Answer:
a) ∆x∆v = 5.78*10^-5
∆v = 1157.08 m/s
b) 4.32*10^{-11}
Explanation:
To solve this problem you use the Heisenberg's uncertainty principle, that is given by:
[tex]\Delta x\Delta p \geq \frac{\hbar}{2}[/tex]
where h is the Planck's constant (6.62*10^-34 J s).
If you assume that the mass of the electron is constant you have:
[tex]\Delta x \Delta (m_ev)=m_e\Delta x\Delta v \geq \frac{\hbar}{2}[/tex]
you use the value of the mass of an electron (9.61*10^-31 kg), and the uncertainty in the position of the electron (50nm), in order to calculate ∆x∆v and ∆v:
[tex]\Delta x \Delta v\geq\frac{\hbar}{2m_e}=\frac{(1.055*10^{-34}Js)}{2(9.1*10^{-31}kg)}=5.78*10^{-5}\ m^2/s[/tex]
[tex]\Delta v\geq\frac{5.78*10^{-5}}{50*10^{-9}m}=1157.08\frac{m}{s}[/tex]
If the electron is a classical particle, the time it takes to traverse the channel is (by using the edge of the uncertainty in the velocity):
[tex]t=\frac{x}{v}=\frac{50*10^{-9}m}{1157.08m/s}=4.32*10^{-11}s[/tex]
In a long distance race, the athletes were expected to take four rounds of the track such that the line of finish was the same as the track was 200 m. (i) What is the total distance to be covered by the athletes? (ii) What is the displacement of the athletes when they touch the finish line? (iii) Is the motion of the athletes uniform or non uniform? (iv) Is the distance moved by and displacement of athletes at the end of the race equal?
Answer:
1) The track is 200 meters long, the athletes do 4 rounds, so the total distance ran is:
4*200 meters = 800 meters
2) The displacement is defined as the difference between the final position and the initial position.
When you are in a track, and you run a full round, you end in the same position where you started, so the total displacement is 0 meters.
3) As they are running in a closed track (for example, a circular track), they must change the direction of motion at some point, so the motion is not uniform (uniform motion happens when the movement is always in the same direction and always at the same speed)
4) no, is not equal because in the end, the total distance is 800 meters and the displacement is 0 meters.
A small, positively charged ball is moved close to a large, positively charged ball. Which describes how the small ball likely responds when it is released?
It will move toward the large ball because like charges repel.
It will move toward the large ball because like charges attract.
It will move away from the large ball because like charges repel.
It will move away from the large ball because like charges attract.
Answer:
C
Explanation:
i took the test
A small, positively charged ball is moved close to a large, positively charged ball. "It will move away from the large ball because like charges repel." The correct option is A.
Charge Interaction: The behavior of charged objects is governed by the fundamental principle that opposite charges attract each other, and like charges repel each other.
Coulomb's Law: Coulomb's Law describes the electrostatic force between two charged objects. It states that the force of attraction or repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Repulsion: Because both the small and large balls have a positive charge, they will exert a repulsive force on each other when they are in close proximity.
Movement Away: When the small ball is released near the large ball, it will experience this repulsive force, causing it to move away from the large ball.
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A small spotlight mounted in the bottom of a swimming pool that is 4.5 m deep emits light in all directions. On the surface of the pool, directly above the light, the area illuminated is a circle. Determine the maximum radius of this circle. The index of refraction of water is 1.33.
Answer:
Maximum radius = 5.1m
Explanation:
For us to get the radius of the circle of light, we have to first calculate the critical angle which is the angle of incidence above which total internal reflection occurs, i.e. the angle of incidence when θ2 = 90° .
At the point where the total internal reflection occurs, the light ray doesn't pass through the interface, thus, this point is on the edge of the circle of light.
From Snell's law, we have:
n_water * sin (θ1) = n_air * sin(θ2)
Thus;
sin(θ1) = n_air/(n_water * sin(θ2))
Since the critical angle is the value of θ1 when θ2 = 90° and that sin(90°) =1, thus;
sin(θ1) = (n_air/n_water) * sin(90°) = n_air/n_water
We are told the Refractive index of water is 1.33. meanwhile the Refractive index of air is not given but it has a constant value of 1.
Thus, we can determine θ1:
sin(θ1) = (nair/nwater) = 1/1.33
sin(θ1) = 1/1.33
(θ1) = sin^(-1)(1/1.33)
(θ1) = 48.75°
The question when looked at critically, depicts a right triangle with vertices including the light and the extremity of the circle, and we know one of its angles(θ1 = 48.75°) and one of its sides(4.5 m).
Thus, from trigonometric ratio, we can determine the radius as;
r/4.5 = tan(θ1)
r = 4.5tan(48.75°) = 5.1 m
Two equal masses m are constrained to move without friction, one on the positive x axis and one on the positive y axis. They are attached to two identical springs (force constant k) whose other ends are attached to the origin. In addition, the two masses are connected to each other by a third spring of force constant k', The springs are chosen so that the system is in equilibrium with all three springs relaxed (length equal to unstretched length). What are the normal frequencies? Find and describe the normal modes
Answer:
Check the explanation
Explanation:
The potential energy (is the energy by virtue of a particular object's location relative to that of other objects. This term is most of the time linked or associated with restoring forces such as a spring or the force of gravity.) seems to be U = mgy [tex](1/2)(k k')(x^2 y^2)[/tex]. In fact, the mgy term has disappeared from the development.
