Explanation:
(a) Formula for average translational kinetic energy of a particle is as follows.
U = [tex]\frac{3}{2}(\frac{RT}{N})[/tex]
where, R = Reydberg's constant
T = absolute temperature
N = Avogadro's number
Therefore, we will calculate value of average translational kinetic energy as follows.
U = [tex]\frac{3}{2}(\frac{RT}{N})[/tex]
= [tex]\frac{3}{2}(\frac{8.314 J/mol K \times 6000 K}{6.023 \times 10^{23} mol^{-1}})[/tex]
= [tex]1.24 \times 10^{-19}[/tex] J
Therefore, value of average translational kinetic energy is [tex]1.24 \times 10^{-19}[/tex] J.
(b) Formula for average kinetic energy is as follows.
K.E = [tex]\frac{1}{2}(\frac{M}{N})v^{2}_{rms}[/tex]
Here, M = molar mass = 1 kg/K mol
And, the average kinetic energy is equal to the average translational kinetic energy.
Hence, K.E = U
[tex]\frac{1}{2}(\frac{M}{N})v^{2}_{rms}[/tex] = [tex]\frac{3}{2}(\frac{RT}{N})[/tex]
[tex]v^{2}_{rms} = \frac{3RT}{M}[/tex]
[tex]v = \sqrt{\frac{3RT}{M}}[/tex]
therefore, we will calculate r.m.s speed of the given atom as follows.
[tex]v = \sqrt{\frac{3RT}{M}}[/tex]
[tex]v = \sqrt{\frac{3 \times 8.314 J/mol K \times 6000 K}{1 kg/K mol}}[/tex]
= 386.84 m/s
Hence, value of r.m.s speed of the given atom is 386.84 m/s.
Following are the solution to the given points:
Given:
Temperature [tex]= 6000\ K[/tex]
To find:
kinetic energy =?
rms speed of the atoms=?
Solution:
For point a)
[tex]\to Avg \ KE =\frac{3}{2}\ KT \\\\[/tex]
[tex]\to KE_{avg} =1.5 \times 1.38 \times 10^{-23} \times 6000 \\\\[/tex]
[tex]=1.5 \times 1.38 \times 10^{-23} \times 6000 \\\\=2.07 \times 10^{-23} \times 6000 \\\\=2.07 \times 10^{-23} \times 6000 \\\\=12.420 \times 10^{-20}\ J[/tex]
For point b)
[tex]\to[/tex] rms speed [tex]V_{rms}[/tex]:
[tex]\to v_{rms}=\sqrt{\frac{3RT}{M}}[/tex]
[tex]=\sqrt{\frac{3 \times 8314 \times 6000}{1}} \\\\=\sqrt{\frac{24942\times 6000}{1}} \\\\=\sqrt{149652000}\\\\=12233.233\\\\ = 12233\ \frac{m}{s}[/tex]
Therefore, the final answer is "[tex]12.420 \times 10^{-20} \ J\ \ and \ \ 12233 \ \frac{m}{s}[/tex]".
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From the following list of words, choose the correct one to complete the statement: absorption, reflection, emission, transmission.
a. Light coming from your computer screen is an example of _________________.
b. Yellow light hitting a yellow banana is an example of _______________.
c. Blue light hitting a yellow banana is an example of _______________.
d. Sunlight passing through a glass door is an example of ______________.
Answer:
a) Emission
b) Reflection
c) Absorption
d) Transmission
Explanation:
a) The screen of computers (most of them LED or LCD) are a bunch of tiny lights that take power of our pc to produce light so they EMMIT light.
b) Sun's light contains all the visible colors of electromagnetic spectrum, when sun light hits an object, due their chemical characteristics the object absorbs a bunch of wavelengths and reflects others, the reflected light is the color we perceive with our eyes. So, for a banana, it absorbs almost all the other colors and reflects only yellow light.
c) As explained on b) a banana absorbs all the other colors except yellow so blue is absorbed on it.
d) When a light hits transparent medium, some rays are reflected and other passes through the medium so that rays are called transmitted and that is the case of Sunlight passing through a glass door.
Final answer:
Correct words are emission for light from a computer screen, reflection for yellow light on a banana, absorption for blue light on a banana, and transmission for sunlight through a glass door. These terms describe how light interacts with different materials through emission, reflection, absorption, and transmission.
Explanation:
From the list of terms provided, the correct words to complete the statements about the behavior of light are:
a. Light coming from your computer screen is an example of emission.
b. Yellow light hitting a yellow banana is an example of reflection.
c. Blue light hitting a yellow banana is an example of absorption.
d. Sunlight passing through a glass door is an example of transmission.
