Answer:
v = 87.46 m/s
Explanation:
The radial acceleration is the centripetal acceleration, whose formula is given as:
[tex]a_c = \frac{v^2}{r}[/tex]
where,
[tex]a_c[/tex] = centripetal acceleration = 17 m/s²
v = planes's speed = ?
r = radius of path = 450 m
Therefore,
[tex]17\ m/s^2 = \frac{v^2}{450\ m}\\\\v^2 = (17\ m/s^2)(450\ m)\\\\v = \sqrt{7650\ m^2/s^2}[/tex]
v = 87.46 m/s
Monochromatic light is incident on a metal surface and electrons are ejected. If the intensity of the light is increased, what will happen to the ejection rate and maximum energy of the electrons
Answer:
Increase the rate and the same maximum energy of the electrons
Explanation:
According to the photoelectric effect we can say:
The number of electrons, or the electric current, has a linear behaviour with the intensity of the light and a constant behaviour whit the frequency. Therefore, the rate of electrons increases.The kinetic energy of the ejected electrons has a linear dependence on the frequency of the light and has a constant behaviour with the intensity. So, we can say there is the same maximum energy.I hope it helps you!
A mountain biker takes a jump in a race and goes airborne. The mountain bike is travelling at 10.0 m/s before it goes airborne. If the mass of the front wheel on the bike is 750 g and has radius 35 cm, what is the angular momentum of the spinning wheel in the air the moment the bike leaves the ground?
Answer:
Explanation:
The formula for angular momentum is
L = mvr where L is the angular momentum, m is the mass of the object, v is the velocity of the object, and r is the radius of the object. The problem we have that prevents us from just throwing those numbers in there is that mass has to be in kg and it's not, and radius has to be in meters and it's not.
Changing the mass to kg:
750 g = .750 kg
Changing the radius to m:
35 cm = .35 m
Now we can fill in the variables with their respective values:
L = .750(10.0)(.35) gives us
[tex]L=2.625\frac{kg*m^2}{s}[/tex]
elastic wire extend by 1.ocm when a load on 20g range from It, what additional load will it be required Cause the futher extension of 2.0cm
Answer:
40g
Explanation:
20g range > 1.0cm
Therefore,
40g range > 2.0cm
The car has a mass of 0·50 kg. The boy
now increases the speed of the car to 6·0
ms-1 . The total radial friction between
the car and the track has a maximum
value of 7.0 N. Show by calculation that
the car cannot continue to travel in the circular path.
Answer:
A solenoid is a type of electromagnet, the purpose of which is to generate a controlled magnetic field through a coil wound into a tightly packed helix. The coil can be arranged to produce a uniform magnetic field in a volume of space when an electric current is passed through it.
The car cannot continue to travel in the circular path, if the radius of the circular track is less than 2.57 m.
What is meant by centripetal force ?Centripetal force is described as the force applied to a body that is travelling in a circular motion and is pointed in the direction towards the center of the circular path.
Here,
Mass of the car, m = 0.5 kg
Velocity of the car, v = 6 m/s
Radial friction between the car and the track, f = 7 N
The necessary centripetal force for the car to execute the circular motion is provided by the maximum radial frictional force between the car and the track.
So, the condition that the car cannot continue to travel in the circular path is that the centripetal force required is greater than the maximum radial friction.
So,
mv²/r > f
0.5 x 6²/r > 7
Therefore, the radius of the circular track,
r < 18/7
r < 2.57 m
Hence,
The car cannot continue to travel in the circular path, if the radius of the circular track is less than 2.57 m.
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RATIO of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is:
1) 7/29
2) 9/31
3) 5/27
4) 5/23
Answer:
[tex]5/27[/tex]
Explanation:
wavelengths for Lyman series
[tex]\lambda=\frac{1}{R(1-\frac{1}{4} })=\frac{4}{3R}[/tex]
wavelengths for Balmer series
[tex]\lambda_B=\frac{1}{R(\frac{1}{4}-\frac{1}{9}) } =\frac{1}{R(\frac{5}{36}) } =\frac{36}{5R}[/tex]
[tex]\frac{ \lambda_L}{ \lambda_B} =\frac{4}{3R} \times\frac{5R}{36} =5/27[/tex]
OAmalOHopeO
The ratio of longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is 5/27. The correct option is 3.
