Parameter, because the data set of all 843 animals in a zoo is a population.
The population of all animals in the Zoo is 843
Proportion = 8%, which is the ratio regarding the population. So 8% is populaton proporiton, i..e Parameter .
What is a zoo?A zoo, short for the zoological garden, is a place where animals are kept in enclosures, cared for, presented to the public, and occasionally bred for conservation efforts. The phrase zoological garden refers to zoology, the study of animals. It is also used to refer to an animal park or menagerie. In the United States alone, over 181 million people visit zoos every year. The goal of the modern zoo, which first appeared in the 19th century in the United Kingdom was to entertain and inspire the public by offering scientific inquiry and later educational exhibits. The London Zoological Gardens, which was opened to the public in 1847 after being opened for scientific study in 1828, is where the abbreviation "zoo" first appeared.
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the mathematical model and parameters that define and fix a coordinate system assigned to a reference frame of physical monuments is:
The mathematical model and parameters that define and fix a coordinate system assigned to a reference frame of physical monuments is Geodetic Datum.
A geodetic datum is a coordinate system used to locate points on the Earth's surface. It defines a reference frame of physical monuments or reference points, which are related to the center of the Earth by a datum transformation. This transformation provides a connection between a global Cartesian coordinate system (such as WGS84) and the local geodetic coordinate system of the region of interest. This connection is specified by a set of parameters that define the position and orientation of the reference frame relative to the global Cartesian coordinate system.
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A charge q = 8 μC is moving with a velocity v = [31 +43]x 106 m/s. If the charge enters a magnetic. field B=0.4k T, then the magnitude of the magnetic force (in N) on the charge is: F=qvx B (A) 4 F=9/15 9 [37+ ujjxk (16 (B) 8 (C) 12 (D) 16 (E) 20 Q7- A charge q = 8 μC is moving with a velocity v = [31 +43]x 106 m/s. If the charge enters a magnetic. field B=0.4k T, then the magnitude of the magnetic force (in N) on the charge is: F=qvx B (A) 4 F=9/15 9 [37+ ujjxk (16 (B) 8 (C) 12 (D) 16 (E) 20 an спо A particle with a charge of 5.0c travels at 2.0 m/s and encounters a magnetic field of 0.0100 T that makes an angle of 46.0 with respect to the x-axis in the xy-plane. Find the force the magnetic field exerts on the particle. FONTEINONA -0.069 N 0.072 N -0.072 N 0.069 N Q7: A positively charged particle q=2 µC enters a uniform magnetic field B= 21 +31 T with a velocity v=4x106 m/s. The magnetic force F(in N) on the particle is: a) -12 1-8 k b) 24 k c) -16 k d) -12 k e) 12î-16ĵ
The force the magnetic field exerts on the particle is 0.072 N with velocity
Charge q = 8 μC is moving with a velocity v = [31 +43] x 106 m/s. If the charge enters a magnetic field B=0.4k T, then the magnitude of the magnetic force (in N) on the charge is given by
F = q x v x B
Given thatq = 8 μC
= 8 x 10-6 C
Velocity v = [31 +43] x 106 m/s
= [31,000,000 + 43,000,000] m/s
= [74,000,000] m/s
Magnetic field B = 0.4k T
= 0.4 x 103 T
TeslaSubstituting these values in the above equation, we get
F = (8 x 10-6) x (74 x 106) x (0.4 x 103)
F = 2.95 N
Therefore, the magnitude of the magnetic force (in N) on the charge is 2.95 N.
Another problem:
Given that a particle with a charge of 5.0 C travels at 2.0 m/s and encounters a magnetic field of 0.0100 T that makes an angle of 46.0 with respect to the x-axis in the xy-plane. We need to find the force the magnetic field exerts on the particle.
The force F on the particle is given by:
F = q x v x B x sin(θ)Where q is the charge of the particle, v is the velocity of the particle, B is the magnetic field and θ is the angle between the velocity of the particle and the magnetic field.
F = 5.0 C x 2.0 m/s x 0.0100 T x sin(46.0)
F = 0.072 N
Therefore, the force the magnetic field exerts on the particle is 0.072 N.