When we talk about light waves interacting with materials, we discuss concepts such as reflection, absorption, and transmission. Reflection occurs when light bounces off an object, such as a yellow light reflecting off a yellow banana. Absorption occurs when an object takes in the light energy, which might later be transformed into other forms of energy like heat, as is the case when a yellow banana absorbs blue light. Lastly, transmission refers to the passage of light through a transparent or semi-transparent material, such as sunlight passing through a glass door.
A 170 g air-track glider is attached to a spring. The glider is pushed in 11.2 cm against the spring, then released. A student with a stopwatch finds that 14 oscillations take 11.0 s. What is the spring constant?
Answer:k = 10.83 N/m²
Explanation: The angular frequency (ω), spring constant (k) and mass is related by the formulae below
ω = √k/m
But ω = 2πf, where f = frequency.
f = number of oscillations /time taken
Number of oscillations = 14, time taken = 11s
f = 14/11 = 1.27Hz.
ω = 2×22/7×1.27
ω = 7.98 rad/s.
By substituting this parameters into ω = √k/m
Where ω = 7.98rad/s, m = 170g = 170/1000 = 0.17kg.
7.98 = √k/0.17
By squaring both sides
(7.98)² = k/ 0.17
k = (7.98)² × 0.17
k = 10.83 N/m²
Final answer:
To find the spring constant (k) of the spring system, we use the period of oscillation formula. After calculating the period of one oscillation (T = 0.7857 s), we solve for k = m/(T/2π)^2 and find that k is approximately 44.1 N/m.
Explanation:
The student asked how to find the spring constant of a spring if a 170 g air-track glider is attached to it, pushed in 11.2 cm, released, and makes 14 oscillations in 11.0 seconds. The spring constant (k) can be found using the formula for the period of a mass-spring system (T = 2π√(m/k)) where m is mass and k is the spring constant.
First, calculate the period of one oscillation by dividing the total time by the number of oscillations: T = 11.0 s / 14 = 0.7857 s. Then rearrange the period formula to solve for k: k = m/(T/2π)2. Convert the mass to kilograms (m = 0.170 kg) and substitute the values to calculate k.
Doing the calculation: k = 0.170 kg / (0.7857 s / 2π)2 gives us the spring constant k. Upon solving, we find that the spring constant is approximately 44.1 N/m.
A motorcycle with two riders weaves dangerously between parked cars in a crowded shopping center parking lot. As the motorcyclists dart between cars, they confront a moving car. Both the car and motorcycle veer to avoid a head-on collision. The motorcycle strikes the side of the oncoming car, throwing riders to the ground. The car stops abruptly, throwing the driver into the windshield. Nearby, Lisa and Paul (two college students) hear the sound of crunching metal and blaring horns and decide to join the small group that has gathered?
Answer:
a
Explanation:
Answer:
A
Explanation:
A train, traveling at a constant speed of 25.8 m/s, comes to an incline with a constant slope. While going up the incline, the train slows down with a constant acceleration of magnitude 1.66 m/s². What is the speed of the train after 8.30 s on the incline?
The final velocity of the train after 8.3 s on the incline will be 12.022 m/s.
Answer:
Explanation:
So in this problem, the initial speed of the train is at 25.8 m/s before it comes to incline with constant slope. So the acceleration or the rate of change in velocity while moving on the incline is given as 1.66 m/s². So the final velocity need to be found after a time period of 8.3 s. According to the first equation of motion, v = u +at.
So we know the values for parameters u,a and t. Since, the train slows down on the slope, so the acceleration value will have negative sign with the magnitude of acceleration. Then
v = 25.8 + (-1.66×8.3)
v =12.022 m/s.
So the final velocity of the train after 8.3 s on the incline will be 12.022 m/s.
answers If visible light and radio waves are both examples of electromagnetic waves, why can’t we see radio waves?
Answer:
Radio Waves:
Radio waves being the lowest-energy form of light and are known to be produced by electrons spiraling around magnetic fields. These Magnetic fields are generated by stars, including our sun, and many weird celestial objects like black holes and neutron stars.
Explanation:
All electromagnetic radiation is light, but we can only see a small portion of this radiation that is the portion we call visible light. Cone-shaped cells in our eyes act as receivers tuned to the wavelengths in this narrow band of the spectrum
Visible light and radio waves are both examples of electromagnetic waves, but visible light has shorter wavelengths that our eyes can detect, while radio waves have longer wavelengths that are outside the range of what our eyes can see.
