Answer:
The amplitude of vibration of the spring is "24 cm"
The periodic vibrating body's motion follows a sinusoidal path. This sinusoidal path is illustrated in the attached picture.
From the picture, it can be clearly seen that the amplitude of the periodic vibration motion is the distance from its mean position to the highest point.
Since the distance of both the highest and the lowest points from the mean position is the same. Therefore, the distance between the lowest and the highest point must be equal to two times the amplitude of the wave.
Amplitude = 24 cm
A load of 25 kg is applied to the lower end and of a steal wire of length 25 m and thickness 3.0mm .The other end of wire is suspeded from a rigid support calculate strain and stress produced in the wire
Answer:
the weight of the wire + 25kg
Explanation:
The image shows a facility that converts the energy of moving water into
electrical energy. What is one advantage of using this technology in place of a
coal-burning power plant?
A. It is fueled by a nonrenewable resource.
B. It causes no harm to ecosystems.
оооо
C. It produces more water pollution.
D. It does not emit greenhouse gases.
Answer:
D. It does not emit greenhouse gases.
Explanation:
D. It does not emit greenhouse gases.
a solenoid that is 98.6 cm long has a cross-sectional area of 24.3 cm2. There are 1310 turns of a wire carrying a current of
Complete question:
A solenoid that is 98.6 cm long has a cross-sectional area of 24.3 cm2. There are 1310 turns of a wire carrying a current of 6.75 A. (a) Calculate the energy density of the magnetic field inside the solenoid. (b) Find the total energy stored in the magnetic field there (neglect end effects).
Answer:
(a) the energy density of the magnetic field inside the solenoid is 50.53 J/m³
(b) the total energy stored in the magnetic field is 0.121 J
Explanation:
Given;
length of the solenoid, L = 98.6 cm = 0.986 m
cross-sectional area of the solenoid, A = 24.3 cm² = 24.3 x 10⁻⁴ m²
number of turns of the solenoid, N = 1310 turns
The magnitude of the magnetic field inside the solenoid is given by;
B = μ₀nI
B = μ₀(N/L)I
Where;
μ₀ is permeability of free space, = 4π x 10⁻⁷ m/A
[tex]B = \frac{4\pi*10^{-7}*1310*6.75}{0.986} \\\\B = 0.01127 \ T[/tex]
(a) Calculate the energy density of the magnetic field inside the solenoid
[tex]u = \frac{B^2}{2 \mu_o}\\\\u = \frac{(0.01127)^2}{2*4\pi *10^{-7}} \\\\u = 50.53 \ J/m^3[/tex]
(b) Find the total energy stored in the magnetic field
U = uV
U = u (AL)
U = 50.53 (24.3 x 10⁻⁴ x 0.986)
U = 0.121 J
7. A sound wave begins traveling through a thin metal rod at one end with a speed that is 15 times the speed of sound in air. If an observer at the other end of the rod hears the sound twice, one from the sound traveling through the rod and one from the sound traveling through the air, with a time delay of 0.12 s, how long is the rod? The speed of sound in air is 343 m/s.
Answer:
L = 44,096 m
Explanation:
The speed of the sound wave is constant therefore we can use the relations of uniform kinematics
v = x / t
the speed of the wave in the bar is
v = 15 v or
v = 15 343
v = 5145 m / s
The sound at the bar goes the distance
L = v t
Sound in the air travels the same distance
L = v_air (t + 0.12)
as the two recognize the same dissonance,
v t = v_air (t +0.12)
t (v- v_air) = 0.12 v_air
t = 0.12 v_air / (v -v_air)
l
et's calculate
t = 0.12 343 / (5145 - 343)
t = 8.57 10-3 s
The length of the bar is
L = 5145 8.57 10-3
L = 44,096 m
Which one of the following actions would make the maxima in the interference pattern from a grating move closer together?
A. Increasing the number of lines per length.
B. Decreasing the number of lines per length.
C. Increasing the distance to the screen.
D. Increasing the wavelength of the laser.
Answer:
Answer:
A. Increasing the number of lines per length.
Two students try to move a heavy box. One pushes with the force of the 20N while the other pulls with a force of 30N in the same direction. What is the work done by each boy after 10 seconds if the box can\t be moved? Show your equation.