What is Lyman and Balmer series?
Lyman and Balmer series are sets of spectral lines in the emission spectrum of hydrogen, which result from the transitions of the electron from higher energy levels to lower energy levels.
The Lyman series consists of spectral lines that are produced by transitions of the electron from higher energy levels to the n=1 energy level. These transitions release energy in the form of ultraviolet photons. The lowest energy level in hydrogen is the n=1 energy level, which is also called the ground state. Therefore, the Lyman series includes the transition of the electron from any energy level greater than or equal to n=2 to the ground state.
The Balmer series consists of spectral lines that are produced by transitions of the electron from higher energy levels to the n=2 energy level. These transitions release energy in the form of visible photons. The lowest energy level in the Balmer series is the n=2 energy level. Therefore, the Balmer series includes the transition of the electron from any energy level greater than or equal to n=3 to the n=2 energy level.
Lyman and Balmer's series are named after the scientists who discovered them. The Lyman series is named after Theodore Lyman, an American physicist who discovered the series in 1906. The Balmer series is named after Johann Balmer, a Swiss mathematician who discovered the series in 1885.
Here in the Question,
The longest wavelength in the Lyman series of the hydrogen spectrum corresponds to the transition from the n = 2 energy level to the n = 1 energy level, while the longest wavelength in the Balmer series corresponds to the transition from the n = 3 energy level to the n = 2 energy level.
The wavelengths of these transitions can be calculated using the Rydberg formula:
1/λ = R(1/n1^2 - 1/n2^2)
where λ is the wavelength of the photon emitted, R is the Rydberg constant (1.097 × 10^7 m^-1), and n1 and n2 are the initial and final energy levels of the electron.
For the longest wavelength in the Lyman series, we have n1 = 2 and n2 = 1, so:
1/λ_lyman = R(1/2^2 - 1/1^2) = 3R/4
For the longest wavelength in the Balmer series, we have n1 = 3 and n2 = 2, so:
1/λ_balmer = R(1/3^2 - 1/2^2) = 5R/36
Therefore, the ratio of the longest wavelengths in the Lyman and Balmer series is:
λ_lyman/λ_balmer = (3R/4)/(5R/36) = 27/20
Simplifying this ratio gives:
λ_lyman/λ_balmer = 27/20
Multiplying both the numerator and denominator by 1/3R, we get:
λ_lyman/λ_balmer = (1/2)/(1/3) = 3/2
Therefore, the ratio of the longest wavelengths in the Lyman and Balmer series is 3:2, or 3/5 in fractional form. Simplifying this ratio gives:
λ_lyman/λ_balmer = 5/3
Taking the reciprocal of both sides, we get:
λ_balmer/λ_lyman = 3/5
Therefore, the correct answer is (3) 5/27.
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A race car goes from a complete stop at the start line to 150 miles per hour in 5 seconds. What is its acceleration? Show your work.
Answer:
Explanation:
150/5 = 30
30mph per 1 second
Two divers, G and H, are at depths 20 m and 40 m respectively
below the water surface in lake. The pressure on G is P, while
the pressure on H is P2 if the atmospheric pressure is equivalent
to 10 m of water, then the value of P2/P1 is.
A. 1.67.
B. 2.00.
C. 0.50.
D. 0.60.
Answer:
B
Explanation:
P1/P1 = 40/20
=2
Uuse Lenz's law to explore what happens when an electromagnet is activated a short distance from a wire loop. You will need to use the right-hand rule to find the direction of the induced current.
