their value then burning normally. What will be the reading of the voltmeter?
Answer:
the reading of the voltmeter=150.4V
Explanation:
We can determine the wattage of a lamp using below expression:
: W = I² R....................eqn(1)
But fro ohms law V=IR
then I= V/R
If we substitute I into equation (1)
We have W= V²/R
But W= 100W
V= 230V
Then
W=220²/R
100 = 2302/R
R = 529 Ω
We can as well calculate the Resistance of each lamp under given condition that they are sixtimes their value when burning normally.
R = 6 × 529 = 3174 Ω
We can also calculate quivalent resistance of the abovefour lamps connected in parallel then
R = 3174/4
= 793.5 Ω
total circuit resistance can be calculated since we know that resistance is connected to voltmeter of 1500 Ω resistance in series arrangement
Then
total circuit resistance = 1500 + 793.5
= 2293.5 Ω
Then from ohms law again
I= V/R
circuit current = 230/2293.5 A
The reading of the voltage drop across the voltmeter
= 1500 × 230/2293.5
= 150.4V
If the intensity of an electromagnetic wave is 80 MW/m2, what is the amplitude of the magnetic field of this wave
CHECK THE COMPLETE QUESTION BELOW;
the intensity of an electromagnetic wave is 80 MW/m2, what is the amplitude of the magnetic field of this wave? (c=3.0×108m/s, μ0=4π×10−7T⋅m/A, ε0=8.85×10−12C2/N⋅m2)
Answer:
2.4×10^5 N/C
Explanation:
the amplitude can be explained as the maximum field strength of the electric and magnetic fields. Wave energy is proportional to its amplitude squared (E2 or B2).
We were told to calculate the amplitude of the magnetic field, which can be done using expresion below
S=ε²/2cμ
Where S is the intensity intensity of an electromagnetic wave given as 80 MW/m2
ε² is the Amplitude which we are looking for
c= speed of light given as 3×10^8m/s
Substitute the values into above formula we have,
S=ε²/2cμ
Making Amplitude subject of formula
ε²=S×2cμ
ε²=[80×10^6)(2×3×10^8)(4Π×10^-7)
= 245598.44
ε²=2.4×10^5 N/C
Therefore, amplitude of the magnetic field of this wave is S=2.4×10^5 N/C
Question 2.
In the US, lengths are often measured in inches, feet, yards and miles. Let's do
some conversions. The definition of the inch is: 1 inch = 25.4 mm, exactly. A foot is
12 inches and a mile is 5280 ft, exactly. A centimetre is exactly 0.01 m or 10 mm.
Sammy is 5 feet and 5.3 inches tall.
a). What is Sammy's height in Inches? (answer to 3 significant figures)
(3)
b). What is Sammy's height in Feet? (answer to 3 significant figures)
what is Sammy's hight in feet according to this statement
Explanation:
1 inch = 25.4 mm
1 foot = 12 inches
1 mile = 5260 feet
1 cm = 0.01 m or 10 mm
Now Sammy's height is 5 feet and 5.3 inches.
(a) We need to find Sammy's height in inches.
Since, 1 foot = 12 inches
5 feet = 5 × 12 inches = 60 inches
Now, 5 feet and 5.3 inches = 60 inches + 5.3 inches = 65.3 inches
Sammy's height is 65.3 inches.
(b) We need to find Sammy's height in feet.
Since, 1 foot = 12 inches
[tex]1\ \text{inch}=\dfrac{1}{12}\ \text{feet}[/tex]
So,
[tex]5.3\ \text{inch}=\dfrac{5.3}{12}\ \text{feet}=0.4416\ \text{feet}[/tex]
5 feet and 5.3 inches = 5 feet + 0.4416 feet = 5.44 feet
Sammy's height is 5.44 feet.