Kindly check the attached image below for the step by step explanation to the question above.
Which statements are true about the flow of blood in the body? Check all that apply.
Answer:
i need some explanation
Explanation:
The correct statements are D, C, and E. Blood flows from the heart to the lungs to pick up oxygen and then to the rest of the body to deliver oxygen, sugar, and nutrients while collecting carbon dioxide.
Understanding the flow of blood in the body is essential. Here are the correct statements regarding blood circulation:
D.) Blood flows from the heart to the lungs to pick up oxygen.C.) Blood picks up carbon dioxide from the cells of the body.E.) Blood delivers sugar and nutrients to cells in the body.The heart pumps oxygen-poor blood to the lungs through the pulmonary circuit where it releases carbon dioxide and picks up oxygen.
The oxygen-rich blood is then pumped through the systemic circuit to the rest of the body, delivering oxygen, sugar, and nutrients to the cells and collecting carbon dioxide to be expelled during the next circulation.
Therefore, the correct statements are D, C, and E.
Complete Question
Which statements are true about the flow of blood in the body? Check all that apply.
A. Blood picks up oxygen from the cells of the body.
B. Blood delivers carbon dioxide to cells in the body.
C. Blood picks up carbon dioxide from the cells of the body.
D. Blood flows from the heart to the lungs to pick up oxygen.
E. Blood delivers sugar and nutrients to cells in the body.
F. Blood flows from the lungs to the heart to pick up oxygen.
Two forces act on a block as shown in the picture.
Right
20 N
Left
10 N
What is the net force on the block?
Answer:
10n to the right
Explanation:
Acceleration is measured in m/s/s (meters per second squared).
True or False
Answer:
true
Explanation:
Answer:true
Explanation:
Acceleration is measured in meters per second squared
After landing on an unexplored Klingon planet, Spock tests for the direction of the magnetic field by firing a beam of electrons in various directions and by observing the following: Electrons moving upward feel a magnetic force in the NW direction; Electrons moving horizontally North are pushed down; Electrons moving horizontally South-East are pushed upward. He naturally concludes that the magnetic field at this landing site is in which direction?
Answer:
Magnetic field is in south west direction .
Explanation:
Let us represent various direction by i , j, k . i representing east , j representing north and k representing vertically upward direction .
magnetic field is represented vectorially as follows
B = B₀ ( - i - j )
In the first case velocity of electron
v = v k
Force = q ( v x B )
= -e [ vk x B₀ ( - i - j ) ]
= evB₀ ( j -i )
Direction of force is north -west .
In the second case velocity of electron
v = vj
Force = -e [ vj x B₀ ( - i - j ) ]
= - evB₀ k
force is downward
In the third case, velocity of electron
v = v( -j +i )
Force = -e [ v( -j +i ) x B₀ ( - i - j ) ]
= 2 evB₀ k
Force is upward.
An electron is confined in a harmonic oscillator potential well. A photon is emitted when the electron undergoes a 3→1 quantum jump. What is the wavelength of the emission if the net force on the electron behaves as though it has a spring constant of 3.6 N/m? (m el = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J, ħ = 1.055 × 10-34 J · s, h = 6.626 × 10-34 J · s)
Answer:
4.74*10^-7 m
Explanation:
TO find the wavelength of the photon you calculate the energy of the photon emitted in a harmonic oscillator:
[tex]E_{m-n}=\hbar \omega(m+\frac{1}{2})-\hbar \omega(n+\frac{1}{2})=\hbar \omega (m-n)\\\\\omega=\sqrt{\frac{k}{m}}\\\\E_{m-n}=\hbar \sqrt{\frac{k}{m}}(m-n)[/tex]
m: initial state = 3
n: final state = 1
k = 3.6N/m
By replacing the values of m for the electron, m,n and ħ you obtain:
[tex]E_{m-n}=(1.055*10^{-34}Js)\sqrt\frac{3.6N/m}{9.11*10^{-31}kg}}(3-1)=4.19*10^{-19}J[/tex]
Furthermore, this energy is equivalent to the expression:
[tex]E_{3-1}=\hbar \omega=\hbar 2\pi \nu=2\pi \hbar\frac{c}{\lambda}\\\\\lambda=\frac{2\pi \hbar c}{E_{3-1}}[/tex]
By replacing you obtain:
[tex]\lambda=\frac{2\pi (1.055*10^{-34}Js)(3*10^8m/s)}{4.19*10^{-19}J}=4.74*10^{-7}m[/tex]
hence, the wavelength of the photon is 4.74*10^-7 m
The wavelength of the emission if the net force on the electron behaves as though it has a spring constant of 3.6 N/m - [tex]4.74\times10^-7 m[/tex]
Formula:The energy of the photon emitted in a harmonic oscillator:
[tex]E_{m-n}=\hbar \omega(m+\frac{1}{2})-\hbar \omega(n+\frac{1}{2})=\hbar \omega (m-n)\\\\\omega=\sqrt{\frac{k}{m}}\\\\E_{m-n}=\hbar \sqrt{\frac{k}{m}}(m-n)[/tex]
Given:m: initial state = 3
n: final state = 1
k = 3.6N/m
Solution:By replacing the values of m for the electron, m, n and ħ you obtain:
this energy is equivalent to the expression:[tex]E_{3-1}=\hbar \omega=\hbar 2\pi \nu=2\pi \hbar\frac{c}{\lambda}\\\\\lambda=\frac{2\pi \hbar c}{E_{3-1}}[/tex]
By replacing you obtain:Thus, the wavelength of the photon is [tex]4.74\times10^-7 m[/tex]
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A 300 MHz electromagnetic wave in air (medium 1) is normally incident on the planar boundary of a lossless dielectric medium with ϵr = 9 (medium 2). What is the wavelength of the incident wave and the wave in medium 2? What are the intrinsic impedances of media 1 and 2? What are the reflection coefficient and the transmission coefficient at the boundary? If the amplitude of the incident electric field is 10 V/m, what are the maximum amplitudes of the total fields in media 1 and 2? A standing wave pattern appears in medium 1. What are the locations of the first minimum and maximum?