Answer:
Explanation:
Time is not part of the Work equation. That's the only conclusion that you can come to.
Work = Force * distance.
Not enough information is given to go any further. You don't have enough information to calculate the distance.
We don't know if the box can be moved or not. It says heavy. 50 N is really not very much.
I would guess that you are intended to answer that the box didn't move, but it's really hard to tell.
A proton, moving north, enters a magnetic field. Because of this field, the proton curves downward. We may conclude that the magnetic field must have a component: _______
a. upward.
b. towards the west.
c. towards the east.
d. towards the north.
e. downward.
Answer:
towards the west
One can conclude that the magnetic field must have a component towards the east. The correct option is c.
What is magnetic field?A magnetic field is a vector field that describes the magnetic influence on moving charges, currents, and magnetic materials.
A moving charge in a magnetic field is subjected to a force that is perpendicular to both its own velocity and the magnetic field.
Every magnet possesses a north as well as a south pole. The opposite poles attract each other, whereas the same poles repel each other.
When you rub a piece of iron against a magnet, the atoms' north-seeking poles line up in the same direction.
Moving north, a proton enters a magnetic field. The proton curves downward as a result of this field. We can conclude that the magnetic field must have an eastward component.
Thus, the correct option is c.
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The hydrogen spectrum has a red line at 656 nm, and a blue line at 434 nm. What is the first order angular separation between the two spectral lines obtained with a diffraction grating with 5000 rulings/cm?
Answer:
Explanation:
grating element or slit width a = 1 x 10⁻² / 5000
= 2 x 10⁻⁶ m
angular width of first order spectral line of wavelength λ
= λ / a
for blue line angular width
= 434 x 10⁻⁹ / 2 x 10⁻⁶ radian
= 217 x 10⁻³ radian
for red line angular width
= 656 x 10⁻⁹ / 2 x 10⁻⁶ radian
= 328 x 10⁻³ radian
difference of their angular width
= 328 x 10⁻³ - 217 x 10⁻³
= 111 x 10⁻³ radian
Ans .
Difference between scissors and nut cracker
A photon has an energy of 2.09×10^-18 kJ .What is its wavelength?
Answer:
wavelength= 1.05 × 10^ -46 m
Explanation:
the formula : λ= hc/E
where; "h" = Planck's constant [6.626 × 10^ -34]
c= speed of light [3.0 × 10^ 8]
you first have to convert the energy of the photon to Joules by dividing the constant by 1000
2.09 × 10^ -18 / 1000 = 2.09 × 10^ -21
then you replace you data into the equation
λ= 6.626 × 10^ -34 × 3.0 × 10^ 8 / 2.09 × 10 ^ -21
first multiply the Planck's constant and the speed of light then divide it by the energy which is in "Joules"
:. λ = 1.05 × 10^ -46
hope this helps
Rank these electromagnetic waves on the basis of their speed (in vacuum). Rank from fastest to slowest.
a. Yellow light
b. FM radio wave
c. Green light
d. X-ray
e. AM radio wave
f. Infrared wave
Answer:
From fastest speed to slowest speed, the electromagnetic waves are ranked as(up to down):
d. X-ray
c. Green light
a. Yellow light
f. Infrared wave
b. FM radio wave
e. AM radio wave
Explanation:
Electromagnetic waves are waves produced as a result of vibrations between an electric field and a magnetic field. The waves have three properties and these properties are frequency, speed and wavelength, which are related by the relationship below
V = Fλ
where:\
V = speed (velocity)
F = frequency
λ = wavelength.
From the relationship above, it is seen that the speed of a wave is directly proportional to its frequency. The higher the frequency, the higher the speed. Therefore, from the list given, the waves with the highest to lowest frequencies/ from left to right are:
X-ray (3×10¹⁹ Hz to 3×10¹⁶Hz), Green light (5.66×10¹⁴Hz), Yellow light (5.17×10¹⁴Hz), Infrared wave (3×10¹¹Hz), FM radio wave (10.8×10⁸Hz to 8.8×10⁷Hz), AM radio wave (1.72 × 10⁶Hz to 5.5×10⁵Hz).