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Frank, a San Francisco hot dog vender, has fallen asleep on the job. When an earthquake strikes, his 300-kg hot-dog cart rolls down Nob Hill which is 50 m high.
A. What is the PE of the cart at the top of Nob hill?
B. What is the Kinetic Energy of the cart at the bottom of the hill?
C. What is the speed of the cart at the bottom of the hill?
(a) The potential energy ( PE ) of the cart at the top of Nob hill is 147,000 J.
(b) The Kinetic Energy of the cart at the bottom of the hill is 147,000 J.
(c) The speed of the cart at the bottom of the hill is 31.3 m/s.
What is the potential energy at top of the hill?
The potential energy ( PE ) of the cart at the top of Nob hill is calculated as follows;
P.E = mgh
where;
m is the mass of the carth is the height above the groundg is acceleration due to gravityP.E = 300 kg x 9.8 m/s² x 50 m
P.E = 147,000 J
The Kinetic Energy of the cart at the bottom of the hill = The potential energy of the cart at the top of Nob hill based on law of conservation of energy.
The speed of the cart at the bottom of the hill is calculated as follows;
v = √ ( 2gh )
v = √ ( 2 x 9.8 x 50 )
v = 31.3 m/s
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smooth surface is also called ......... surface
Answer:
Plane (or) regular surface
Explanation:
A smooth surface is also called as plane surface. (It is like a mirror)
Tom rides his skateboard 2.4km in 20 mins and Max rides his scooter 3.6km in 30 mins. Who is moving at a faster rate (speed)? Choose the correct formula and show your work. (what you are plugging into the calculator) Use proper units in your answer.
Answer:
The are both moving at the same speed
Explanation:
Given the following :
Tom = 2.4km in 20 minutes
Max = 3.6km in 30 minutes
To calculate the rider moving at a faster spedd, we need to calculate the speed of each rider.
Speed = distance / time
Tom's speed :
Distance = 2.4km = 2.4 × 1000 = 2400meters
Time = 20 minutes = 20 × 60 = 1200 seconds
Speed = (2400 / 1200) = 2 meter per second
Max's speed :
Distance = 3.6km = 3.6 × 1000 = 3600meters
Time = 30 minutes = 30 × 60 = 1800 seconds
Speed = (3600 / 1800) = 2 meter per second
Both Tom and Max are riding at the same speed(rate)
Which electrode is the anode and what is the cell potential in a standard lead-cobalt cell? a)The anode is the lead electrode and the cell potential is +0.15 V. b)The anode is the lead electrode and the cell potential is +0.39 V. c)The anode is the cobalt electrode and the cell potential is +0.15 V. d)The anode is the cobalt electrode and the cell potential is +0.39 V.
The correct answer is d) The anode is the cobalt electrode and the cell potential is +0.39 V. In a standard lead-cobalt cell, the anode is the cobalt electrode and the cell potential is +0.39 V.
This is because the cobalt electrode has a higher reduction potential than the lead electrode, meaning that electrons will flow from the cobalt to the lead electrode. The cell potential is the difference in the reduction potentials of the two electrodes, and since the cobalt electrode has a higher reduction potential, the cell potential is positive. The cell potential is measured in volts, and in this case it is +0.39 V.
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What is the difference between a series circuit and Parrallel circuit
The primary differences between a series circuit and a parallel circuit are determined by the amount of current passing through each component in the circuit.
In a series circuit, the amount of current passing through each element is the same.
In contrast, a parallel circuit divides the current flow because the components are arranged in parallel to one another. The source's current and the current flowing through each of these components will be divided.
Series circuits have the following benefits: They are easy to grasp, have a straightforward design, do not overheat easily, have a greater output voltage so we can add more powerful appliances, and carry the same current throughout the circuit.
Benefits of parallel circuits: If one component in a parallel circuit is destroyed, the current still flows through the remaining components, allowing the remaining components to function as intended. A new component can be easily connected or disconnected in a parallel circuit without impairing the operation of another component.
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HELP PLS I CANT FIND THHE ANSWER ANYWHERE IM BEING TIMED TOO!!
Answer:
I think It's magna! Let me know if It's right.