Explanation:Visible light and radio waves are both examples of electromagnetic waves, but they have different wavelengths. Visible light has a shorter wavelength than radio waves, which is why we can see it. Our eyes are sensitive to the wavelengths of visible light, but not to the longer wavelengths of radio waves.
The human eye can detect wavelengths within a certain range, known as the visible spectrum, which includes the colors of the rainbow. Radio waves have much longer wavelengths, ranging from meters to kilometers. These longer wavelengths are outside the range of what our eyes can detect, so we cannot see radio waves.
However, even though we can't see radio waves, we can still use them for various purposes, such as wireless communication, radar, and satellite transmission.
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Which of Galileo's observations directly disproved Ptolemy's epicycle model of the Solar System, showing that the Sun is at the center and not Earth?
Answer:
Venus observation.
Explanation:
Galileo had learned regarding the heliocentric (Sun-centered) idea of Copernicus, and acknowledged it. However, the theory was proven by Galileo's observations of Venus. Galileo concluded that Venus should travel round the Sun, sometimes passing behind and then beyond, instead of directly rotating around the Earth.
Recall the observed behavior of the compass during the mapping of the magnetic field. Which of the following descriptions best matches the behavior you observed? Two correct answers required for full credit.
A. Where the field is strong the compass needle readily and quickly aligns with rapid oscillations around the equilibrium direction.
B. Where the field is strong the compass needle slowly oscillates around the final equilibrium position.
C. Where the field is weak the compass needle rapidly oscillates around the final equilibrium position.
D. Where the field is weak the compass needle slowly oscillates around the final equilibrium position.
E. Where the field is weak the compass needle readily and quickly aligns with rapid oscillations around the equilibrium direction.
Answer:
Option A & B
Explanation:
This is cause the compass needle is magnetized anointed in such a way that it responds to magnetic field strength.
The amplitude of a sound wave is measured in terms of its maximum gauge pressure. By what factor does the amplitude of a sound wave increase if the sound level goes up by 26.0 dB?
Answer:
The amplitude of wave increases by a factor of 20
Explanation:
The Sound level in decibel β is described as
[tex]\beta =(10dB)log(\frac{I}{I_{o} })[/tex]
Where I₀=10⁻¹²W/m² is reference intensity
Suppose β₁ is initial sound intensity and β₂ is final sound intensity.Therefore the change in sound intensity is given as
β₁-β₂=26.0 dB
[tex](10dB)log(\frac{I_{2} }{I_{o}} )-(10dB)log(\frac{I_{1} }{I_{o}} )=26.0dB\\(10dB)[log(\frac{I_{2} }{I_{o}} )-log(\frac{I_{1} }{I_{o}} )]=26.0dB\\log(\frac{\frac{I_{2}}{I_{o}} }{\frac{I_{1}}{I_{o}} })=\frac{26dB}{10dB}\\ log\frac{I_{2}}{I_{1}}=2.6\\ \frac{I_{2}}{I_{1}}=10^{2.6}[/tex]
The intensity of sound is directly proportional to the amplitude of wave squared
So
I∝A²
[tex]\frac{I_{1}}{I_{2}}=(\frac{A_{1}}{A_{2}})^{2}\\ (\frac{A_{1}}{A_{2}})=\sqrt{(\frac{I_{1}}{I_{2}})}\\ (\frac{A_{2}}{A_{1}})=\sqrt{(\frac{I_{2}}{I_{1}})}\\ (\frac{A_{2}}{A_{1}})=\sqrt{10^{2.6} }\\ (\frac{A_{2}}{A_{1}})=20[/tex]
Therefore the amplitude of wave increases by a factor of 20
Three resistors are connected into the section of the circuit described by the diagram. Then the wire is cut at point x, and the two cut ends of the wire are separated. Through which of the three resistors, if any, does current still flow?
A. None of the resistors
B. All three resistors
C. R1 only
D. R1 and R2 only
Answer:
C. R1 only
Explanation:
As the wire is cut at x, there will be no current through the resistors R2 and R3. Then the current will only go from a to b through the R1 resistor.
Another way to think about this is that once the wire is cut at x, there is now infinite resistance at the point of cutting; therefore, the current can no longer flow through R2 and R3 resistors, but now it only flows through the R1 resistor.
Therefore, only choice C is correct.
A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble during the same amount of time. Which object has the greatest value for each of these quantities?
Answer: pebble has the greatest value of acceleration due to its low mass.