Answer:
Wavelength of the incident wave in air = 1 m
Wavelength of the incident wave in medium 2 = 0.33 m
Intrinsic impedance of media 1 = 377 ohms
Intrinsic impedance of media 2 = 125.68 ohms
Check the explanation section for a better understanding
Explanation:
a) Wavelength of the incident wave in air
The frequency of the electromagnetic wave in air, f = 300 MHz = 3 * 10⁸ Hz
Speed of light in air, c = 3 * 10⁸ Hz
Wavelength of the incident wave in air:
[tex]\lambda_{air} = \frac{c}{f} \\\lambda_{air} = \frac{3 * 10^{8} }{3 * 10^{8}} \\\lambda_{air} = 1 m[/tex]
Wavelength of the incident wave in medium 2
The refractive index of air in the lossless dielectric medium:
[tex]n = \sqrt{\epsilon_{r} } \\n = \sqrt{9 }\\n =3[/tex]
[tex]\lambda_{2} = \frac{c}{nf}\\\lambda_{2} = \frac{3 * 10^{6} }{3 * 3 * 10^{6}}\\\lambda_{2} = 1/3\\\lambda_{2} = 0.33 m[/tex]
b) Intrinsic impedances of media 1 and media 2
The intrinsic impedance of media 1 is given as:
[tex]n_1 = \sqrt{\frac{\mu_0}{\epsilon_{0} } }[/tex]
Permeability of free space, [tex]\mu_{0} = 4 \pi * 10^{-7} H/m[/tex]
Permittivity for air, [tex]\epsilon_{0} = 8.84 * 10^{-12} F/m[/tex]
[tex]n_1 = \sqrt{\frac{4\pi * 10^{-7} }{8.84 * 10^{-12} } }[/tex]
[tex]n_1 = 377 \Omega[/tex]
The intrinsic impedance of media 2 is given as:
[tex]n_2 = \sqrt{\frac{\mu_r \mu_0}{\epsilon_r \epsilon_{0} } }[/tex]
Permeability of free space, [tex]\mu_{0} = 4 \pi * 10^{-7} H/m[/tex]
Permittivity for air, [tex]\epsilon_{0} = 8.84 * 10^{-12} F/m[/tex]
ϵr = 9
[tex]n_2 = \sqrt{\frac{4\pi * 10^{-7} *1 }{8.84 * 10^{-12} *9 } }[/tex]
[tex]n_2 = 125.68 \Omega[/tex]
c) The reflection coefficient,r and the transmission coefficient,t at the boundary.
Reflection coefficient, [tex]r = \frac{n - n_{0} }{n + n_{0} }[/tex]
You didn't put the refractive index at the boundary in the question, you can substitute it into the formula above to find it.
[tex]r = \frac{3 - n_{0} }{3 + n_{0} }[/tex]
Transmission coefficient at the boundary, t = r -1
d) The amplitude of the incident electric field is [tex]E_{0} = 10 V/m[/tex]
Maximum amplitudes in the total field is given by:
[tex]E = tE_{0}[/tex] and [tex]E = r E_{0}[/tex]
E = 10r, E = 10t
A helicopter, which starts directly above you, lands at a point that is 4.50 km from your present location and in a direction that is 25° north of east. You want to meet the helicopter at it's landing site, however, you must travel along streets that are oriented either east-west or north-south. What is the minimum distance you must travel to reach the helicopter?
Answer:
5.98 km
Explanation:
This question can be easily solved by using the trigonometric properties of a right angled triangle.
See attachment for pictorial explanation
To get x we have
Sinθ = opp / hyp
Sin25 = x / 4.5
x = 4.5 sin 25
x = 4.5 * 0.423
x = 1.9 km
To get y, we have
Cosθ = adj / hyp
Cos25 = y / 4.5
y = 4.5 cos 25
y = 4.5 * 0.906
y = 4.08 km
x + y = 1.9 + 4.09 = 5.98 km
Thus, the minimum distance required is 5.98 km
Final answer:
To find the minimum distance to the helicopter, calculate the eastward and northward components using trigonometry and sum them.
Explanation:
The minimum distance you must travel to reach the helicopter is determined by decomposing the direct diagonal path into two perpendicular paths that correspond to the grid of streets running east-west and north-south. Since the direction to the helicopter is 25° north of east, you can use trigonometry to find the lengths of the east and north legs of your journey. Using the cosine function for the eastward distance (cos(25°) × 4.50 km) and the sine function for the northward distance (sin(25°) × 4.50 km), you can calculate the exact distances you need to travel east and north:
Eastward distance = cos(25°) × 4.50 km
Northward distance = sin(25°) × 4.50 km
Sum these two distances to get the total minimum distance you need to travel.