The gravitational force exerted on a star by a planet is
- stronger than that exerted on the planet by the star and in the same direction
- weaker than that exerted on the planet by the star and in the same direction
- equal to that exerted on the planet by the star and in the same direction
- equal to that exerted on the planet by the star and in the opposite direction
The gravitational force exerted on a star by a planet is equal to that exerted on the planet by the star and in the opposite direction.
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This principle applies to the gravitational force as well. The force of gravity between two objects depends on their masses and the distance between them.
In the case of a star and a planet, both objects exert a gravitational force on each other. The force exerted by the star on the planet is equal in magnitude to the force exerted by the planet on the star. However, the direction of the forces is opposite. The star attracts the planet with a force, while the planet attracts the star with an equal force but in the opposite direction.
Therefore, the correct answer is: The gravitational force exerted on a star by a planet is equal to that exerted on the planet by the star and in the opposite direction.
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A 222 kg snowmobile is traveling at 24.21 m/s. How fast would a 306.3 kg snowmobile need to travel in order to have the same momentum?
The velocity is 17.5 m/s.
What is the momentum?Momentum is a measure of an object's motion and is defined as the product of its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.
Momentum of the snowmobile = 222 kg * 24.21 m/s.
= 5374.62 Kgm/s
Velocity of the other snowmobile = 5374.62 Kgm/s/306.3 kg
= 17.5 m/s
Thus we observe that the momentum can be used to obtain the velocity of the object we have here. In physics, momentum is a vector quantity, meaning it has both magnitude and direction.
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if the electric flux through a closed surface is zero, the electric field at points on that surface must be zero.
True, if the electric flux through a closed surface is zero, the electric field at points on that surface must be zero.
What does a closed surface's electric flux look like?
The charge encapsulated divided by the permittivity is equal to the total electric flux out of a closed surface. The electric field is multiplied by the surface area projected in a plane perpendicular to the field to get the electric flux across a region.
If there is a net outward flow, the electric flux through a closed surface is positive; if there is a net inward flow, it is negative. If there is a source inside the closed surface, we have a net outward flux, and if there is a sink inside the closed surface, we have a net inward flux. Zero field implies zero flux, but zero flux does not imply zero field.
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8. A jaguar runs 4200 meters at the speed of 400 meters per minute. How
much time did this take? (You can use the speed triangle if it helps! Write
the formula, plug in the numbers, and write the answer with a box around it
Answer:
10.5min
Explanation:
Given parameters:
Distance = 4200m
Speed = 400m/min
Unknown:
Time taken for this run = ?
Solution:
Speed is the distance divided by the time taken.
Speed = \(\frac{distance }{time }\)
Time = \(\frac{distance}{speed }\)
Now insert the parameters and solve;
Time = \(\frac{4200}{400}\) = 10.5min
enter your answer in the provided box. determine the change in entropy (δssys), for the expansion of 0.900 mole of an ideal gas from 2.00 l to 3.00 l at constant temperature. j/k
Therefore, the change in entropy of the system, δSSys, is 3.23 J/K.
Entropy (S) is the measure of the disorder or randomness of a system.
When a gas expands from a small volume to a large volume at constant temperature, the entropy of the gas system increases.
Therefore, we can use the formula
δSSys=nRln(V2/V1),
where n = 0.900 mole, R is the universal gas constant, V1 = 2.00 L, and V2 = 3.00 L.
We use R = 8.314 J/mol-K as the value for the universal gas constant.
δSSys=nRln(V2/V1)
δSSys=(0.900 mol)(8.314 J/mol-K) ln(3.00 L / 2.00 L)
δSSys= 0.900 mol x 8.314 J/mol-K x 0.4055
δSSys = 3.23 J/K
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What wavelength photon would have the same energy as a 145-gram baseball moving 30.2 m/s ?
Answer:
Approximately \(3.01 \times 10^{-27}\; {\rm m}\) (when measured in a vacuum.)
Explanation:
Apply unit conversion and ensure that the mass of the baseball is in standard units (kilograms):
\(m = 145\; {\rm g} = 0.145\; {\rm kg}\).
The kinetic energy of the baseball will be:
\(\displaystyle E = \frac{1}{2}\, m\, v^{2}\),
Where \(v = 30.2\; {\rm m\cdot s^{-1}}\) is the speed of the baseball.