This corresponds to the speed from highest to lowest from left to right.
A train moving west with an initial velocity of 20 m/s accelerates at 4 m/s2 for 10 seconds. During this tim
moves a distance of
meters.
Answer:
400m
Explanation:
[tex]x = v_{0}t + \frac{at^{2} }{2} \\x = 20*10+\frac{4*10x^{2} }{2} = 400m[/tex]two bodies A and B with some asses 20 kg and 30 kg respectively above the ground which have greater potential
Answer:
B has greater potential
Explanation:
We know;
Potential Energy (PE) = mgh
where, m=mass of body
g=acceleration due to gravity
h=height of body
From the formula,
PE is directly proportional to the mass of the body
so the body with greater mass has greater potential.
Radio station WCCO in Minneapolis broadcasts at a frequency of 830 kHz. At a point some distance from the transmitter, the magnetic-field amplitude of the electromagnetic wave from WCCO is 4.82×10-11 T.A) Calculate the wavelength.B) Calculate the wave number.C) Calculate the angular frequency.
D) Calculate the electric-field amplitude.
Answer:
A
[tex]\lambda = 361.45 \ m[/tex]
B
[tex]k = 0.01739 \ rad/m[/tex]
C
[tex]w = 5.22 *10^{6} \ rad/s[/tex]
D
[tex]E = 0.01446 \ N/C[/tex]
Explanation:
From the question we are told that
The frequency is [tex]f = 83 0 \ kHz = 830 *10^{3} \ Hz[/tex]
The magnetic field amplitude is [tex]B = 4.82*10^{-11} \ T[/tex]
Generally wavelength is mathematically represented as
[tex]\lambda = \frac{c}{f}[/tex]
where c is the speed of light with value [tex]c = 3.0*10^{8} \ m/s[/tex]
=> [tex]\lambda = \frac{3.0*10^{8}}{ 830 *10^{3}}[/tex]
=> [tex]\lambda = 361.45 \ m[/tex]
Generally the wave number is mathematically represented as
[tex]k = \frac{2 \pi }{\lambda }[/tex]
=> [tex]k = \frac{2 * 3.142 }{ 361.45 }[/tex]
=> [tex]k = 0.01739 \ rad/m[/tex]
Generally the angular frequency is mathematically represented as
[tex]w = 2 * \pi * f[/tex]
=> [tex]w = 2 * 3.142 * 830*10^{3}[/tex]
=> [tex]w = 5.22 *10^{6} \ rad/s[/tex]
The the electric-field amplitude is mathematically represented as
[tex]E = B * c[/tex]
=> [tex]E = 4.82 *10^{-11} * 3.0*10^{8}[/tex]
=> [tex]E = 0.01446 \ N/C[/tex]
This question involves the concepts of wavelength, frequency, wave number, and electric field.
a) The wavelength is "361.44 m".
b) The wave number is "0.0028 m⁻¹".
c) The angular frequency is "5.22 x 10⁶ rad/s".
d) The electric field amplitude is "0.0145 N/C".
a)
The wavelength can be given by the following formula:
[tex]c=f\lambda[/tex]
where,
c = speed of light = 3 x 10⁸ m/s
f = frequency = 830 KHz = 8.3 x 10⁵ Hz
λ = wavelength = ?