Answer:
Explanation:
According to the Fleming's right hand rule, if we spread our right hand such that the thumb, fore finger and the middle finger are mutually perpendicular to each other, then the thumb indicates the direction of force, fore finger indicates the direction of magnetic field, then the middle finger indicates the direction of induced current.
According to the Lenz's law, the direction of induced emf is such that it always opposes the cause due to which it is produced.
1. Estimate the buoyant force that air exerts on a man. (To do this, you can estimate his volume by knowing his weight and by assuming that his weight density is about equal to that of water. Assume his weight is 940 N.) answer in N
2.On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 17000 N.
(a) What is the weight of the displaced air?
answer in N
(b) What is the volume of the displaced air?
answer in m^3
Solution :
1. We know that : Buoyant force = weight of the liquid displace
= volume displaced x density of the fluid
Now volume of the man = [tex]$\frac{\text{mass}}{\text{density}}$[/tex]
Mass = weight / g
[tex]$=\frac{940}{9.8}$[/tex]
= 95.92 kg
And density = 1000 [tex]kg/m^3[/tex]
Therefore,
[tex]$\text{volume} = \frac{\text{mass}}{\text{density}}$[/tex]
[tex]$=\frac{95.92}{1000}$[/tex]
= 0.0959 [tex]m^3[/tex]
We know density of air = 1.225 [tex]kg/m^3[/tex]
∴ Mass of air displaced = 0.0959 x 1.225
= 0.1175 kg
Weight of the air displaced = 1.1515 N
Therefore, the buoyant force = 1.1515 N
2). As the balloon is not accelerated, the net force acting on it is zero.
Thus the weight that acts downwards = buoyant force upwards
So, the weight of the air displaced = weight of the balloon
= 17000 N
Therefore, the mass of the air displaced = volume of the air displaced (volume of the balloon) x density of air
[tex]$\frac{17000}{9.8} = \text{volume of air} \times 1.225$[/tex]
[tex]$\text{Volume of air displaced} = \frac{1700}{9.8 \times 1.225}$[/tex]
= 1416.0766 [tex]m^3[/tex]
Ayudaaa :(
Calcula la resistencia total del siguiente circuito eléctrico.
A 150g copper bowl contains 220g of water, both at 20.0oC, A very hot 300 g copper cylinder is dropped into the water, causing the water to boil, with 5.00 g being converted to steam. The final temperature of the system is 100oC, Neglect energy transfers with the environment.
a) How much energy (in calories) is transfered to the water as heat?
b) How much to the bowl?
c) What is the original temperature of the cylinder?
We have that the energy (in calories) is transferred to the water as heat,to the bowl and the original temperature of the cylinder is mathematically given as
Qw=20.3 kcal Q= 1.11 kcal Ti=873°CEnergy
Generally the equation for the is mathematically given as
(a)
The heat transferred to the H20
Qw= CwMwdT+Lvms
Qw=((220g)(100°C-20.0T)+(539 caVg)(5.00 g)
Qw=20.3 kcal .
(b)
The heat transferred to the bowl is
Qb= CbmbdT
Q= (0.0923 cal/gC)(150g)(100°C-20.0°C)
Q= 1.11 kcal
(c)
original temperature of the cylinder
-Qw- Qb = CcMc(T2-T1)
[tex]T1=\frac{Qw+Qm}{CcMc}+T2[/tex]
T1=873C
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Question 3 of 10
What has the same value no matter where it is located in the universe?
A. Volume
B. Weight
C. Mass
D. Density
Reset Selection
Answer:
C. Mass
Explanation:
In order to test an intentionally weak adhesive, the bottom of the small 0.15-lb block is coated with adhesive and then the block is pressed onto the turntable with a known force. The turntable starts from rest at t = 0 and uniformly accelerates with a = 2 rad/s^2. If the adhesive fails at exactly t = 3 s, then determine:
a. the magnitude of the ultimate shear force that the adhesive supports
b. the angular displacement of the turntable at the time of failure
Answer:
answer
Explanation:
it is the answer which was presented in the year
g Light that is incident upon the eye is refracted several times before it reaches the retina. As light passes through the eye, at which boundary does most of the overall refraction occur?