\(\begin{aligned}E &= \frac{1}{2}\, m\, v^{2} \\ &= \frac{1}{2}\, (0.145)\, (30.2)^{2}\; {\rm J} \\ &= 66.12290\; {\rm J}\end{aligned}\).
The energy of a photon of frequency \(f\) is:
\(E = h\, f\),
Where \(h \approx 6.62607 \times 10^{-34}\; {\rm m^{2}\cdot kg \cdot s^{-1}}\) is Planck's constant.
When measured in a vacuum where speed of light is \(c \approx 3.00 \times 10^{8}\; {\rm m\cdot s^{-1}}\), the wavelength \(\lambda\) of this photon will be:
\(\displaystyle \lambda = \frac{c}{f}\).
\(\displaystyle f = \frac{c}{\lambda}\).
Hence, the expression for the energy of this photon can be rewritten as:
\(\displaystyle E = h\, f = \frac{h\, c}{\lambda}\).
Rearrange this equation to find \(\lambda\):
\(\displaystyle \lambda &= \frac{h\, c}{E}\).
Assuming that the energy of this photon to be equal to the kinetic energy of that baseball, \(66.12290\; {\rm J}\):
\(\begin{aligned}\lambda &= \frac{h\, c}{E} \\ &\approx \frac{(6.62607\times 10^{-34})\, (3.00 \times 10^{8})}{(66.12290)}\; {\rm m} \\ &\approx 3.01 \times 10^{-27}\; {\rm m}\end{aligned}\).
A 30 kg box is pushed along a horizontal surface. The person pushing the box pushes with a constant force of 300 N directed at an angle of 30° below the horizontal. If the box starts from rest and reaches a speed of 5 m/s after only 2 seconds of pushing, find the force of friction acting on the box.
Answer:
aye son yall think if i keep answering these questions incorrectly.. they'll find out what im doing and take my li points back?
Explanation:
how does density play a part in determining how unlike air masses react
Identification of compounds can benefit from density. It is also a useful feature since it connects (or acts as a conversion factor between) a substance's mass and volume. Volume and mass are extended (or extrinsic) qualities of matter that are quantity dependent.
What is the density playing a part in air masses detection?The force of an air mass acting on the earth's surface is known as atmospheric pressure. Remember that wind currents are created when the densities of two separate air masses differ.
Our wind currents are driven by the atmospheric pressure density, and denser air exerts a higher pressure than less dense air. Compared to the cold and dry air, the warm and humid air is less dense. The less dense air will then float on top of the thicker air in certain regions.
Therefore, Warm air masses rise while cold air masses descend because they are less dense.
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A 70mm long blockhas cross-section of 50mm by 10mm the block is subjected to forces 60KN (tension) on the 50mm by 10mm face and 110KN (Compression) on the 70mm by 10mm face Determine the force to be applied on the 70mm by 50mm face such that there is no change in volume
Answer:
970 kN
Explanation:
The length of the block = 70 mm
The cross section of the block = 50 mm by 10 mm
The tension force applies to the 50 mm by 10 mm face, F₁ = 60 kN
The compression force applied to the 70 mm by 10 mm face, F₂ = 110 kN
By volumetric stress, we have that for there to be no change in volume, the total pressure applied by the given applied forces should be equal to the pressure removed by the added applied force
The pressure due to the force F₁ = 60 kN/(50 mm × 10 mm) = 120 MPa
The pressure due to the force F₂ = 110 kN/(70 mm × 10 mm) = 157.142857 MPa
The total pressure applied to the block, P = 120 MPa + 157.142857 MPa = 277.142857 MPa
The required force, F₃ = 277.142857 MPa × (70 mm × 50 mm) = 970 kN
Three 20W resistors are connected in series across a 120 V generator. What is the total resistance of the circuit and what current flows in the circuit?
The total resistance and current flowing through the circuit is equal to 60 Ohms and 2 Amperes respectively.
Given the following data:
Resistors = 20 Ohms.
Voltage = 120 Volts.