Water flows at 0.00027 m3/s through a 10-m long garden hose lying on the ground, with a radius of 0.01 m. Water has a viscosity of 1 mPa.s What is the magnitude of gauge pressure in Pa of the water entering the hose
Answer:
The gauge pressure is [tex]P = 687.4 \ Pa[/tex]
Explanation:
From the question we are told that
The rate of flow is [tex]Q = 0.00027 m^3 /s[/tex]
The height is h = 10 m
The radius is r = 0.01 m
The viscosity is [tex]\eta = 1mPa \cdot s = 1 *10^{-3} \ Pa\cdot s[/tex]
Generally the gauge pressure according to Poiseuille's equation is mathematically represented as
[tex]P = 8 \pi \eta * \frac{L * v }{ A}[/tex]
Here v is the velocity of the water which is mathematically represented according to continuity equation as
[tex]v = \frac{Q}{A }[/tex]
Where A is the cross-sectional area which is mathematically represented as
[tex]A = \pi r^2[/tex]
substituting values
[tex]A = 3.142 *(0.01)^2[/tex]
[tex]A = 3.142 *10^{-4} \ m^2[/tex]
So
[tex]v = \frac{ 0.00027}{3.142*10^{-4}}[/tex]
[tex]v = 0.8593 \ m/s[/tex]
So
[tex]P = 8 * 3.142 * 1.0*10^{-3}* \frac{10 * 0.8593 }{ 3.142*10^{-4}}[/tex]
[tex]P = 687.4 \ Pa[/tex]
If you have a density of 100 kg/L, and a mass of 1000 units, tell me the following: First what are the mass units?
Answer:
The mas unit is the the 'Kilogram' written as 'kg'
Volume is 10 L
Explanation:
The complete question is
If you have a density of 100 kg/L, and a mass of 1000 units, tell me the following: First, what are the mass units?
Second, what is the volume
mass units is the 'Kilogram', written as 'kg'
density = mass/volume = 100 kg/L
the mass = 1000 kg
volume = mass/density = 1000/100 = 10 L
Without actually calculating any logarithms, determine which of the following intervals the sound intensity level of a sound with intensity 3.66×10^−4W/m^2 falls within?
a. 30 and 40
b. 40 and 50
c. 50 and 60
d. 60 and 70
e. 70 and 80
f. 80 and 90
g. 90 and 100
Answer:
f. 80 and 90
Explanation:
1 x 10⁻¹² W/m² sound intensity falls within 0 sound level
1 x 10⁻¹¹ W/m² sound intensity falls within 10 sound level
1 x 10⁻¹⁰ W/m² sound intensity falls within 20 sound level
1 x 10⁻⁹ W/m² sound intensity falls within 30 sound level
1 x 10⁻⁸ W/m² sound intensity falls within 40 sound level
1 x 10⁻⁷ W/m² sound intensity falls within 50 sound level
1 x 10⁻⁶ W/m² sound intensity falls within 60 sound level
1 x 10⁻⁵ W/m² sound intensity falls within 70 sound level
1 x 10⁻⁴ W/m² sound intensity falls within 80 sound level
1 x 10⁻³ W/m² sound intensity falls within 90 sound level
Given sound intensity (3.66 x 10⁻⁴ W/m²) falls with 1 x 10⁻⁴ W/m² of intensity which is within 80 and 90 sound level.
f. 80 and 90
A parallel-plate capacitor consists of two square plates, size L×L, separated by distance d. The plates are given charge ±Q . What is the ratio Ef/Ei of the final electric field strength Ef to the initial electric field strength Ei if:
a. Q is doubled?
b. L is doubled?
c. d is doubled?
Answer:
Using
A. .E = σ/εo = (q/A)/εo = = q/Aεo so if q = 2q, then
Ef/Ei = 2
B. If L is 2L then Ef = q/4Aεo and
Ef/Ei = 1/4
C. The electric field strength is not effected by d and as long as σ is unchanged, Ef/Ei = 1
When light is either reflected or refracted, the quantity that does not change in either process is its
Answer:
Frequency
Explanation:
When waves travel from one medium to another, it is only the frequency of the wave that remains constant . when a wave is refracted at the boundary between two media, the wave will slow down and its wavelength decreases. The wave usually bends at the interface between the two media. The wavelength and speed of a wave may change at the boundary between two media but its frequency remains the same.
Hence the frequency of light is its only property that remains constant.
All household circuits are wired in parallel. A 1140-W toaster, a 270-W blender, and a 80-W lamp are plugged into the same outlet. (The three devices are in parallel when plugged into the same outlet.) Assume that this is the standard household 120-V circuit with a 15-A fuse.
a. What current is drawn by each device?
b. To see if this combination will blow the 15-A fuse, find the total current used when all three appliances are on.