Answer
Explanation
:giác mạc
Two long straight wires are suspended vertically. The wires are connected in series, and a current from a battery is maintained in them. What happens to the wires? What happens if the battery is replaced by an a-c source?
Answer:
(i) When a battery is connected inseries to two long parallel wires, the currents in the two wires will be in opposite directions. Due to which a force of repulsion will be acting between them and they are moving further apart.
(ii) When a battery is connected in parallel to two long parallel wires, the currents in the two wires will be in same direction. Due to it, a force of attraction will be acting between them and they are coming closer to each other.
hope it's help you ....!!!!!
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Explanation:
Hope it will helps you lot!
Earth’s Moon has a diameter of 3,474 km and orbits at an average distance of 384,000 km. At that distance it subtends and angle just slightly larger than half a degree in Earth’s sky. Pluto’s moon Charon has a diameter of 1,186 km and orbits at a distance of 19,600 km from the dwarf planet. Compare the appearance of Charon in Pluto’s skies with the Moon in Earth’s skies. Describe where in the sky Charon would appear as seen from various locations on Pluto.
The reason for arriving at the above solutions is as follows:
The given dimensions and distance from the Earth of the Moon are;
The diameter of the Moon, d = 3,474 km
The average distance of the Moon from the Earth, R = 384,000 km
Required:
The comparison between Charon's appearance in Pluto and the Moon's appearance on Earth Earth
Solution:
The distance of the Moon's travels in an orbit, C = 2·π·R
∴ C = 2 × π × 384,000 km
The angle subtended by the Moon, θ = d/C × 360°
∴ θ = 3,474/(2 × π × 384,000) × 360° ≈ 0.518°
Pluto's moon Charon, has the following parameters;
The diameter of the Charon, d₂ = 1,186 km
The average distance of the Charon from Pluto, R₂ = 19,600 km
Therefore, the distance of the Moon's travels in an orbit, C₂ = 2·π·R₂
∴ C₂ = 2 × π × 19,600 km
The angle subtended by the Moon, θ₂ = d₂/C₂ × 360°
∴ θ₂ = 1,186/(2 × π × 19,900) × 360° ≈ 3.415°
The angle subtended by Charon in Pluto's sky ≈ 3.415°
Charon therefore, appears 7 times larger in Pluto's skies than the Moon's appearance in Earth's skies
Required:
The appearance of Charon as seen from different locations on Pluto
Solution:
Charon is gravitationally locked to Pluto, therefore, the same side of Pluto is faced with the same side of Charon
Therefore;
Charon appears constantly overhead from the side of Pluto locked to CharonCharon appears constantly at the horizon from the poles on either side of the axis of rotation of Pluto and CharonLearn more about Pluto's moon Charon here:
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Which of the following statements about magnetism is TRUE?
a) The direction of the magnetic force on a current-carrying wire is parallel to the wire.
b) Magnetic poles always occur in pairs (N and S).
c) Magnetic field lines begin at south poles and end on north poles.
d) Moving charges do not experience a force in magnetic fields.
Two circular coils are concentric and lie in the same plane.The inner coil contains 120 turns of wire, has a radius of 0.012m,and carries a current of 6.0A. The outer coil contains 150turns and has a radius of 0.017 m. What must be the magnitudeand direction (relative to the current in the inner coil) ofthe current in the outer coil, such that the net magnetic field atthe common center of the two coils is zero?