How to determine the total resistance.Since the three resistors are connected in series, we would calculate their total resistance by adding them up as follows:
RT = R1 + R2 + R3
RT = 20 + 20 + 20
RT = 60 Ohms.
Next, we would determine the current that is flowing through the circuit by applying Ohm's law.
From Ohm's law, we have:
V = IR
I = V/R
I = 120/60
I = 2 Amperes.
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If a falling object is covering 50 metre distance in 5 seconds, how much time it will take to cover 72 metres?
Answer:
7.2 seconds
Explanation:
50=5
72=t, criss-cross, t=72 (5)/50
DC current is less than AC current
true\false
Answer:
False
Explanation:
.......................
What is artificial insemination as used in animal production
Answer:
i hope this helps!
Explanation:
Artificial Insemination (AI) is an Assisted Reproductive Technology (ART) used worldwide to deposit stored semen directly into a cow or heifer's uterus. It is a tool for improving reproductive performance and genetic quality of livestock.
source: https://nwdistrict.ifas.ufl.edu/phag/2020/05/29/tips-for-successful-artificial-insemination-of-cattle/
julia performs an experiment to measure the wavelength of four different waves and records her data in the table below.a 2-column table with 4 rows titled julia's waves. the first column labeled wave has entries 1, 2, 3, 4. the second column labeled information has entries this wave has 3 centimeter amplitude, the distance from the midpoint to the crest is 6 centimeters, the distance from the midpoint to the trough is 12 centimeters, this wave has a 4 centimeter amplitude.which accurately ranks the waves from the lowest energy wave to the highest energy wavehow has the change in media affected the frequency of the wave?
A wave's frequency varies when it moves from one medium to another. This is due to the fact that a wave's wavelength doesn't change when it enters a different medium, but its speed does. This is referred to as the frequency-wavelength relationship of the wave.
Based on the information provided in the table, the waves can be ranked from lowest energy to highest energy as follows: wave 1, wave 2, wave 3, and wave 4.
This is because wave energy is directly proportional to its amplitude and frequency, and in this case, the amplitude of wave 1 is the lowest, followed by wave 2, wave 3, and wave 4.
When a wave travels from one medium to another, its frequency changes.
This is because the speed of the wave changes when it enters a different medium, while its wavelength remains constant. This is known as the wave's frequency-wavelength relationship.
When the wave enters a denser medium, its speed decreases, and its frequency decreases as well. On the other hand, when the wave enters a less dense medium, its speed increases, and its frequency increases as well. Therefore, the change in media can affect the frequency of the wave.
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what must the coefficient of static friction be for a car traveling at 115 km/h around the same turn?
Generally, the coefficient of static friction should be at least 0.7 for a car traveling at this speed, but this value could be higher depending on the specific conditions.
The coefficient of static friction, or μs, is the ratio of the maximum static force that can be applied without causing slipping to the normal force between two surfaces. The coefficient is affected by the surfaces in contact and the material they are made of.
The tires of a car also have an effect on the coefficient of static friction. Tires with a greater tread depth can provide better grip on the road and therefore have a higher coefficient of static friction than tires with a shallow tread. Tire pressure also plays a role, as low pressure can reduce the coefficient of static friction.
The weight of the vehicle is also an important factor. Heavier vehicles tend to have a higher coefficient of static friction, as the greater mass increases the normal force between the car and the surface.
In conclusion, the coefficient of static friction for a car traveling at 115 km/h around a turn depends on several factors, including the road surface, the vehicle's tires, and the vehicle's weight.
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I need answers to these physics problems. (See picture). Also, i'm not sure if the one's I circled are correct
The length of the vector is proportional to the size of the force.
The wheelchair is not accelerating, so the forces on it are balanced.
In a free-body diagram of the wheelchair, force due to gravity points down, normal force points up, force pushing the wheelchair points forward, friction resisting the motion points backward.
For the force diagram:
In picture 1: F gravity points down; F normal points upIn picture 2: F gravity points down; F tension points upIn picture 3: F gravity points down; F spring points up.What are forces?Forces are a push or pull agents that causes a change in the state of a body when they are applied to the body.
Unbalanced forces cause acceleration of a body.
In a free-body diagram, the mass (force) on an object is represented by a vector.
