A pure tone with frequency f1 = 800 Hz is modulated by frequency f2 = 160 Hz. The primary sidebands are 960 Hz and 640 Hz. The virtual pitch heard will be the related fundamental, 800 Hz.
In physics, the term frequency refers to the number of waves passing through a fixed point in unit time. It also represents the number of cycles or oscillations an object undergoes per unit time in periodic motion.
The wave frequency (f,) is the number of waves passing through a point in one second. Frequency is measured in Hertz (Hz). One hertz equals one wave per second. Frequency is also called cycles per second or time frequency. The usual symbol for frequency is the Latin letter f or the Greek letter ν (nu).
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A boy is watching his grandfather fire an old cannon. He notices that whenever the cannonball is fired, it moves with a very high velocity to the right. He also notices that when the cannonball is fired, the cannon moves very slowly to the left. How does conservation of momentum explain these observations?.
Since the system's total momentum was zero before the cannon was fired, the momentum of the projectile and the cannon must be equal and opposing. The cannon will have a lower velocity since it has a lot greater mass.
Law of conservation of momentum states that total momentum of system remains conserved in the absence of external force.
As we know that know external no force is acting in the on the system therefore momentum should be conserved according to the law of the conservation of momentum.
As we know that momentum is given by the formula
momentum = mass × velocity
initially momentum of the system is equal to zero because the velocity of the system is zero.
After fire ball move with high velocity means we have some momentum in the direction of the ball's motion but according to the law of the conservation there should be some momentum in the opposite direction which will cancel out the momentum of the ball therefore cannon will also move in opposite direction.
But as we know that momentum = mass × velocity
As the mass of the cannon is much higher than the mass of the ball therefore less velocity can generate the same amount of the momentum that is required to the cancel the momentum of the ball .
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a ball is shot from the ground straight up into the air with initial velocity of 48 ft/sec. assuming that the air resistance can be ignored, how high does it go?
The ball goes up to 35.83 ft high. The result is obtained by using the formula of motion with constant acceleration.
What is motion with a constant acceleration?A motion along a straight line with a constant acceleration is a motion which the initial and final velocity change. There are 3 important formulas in this case for vertical motion.
v₁ = v₀ + gt
v₁² = v₀² + 2gh
h = v₀t + 1/2 gt²
Where
v₀ = initial velocity (m/s)v₁ = final velocity (m/sg = acceleration due to gravity (9.8 m/s²)t = time (s)h = height (m)Note: If the object goes up, the value of g is (-).
A ball moves from the ground straight up with a velocity of 48 ft/sec. Find the height of the ball!
First, we change the unit of initial velocity.
v₀ = 48 ft/sec
v₀ = 48 × 0.3048 m/s
v₀ = 14.63 m/s
The ball will go up to a certain height. At the maximum height, the velocity of the ball is 0. Thus, we can use the following formula to find h.
v₁² = v₀² - 2gh
0 = (14.63)² - 2(9.8)h
214.04 = 19.6h
h = 10.92 m
h = 10.92/0.3048 ft
h = 35.83 ft
Hence, the ball will go straight up to a height of 35.83 ft.
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A passenger weighing 500N is inside an elevator weighing 24500 N that rises 30 m every minute. How much power is needed for the elevator’s trip?
A passenger weighing 500N is inside an elevator weighing 24500 N that rises 30 m every minute is 12500 W (12.5 kW).
What is Power?
Power is the amount of work that is done per unit of time. It can be associated with the speed of a change of energy within a system, or the time it takes to perform a job.
There are different types of power,
Mechanical power: is that work performed by an individual or a machine in a certain period of time.
Electric power: which is the result of the multiplication of the potential difference between the ends of a load and the current flowing there.
P= W/t
Where, P- Power,
W- Work
T- Time
The total weight of the passenger + elevator is
Fg = 500+24500
= 25000
The total work done to rise the elevator + passenger is equal to the product between the total weight and the distance covered during the trip (d = 30 m):
W = Fgd
= 25000×30
=7,50,000 J.