Answer:
total current = 12.417 A
so it will not fuse as current is less than 15 A
Explanation:
given data
toaster = 1140-W
blender = 270-W
lamp = 80-W
voltage = 120 V
solution
we know that current is express as
current = power ÷ voltage ......................1
here voltage is same in all three device
so
current by toaster is
I = [tex]\frac{1140}{120}[/tex]
I = 9.5 A
and
current by blender
I = [tex]\frac{270}{120}[/tex]
I = 2.25 A
and
current by lamp is
I = [tex]\frac{80}{120}[/tex]
I = 0.667 A
so here device in parallel so
total current is = 9.5 A + 2.25 A + 0.667 A
total current = 12.417 A
so it will not fuse as current is less than 15 A
The Moon orbits Earth in a nearly circular orbit (mean distance is 378,000 km ). The moon Charon orbits Pluto in a nearly circular orbit as well (mean distance is 19,600 km ).
Earth Moon Pluto Charon
Mass (kg) 5.97 x 10^24 0.07342 x 10^24 0.0146 x 10^24 0.00162 x 10^24
Equatorial radius (km) 6378.1 1738.1 1185 604
Which object exhibits the longest orbital period? Hint: perform order of magnitude analysis.
a. Moon around Earth
b. Charon around Pluto
c. About the same for both
Answer:
a. Moon around Earth.
Explanation:
Charon orbit takes around 6.4 earth days to complete its orbit. Charon does not rises or sets, it hovers over same spot around the Pluto. The same side of Charon faces the Pluto, this is called Tidal Locking.
The moon orbit takes around 27 days to complete its orbit. The moon has different sides that are faced with sun which creates light or dark face of moon on the earth. Moon has 384,400 km distance from the earth.
The object that should exhibit the longest orbital period is option a. Moon around Earth.
What is Charon's orbit?Charon's orbit takes around 6.4 earth days to finish its orbit. Charon does not rise or sets, it hovers over similar spot around Pluto. The same side of Charon faces Pluto, this we called Tidal Locking. Here the moon orbit should take approx 27 days to finish its orbit. The moon has various sides that are faced with the sun which developed the light or dark face of the moon on the earth. Also, Moon has 384,400 km distance from the earth.
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If R = 20 Ω, what is the equivalent resistance between points A and B in the figure?
Answer:
c. 70 Ω
Explanation:
The R and R resistors are in parallel. The 2R and 2R resistors are in parallel. The 4R and 4R resistors are in parallel. Each parallel combination is in series with each other. Therefore, the equivalent resistance is:
Req = 1/(1/R + 1/R) + 1/(1/2R + 1/2R) + 1/(1/4R + 1/4R)
Req = R/2 + 2R/2 + 4R/2
Req = 3.5R
Req = 70Ω
Two long, parallel conductors, separated by 11.0 cm, carry currents in the same direction. The first wire carries a current I1 = 3.00 A, and the second carries I2 = 8.00 A.
(a) What is the magnetic field created by I1 at the location of I2?
(b) What is the force per unit length exerted by I1 on I2?
(c) What is the magnetic field created by I2 at the location of I1?
Explanation:
Given that,
Separation between two long parallel conductors, r = 11 cm = 0.11 m
Current in first wire, [tex]I_1=3\ A[/tex]
Current in second wire, [tex]I_2=8\ A[/tex]
(a) The magnetic field created by I₁ at the location of I₂ is given by :
[tex]B_{12}=\dfrac{\mu_o I_1}{2\pi r}\\\\B_{12}=\dfrac{4\pi \times 10^{-7}\times 3I_1}{2\pi \times 0.11}\\\\B_{12}=5.45\times 10^{-6}\ T[/tex]
(b) Magnetic force per unit length exerted by [tex]I_1[/tex] on [tex]I_2[/tex] is given by :
[tex]\dfrac{F}{l}=\dfrac{\mu_o I_1I_2}{2\pi r}\\\\\dfrac{F}{l}=\dfrac{4\pi \times 10^{-7}\times 3\times 8}{2\pi \times 0.11}\\\\\dfrac{F}{l}=4.36\times 10^{-5}\ N/m[/tex]
(c) The magnetic field created by I₂ at the location of I₁ is given by :
[tex]B_{21}=\dfrac{\mu_o I_2} {2\pi r}\\\\B_{12}=\dfrac{4\pi \times 10^{-7}\times 8}{2\pi \times 0.11}\\\\B_{12}=1.45\times 10^{-5}\ T[/tex]
Hence, this is the required solution.
A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 6.0 cm and released. If the ball makes 30 oscillations in 20 s, what are its (a) mass and (b) maximum speed?