Problem (2) A 16 kg cylinder, initially at rest, is held by a cord connected to a grooved drum whose mass is 20 kg. The drum has an outer radius �% = 250 mm and an inner radius of �& = 160 mm. If the drum experiences a constant frictional moment of 3 N∙m at O, how far has the cylinder dropped when it has a downward velocity of 2 m/s? Neglect the mass of the cord and treat the drum as a thin disk. Use the Principle of Work and Energy.
Answer:
Explanation:
The solution to the problem is given in the pictures attached below; the three pictures explains the problem fully and I hope it helps you. Thank you
g Two cars, car 1 and car 2 are traveling in opposite directions, car 1 with a magnitude of velocity v1=13.0 m/s and car 2 v2= 7.22 m/s. If car 1’s exhaust system is loud enough to be heard by car 2 and the frequency fe produced from the exhaust is 2.10 kHz. What frequencies would be heard by car 2 when the cars are approaching, passing, and retreating from one another?
Answer:
When they are approaching each other
[tex]f_a = 2228.7 \ Hz[/tex]
When they are passing each other
[tex]f_a = 2100Hz[/tex]
When they are retreating from each other
[tex]f_a = 1980.7 Hz[/tex]
Explanation:
From the question we are told that
The velocity of car one is [tex]v_1 = 13.0 m/s[/tex]
The velocity of car two is [tex]v_2 = 7.22 m/s[/tex]
The frequency of sound from car one is [tex]f_e = 2.10 kHz[/tex]
Generally the speed of sound at normal temperature is [tex]v = 343 m/s[/tex]
Now as the cars move relative to each other doppler effect is created and this can be represented mathematically as
[tex]f_a = f_o [\frac{v \pm v_o}{v \pm v_s} ][/tex]
Where [tex]v_s[/tex] is the velocity of the source of sound
[tex]v_o[/tex] is the velocity of the observer of the sound
[tex]f_o[/tex] is the actual frequence
[tex]f_a[/tex] is the apparent frequency
Considering the case when they are approaching each other
[tex]f_a = f_o [\frac{v + v_o}{v - v_s} ][/tex]
[tex]v_o = v_2[/tex]
[tex]v_s = v_1[/tex]
[tex]f_o = f_e[/tex]
Substituting value
[tex]f_a = 2100 [\frac{343 + 7.22}{ 343 - 13} ][/tex]
[tex]f_a = 2228.7 \ Hz[/tex]
Considering the case when they are passing each other
At that instant
[tex]v_o = v_s = 0m/s[/tex]
[tex]f_o = f_e[/tex]
[tex]f_a = f_o [\frac{v }{v } ][/tex]
[tex]f_a = f_o[/tex]
Substituting value
[tex]f_a = 2100Hz[/tex]
Considering the case when they are retreating from each other
[tex]f_a = f_o [\frac{v - v_o}{v + v_s} ][/tex]
[tex]v_o = v_2[/tex]
[tex]v_s = v_1[/tex]
[tex]f_o = f_e[/tex]
Substituting value
[tex]f_a = 2100 [\frac{343 - 7.22}{343 + 13} ][/tex]
[tex]f_a = 1980.7 Hz[/tex]
Suppose a 2.0×10−62.0×10−6-kgkg dust particle with charge −1.0×10−9C−1.0×10−9C is moving vertically up a chimney at speed 6.0 m/sm/s when it enters the +2000-N/CN/C E⃗ E→ field pointing away from a metal collection plate of an electrostatic precipitator. The particle is 4.0 cmcm from the plate at that instant. Find the time needed for the particle to hit the plate. Express your answer with the
Answer:
Explanation:
mass of particle m = 2 x 10⁻⁶ kg
charge q = 1 x 10⁻⁹ C
electric field E = 2000 N/C
force on charge = E q
= 2000 x 1 x 10⁻⁹
acceleration = force / mass
= 2000x10⁻⁹ / 2 x 10⁻⁶
= 1 m /s²
initil velocity u = 6 m /s
distance s = 4 x 10⁻²
time = t
s = ut + .5 t²
4 x 10⁻² = 6t + .5 x 1 x t²
t² + 12t - .08 = 0
= .0067 s .
= 6.7 ms .
A favorite physics demonstration at the University of Texas at Austin is a giant skateboard about 6 feet long, with about the same mass as a physics professor. Suppose the skateboard rolls with negligible friction on the level classroom floor. The professor is standing at rest on the skateboard, of length L, and the end of the board opposite to the professor is a distance d from the wall. d L If the professor and board have the same mass, and if the professor slowly walks towards the wall, how far is he from the wall when he stops at the opposite end of the skateboard from where he started? (Note his initial distance from the wall is d + L.)
Answer:[tex]d+\frac{L}{2}[/tex]
Explanation:
Given
Length of skateboard is L
distance of skateboard from the wall is d
Suppose mass of skateboard is M
so mass of Professor is M
When Professor moves towards wall skateboard started moving away from wall.
If the professor moves L distance on the skateboard
Therefore relative displacement of the skateboard is
[tex]=\frac{ML}{M+M}[/tex]
[tex]=\frac{L}{2}[/tex]
Therefore professor is at a distance of [tex]d+\frac{L}{2}[/tex] from wall
Final answer:
The professor is 0 meters from the wall when he stops at the opposite end of the skateboard from where he started.
Explanation:
To solve this problem, we can apply the principle of conservation of momentum. The initial momentum of the system, consisting of the professor and the skateboard, is equal to the final momentum of the system. Initially, both the professor and the skateboard are at rest, so the initial momentum is zero.