The power needed for the trip is equal to the ratio between the work done (W) and the time taken (t):
P = W/t
Since the time taken is t = 1 min = 60 s, the power needed is
P = 750000 / 60
= 12,500 W
P = 12.5 kW
Thus, Power was calculated as P = 12.5 kW.
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what is the greatest average speed ????v of blood flow at 37∘c37∘c in an artery of radius 2.25 mm2.25 mm if the flow is to remain laminar? take the density of blood to be 1025 kg/m3,1025 kg/m3, and the viscosity to be 2.084×10−3 pa·s.
Average speed of blood flow is given by:
V = n*Re/(rho*d)
n = viscosity of blood = 2.084*10^-3 Pa.s
Re = max reynolds number for which flow remains laminar = 2000
rho = density of blood = 1025 kg/m^3
d = diameter of artery = 2*radius = 2*2.50 mm = 5.0*10^-3 m
So,
V = 2.084*10^-3*2000/(1025*5.0*10^-3)
V = 0.813 m/sec
On a train moving , 75 m/s you roll a ball towards the front of the train with a speed of 5m/s. Your friend standing some unknown distance away from you catches it. To a person outside the train, the ball traveled 220m until it was caught. How far away is your friend standing from you?
The distance of your friend from you is 15.7 m.
What is the time of motion of ball?
The time take for the ball to travel to you friend is calculated by applying the principle of relative velocity as shown below.
( Vt - Vb ) t = d
where;
Vt is the velocity of the trainVb is the velocity of the ballt is the time of motion of the balld is the distance travelled by the ball( Vt - Vb ) t = d
(75 - 5) t = 220
70t = 220
t = 220 / 70
t = 3.14 s
The distance of your friend from you is calculated as;
d1 = 5 m/s x 3.14 s
d1 = 15.7 m
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A 1500-kg car moving at 25 m/s hits an initially uncompressed horizontal spring with spring constant of 2. 0 ? 106 n/m. What is the maximum compression of the spring? (neglect the mass of the spring. ).
A 1500-kg car moving around 25 m/s collides with a horizontal spring that is initially uncompressed but has a spring stiffness of 2.0?106 n/m as well as a max compress of x = 0.68 meters.
What is another word for compression?Compress, constrict, contract, inflate, and shrink are a few words that frequently replace the word compress. While all of these phrases refer to "decreasing in bulk or area," compress indicates squeezing over resistance into a constricted area with a certain shape.
Briefing:Considering that,
The automobile weighs 1500 kg.
Vehicle speed, v = 25 m/s
spring's spring constant, k=2×10⁶ N/m
Let x be the greatest distance the spring may compress before breaking,
1/2mv²=1/2kx²
1/2mv²=1/2kx²
x=[tex]\sqrt{mv^{2} /k}[/tex]
x=[tex]\sqrt{1500*25x^{2} /2*10^{6} }[/tex]
x = 0.68 meters
The spring is thereby compressed by 0.68 meters.
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Three identical rods are welded together to form a Y- shaped figure. The cross-sectional area of each rod is A, and they have length L and thermal conductivity k. The free end of rod 1 is maintained at T1 and the free ends of rods 2 and 3 are maintained at a lower temperature T0. You may assume that there is no heat loss from the surfaces of the rods What is TJ, the temperature of the junction point?
The temperature of the junction point = [tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]
What is Temperature ?Temperature is a unit used to describe hotness or coldness. It can be stated in terms of any number of arbitrary scales and shows the direction in which heat energy will naturally flow, i.e., from a hotter body to a colder body (one at a lower temperature). Temperature does not equal the energy of a thermodynamic system; for instance, an iceberg has a far larger total thermal energy than a match, despite the fact that a match is burning at a much higher temperature.