Explanation:
According to newton's second law of motion,
Force = mass × acceleration
For boulder,
Acceleration = Force/mass
Force acting on boulder is 200N
Its mass is 100kg
Acceleration = 200/100
Acceleration = 2m/s²
Similarly for pebble,
Force on pebble = 200N (the same as boulder)
Its mass is 130g = 0.13kg(has to be converted to the standard unit which is kg)
Its acceleration = 200/0.13
Acceleration of pebble = 1538.5m/s²
Since the question doesn't specify what to compare, we will compare their accelerations.
Therefore, pebble has the greatest value of acceleration due to its low mass.
A flea jumps straight up to a maximum height of 0.490 m . How long is the flea in the air from the time it jumps to the time it hits the ground?
Answer:
0.62 s
Explanation:
given,
maximum height of the flea = 0.49 m
velocity at maximum height = 0 m/s
now, calculating initial velocity
using equation of motion
[tex]v^2 = u^2 + 2 g h[/tex]
[tex]0^2 = u^2 - 2\times 9.8 \times 0.49[/tex]
[tex]u^2 = 9.604[/tex]
[tex]u = 3\ m/s[/tex]
now, calculating time he take to reach at the highest point
v = u + g t
0 = 3 - 9.8 x t
9.8 t = 3
t = 0.31 s
Time it will be in air will be twice the time it took to reach to the maximum height.
Time for which it was in air = 2 x 0.31 s = 0.62 s
If a substance can be separated by physical means and it is not the same throughout, what is it?
A: a homogeneous solution
B: a heterogeneous mixture
C: a pure substance
D: an element
E: a compound
Answer:
Option (B)
Explanation:
A heterogeneous mixture is usually defined as a combination of two or more chemical substances. It can be also elements as well as compounds. These contrasting components can be easily separated from one another by means of physical process. These are comprised of substances that are not even everywhere. There is variation in it.
Thus, the correct answer is option (B).
Answer:
B: a heterogeneous mixture
Explanation:
If the components of a substance can be separated by the physical means then the substance is a mixture and its component have not undergone any kind of chemical change with their original molecular structure.
The mixtures are of two types homogeneous and heterogeneous.
Homogeneous mixtures have a uniform composition of its components throughout the mixture whereas heterogeneous mixtures have a non-uniform composition of its constituents in the mixture.Describe a situation that includes no less than four charges of any magnitude, but they combine so that another location, p, has no net electric field at that point. Describe where those charges could be or what magnitudes they could be
Answer:
Four charges of equal magnitude sitting at the vertices of a square
Explanation:
We can arrive at such a situation by thinking of a simple example first, a configuration of two charges. The force acting on the middle point of a straight line joining the two points(charges) will be zero. That is, the net Electric field will be zero as they cancel out being equal in magnitude and opposite in direction.
Now, we can extend this idea to a square having charge q at each vertex. If we put 'p' at the geometric center, we can see that the Electric fields along the diagonals cancel out due to the charges at the diagonally opposite vertices(refer to the figure attached). Actually, the only requirement is that the diagonally opposite charges are equal.
We can further take this to 3 dimensions. Consider a cube having charges of equal magnitude at each vertex. In this case, the point 'p' will yet again be the geometric center as the Electric field due to the diagonally opposite charges will cancel out.
A train travels due south at 25 m/s (relative to the ground) in a rain that is blown toward the south by the wind. The path of each raindrop makes an angle of 66° with the vertical, as measured by an observer stationary on the ground. An observer on the train, however, sees the drops fall perfectly vertically. Determine the speed of the raindrops relative to the ground.
Answer:
Explanation:
Given
Train travels towards south with a velocity if [tex]v_t=25\ m/s[/tex]
Rain makes an angle of [tex]\theta =66^{o}[/tex] with vertical
If an observer sees the drop fall perfectly vertical i.e. horizontal component of rain velocity is equal to train velocity
suppose [tex]v_r[/tex] is the velocity of rain with respect to ground then
[tex]v_r\sin\theta =v_t[/tex]
[tex]v_r\times \sin (66)=25[/tex]
[tex]v_r=27.36\ m/s[/tex]
Therefore velocity of rain drops is 27.36 m/s
A uniform plank of length 6.1 m and mass 33 kg rests horizontally on a scaffold, with 1.6 m of the plank hanging over one end of the scaffold. L l x How far can a painter of mass 60 kg walk on the overhanging part of the plank x before it tips? The acceleration of gravity is 9.8 m/s 2 . Answer in units of m.