Therefore,
[tex]3\ x\ 10^8\ m/s=(8.3\ x\ 10^5\ Hz)\lambda\\\\\lambda=\frac{3\ x\ 10^8\ m/s}{8.3\ x\ 10^5\ Hz}\\\\[/tex]
λ = 361.44 m
b)
The wave number can be given by the following formula:
[tex]wave\ number = \frac{1}{\lambda} = \frac{1}{361.44\ m}[/tex]
wave number = 0.0028 m⁻¹
c)
The angular frequency is given as follows:
[tex]\omega = 2\pi f = (2)(\pi)(8.3\ x\ 10^5\ Hz)[/tex]
ω = 5.22 x 10⁶ rad/s
d)
The electric field amplitude can be given by the following formula:
[tex]\frac{E}{B} = c\\\\c(B)=E\\\\E = (3\ x\ 10^8\ m/s)(4.82\ x\ 10^{-11}\ T)\\[/tex]
E = 0.0145 N/C
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Lasers are classified according to the eye-damage danger they pose. Class 2 lasers, including many laser pointers, produce visible light with no greater than 1.0 mW total power. They're relatively safe because the eye's blink reflex limits exposure time to 250 ms.
Requried:
a. Find the intensity of a 1-mW class 2 laser with beam diameter 2.0 mm .
b. Find the total energy delivered before the blink reflex shuts the eye.
c. Find the peak electric field in the laser beam.
Answer:
a) 318.2 W/m^2
b) 2.5 x 10^-4 J
c) 1.55 x 10^-8 v/m
Explanation:
Power of laser P = 1 mW = 1 x 10^-3 W
exposure time t = 250 ms = 250 x 10^-3 s
If beam diameter = 2 mm = 2 x 10^-3 m
then
cross-sectional area of beam A = [tex]\pi d^{2} /4[/tex] = (3.142 x [tex](2*10^{-3} )^{2}[/tex])/4
A = 3.142 x 10^-6 m^2
a) Intensity I = P/A
where P is the power of the laser
A is the cros-sectional area of the beam
I = ( 1 x 10^-3)/(3.142 x 10^-6) = 318.2 W/m^2
b) Total energy delivered E = Pt
where P is the power of the beam
t is the exposure time
E = 1 x 10^-3 x 250 x 10^-3 = 2.5 x 10^-4 J
c) The peak electric field is given as
E = [tex]\sqrt{2I/ce_{0} }[/tex]
where I is the intensity of the beam
E is the electric field
c is the speed of light = 3 x 10^8 m/s
[tex]e_{0}[/tex] = 8.85 x 10^9 m kg s^-2 A^-2
E = [tex]\sqrt{2*318.2/3*10^8*8.85*10^9}[/tex] = 1.55 x 10^-8 v/m
(a) The intensity of laser beam is [tex]318.2 \;\rm W/m^{2}[/tex].
(b) The total energy delivered before the blink reflex shuts the eye is [tex]2.5 \times 10^{-4} \;\rm J[/tex].
(c) The required value of peak electric field in the laser beam is [tex]1.55 \times 10^{-8} \;\rm V/m[/tex].
Given data:
The power of laser is, [tex]P=1 \;\rm mW = 1 \times 10^{-3} \;\rm W[/tex].
The exposure time is, [tex]t = 250\;\rm ms = 250 \times 10^{-3} \;\rm s[/tex].
The beam diameter is, [tex]d = 2 \;\rm mm = 2 \times 10^{-3} \;\rm m[/tex].
a)
The standard expression for the intensity of beam is given as,
I = P/A
Here, P is the power of the laser and A is the cross-sectional area of the beam. And its value is,
[tex]A =\pi /4 \times d^{2}\\\\A =\pi /4 \times (2 \times 10^{-3})^{2}\\\\A =3.142 \times 10^{-6} \;\rm m^{2}[/tex]
Then intensity is,
[tex]I = (1 \times 10^{-3})/(3.142 \times 10^{-6})\\\\I =318.2 \;\rm W/m^{2}[/tex]
Thus, the intensity of laser beam is [tex]318.2 \;\rm W/m^{2}[/tex].
(b)
The expression for the total energy delivered is given as,
E = Pt
Solving as,
[tex]E = 1 \times 10^{-3} \times (250 \times 10^{-3})\\\\E = 2.5 \times 10^{-4} \;\rm J[/tex]
Thus, the total energy delivered before the blink reflex shuts the eye is [tex]2.5 \times 10^{-4} \;\rm J[/tex].