When the professor walks towards the wall, he exerts a force on the ground, causing an equal and opposite force on him (according to Newton's third law). This force propels the skateboard forward, resulting in a change in momentum of the professor-skateboard system. The total momentum is conserved during this process.
When the professor reaches the opposite end of the skateboard, he comes to a stop. At this point, the skateboard would have moved a certain distance, which we'll call x. If the professor and the board have the same mass, the professor would have moved a distance equal to (d + x) from the wall, while the board would have moved a distance equal to x from the wall.
From the conservation of momentum, we can write:
(0) + (m)(v) = (m)(v) + (M)(V)
Here, m represents the mass of the professor, v represents his initial velocity, M represents the mass of the skateboard, and V represents its final velocity.
Since the professor starts from rest, his initial velocity v is zero. The final velocity V of the skateboard can be calculated using the equation:
(m)(v) = (M)(V)
From the given information, we know that the professor's mass is equal to the skateboard's mass, so m = M. Plugging this into the equation, we get:
(M)(0) = (M)(V)
This simplifies to:
0 = V
Since the final velocity V of the skateboard is zero, we can conclude that the professor comes to a stop at the opposite end of the skateboard. Therefore, he would be a distance x from the wall. To find the value of x, we need to analyze the forces and motion of the system.
When the professor exerts a force on the ground, causing an equal and opposite force on him, the system experiences a net force. According to Newton's second law, the net force on the system is equal to the product of the mass of the system and its acceleration.
Let's define the positive direction as the direction the professor is moving towards the wall. The net force on the system in the positive direction is:
F_net = F_applied - F_opposing
Where F_applied is the force exerted by the professor on the ground, and F_opposing is the sum of all the opposing forces, such as friction.
Since the skateboard rolls with negligible friction, the opposing forces can be considered negligible. Therefore, we have:
F_net = F_applied
From Newton's second law, we can write:
F_net = (M + m)a
Where a is the acceleration of the system.
Plugging in the given information, we have:
150 N = (2M)a
Solving for a gives:
a = 75 N / M
Now, let's consider the motion of the skateboard. Since there is no friction, the only horizontal force acting on the skateboard is the force exerted by the professor on the ground. This force causes the skateboard to accelerate in the positive direction.
The distance x is related to the acceleration a and the time taken t to reach the opposite end of the skateboard. We can use the kinematic equation:
x = (1/2)at^2
Since the professor is initially at rest and comes to a stop at the opposite end, his final velocity vf is zero. We can use the equation:
vf = vi + at
Where vi is the initial velocity of the professor, and a is the acceleration.
Since the professor is initially at rest, his initial velocity vi is zero. Plugging in the known values, we have:
0 = 0 + (75 N / M)t
This simplifies to:
t = 0
Since the time t is zero in this case, the professor reaches the opposite end of the skateboard instantaneously. Therefore, the distance x is also zero.
In conclusion, the professor is 0 meters from the wall when he stops at the opposite end of the skateboard from where he started.
A small airplane is sitting at rest on the ground. Its center of gravity is 2.58 m behind the nose of the airplane, the front wheel (nose wheel) is 0.800 m behind the nose, and the main wheels are 3.02 m behind the nose. What percentage of the airplane's weight is supported by the nose wheel?
Answer:
The percentage of the weight supported by the front wheel is A= 19.82 %
Explanation:
From the question we are told that
The center of gravity of the plane to its nose is [tex]z = 2.58 m[/tex]
The distance of the front wheel of the plane to its nose is [tex]l = 0.800\ m[/tex]
The distance of the main wheel of the plane to its nose is [tex]e = 3.02 \ m[/tex]
At equilibrium the Torque about the nose of the airplane is mathematically represented as
[tex]mg (z- l) - G_B *(e - l) = 0[/tex]
Where m is the mass of the airplane
[tex]G_B[/tex] is the weight of the airplane supported by the main wheel
So
[tex]G_B =\frac{mg (z-l)}{(e - l)}[/tex]
Substituting values
[tex]G_B =\frac{mg (2.58 -0.8 )}{(3.02 - 0.80)}[/tex]
[tex]G_B = 0.8018 mg[/tex]
Now the weight supported at the frontal wheel is mathematically evaluated as
[tex]G_F = mg - G_B[/tex]
Substituting values
[tex]G_F = mg - 0.8018mg[/tex]
[tex]G_F = (1 - 0.8018) mg[/tex]
[tex]G_F = 0.1982 mg[/tex]
Now the weight of the airplane is = mg
Thus percentage of this weight supported by the front wheel is [tex]A = 0. 1982 *100 =[/tex] 19.82 %
After a switch is thrown to replace the battery in a DC LR circuit with a conducting wire (so that the circuit is still left complete), the time constant represents:
a. the time rate of change of the current in the circuit.b. the time rate of change of the induced emf in the circuit.c. the magnitude of the ratio of the current to the time rate of change of the current.d. all of the above.e. only (a) and (b) above
Answer:
c. the magnitude of the ratio of the current to the time rate of change of the current
Explanation:
In a LR circuit where battery is connected , the expression for decay of current is given by
[tex]i = i_0e^{-\frac{t}{\lambda}[/tex] where i is instantaneous current at time t , i₀ is maximum current , λ is constant .
differentiating on both sides with respect to t
di / dt = [tex]- \frac{i_0}{\lambda} e^{-\frac{t}{\lambda}[/tex]
[tex]\lambda = - \frac{i}{\frac{di}{dt} }[/tex]
So time constant is equal to magnitude of ratio of current to time rate of change of current .