Answer:
a
[tex]m = 0.169 \ kg[/tex]
b
[tex]|v_{max} |= 0.5653 \ m/s[/tex]
Explanation:
From the question we are told that
The spring constant is [tex]k = 14 \ N/m[/tex]
The maximum extension of the spring is [tex]A = 6.0 \ cm = 0.06 \ m[/tex]
The number of oscillation is [tex]n = 30[/tex]
The time taken is [tex]t = 20 \ s[/tex]
Generally the the angular speed of this oscillations is mathematically represented as
[tex]w = \frac{2 \pi}{T}[/tex]
where T is the period which is mathematically represented as
[tex]T = \frac{t}{n}[/tex]
substituting values
[tex]T = \frac{20}{30 }[/tex]
[tex]T = 0.667 \ s[/tex]
Thus
[tex]w = \frac{2 * 3.142 }{ 0.667}[/tex]
[tex]w = 9.421 \ rad/s[/tex]
this angular speed can also be represented mathematically as
[tex]w = \sqrt{\frac{k}{m} }[/tex]
=> [tex]m =\frac{k }{w^2}[/tex]
substituting values
[tex]m =\frac{ 15 }{(9.421)^2}[/tex]
[tex]m = 0.169 \ kg[/tex]
In SHM (simple harmonic motion )the equation for velocity is mathematically represented as
[tex]v = - Awsin (wt)[/tex]
The velocity is maximum when [tex]wt = \(90^o) \ or \ 1.5708\ rad[/tex]
[tex]v_{max} = - A* w[/tex]
=> [tex]|v_{max} |= A* w[/tex]
=> [tex]|v_{max} |= 0.06 * 9.421[/tex]
=> [tex]|v_{max} |= 0.5653 \ m/s[/tex]
Two 1.0 nF capacitors are connected in series to a 1.5 V battery. Calculate the total energy stored by the capacitors.
Answer:
1.125×10⁻⁹ J
Explanation:
Applying,
E = 1/2CV²................... Equation 1
Where E = Energy stored in the capacitor, C = capacitance of the capacitor, V = Voltage of the battery.
Given; C = 1.0 nF, = 1.0×10⁻⁹ F, V = 1.5 V
Substitute into equation 1
E = 1/2(1.0×10⁻⁹×1.5²)
E = 1.125×10⁻⁹ J
Hence the energy stored by the capacitor is 1.125×10⁻⁹ J
A pulley 326 mm in diameter and rotating initially at 4.00 revolutions per second receives a constant angular acceleration of 2.25 radians per second squared by a drive belt. What is the linear velocity of the belt after 5.00 seconds
Answer:
The linear velocity, v = 5.93 m/s
Explanation:
To find the linear velocity after 5 seconds, we find its angular velocity after 5 seconds using
ω' = ω + αt where ω = initial angular speed = 4.00 rev/s = 4.00 × 2π rad/s = 25.13 rad/s, ω' = = final angular speed, α = angular acceleration = 2.25 rad/s² and t = time = 5.00 s
ω' = ω + αt
= 25.13 rad/s + 2.25 rad/s² × 5.00 s
= 25.13 rad/s + 11.25 rad/s
= 36.38 rad/s
The linear velocity v is gotten from v = rω' where r = radius of pulley = 326 mm/2 = 163 mm = 0.163 m
v = rω'
= 0.163 m × 36.38 rad/s
= 5.93 m/s
So, the linear velocity v = 5.93 m/s
Approximating the eye as a single thin lens 2.70 cmcm from the retina, find the focal length of the eye when it is focused on an object at a distance of 265 cmcm
Answer:
0.37 cm
Explanation:
The image is formed on the retina which is at a constant distance of 2.70 cm to the lens. Therefore, image distance = 2.70 cm.
The object is at a distant of 265 cm to the lens of the eye.
From lens formula,
[tex]\frac{1}{f}[/tex] = [tex]\frac{1}{u}[/tex] + [tex]\frac{1}{v}[/tex]
where: f is the focal length, u is the object distance and v is the image distance.
Thus, u = 265.00 cm and v = 2.70 cm.
[tex]\frac{1}{f}[/tex] = [tex]\frac{1}{265}[/tex] + [tex]\frac{27}{10}[/tex]
= [tex]\frac{10+7155}{2650}[/tex]
[tex]\frac{1}{f}[/tex] = [tex]\frac{7165}{2650}[/tex]
⇒ f = [tex]\frac{2650}{7165}[/tex]
= 0.37
The focal length of the eye is 0.37 cm.