According to the given information
[tex]T_{1} - T_{j} = 2 ( T_{j} - T_{0})[/tex]
Q/t = K × A ×([tex]T_{1} - T_{j}[/tex] )/L
However you have the Y shape so that half the heat transfer goes into each part of the Y. So you need a factor of 2 when you add in the Y parts.
(Q/t)bottom = 2x(Q/t)top
[tex]T_{1} - T_{j} = 2 ( T_{j} - T_{0})[/tex]
[tex]T_{1} + 2T_{0} = 3T_{j}[/tex]
[tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]
The temperature of the junction point = [tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]
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how fast (in rpm ) must a centrifuge rotate if a particle 3.1 cm from the axis of rotation is to experience an acceleration of 200000 g 's?
The value of the speed will be [tex]2.7\times 10^4rm[/tex]
We have,
Radius of particle = 3.1 cm
Acceleration of particle = 20000 g's
As we know,
The value of acceleration can be determined by using the formula:
[tex]a & =v^2 / r \\v & =\sqrt{a r}{ }^2=a r \\[/tex], where, v = velocity, a = acclreation, and r = radius of particle
So, putting the value of "a" and 'r" in the above formula:
[tex]$$\begin{aligned}& =\sqrt{(200000 \mathrm{~g})\left(3.1 \times 10^2 \mathrm{~m}\right)} \\v & =\sqrt{(200000)\left(9.8 \mathrm{~m} / \mathrm{s}^2\right)\left(3.1 \times 10^{-2} \mathrm{~m}\right)} \\v & =1.745 \times 10^2 \mathrm{~m} / \mathrm{s} \\& =\left(1.745 \times 10^2 \mathrm{~m} / \mathrm{s}\right) \frac{1 \mathrm{rev}}{(2 \pi)\left(6.2 \times 10^{-2} \mathrm{~m}\right)}\left(\frac{60 \mathrm{~m}}{1 \mathrm{~min}}\right) \\& =2.7 \times 10^4 \mathrm{rm}\end{aligned}$$[/tex]
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if a jumper falls for one minute through upper winds averaging 30 knots from the west, how far will the jumper drift? in what direction?
A jumper will drift half a mile if they fall for one minute through winds that are blowing from the west at an average speed of 30 knots.
Explain about the Distance?Distance is an object's overall movement, regardless of direction. Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has travelled.
The distance between two objects, points, lines, etc., in any direction. the condition or occurrence of being away from another object or person in space; distance. an area that is linear: Seven miles is too far to go in an hour of walking.
The entire path an object has taken can be used to define the distance of an object. an illustration If a car drives 5 km east, then turns to head north for 8 km, the final distance driven by the car must be 13 km.
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A 0,200-kg piece of lead at 100.0°C is dropped into a calorimeter. The calorimeter is a copper can of mass
5.00 x 102 kg and already contains 0.100 kg of water at 20.0°C. Calculate the final temperature if the specific heats of water, lead, and copper are 4.20 x 103 J/kg.K, 1.30 x 102 J/kg.K, and 4.00 x 103 J/kg:K respectively.
Answer:
24.5°C
Explanation:
An ideal gas is initially in a state that corresponds to point 1 on the graph above, where it has pressure P1 volume V1, and temperature T1. The gas undergoes an isothermal process represented by the curve shown, which takes it to a final state 3 at temperature T3. If T2 and T4 are the temperatures the gas would have at points 2 and 4, respectively, which of the following relationships is true? a. t1
b. t1
c. t1
d. t1=t2
e. t1=t4
The following relationship is true T1 < T2.
An ideal gas is defined as a gas in which all collisions between atoms or molecules are perfectly elastic and no intermolecular attractive forces occur. It can be thought of as a collection of perfectly rigid spheres that collide but do not interact.
The volume of gas particles is negligible. Gas particles are the same size and have no intermolecular forces as other gas particles. Gas particles move randomly according to Newton's laws of motion. Gas particles undergo perfectly elastic collisions without losing energy. This is the relationship between four variables and describes the state of the gas.