A point source of light is submerged 3.3 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have? Take the refraction index of water to be 1.333.
Answer:
Maximum Radius = 2.89m
Explanation:
The maximum radius will be determined by the angle of incidence which is equal to the critical angle. Now, any angle larger than that will make the light to be totally internally reflected. Hence, we can figure out that angle from Snell’s law where the refracted angle is 90°, and then use the tangent function.
From Snell's law;
n_air*sin90° = n_water*sin(θ _c)
Where;
θ_c is the critical angle
Refractive index of water; n_water = 1.333
Refractive index of air;n_air = 1
Thus;
1*1 = 1.33sinθ_c
sinθ_c = 1/1.33
θ_c = sin^(-1)0.7519
θ_c = 48.76°
Like I said earlier, we'll use tangent to find the radius.
Thus;
tanθ_c = d/R
From the question, d = 3.3m
Thus;
3.3/tan48.76 = R
So, R = 2.89m
A child on a 2.4 kg scooter at rest throws a 2.2 kg ball. The ball is given a speed of 3.1 m/s and the child and scooter move in the opposite directions at 0.45 m/s. Find the child's mass.
Answer:
The child's mass is 14.133 kg
Explanation:
From the principle of conservation of linear momentum, we have;
(m₁ + m₂) × v₁ + m₃ × v₂ = (m₁ + m₂) × v₃ - m₃ × v₄
We include the negative sign as the velocities were given as moving in the opposite directions
Since the child and the ball are at rest, we have;
v₁ = 0 m/s and v₂= 0 m/s
Hence;
0 = m₁ × v₃ - m₂ × v₄
(m₁ + m₂)× v₃ = m₃ × v₄
Where:
m₁ = Mass of the child
m₂ = Mass of the scooter = 2.4 kg
v₃ = Final velocity of the child and scooter = 0.45 m/s
m₃ = Mass of the ball = 2.4 kg
v₄ = Final velocity of the ball = 3.1 m/s
Plugging the values gives;
(m₁ + 2.4)× 0.45 = 2.4 × 3.1
(m₁ + 2.4) = 16.533
∴ m₁ + 2.4 = 16.533
m₁ = 16.533 - 2.4 = 14.133 kg
The child's mass = 14.133 kg.
Ehren is trying to increase his mile run from eight to six minutes. He has decided to run some sandy hills near his home. Which principle of overload is at work? progression time frequency intensity
Answer:
The correct answer is intensity.
Explanation:
The principle of overload is a basic sports fitness training concept which means that in order to improve, athletes must continually work harder as they their bodies adjust to existing workouts. Thus, overloading also plays a role in skill learning.
Now, since erhen wants to increase his mile run from eight to six minutes by run some sandy hills near his home, it means the principle at work is making his training runs more intense for better speed results. Thus the principle at work is intensity because he is trying to do something that makes him run faster.
Final answer:
Ehren is employing the Overload Principle, focusing on the component of intensity to improve his mile run time by running up sandy hills. This method increases resistance and is aligned with the Progression Principle to safely enhance his fitness and performance.
Explanation:
Ehren is working on improving his mile run time and has decided to include running up sandy hills as part of his training. This implementation of intensity in his workouts is a component of the Overload Principle. The principle of overload necessitates a "greater than normal workload or exertion" for an individual to improve in aspects such as aerobic endurance, muscular strength, endurance, and flexibility. By running on sandy hills, Ehren increases the resistance and difficulty compared to running on a flat surface, thus intensifying his training sessions to drive physiological adaptations.
The Progression Principle is also at play here, which entails the gradual increase in stress placed on the body to safely enhance fitness without risking overuse or injury. This principle aligns with the Overload Principle, as it supports the idea of incrementally adding stress to the body through exercises to foster continual improvements. Overall, Ehren's choice to run sandy hills is applying both the intensity and progression components of the overload to achieve his goal of increasing his running pace.
A sound is traveling through the air with a temperature of 35•C. The sound wave has a wavelength of 0.75 meters. What is the frequency of the sound
Answer:
f = 687.85 Hz
Explanation:
Given that,
The wavelength of sound wave, [tex]\lambda=0.75\ m[/tex]
We need to find the frequency of the sound wave. The relation between wavelength and frequency is given by :
[tex]v=f\lambda[/tex]
v is speed of sound at T = 35°C = 308.15 K
[tex]v=331+0.6T\\\\v=331+0.6\times 308.15 \\\\v=515.89\ m/s[/tex]
So,
[tex]f=\dfrac{v}{\lambda}\\\\f=\dfrac{515.89}{0.75}\\\\f=687.85\ Hz[/tex]
So, the frequency of the sound is 687.85 Hz.
Final answer:
To calculate the frequency of a sound wave, use the formula frequency = speed of sound / wavelength. For this specific scenario, the frequency of the sound wave is 3400 Hz.
Explanation:
The frequency of the sound wave can be calculated using the formula:
frequency = speed of sound / wavelength
Given that the speed of sound in air is 340 m/s and the wavelength is 0.10 m, we can plug in the values to find the frequency:
frequency = 340 m/s / 0.10 m = 3400 Hz
Therefore, the frequency of the sound wave is 3400 Hz.