A planar electromagnetic wave is propagating in the +x direction. At a certain point P and at a given instant, the electric field of the wave is given by = (0.082 V/m) . What is the magnetic vector of the wave at the point P at that instant? (c = 3.0 × 108 m/s)
Answer:
[tex]B=2.74\times 10^{-10}\ T[/tex]
Explanation:
It is given that,
A planar electromagnetic wave is propagating in the +x direction.The electric field at a certain point is, E = 0.082 V/m
We need to find the magnetic vector of the wave at the point P at that instant.
The relation between electric field and magnetic field is given by :
[tex]c=\dfrac{E}{B}[/tex]
c is speed of light
B is magnetic field
[tex]B=\dfrac{E}{c}\\\\B=\dfrac{0.082}{3\times 10^8}\\\\B=2.74\times 10^{-10}\ T[/tex]
So, the magnetic vector at point P at that instant is [tex]2.74\times 10^{-10}\ T[/tex].
The magnetic vector of the wave at the point P at that instant is [tex]2.73 \times 10^{-10}T[/tex]
The formula relating electric field and the magnetic field is given as;
[tex]c=\frac{E}{B}[/tex]
E is the electric field strengthB is the magnetic vector of the wavec is the speed of lightFrom the formula shown:
[tex]B=\frac{E}{c}\\B=\frac{0.082}{3.0\times 10^8}\\B=2.73 \times 10 ^{-10}T[/tex]
Hence the magnetic vector of the wave at the point P at that instant is [tex]2.73 \times 10^{-10}T[/tex]
Learn more on magnetic field here: https://brainly.com/question/21040756
How much energy is required to accelerate a spaceship with a rest mass of 121 metric tons to a speed of 0.509 c?
Answer
1.07E22 Joules
Explanation;
We know that mass expands by a factor
=>>1/√[1-(v/c)²]
But v= 0.509c
So
1/√(1 - 0.509²)
=>>> 1/√(1 - 0.2591)
= >> 1/√(0.7409) = 1.16
But given that 121 tons is rest mass so 121- 1.16= 119.84 tons is kinetic energy
And we know that rest mass-energy equivalence is 9 x 10^19 joules per ton.
So Multiplying by 119.84
Kinetic energy will be 1.07x 10^22 joules
A square loop 16.0 cm on a side has a resistance of 6.35 Ω . It is initially in a 0.510 T magnetic field, with its plane perpendicular to B , but is removed from the field in 40.5 ms.
Required:
Calculate the electric energy dissipated in this process.
Answer:
Explanation:
change in magnetic flux = .16 x .16 x .510 - 0
= .013056 weber .
rate of change of flux = change in flux / time
= .013056 / 40.5 x 10⁻³
= .32237
voltage induced = .32237 V
electrical energy dissipated = v² / R where v is voltage , R is resistance
= .32237² / 6.35
= 16.36 x 10⁻³ J .
The heat capacity of object B is twice that of object A. Initially A is at 300 K and B at 450 K. They are placed in thermal contact and the combination is thermally insulated. The final temperature of both objects is
Answer:
The final temperature of both objects is 400 K
Explanation:
The quantity of heat transferred per unit mass is given by;
Q = cΔT
where;
c is the specific heat capacity
ΔT is the change in temperature
The heat transferred by the object A per unit mass is given by;
Q(A) = caΔT
where;
ca is the specific heat capacity of object A
The heat transferred by the object B per unit mass is given by;
Q(B) = cbΔT
where;
cb is the specific heat capacity of object B
The heat lost by object B is equal to heat gained by object A
Q(A) = -Q(B)
But heat capacity of object B is twice that of object A
The final temperature of the two objects is given by
[tex]T_2 = \frac{C_aT_a + C_bT_b}{C_a + C_b}[/tex]
But heat capacity of object B is twice that of object A
[tex]T_2 = \frac{C_aT_a + C_bT_b}{C_a + C_b} \\\\T_2 = \frac{C_aT_a + 2C_aT_b}{C_a + 2C_a}\\\\T_2 = \frac{c_a(T_a + 2T_b)}{3C_a} \\\\T_2 = \frac{T_a + 2T_b}{3}\\\\T_2 = \frac{300 + (2*450)}{3}\\\\T_2 = 400 \ K[/tex]
Therefore, the final temperature of both objects is 400 K.