(c)
The expression for the peak electric field is given as,
[tex]E = \sqrt{\dfrac{2I}{c \times \epsilon_{0}}}[/tex]
Solving as,
[tex]E = \sqrt{\dfrac{2 \times 318.2}{(3 \times 10^{8}) \times (8.85 \times 10^{9})}}\\\\E =1.55 \times 10^{-8} \;\rm V/m[/tex]
Thus, the required value of peak electric field in the laser beam is [tex]1.55 \times 10^{-8} \;\rm V/m[/tex].
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When you shine a beam of light, which is composed of just two different colors, red and green, onto a diffraction grating which color gets diffracted more
Answer:
The diffraction grating separates light into colors as the light passes through the many fine slits of the grating. This is a transmission grating. ... The prism separates light into colors because each color passes through the prism at a different speed and angle.
A 0.2-stone is attached to a string and swung in a circle of radius 0.6 m on a horizontal and frictionless surface. If the stone makes 150 revolutions per minute, the tension force of the string on the stone is:
Answer:
2960 N
Explanation:
Convert rev/min to rad/s:
150 rev/min × (2π rad/rev) × (1 min / 60 s) = 50π rad/s
Sum of forces in the centripetal direction:
∑F = ma
T = m v² / r
T = m ω² r
T = (0.2 kg) (50π rad/s)² (0.6 m)
T = 2960 N
An 1,820 W toaster, a 1,420 W electric frying pan, and a 55 W lamp are plugged into the same outlet in a 15 A, 120 V circuit. (The three devices are in parallel when plugged into the same socket.)
Required:
a. What current is drawn by each device?
b. Will this combination blow the 15-A fuse?
Answer:
toaster- 15.1A
electric frying pan- 11.8 A
lamp- 0.5 A
b) The combination will blow the fuse.
Explanation:
When devices are connected in parallel, the potential difference across each of the devices is the same but the current through each is different. Hence;
V= 120 V
Power= IV
For the toaster;
I= 1820/120 = 15.1 A
For the electric frying pan;
I= 1420/120 = 11.8 A
For the lamp;
55/120 = 0.5 A
Total current = 15.1 +11.8 + 0.5 = 27.4 A
The combination will blow the fuse.
Explanation:
step one:
Given data
power of toaster= 1,820 W
power of electric frying pan= 1,420 W
power of lamp= 55 W
current of the outlet= 15 A
voltage of outlet = 120 V
step two
since all three appliances are connected in parallel to the socket outlet, they will use the same voltage of 120 V and the currents will be different across each appliance,
Hence the current across the Toaster will be I₁
using P=I₁V we have
I₁= P/V
I₁= 1820/120 = 15.16 A
A. The current drawn by each device
the current across the electric frying pan will be I₂
using P=I₂V we have
I₂= P/V
I₂= 1420/120 = 11.83 A
the current across the lamp will be I₃
using P=I₃V we have
I₃= P/V
I₃= 55/120 = 0.45 A
therefore the total current drawn by all appliances will be
Total current = I₁+I₂+I₃= 15.16 +11.83+ 0.45= 27.44
B. Will this combination blow the 15-A fuse?
27.44 A > 15 A by 45% ...and this will make fuse to blow
An engine causes a car to move 10 meters with a force of 100 N. The engine produces 10,000 J of energy. What is the efficiency of this engine?
Answer:
10%
Explanation:
Efficiency = work done / energy used
e = (10 m × 100 N) / (10,000 J)
e = 0.1
The efficiency is 0.1, or 10%.
Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute. What is their speed?
Explanation:
We know that,
[tex]v(wave \: speed) = f(frequency) \times \alpha (wavelength)[/tex]
frequency (f) = 1 / t (sec) = 8/60 = 0.13 Hz
V ( wave speed) = 0.13 * 120 = 16 m/sec
The speed of the given wave is equal to 15.96 m/s.
What are frequency and wavelength?The frequency of the wave can be defined as the number of oscillations of a wave in one second. The frequency has S.I. units which can be expressed as per second or hertz (Hz).
The wavelength can be described as the distance between the two adjacent points in phase. Two crests or two troughs of a wave are separated by a distance is called wavelength.