The length of the vector is proportional to the size of the force. Suppose you push a wheelchair forward at constant velocity. The wheelchair is not accelerating, so the forces on it are balanced. In a free-body diagram of the wheelchair, the vector for the force due to gravity points down, the vector for the normal force points up, the vector for your force pushing the wheelchair points forward, and the vector for the force of friction resisting the motion points backward.
Considering the picture visual representation of the forces between many interacting objects or the force diagram:
In picture 1: F gravity points down; F normal points up
In picture 2: F gravity points down; F tension points up
In picture 3: F gravity points down; F spring points up.
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this si a 2 part question84) A shock absorber is designed to quickly damp out the oscillations that a car would otherwise make because it is suspended on springs. (a) Find the period of oscillation of a 1610-kg car that is suspended by springs that make an effective force constant of 5.75×104 N/m. (b) Find the damping constant b that will reduce the amplitude of oscillations of this car by a factor of 5.00 within a time equal to half the period of oscillation.
Given data
*The given mass of the car is m = 1610 kg
*The given effective force constant is k = 5.75 × 10^4 N/m
(a)
The formula for the period of oscillation of a 1610 kg car is given as
\(T=2\pi\sqrt[]{\frac{m}{k}}\)Substitute the known values in the above expression as
\(\begin{gathered} T=2\times3.14\times\sqrt[]{\frac{1610}{5.75\times10^4}} \\ =1.05\text{ s} \end{gathered}\)Hence, the time period of oscillation of a 1610 kg car is T = 1.05 s
(b)
As from the given data, the amplitude of the oscillation of the car decreases by a factor of 5.00. Then, the expression for the amplitude of the oscillation, and the damping constant (b) is calculated as
\(A=A_0e^{-\frac{bt}{2m}}\)Substitute the known values in the above expression as
\(\begin{gathered} \frac{A_0}{5.0}=A_0e^{-\frac{bt}{2m}} \\ bt=2m\ln (5.0)_{} \\ b(\frac{T}{2})=2m\ln (5.0) \\ b=\frac{4m\ln (5.0)}{T} \\ =\frac{4\times1610\times\ln (5.0)}{1.05} \\ =9871.2\text{ kg/s} \end{gathered}\)Hence, the damping constant is b = 9871.2 kg/s
which of the following does not influence the speed of water in a
stream?
a. gradient
b. discharge
c. channel geometry
d. flow
Pption d. flow does not independently influence the speed of water in a stream. Instead, it is an outcome determined by the combined effects of gradient, discharge, and channel geometry.
The flow itself, or the rate at which water moves in a stream, is not an independent factor that influences the speed of water in a stream. Instead, it is a result of other factors such as gradient, discharge, and channel geometry.
a. Gradient: The gradient, or slope, of the stream affects the speed of water. Steeper gradients generally lead to faster-flowing water.
b. Discharge: The discharge of a stream, which refers to the volume of water passing through a given point in a specified amount of time, directly affects the speed of water. Higher discharge results in faster flow.
c. Channel geometry: The shape and dimensions of the stream channel also influence the speed of water. Wider and deeper channels tend to have slower flow, while narrower and shallower channels often lead to faster flow.
Therefore, option d. flow does not independently influence the speed of water in a stream. Instead, it is an outcome determined by the combined effects of gradient, discharge, and channel geometry.
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The table shows data about lightning and thunder.
Lightning and Thunder Data
Occurrence Lightning
Observed Thunder Heard Distance to
Lightning (m)
A 8:00:00 p.m. 8:00:01 p.m. 330
B 5:30:00 p.m. 5:30:04 p.m. 1,320
C 6:45:00 p.m. 6:45:06 p.m. 1,980
D 7:20:00 p.m. 7:21:00 p.m. 19,800
According to the table, how fast does the sound of thunder travel?
Answer:
Explanation:
If the question is set up correctly here, we can solve this correctly.
Lightning and Thunder Data
Occurrence Lightning
Observed Thunder Heard Distance to ---- We need this
Lightning (m)
A 8:00:00 p.m. 8:00:01 p.m. 330
B 5:30:00 p.m. 5:30:04 p.m. 1,320
C 6:45:00 p.m. 6:45:06 p.m. 1,980 ---- We need this
D 7:20:00 p.m. 7:21:00 p.m. 19,800
6:45:06 - 6:45:00 = 6
So 6 seconds. We also get 1980. So we do 1980/6, which is 330(m)?