Blood flow rates in the umbilical cord can be found by measuring the Doppler shift of the ultrasound signal reflected by the red blood cells. If the source emits a frequency f, what is the measured reflected frequency fR? Assume that all of the red blood cells move directly toward the source. Let c be the speed of sound in blood and v be the speed of the red blood cells.
Answer:
fR = f(c + v)/c
Explanation:
The speed of a wave is its frequency x wavelenght. Therefore,
Frequency is speed of wave over the wavelength.
Since the source (ultrasound machine) is stationary, and the receiver red blood cell is moving towards it. The wavelenght of the wave sent out towards the observer is c/f
The speed of the reflected sound wave is (c + v), so that the reflected frequency fR is given by
fR = f(c + v)/c
The measured reflected frequency ( fR) in Doppler-shifted ultrasound, when blood cells move towards the source, is calculated using the formula fR = f * (c + v) / c, where f is the original frequency, c is the speed of sound in blood, and v is the velocity of blood cells.
The question relates to the principle of the Doppler effect and its application in calculating the velocity of blood flow using Doppler-shifted ultrasound. The Doppler effect occurs when a wave source and an observer are in relative motion, resulting in a change in the observed frequency. Specifically, when the blood cells move towards the ultrasound source, the frequency of the reflected ultrasound increases. This change in frequency can be measured for diagnostic purposes.
To find the measured reflected frequency fR when blood cells are moving towards the source, you can use the formula:
fR = f * (c + v) / c
Where,
f = original frequency of the ultrasound
c = speed of sound in blood (or human tissue)
v = velocity of blood cells relative to the ultrasound source
A sphere of radius 5.00 cm carries charge 3.00 nC. Calculate the electric-field magnitude at a distance 4.00 cm from the center of the sphere and at a distance 6.00 cm from the center of the sphere if the sphere is a solid insulator with the charge spread uniformly throughout its volume. Express your answers in newtons per coulomb separated by a comma. Repeat part A if the sphere is a solid conductor.
Answer:
a) E = 8.63 10³ N /C, E = 7.49 10³ N/C
b) E= 0 N/C, E = 7.49 10³ N/C
Explanation:
a) For this exercise we can use Gauss's law
Ф = ∫ E. dA = [tex]q_{int}[/tex] /ε₀
We must take a Gaussian surface in a spherical shape. In this way the line of the electric field and the radi of the sphere are parallel by which the scalar product is reduced to the algebraic product
The area of a sphere is
A = 4π r²
if we use the concept of density
ρ = q_{int} / V
q_{int} = ρ V
the volume of the sphere is
V = 4/3 π r³
we substitute
E 4π r² = ρ (4/3 π r³) /ε₀
E = ρ r / 3ε₀
the density is
ρ = Q / V
V = 4/3 π a³
E = Q 3 / (4π a³) r / 3ε₀
k = 1 / 4π ε₀
E = k Q r / a³
let's calculate
for r = 4.00cm = 0.04m
E = 8.99 10⁹ 3.00 10⁻⁹ 0.04 / 0.05³
E = 8.63 10³ N / c
for r = 6.00 cm
in this case the gaussine surface is outside the sphere, so all the charge is inside
E (4π r²) = Q /ε₀
E = k q / r²
let's calculate
E = 8.99 10⁹ 3 10⁻⁹ / 0.06²
E = 7.49 10³ N/C
b) We repeat in calculation for a conducting sphere.
For r = 4 cm
In this case, all the charge eta on the surface of the sphere, due to the mutual repulsion between the mobile charges, so since there is no charge inside the Gaussian surface, therefore the field is zero.
E = 0
In the case of r = 0.06 m, in this case, all the load is inside the Gaussian surface, therefore the field is
E = k q / r²
E = 7.49 10³ N / C
An imaginary cubical surface of side L has its edges parallel to the x-, y- and z-axes, one corner at the point x = 0, y = 0, z = 0 and the opposite corner at the point x=L, y=L, z=L. The cube is in a region of uniform electric field E⃗ =E1i^+E2j^, where E1 and E2 are positive constants. Calculate the electric flux through the cube face in the plane x = 0 and the cube face in the plane x=L. For each face the normal points out of the cube.
Find the given attachment for solution
The electric flux trough x = 0 plane is = - EL² and the electric flux trough x = l plane is = EL².
What is electric flux?Although an electric field cannot flow by itself, electric flux in electromagnetism is a measure of the electric field passing through a specific surface.
An electric field surrounds an electric charge, such as a solitary electron in space. Field lines have no physical significance and are merely a graphic representation of field strength and direction.
The number of "lines" per unit area, also known as the electric flux density, is inversely proportional to the electric field strength. The total number of electric field lines passing through a surface determines the amount of electric flux.
Hence, electric flux trough x = 0 plane is = - EL² and the electric flux trough x = l plane is = EL².