Answer:
Explanation:
consider the principle of moment
when a system is in equilibrium, the clockwise moment (torque) about the pivot is equal to the counterclockwise moment ( torque). Since the plank is uniform the weight of the plank act at the middle which = 6.1 m / 2 = 3.05 m
the distance that can support the weight of the man = d
mass of the man = 70
70 × d = 33 × ( 3.05 - 1.6)
d = 47.85 / 60 = 0.798 m, if the man work beyond this point he will fall.
u are holding the axle of a bicycle wheel with radius30 cm and mass 1.05 kg. You get the wheel spinning at arate of 77 rpm and then stop it by pressing the tire againstthe pavement. You notice that it takes 1.37 s for the wheelto come to a complete stop. What is the angular accelerationof the wheel
Answer:
-5.9 rad/s^{2}
Explanation:
radius (r) = 30 cm = 0.3 m
mass (m) = 1.05 kg
initial speed (u) = 77 rpm
final speed (v) = 0 rpm
time (t) = 1.37 s
angular acceleration =[tex]\frac{(final speed-initial speed)rad/s}{time}[/tex]
therefore
initial speed (U) = 77 rpm = 77 x (2π/60) = 8.06 rad/s
final speed (v) = 0 rpm = 0 rad/s
angular acceleration = [tex]\frac{0-8.06}{1.37}[/tex] = -5.9 rad/s^{2}
Answer:
-5.886 rad/s^2.
Explanation:
radius, r = 30 cm
= 0.3 m
mass, m
= 1.05 kg
initial speed, wo = 77 rpm
Converting from rpm to rad/s,
= 77 rpm * 2pi rad * 1 min/60 s
= 8.063 rad/s
final speed, wi = 0 rad/s
time, t = 1.37 s
angular acceleration = Δw/Δt
= (wi - wo)/t
= 8.063/1.37
= -5.886 rad/s^2.
Austin left the park traveling 4 mph. Then, 3 hours later, Wyatt left traveling the same direction at 10 mph. How long until Wyatt catches up with Austin?
ANSWER: 2 hours
EXPLANATION: After three hours Austin has traveled 12 miles. Wyatt will start up and in an hour will be at 10 miles, but by that time Austin will be at 16 miles. One more mile and Wyatt will be at 20 miles and so will Austin. So that would make the answer 2 hours.
1. Our entire solar system orbits around the center of the Milky Way Galaxyabout once every 230 million years.
2. The Milky Way and Andromeda galaxies are among a few dozen galaxies that make up our Local Group.
3. The Sun appears to rise and set in our sky because Earth orbitsonce each day.
4. You are one year older each time Earth rotatesabout the Sun.
5. On average, galaxies are getting farther apart with time, which is why we say our universeis expanding.
6. Our solar systemis moving toward the star Vega at about 70,000 km/hr.
Answer: Hello! Apparently, your question is incomplete. Those were sentences in which you had to complete with missing information, so here we go:
1- Our entire solar system orbits around the center of the MILKY WAY GALAXY about once every 230 million years.
2- The Milky Way and Andromeda galaxies are among a few dozen galaxies that make up our LOCAL GROUP.
3 - The Sun appears to rise and set in our sky because Earth ROTATES once each day.
4 - You are one year older each time Earth ORBITS about the Sun.
5 - On average, galaxies are getting farther apart with time, which is why we say our UNIVERSE is expanding.
6 - Our SOLAR SYSTEM is moving toward the star Vega about 70,000 km/hr.
Xenon fluoride can be prepared by heating a mixture of Xe and F2 gases to a high temperature in a pressure-proof container. Assume that xenon gas was added to a 0.25 liter container until its pressure reached 0.12 atm at 0.0°C. Fluorine gas was then added until the total pressure reached 0.72 atm at 0.0°C. After the reaction was complete, the xenon was consumed completely, and the pressure of the F2 remaining in the container was 0.36 atm at 0.0°C. What is the empirical formula of the xenon fluoride?
Answer:
XeF₄
Explanation:
Dalton law's of partial pressure states that the total pressure equal to the sum of the partial pressure of the individual gases that make up the mixture.
Pt = Pxe + Pf₂
0.72 = 0.12 + Pf₂
0.72 - 0.12 = Pf₂
0.60 atm = Pf₂
after the the reaction was complete, the pressure of F₂ remaining = 0.36 atm
pressure of the consumed F₂ = 0.60 - 0.36 = 0.24 atm
Pxe / total pressure = number of mole / total number of mole of gas present
0.24 / 0.72 = nf / nt
0.12 / 0.72 = nxe / nt
comparing the two
(1/ 3) / ( 1/6) = (nf/ nt) / ( nxe/ nt)
nf / nxe = 2 / 1
the emperical formula = XeF₄
The empirical formula of the xenon fluoride is :
-XeF₄
"Dalton law's of partial pressure"It states that the Total pressure break even with to the whole of the fractional weight of the person gasses that make up the blend.