If the unit is meters, then the sound of thunder travels at 330(m)
8. The mediator particle for gravitational force is on
(1 Point)
gluon
vector boson
photon
gravitone
Answer:
Gravitone
Explanation:
In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravity. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with renormalization in general relativity.
A study of classical waves tells us that a standing wave can be expressed as a sum of two travelling waves. Quantum-Mechanical travelling waves, discussed in Chapter 4, is of the form φ(x,t) = Ae^i(kw=wt) Show that the infinite well’s standing wave function can be expressed as a sum of two traveling waves.
In quantum mechanics, the wavefunction of a particle in an infinite well can be described as a standing wave, which is a superposition of two traveling waves propagating in opposite directions.
The standing wave function in an infinite well is given by:
ψ(x, t) = A sin(kx) e^(-iωt)
Using the Euler's formula, we can rewrite the sine function as a sum of exponential functions:
sin(kx) = (1/2i) * (e^(ikx) - e^(-ikx))
Substituting this back into the standing wave function, we have:
ψ(x, t) = A (1/2i) * (e^(ikx) - e^(-ikx)) * e^(-iωt)
Simplifying the expression, we obtain:
ψ(x, t) = (A/2i) * (e^(ikx - iωt) - e^(-ikx - iωt))
Now, we can define two traveling waves:
ψ_1(x, t) = (A/2i) * e^(ikx - iωt)
ψ_2(x, t) = (A/2i) * e^(-ikx - iωt)
The superposition of these two traveling waves gives us the standing wave function:
ψ(x, t) = ψ_1(x, t) + ψ_2(x, t)
Therefore, we have shown that the infinite well's standing wave function can be expressed as a sum of two traveling waves propagating in opposite directions.
By expressing the sine function in terms of exponential functions and defining two traveling waves, we can show that the infinite well's standing wave function can be written as the sum of these two traveling waves. This demonstrates the connection between standing waves and the superposition of traveling waves in the context of quantum mechanics.
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Astronomers observe a spectral analysis of a distant star where a particular element has a spectral line with a wavelength of 663 nm. In the laboratory, the same element has a spectral line with a wavelength of 645 nm.
a. How fast is the star moving, and in what direction is it moving?
b. The same element on Earth’s surface is observed from a space shuttle orbiting at 7800 m/s,
350 km above Earth. Is the same shift in the spectral line seen from the space shuttle? Why or why not?
Answer:
(a). The velocity of star is \(8.1\times10^{6}\ m/s\) and the direction of star toward the earth.
(b). The shift is 0.0168 nm.
Explanation:
Given that,
Wavelength of spectral line = 663 nm
Wavelength of spectral line in lab = 645 nm
(a). We need to calculate the velocity
Using doppler's effect
\(\Delta \lambda=\dfrac{v}{c}\lambda\)
Where, \(\Delta\lambda\)= change in wavelength
v = velocity
c = speed of light
Put the value into the formula
\(663-645=\dfrac{v}{3\times10^{8}}\times663\)
\(v=\dfrac{3\times10^{8}(663-645)}{663}\)
\(v=8144796.38\ m/s\)
\(v=8.1\times10^{6}\ m/s\)
The direction of star toward the earth.
(b). Speed = 7800 m/s
We need to calculate the shift
Using formula of shift
\(\Delta \lambda=\lambda(\sqrt{\dfrac{1+\dfrac{v}{c}}{1-\dfrac{v}{c}}}-1)\)
Put the value into the formula
\(\Delta \lambda=645\times(\sqrt{\dfrac{1+\dfrac{7800}{3\times10^{8}}}{1-\dfrac{7800}{3\times10^{8}}}}-1)\)
\(\Delta\lambda=0.0168\ nm\)
This shift is small compare to the the movement of Earth around the sun.
Hence, (a). The velocity of star is \(8.1\times10^{6}\ m/s\) and the direction of star toward the earth.
(b). The shift is 0.0168 nm.