The relationship between wavelength (λ), frequency (ν), and wave speed (V):
V = νλ
Given, the frequency of the wave, ν = 8 min⁻¹ = 0.133 s⁻¹
The wavelength of the wave, λ = 120 m
The speed of the waves can calculate from the above-mentioned relationship:
V = νλ = 120 × 0.133 = 15.96 m/s
Therefore, the speed of the wave is equal to 15.96 m/s.
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NASA is doing research on the concept of solar sailing. A solar sailing craft uses a large, low-mass sail and the energy and momentum of sunlight for propulsion.
A) Should the sail be absorptive or reflective? Why?
B)The total power output of the sun is 3.90 × 1026 W . How large a sail is necessary to propel a 1.06 × 104 kg spacecraft against the gravitational force of the sun?
Answer:
A = 6.8 km²
Explanation:
A) The sail should be reflective. This is so that, it can produce the maximum radiation pressure.
B) let's begin with the formula used to calculate the average solar sail in orbit around the sun. Thus;
F_rad = 2IA/c
I is given by the formula;
I = P/(4πr²)
Thus;
F_rad = (2A/c) × (P/(4πr²)) = PA/2cπr²
Where;
A is the area of the sail
r is the distance of the sail from the sun
c is the speed of light = 3 × 10^(8) m/s
P is total power output of the sun = 3.90 × 10^(26) W
Now,F_rad = F_g
Where F_g is gravitational force.
Thus;
PA/2cπr² = G•m•M_sun/r²
r² will cancel out to givw;
PA/2cπ = G•m•M_sun
Making A the subject, we have;
A = (2•c•π•G•m•M_sun)/P
Now, m = 1.06 × 10⁴ kg and M_sun has a standard value of 1.99 × 10^(30) kg
G is gravitational constant and has a value of 6.67 × 10^(-11) Nm²/kg²
Thus;
A = (2 × 3 × 10^(8) × π × 6.67 × 10^(-11) × 1.06 × 10^(4) × 1.99 × 10^(30))/(3.90 × 10^(26))
A = 6.8 × 10^(6) m² = 6.8 km²
2.5: Một người nặng 72kg ngồi trên sàn treo nặng 12kg như hình vẽ. Hỏi người đó
phải kéo dây với một lực bằng bao nhiêu để sàn chuyển động nhanh dần đều lên cao
được 3m trong thời gian là 2s. Tính áp lực của người đó lên sàn.
Answer:
english
Explanation:
Atoms are the particles that all matter is made from. When two or more kinds of atoms combine, they form _______. A. pure elements B. molecules C. metals D. the periodic table
Answer:
Atoms are the particles that all matter is made from. When two or more kinds of atoms combine, they form pure elements
The answer is option A
Answer:
its molecues
Explanation:
A cylinder is given a push and then rolls up an inclined plane. If the origin is the starting point, sketch the position, velocity, and acceleration of the cylinder vs. time as it goes up and then down the plane.