Pt = Pxe + Pf₂0.72 = 0.12 + Pf₂0.72 - 0.12 = Pf₂0.60 atm = Pf₂Pressure of F₂ remaining = 0.36 atm
Pressure of the consumed F₂ = 0.60 - 0.36 = 0.24 atm
Pxe / total pressure = number of mole / total number of mole of gas present
0.24 / 0.72 = nf / nt
0.12 / 0.72 = nxe / nt
comparing the two:
(1/ 3) / ( 1/6) = (nf/ nt) / ( nxe/ nt)
nf / nxe = 2 / 1
The emperical formula = XeF₄
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A water break at the entrance to a harbor consists of a rock barrier with a 50.0-m-wide opening. Ocean waves of 20.0-m wavelength approach the opening straight on. At what angles to the incident direction are the boats inside the harbor most protected against wave action?
The angles to the incident direction are the boats inside the harbor most protected against wave action will be 23.57 °
What is diffraction ?Diffraction is the phenomenon that occur when a wave of light encounter an obstacle or a slit generally.
considering wide opening of harbor as thickness d
the ocean wave as light source (coherent )
boats inside the harbor as screen where diffraction pattern is going to happen
so , destructive interference should happen (to minimize the amplitude of wave ) in order to save the boats from its effect
n * lambda = d sin (theta )
n=1 ( first order minima )
sin(theta ) = lambda / d
sin( theta ) = 20 /50
sin(theta) = 2/5
theta = sin inverse (2/5)
theta = 23.57 °
The angles to the incident direction are the boats inside the harbor most protected against wave action will be 23.57 °
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An electric drill starts from rest and rotates with a constant angular acceleration. After the drill has rotated through a certain angle, the magnitude of the centripetal acceleration of a point on the drill is twice the magnitude of the tangential acceleration. What is the angle?
Answer:
Explanation:
Given
magnitude of centripetal acceleration is twice the magnitude of tangential acceleration
Suppose [tex]\theta [/tex] is theta angle rotated by electric drill
it is given that it starts from rest i.e. [tex]\omega _0=0[/tex]
suppose [tex]\omega [/tex] and [tex]\alpha [/tex] is the final angular velocity and angular acceleration
using rotational motion equation
[tex]\omega ^2-\omega _0^2=2\times \alpha \times \theta [/tex]
where [tex]\theta [/tex]=angle turned by drill
[tex]\omega _0[/tex]=initial angular velocity
[tex]\omega [/tex]=final angular velocity
[tex]\alpha [/tex]=angular acceleration
[tex]\omega ^2-0=2\times \alpha \times \theta [/tex]
[tex]\omega ^2=2\alpha \theta ---1[/tex]
It is also given that centripetal acceleration is twice the magnitude of tangential i.e.
[tex]\omega ^2r=\alpha \times r[/tex]
where r=radial distance of any point from axis of drill
i.e. [tex]\omega ^2=\alpha [/tex]
substitute this value to equation 1
we get
[tex]\theta =\frac{\omega ^2}{2\alpha }[/tex]
[tex]\theta =1\ rad[/tex]
In The Funeral of St. Bonaventure, Francisco de Zurbarán used the principle of __________ to create emphasis and focal point.
Answer:
In The Funeral of St. Bonaventure, Francisco de Zurbarán used the principle of _contrast_ to create emphasis and focal point
Explanation:
Contrast relates to the combination of opposing components and effects as an art theory. Lighter and darker colours, polished and rough materials, large and small shapes. Contrast can be used for the production of diversity visual interest and excitement.
A certain spacecraft is x AU (Astronomical Units) from Earth. How long in seconds does it take for a signal to reach the Earth after it is transmitted from the spacecraft? Hint: An AU is about 149.9 Million Km, and light moves at 299,800 Km/s. Indicate your answer to the nearest whole second.
Answer:
The time taken for a signal to reach the Earth after it is transmitted from the spacecraft is (500x) seconds
Explanation:
Distance of spacecraft from Earth = x AU = x × 149.9×10^6 Km = (149.9×10^6x) Km
Speed of light = 299,800Km/s
Time taken for a signal to reach the Earth after it is transmitted from the spacecraft = distance of spacecraft from Earth ÷ speed of light = (149.9×10^6x)Km ÷ 299,800Km/s = (500x) seconds
You are standing in an elevator that is accelerating upward at 2 m/s2. What is the normal force acting on you by the elevator if your mass is 70 kg?