Answer:
[tex]I_2=6.8A[/tex]
Explanation:
From the question we are told that:
Turns of inner coil [tex]N_1=120[/tex]
Radius of inner coil [tex]r_1=0.012m[/tex]
Current of inner coil [tex]I_1=6.0A[/tex]
Turns of Outer coil [tex]N_2=150[/tex]
Radius of Outer coil [tex]r_2=0.017m[/tex]
Generally the equation for Magnetic Field is mathematically given by
[tex]B =\frac{ \mu N I}{2R}[/tex]
Therefore
Condition for the net Magnetic field to be zero
[tex]\frac{N_1* I_1}{( 2 * r_1 )}=\frac{N_2 * I_2}{2 * r_2}[/tex]
[tex]I_2=\frac{(N_1* I_1)*(( 2 * r_2)}{( 2 * r_1)*N_2}[/tex]
[tex]I_2=\frac{(120*6.0)*(( 2 * 0.017)}{( 2 * 0.012)*150}[/tex]
[tex]I_2=6.8A[/tex]
Which of the following measures is equal to 700 km?
Answer:
1km=1000m
700km=
700×1000=700000
=700000metres
hope this helps
A roller coaster has a total track length of 500 yards. A complete ride on the roller coaster is considered two times around the track. The start and stop places for the ride are virtually the same. What are the distance and displacement for a ride on the roller coaster? Explain your answers.
Answer:
Explanation:
its 1000 yards if its going around the track 2 times and that if one whole around the track is 500 its 500 x 2
A 1.50 kg book is sliding along a rough horizontal surface. At point A it is moving at 3.21 m/s , and at point B it has slowed to 1.25 m/s .
Part A
How much work was done on the book between A and B ?
Part B
If -0.750J of work is done on the book from B to C , how fast is it moving at point C ?
Part C
How fast would it be moving at C if 0.750J of work were done on it from B to C ?
I assume friction is the only force acting on the book as it slides.
(A) By the work-energy theorem, the total work performed on the book as it slides is equal to the change in its kinetic energy:
W = ∆K
W = 1/2 (1.50 kg) (1.25 m/s)² - 1/2 (1.50 kg) (3.21 m/s)²
W ≈ -6.56 J
(B) Using the work-energy theorem again, the speed v of the book at point C is such that
-0.750 J = 1/2 (1.50 kg) v ² - 1/2 (1.50 kg) (1.25 m/s)²
==> v = 0.750 m/s
(C) Take the left side to be positive, then solve again for v.
0.750 J = 1/2 (1.50 kg) v ² - 1/2 (1.50 kg) (1.25 m/s)²
==> v ≈ 1.60 m/s
a standard bathroom scale is placed on an elevator. A 34 kg boy enters the elevator on the first floor and steps on the scale. What will the scale read (in newtons) when the elevator begins to accelerate upward at 0.4 m/s2
Answer:F = 255 N
Explanation:
It is given that,
Mass of the boy, m = 25 kg
Acceleration of the elevator,
The elevator is accelerating in upward direction. The net force acting on the boy is given by :
g is the acceleration due to gravity
F = 255 N
The scale reading is 255 N as it begins to accelerate upward. hence, this is the required solution.
krichoffs law of current questions
Answer:
Explanation:
Kirchhoff's Current Law, often shortened to KCL, states that “The algebraic sum of all currents entering and exiting a node must equal zero.
#I AM ILLITERATE
Light of a given wavelength is used to illuminate the surface of a metal, however, no photoelectrons are emitted. In order to cause electrons to be ejected from the surface of this metal you should: ___________
a. use light of the same wavelength but increase its intensity.
b. use light of a shorter wavelength.
c. use light of the same wavelength but decrease its intensity.
d. use light of a longer wavelength.
Answer:
use light of the same wavelength but decrease it's intensity
Two masses of 3 kg and 5 kg are connected by a light string that passes over a smooth polley as shown in the Figure.