A 5.0 kg block hangs from a spring with spring constant 2000 N/m. The block is pulled down 5.0 cm from the equilibrium position and given an initial velocity of 1.0 m/s back towards equilibrium. a) What is the total mechanical energy of the motion
Answer:
Explanation:i think this would help u
what is the area of velocity time graph
A homeowner purchases insulation for her attic rated at R-15. She wants the attic insulated to R-30. If the insulation she purchased is 10 cm thick, what thickness does she need to use
Answer:
she need to use 20 cm thick
Explanation:
given data
wants the attic insulated = R-30
purchased = 10 cm thick
solution
as per given we can say that
10 cm is for the R 15
but she want for R 30
so
R 30 thickness = [tex]\frac{30}{15} \times 10[/tex]
R 30 thickness = 20 cm
so she need to use 20 cm thick
A 25 cm diameter circular saw blade spins at 3500 rpm. How fast would you have to push a straight hand saw to have the teeth move through the wood at the same rate as the circular saw teeth
Answer:
The answer is "45.79 m/s"
Explanation:
Given values:
diameter= 25 cm
w= 3500 rpm
Formula:
[tex]\boxed{v=w \times r} \ \ \ \ \ \ _{where} \ \ \ w = \frac{rad}{s} \ \ \ and \ \ \ r = meters[/tex]
Calculating r:
[tex]r= \frac{diameter}{2}[/tex]
[tex]=\frac{25}{2}\\\\=12.5 \ cm[/tex]
converting value into meters: [tex]12.5 \times 10^{-2} \ \ meter[/tex]
calculating w:
[tex]w= diameter \times \frac{2\pi}{60}\\[/tex]
[tex]= 3500 \times \frac{2\times 3.14}{60}\\\\= 3500 \times \frac{2\times 314}{6000}\\\\= 35 \times \frac{314}{30}\\\\= 35 \times \frac{314}{30}\\\\=\frac{10990}{30}\\\\=\frac{1099}{3}\\\\=366.33[/tex]
w= 366.33 [tex]\ \ \frac{rad}{s}[/tex]
Calculating v:
[tex]v= w\times r\\[/tex]
[tex]= 366.33 \times 12.5 \times 10^{-2}\\\\= 366.33 \times 12.5 \times 10^{-2}\\\\= 4579.125 \times 10^{-2}\\\\\boxed{=45.79 \ \ \frac{m}{s}}[/tex]
QUESTION 27
The titanium shell of an SR-71 airplane would expand when flying at a speed exceeding 3 times the speed of sound. If the skin of the
plane is 400 degrees C and the linear coefficient of expansion for titanium is 5x10-6/C when flying at 3 times the speed of sound, how
much would a 10-meter long (originally at oC) portion of the airplane expand? Write your final answer in centimeters and show all of your
work.
Answer:
2 cm.
Explanation:
Data obtained from the question include the following:
Original Length (L₁ ) = 10 m
Initial temperature (T₁) = 0°C
Final temperature (T₂) = 400°C
Linear expansivity (α) = 5×10¯⁶ /°C
Increase in length (ΔL) =..?
Next, we shall determine the temperature rise (ΔT).
This can be obtained as follow:
Initial temperature (T₁) = 0°C
Final temperature (T₂) = 400°C
Temperature rise (ΔT) =..?
Temperature rise (ΔT) = T₂ – T₁
Temperature rise (ΔT) = 400 – 0
Temperature rise (ΔT) = 400°C
Thus, we can obtain the increase in length of the airplane by using the following formula as illustrated below:
Linear expansivity (α) = increase in length (ΔL) /Original Length (L₁ ) × Temperature rise (ΔT)
α = ΔL/(L₁ × ΔT)
Original Length (L₁ ) = 10 m
Linear expansivity (α) = 5×10¯⁶ /°C
Temperature rise (ΔT) = 400°C
Increase in length (ΔL) =..?
α = ΔL/(L₁ × ΔT)
5×10¯⁶ = ΔL/(10 × 400)
5×10¯⁶ = ΔL/4000
Cross multiply
ΔL = 5×10¯⁶ × 4000
ΔL = 0.02 m
Converting 0.02 m to cm, we have:
1 m = 100 cm
Therefore, 0.02 m = 0.02 × 100 = 2 cm.
Therefore, the length of the plane will increase by 2 cm.
For a proton (mass = 1.673 x 10–27 kg) moving with a velocity of 2.83 x 104 m/s, what is the de Broglie wavelength (in pm)?
Answer:
The value of de Broglie wavelength is 14.0 pm
Explanation:
Given;
mass of proton, m = 1.673 x 10⁻²⁷ kg
velocity of the proton, v = 2.83 x 10⁴ m/s
De Broglie wavelength is given as;
[tex]\lambda = \frac{h}{mv}[/tex]
where;
h is planck's constant = 6.626 x 10⁻³⁴ kgm²/s
m is mass of the proton
v is the velocity of the proton
[tex]\lambda = \frac{6.626*10^{-34}}{(1.673*10^{-27})(2.83*10^4})} \\\\\lambda = 1.40 *10^{-11} \ m\\\\\lambda = 14.0 \ pm[/tex]
Therefore, the value of de Broglie wavelength is 14.0 pm