Learn more about electric flux here:
https://brainly.com/question/14544020
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If an arrow is shot upward on the moon with a velocity of 58 m/s, its height (in meters) after t seconds is given by H = 58t − 0.83t2. (a) Find the velocity of the arrow after two seconds. m/s (b) Find the velocity of the arrow when t = a. m/s (c) When will the arrow hit the surface? (Round your answer to one decimal place.) t = s (d) With what velocity will the arrow hit the surface? m/s
Answer:
a) v = 54.7m/s
b) v = (58 - 1.66a) m/s
c) t = 69.9 s
d) v = -58.0 m/s
Explanation:
Given;
The height equation of the arrow;
H = 58t - 0.83t^2
(a) Find the velocity of the arrow after two seconds. m/s;
The velocity of the arrow v can be given as dH/dt, the change in height per unit time.
v = dH/dt = 58 - 2(0.83t) ......1
At t = 2 seconds
v = dH/dt = 58 - 2(0.83×2)
v = 54.7m/s
(b) Find the velocity of the arrow when t = a. m/s
Substituting t = a into equation 1
v = 58 - 2(0.83×a)
v = (58 - 1.66a) m/s
(c) When will the arrow hit the surface? (Round your answer to one decimal place.) t = s
the time when H = 0
Substituting H = 0, we have;
H = 58t - 0.83t^2 = 0
0.83t^2 = 58t
0.83t = 58
t = 58/0.83
t = 69.9 s
(d) With what velocity will the arrow hit the surface? m/s
from equation 1;
v = dH/dt = 58 - 2(0.83t)
Substituting t = 69.9s
v = 58 - 2(0.83×69.9)
v = -58.0 m/s
A point charge q1 is at the center of a sphere of radius 20 cm. Another point charge q2 = 10 nC is located at a distance r = 10 cm from the center of the sphere. If the net flux through the surface of the sphere is 800 N.m2/C, find q1.
Answer:
q₁ = -2.92 nC
Explanation:
Given;
first point charge, q₁ = ?
second point charge, q₂ = 10 nC
net flux through the surface of the sphere, Φ = 800 N.m²/C
According to Gauss’s law, the flux through any closed surface (Gaussian surface), is equal to the net charge enclosed divided by the permittivity of free space.
[tex]\phi = \frac{q_{enc.}}{\epsilon_o}[/tex]
where;
Φ is net flux
[tex]q_{enc.}[/tex] net charge enclosed
ε₀ is permittivity of free space.
[tex]q_{enc.}[/tex] = Φε₀
= 800 x 8.85 x 10⁻¹²
= 7.08 x 10⁻⁹ C
[tex]q_{enc.}[/tex] = 7.08 nC
q₁ + q₂ = [tex]q_{enc.}[/tex]
q₁ = [tex]q_{enc.}[/tex] - q₂
q₁ = 7.08nC - 10 nC
q₁ = -2.92 nC
106 grams of liquid water are in a cylinder with a piston maintaining 1 atm (101325 Pa) of pressure. It is exactly at the boiling point of water, 373.15 K. We then add heat to boil the water, converting it all to vapor. The molecular weight of water is 18 g/mol and the latent heat of vaporization is 2260 J/g. 1) How much heat is required to boil the water?
Answer:
239.55 KJ
Explanation:
Given:
Mass 'm' = 106 g
Latent heat of vaporization'L'= 2260 J/g.
Molecular weight of water'M' = 18 g/mol
Pressure 'P' = 101325 Pa
Temperature 'T' = 373.15 K
Using the formula of phase change, in order to determine the amount of heat required, we have
Q = mL
Q = 106 x 2260
Q = 239560J = 239.55 KJ
A proton travels through uniform magnetic and electric fields. The magnetic field is in the negative x direction and has a magnitude of 2.85 mT. At one instant the velocity of the proton is in the positive y direction and has a magnitude of 2840 m/s. At that instant, what is the magnitude of the net force acting on the proton if the electric field is (a) in the positive z direction and has a magnitude of 5.38 V/m, (b) in the negative z direction and has a magnitude of 5.38 V/m, and (c) in the positive x direction and has a magnitude of 5.38 V/m
Answer:
Explanation:
a ) Magnetic force on proton
= B q v , B is magnetic field , q is charge with velocity v
= 2.85 x 10⁻³ x 1.6 x 10⁻¹⁹ x 2840
= 12.95 x 10⁻¹⁹ N
Its direction will be towards positive z - direction according to Fleming's left hand rule.
force on proton due to electric field = charge x electric field.
= 1.6 x 10⁻¹⁹ x 5.38
= 8.608 x 10⁻¹⁹ N
this force will be along the field ie in positive z direction so both the forces are acting in the same direction so they will add up.
total force = (12.95 + 8.608)x 10⁻¹⁹
= 21.558 x 10⁻¹⁹ N .
b ) in this case , both the forces are acting in opposite direction . net force
= (12.95 - 8.608)x 10⁻¹⁹
= 4.342 x 10⁻¹⁹ N
c ) In this case both the forces are acting perpendicular to each other
resultant = √(12.95² + 8.608²) x 10⁻¹⁹ N
= 15.54 x 10⁻¹⁹ N .
Derive the equation relating the total charge QQ that flows through a search coil (Conceptual Example 29.3) to the magnetic-field magnitude BB. The search coil has NN turns, each with area AA, and the flux through the coil is decreased from its initial maximum value to zero in a time ΔtΔt. The resistance of the coil is RR, and the total charge is Q=IΔtQ=IΔt, where II is the average current induced by the change in flux.
Answer:
Explanation:
flux through the coil = NBA
Change in flux = NBA - 0 = NBA
rate of change of flux = NBA / Δt
emf induced = NBA / Δt
current i = emf / resistance
= NBA / (RΔt)
Charge flowing through the search coil
= NBA Δt/ (RΔt)
Q = NBA/R
force= mass x acceleration
Which object would have the greatest force?
Answer:the object with the highest mass and with the highest acceleration
Explanation:
Force is directly proportional to mass
The higher the mass, the higher the force