Answer:
784 N.
Explanation:
The expression for the Normal reaction acting on a body inside an elevator that is moving upward is given as
R = m(g+a)................. Equation 1
Where R = normal reaction, g = acceleration due to gravity, a = acceleration, m = mass .
Given: m = 70 kg, a = 2 m/s²
Constant: g = 9.8 m/s²
Substitute into equation 1
R = 70(2+9.2)
R = 70(11.2)
R = 784 N.
Hence the normal force = 784 N.
A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation x(t)= α t2− β t3, where α = 1.53 m/s2 and β = 4.80×10−2 m/s3. Calculate the average velocity of the car for each time interval:_______.
a) t = 0 to t = 2.00 s.
b) t = 0 to t = 4.00 s.
c) t = 2.00 s to t = 4.00 s.
Answer:
(a) [tex]V_{avg}=2.868m/s[/tex]
(b) [tex]V_{avg}=5.352m/s[/tex]
(c) [tex]V_{avg}=7.836m/s[/tex]
Explanation:
Given data
x(t)=αt²-βt³
α=1.53m/s²
β=0.0480m/s³
First we need to find distance x at these time so
x(t)=1.53t²-0.0480t³
at t=0
x(0)=1.53(0)²-0.0480(0)³=0m
at t=2
x(2)=1.53(2)²-0.0480(2)³=5.736m
at t=4s
x(4)=1.53(4)²-0.0480(4)³=21.408 m
For(a) Average velocity at t=0s to t=2s
The average velocity is given as
Vavg=Δx/Δt
[tex]V_{avg}=\frac{x_{f}-x_{i} }{t_{f}-t_{i}}\\ As\\x(0)=0m\\x(2)=5.736m\\V_{avg}=\frac{5.736m-0m }{2s-0s}\\V_{avg}=2.868m/s[/tex]
For(b) Average velocity at t=0s to t=4s
The average velocity is given as
Vavg=Δx/Δt
[tex]V_{avg}=\frac{x_{f}-x_{i} }{t_{f}-t_{i}}\\ As\\x(0)=0m\\x(4)=21.408m\\V_{avg}=\frac{21.408m-0m }{4s-0s}\\V_{avg}=5.352m/s[/tex]
For(c) Average velocity at t=2s to t=4s
The average velocity is given as
Vavg=Δx/Δt
[tex]V_{avg}=\frac{x_{f}-x_{i} }{t_{f}-t_{i}}\\ As\\x(2)=5.736m\\x(4)=21.408m\\V_{avg}=\frac{21.408m-5.736m }{4s-2s}\\V_{avg}=7.836m/s[/tex]
Final answer:
The average velocity of the Honda Civic over the time intervals from t=0 to t=2.00 s is 2.868 m/s, from t=0 to t=4.00 s is 5.352 m/s, and from t=2.00 s to t=4.00 s is 7.836 m/s, calculated using the given equation and the variables α and β.
Explanation:
To find the average velocity of the Honda Civic over specific time intervals using the equation x(t) = α t^2 - β t^3, where α = 1.53 m/s^2 and β = 4.80×10^-2 m/s^3, we must calculate the change in position (Δx) over the change in time (Δt) for each interval.
a) t = 0 to t = 2.00 s
Initial position, x(0) = 0 (since any term with t = 0 results in 0).
Final position, x(2) = 1.53×2^2 - 4.80×10^-2×2^3 = 6.12 - 0.384 = 5.736 m.
Δx = 5.736 - 0 = 5.736 m, Δt = 2 s.
Average velocity = Δx/Δt = 5.736 m / 2 s = 2.868 m/s.
b) t = 0 to t = 4.00 s
Final position, x(4) = 1.53×4^2 - 4.80×10^-2×4^3 = 24.48 - 3.072 = 21.408 m.
Δx = 21.408 - 0 = 21.408 m, Δt = 4 s.
Average velocity = Δx/Δt = 21.408 m / 4 s = 5.352 m/s.
c) t = 2.00 s to t = 4.00 s
Using the previously calculated final positions for t = 2 and t = 4:
Δx = 21.408 - 5.736 = 15.672 m, Δt = 4 s - 2 s = 2 s.
Average velocity = Δx/Δt = 15.672 m / 2 s = 7.836 m/s.
Vector A is 3.00 units in length and points along the positive x-axis. Vector B is 4.00 units in length and points along the negative y-axis. Use graphical methods to find the magnitude and direction of the following vectors:
To find the magnitude and direction of the resultant vector R, we can use graphical methods. First, find the components of vectors A and B along the x and y axes. Then, use the Pythagorean theorem to find the magnitude of R and the inverse tangent function to find the direction of R.