QL
Determine:
i. the tension in the string,
ii. the acceleration of each mass, and
iii. the distance each mass moves in the first second of motion if they start from rest
i. [tex]T = 36.8\:\text{N}[/tex]
ii. [tex]a = 2.45\:\text{m/s}^2[/tex]
iii. [tex]x = 1.23\:\text{m}[/tex]
Explanation:
Let's write Newton's 2nd law for each object. We will use the sign convention assigned for each as indicated in the figure. Let T be the tension on the string and assume that the string is inextensible so that the two tensions on the strings are equal. Also, let a be the acceleration of the two masses. And [tex]m_1 = 3\:\text{kg}[/tex] and [tex]m_2 = 5\:\text{kg}[/tex]
Forces acting on m1:
[tex]T - m_1g = m_1a\:\:\:\:\:\:\:(1)[/tex]
Forces acting on m2:
[tex]m_2g - T = m_2a\:\:\:\:\:\:\:(2)[/tex]
Combining Eqn(1) and Eqn(2) together, the tensions will cancel out, giving us
[tex]m_2g - m_1g = m_2a + m_1a[/tex]
or
[tex](m_2 - m_1)g = (m2 + m_1)a[/tex]
Solving for a,
[tex]a = \left(\dfrac{m_2 - m_1}{m_2 + m_1}\right)g[/tex]
[tex]\:\:\:\:= \left(\dfrac{5\:\text{kg} - 3\:\text{kg}}{5\:\text{kg} + 3\:\text{kg}}\right)(9.8\:\text{m/s}^2)[/tex]
[tex]\:\:\:\:= 2.45\:\text{m/s}^2[/tex]
We can solve for the tension by using this value of acceleration on either Eqn(1) or Eqn(2). Let's use Eqn(1).
[tex]T - (3\:\text{kg})(9.8\:\text{m/s}^2) = (3\:\text{kg})(2.45\:\text{m/s}^2)[/tex]
[tex]T = (3\:\text{kg})(9.8\:\text{m/s}^2) + (3\:\text{kg})(2.45\:\text{m/s}^2)[/tex]
[tex]\:\:\:\:= 29.4\:\text{m/s}^2 + 7.35\:\text{m/s}^2 = 36.8\:\text{N}[/tex]
Assuming that the two objects start from rest, the distance that they travel after one second is given by
[tex]x = \frac{1}{2}at^2 = \frac{1}{2}(2.45\:\text{m/s}^2)(1\:\text{s})^2 = 1.23\:\text{m}[/tex]
What is the order of magnitude of the distance of Sun to nearest star in meters?
Answer:
Approximating the Milky Way as a disk and using the density in the solar neighborhood, there are about 100 billion stars in the Milky Way.
Explanation:
Since we are making an order of magnitude estimate, we will make a series of simplifying assumptions to get an answer that is roughly right.
Let's model the Milky Way galaxy as a disk.
The volume of a disk is:
V
=
π
⋅
r
2
⋅
h
Plugging in our numbers (and assuming that
π
≈
3
)
V
=
π
⋅
(
10
21
m
)
2
⋅
(
10
19
m
)
V
=
3
×
10
61
m
3
Is the approximate volume of the Milky Way.
Now, all we need to do is find how many stars per cubic meter (
ρ
) are in the Milky Way and we can find the total number of stars.
Let's look at the neighborhood around the Sun. We know that in a sphere with a radius of
4
×
10
16
m there is exactly one star (the Sun), after that you hit other stars. We can use that to estimate a rough density for the Milky Way.
ρ
=
n
V
Using the volume of a sphere
V
=
4
3
π
r
3
ρ
=
1
4
3
π
(
4
×
10
16
m
)
3
ρ
=
1
256
10
−
48
stars /
m
3
Going back to the density equation:
ρ
=
n
V
n
=
ρ
V
Plugging in the density of the solar neighborhood and the volume of the Milky Way:
n
=
(
1
256
10
−
48
m
−
3
)
⋅
(
3
×
10
61
m
3
)
n
=
3
256
10
13
n
=
1
×
10
11
stars (or 100 billion stars)
Is this reasonable? Other estimates say that there are are 100-400 billion stars in the Milky Way. This is exactly what we found.
Answer:
Mercury, 46,001,272 km from the sun at the nearest point.
Explanation:
What is hydroelectric power ?
Answer quickly..!
Answer:
It's electricity produced from hydropower. It's also a form of energy that controls the power of water motion.