Explanation:To find the magnitude and direction of the resultant Vector B, with a magnitude of 4 units, points along the negative y-axis, so its x-component is 0 and its y-component is -4.
To find the components of R, we can simply add the corresponding components of A and B: Rx = Ax + Bx
= 3 + 0 = 3, Ry = Ay + By = 0 + (-4) = -4.
Using the Pythagorean theorem, we can find the magnitude of R: R = sqrt(Rx^2 + Ry^2)
= sqrt(3^2 + (-4)^2) = sqrt(9 + 16) = sqrt(25) = 5 units.
To find the direction of R, we can use the inverse tangent function: Rtheta = atan(Ry/Rx)
= atan((-4)/3)
= atan(-4/3) = -53.13 degrees.
However, since vector B points along the negative y-axis, the direction of R is 90 degrees minus the calculated angle: Rtheta = 90 - 53.13 = 36.87 degrees.
Therefore, the magnitude of R is 5 units and it points at an angle of 36.87 degrees north of the x-axis.
According to the animation, in the first half of the lunar cycle, the waxing, bright part of the moon appears on the ____ side of the Earth. After full moon when the moon is waning, the illuminated part of the moon appears on the ______ side.
Answer: Blanks in order are: Right, Left
Explanation:
The moon rotates around the Earth. It completes its rotation in roughly 29.5 days which is known as the lunar cycle. The first half of rotation is known as waxing and in this the moon starts to become a full moon so bright side of the moon appears on the left side of Earth. After this ends, the waning part starts which means the decreasing of light of moon so bright side is on the left side of the Earth.
During the first half of the lunar cycle, the bright part of the moon (waxing moon) appears on the right side and after the full moon, the lit part of the moon (waning moon) appears on the left side.
Explanation:According to the animation, in the first half of the lunar cycle, the waxing, or growing, bright part of the moon appears on the right side (from an observer in the northern hemisphere). This phase is known as a waxing moon. After the full moon when the moon starts to shrink, or wane, the illuminated part of the moon appears on the left side. This phase is known as a waning moon.
Learn more about Lunar CycleSuppose that the voltage of the battery in the circuit is 3.3 V, the magnitude of the magnetic field (directed perpendicularly into the plane of the screen) is 0.66 T, and the length of the rod between the rails is 0.19 m. Assuming that the rails are very long and have negligible resistance, find the maximum speed attained by the rod after the switch is closed.
Answer:
Maximum velocity of rod will be equal to 26.315 m/sec
Explanation:
We have given voltage of the battery in the circuit V = 3.3 volt
Magnetic field B = 0.66 Tesla
Length of the rod l = 0.19 m
We know that emf is given by e = BVl
We have to find the maximum velocity of the rod
Here velocity is maximum
So [tex]e=v_{max}Bl[/tex]
So [tex]3.3=v_{max}\times 0.66\times 0.19[/tex]
[tex]v_{max}=26.315m/sec[/tex]
So maximum velocity of rod will be equal to 26.315 m/sec
Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1050 kg and was approaching at 6.00 m/s due south. The second car has a mass of 750 kg and was approaching at 25.0 m/s due west.
Answer:
v = 11.0 m/s at 198.6° (18.6° south of west)
ΔKE = -145 kJ
Explanation:
I assume you want to find the final velocity and the change in kinetic energy.
Take east to be +x and north to be +y.
Momentum is conserved in the x direction:
(1050 kg) (0 m/s) + (750 kg) (-25.0 m/s) = (1050 kg + 750 kg) vₓ
vₓ = -10.4 m/s
Momentum is conserved in the y direction:
(1050 kg) (-6.00 m/s) + (750 kg) (0 m/s) = (1050 kg + 750 kg) vᵧ
vᵧ = -3.50 m/s
The magnitude of the final velocity is:
v² = (-10.4 m/s)² + (-3.50 m/s)²
v = 11.0 m/s
The direction of the final velocity is:
θ = atan(-3.50 m/s / -10.4 m/s)
θ = 198.6°
The initial kinetic energy is:
KE₀ = ½ (1050 kg) (6.00 m/s)² + ½ (750 kg) (25.0 m/s)²
KE₀ = 253,275 J
The final kinetic energy is:
KE = ½ (1800 kg) (11.0 m/s)²
KE = 108,682 J
The change in kinetic energy is:
ΔKE = 108,682 J − 253,275 J
ΔKE ≈ -145,000 J
Which of the following are molecules?
Answer:
b c and e
Explanation:
Answer: C, D, and E are all molecules!