Explanation:
One pro about hydroelectric power is that it's renewable energy. But one con about hydroelectric power is that it can impact the environment in a negative way.
A cylindrical wire made of an unknown alloy hangs from a support in the ceiling. You measure the relaxed length of the wire to be 16 m long; and the radius of the wire to be 3.5 m. When hang a 5 kg mass from the wire, you measure that it stretches a distance of 4 x 10 m The average bond length between atoms is 2.3 x 10^0 m for th alloy.
Required:
What is the stiffness of a typical interatomic bond in the alloy
Answer: hello some of your values are wrongly written hence I will resolve your question using the right values
answer:
stiffness = 1.09 * 10^-6 N/m
Explanation:
Given data:
Length ( l ) = 16 m
radius of wire ( r ) = 3.5 m
mass ( m ) = 5kg
Distance stretched ( Δl ) = 4 * 10^-3 m ( right value )
average bond length ( between atoms ) = 2.3 * 10^-10 m ( right value)
first step : calculate the area
area ( A ) = πr^2 = π * ( 3.5)^2 = 38.48 m^2
γ = MgL / A Δl
= [ (5 * 9.81 * 16 ) / ( 38.48 * (4.3*10^-3) ) ]
= 784.8 / 0.165 = 4756.36 N/m^2
hence : stiffness = γ * bond length
= 4756.36 * 2.3 * 10^-10 = 1.09 * 10^-6 N/m
In these formulas, it is useful to understand which variables are parameters that specify the nature of the wave. The variables E0E0E_0 and B0B0B_0 are the __________ of the electric and magnetic fields. Choose the best answer to fill in the blank.
1. There is a famous intersection in Kuala Lumpur, Malaysia, where thousands of vehicles pass each hour. A 750 kg Tesla Model S traveling south crashes into a 1250 kg Ford F-150 traveling east. What are the initial speeds of each vehicle before collision if they stick together after crashing into each other and move at an angle of 320 and a common velocity of 18 m/s.
Solution :
Let the positive [tex]x-axis[/tex] is along the East and the positive [tex]y[/tex] direction is along the north.
Given :
Mass of the Tesla car, [tex]m_1[/tex] = [tex]750 \ kg[/tex]
Mass of the Ford car, [tex]m_2 = 1250 \ kg[/tex]
Now let the initial velocity of Tesla car in the south direction be = [tex]-v_1j[/tex]
The initial momentum of Tesla car, [tex]p_1 = -750 \ v_1[/tex]
Let the initial velocity of Ford car in the east direction be = [tex]v_2 \ i[/tex]
So the initial momentum of the Ford car is [tex]p_2=1250\ v_2 \ i[/tex]
Therefore, the initial velocity of both the cars is [tex]p_i = p_1+p_2[/tex]
[tex]=1250 \ v_2 \ i - 750\ v_1 \ j[/tex]
Now the final velocity of both the cars is [tex]v = 18 \ m/s[/tex]
So the vector form is :
[tex]v = 18\cos 32\ i-18 \sin 32 \ j[/tex]
[tex]= 15.26 \ i - 9.54 \ j[/tex]
Therefore the momentum after the accident is
[tex]p_f=(m_1+m_2) \times v[/tex]
[tex]=(750+1250) \times (15.26 \ i - 9.54 \ j)[/tex]
[tex]= 30520\ i -19080\ j[/tex]
According to the law of conservation of momentum, we know
[tex]p_i = p_f[/tex]
[tex]1250 \ v_2 \ i - 750\ v_1 \ j[/tex] [tex]= 30520\ i -19080\ j[/tex]
[tex]1250 \ v_2 = 30520[/tex]
[tex]v_2=24.4 \ m/s[/tex]
From, [tex]750\ v_1 = 19080[/tex]
We get, [tex]v_1=25.4 \ m/s[/tex]
Therefore the speed of Tesla car before collision = 25.4 m/s
The speed of ford car before collision = 24.4 m/s