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(b) Explain the behaviour of the light at points Y and Z.
ray of
light
not to scale
Help
At a point, Y refraction is observed and the light ray is moving away from the normal means going from the denser to the rarer medium, at point Z, the light ray is moving towards the normal, which means travelling in the denser medium.
What is Refraction?The redirection of a wave as it travels through one medium and into another is called refraction. The wave's altered speed or a shift in the medium might both result in a redirection. Refraction of light is governed by Snell's rule, which states that for a given set of media, the ratio of the sines of the angle of incidence and angle of refraction is equal to the phase velocities (v1/v2) or, alternatively, the refractive indices (n2/n1) of the two media.
What is a Denser medium?A medium is said to be optically denser if the speed of light is lower in it. In terms of optical density, glass is a denser medium than air.
Hence, at a point, Y refraction is observed and the light ray is moving away from the normal means going from the denser to the rarer medium, at point Z, the light ray is moving towards the normal, which means travelling in the denser medium.
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Any external force that acts against movement is called __________. A. Gravityb. Efficiencyc. Resistanced. Momentum.
Answer:
the answer is resistance
how much work does an elevator motor do to lift a 1500 kg elevator a height of 100 m ? express your answer with the appropriate units.
1.47 MJ work does an elevator motor do to lift a 1500 kg elevator a height of 100 m.
What is work in a physics?In physics, the term "work" refers to the energy transfer that takes place when an item is displaced over a distance by such an external force, at least a portion of which is supplied in the displacement direction. Stimulates into an object to cause some displacement is what is referred to as work. The ability to perform tasks is referred to as energy. The work is consistently the same.
Briefing:Work is simply the result of force multiplied by distance, so:
Work = Force * Distance
In this instance, force is simply equal to the elevator's weight, so:
Work = mass * gravity * distance
Work = 1500 kg * 9.8 m/s^2 * 100 m
Work = 1,470,000 J = 1.47 MJ
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the pendulum consists of a 14-kgkg uniform disk and a 3-kgkg uniform slender rod. it is released from rest in the position shown. suppose that lll
The angular velocity of the pendulum at the bottom is 2.82 rad/s.
The length of the pendulum rod is 1.5ma nd the radius of the pendulum is 0.8m. The mass of the pendulum bob is 14kg and the mass of the rod is 3 kg.
When the pendulum is dropped,
Rotational kinetic energy = Potential energy
Iw²/2 = Mg(L+R) + mgL
Where,
L is the length of the rod and the R is the radius of the bob and I is the moment of inertia of the system while W is the angular speed,
[mL²/3 + MR² + M(L+R)²]W²/2 = Mg(L+R) + mgL
Now, solving the above complex equation,
W = 2.82 rad/s.
So, the angular speed of the pendulum is 2.82 rad/s.
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Complete question- The pendulum consists of a 14 kg uniform disk and a 3 kg uniform slender rod. It is released from rest in the position shown. Suppose that L = 1.5 m. Determine the angular velocity, measured clockwise, when it rotates clockwise 90 degrees.
given the mass of the rubber in the balloon is 1.10 g, what is the net vertical force (in n) on the balloon if it is let go? you can neglect the volume of the rubber. n (upward)
The vertical component of force is 10.78N
The need is to find what would be the net vertical force (in n) on the balloon if it were released, given that the rubber in the balloon weighs 1.10g.The relationship between an object's mass and the amount of force required to accelerate it is outlined in Newton's second law of motion. F=ma, or the force acting on an object is equal to its mass times acceleration, is a common way to express Newton's second law. Therefore, more force is required to accelerate an object with more mass. Neglecting the volume of rubber , additionally, an object accelerates more quickly the more force it is under.[tex]F=ma\\\\F=1.10 * 9.81\\\\F=10.78N[/tex]To learn more about Newton's second law of motion-
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"Which of the following characteristics of Earth's relationship to the Sun explains the existence of Earth's seasons? Choose all that apply: ANSWER: Earth's axis always points in the same direction relative to the stars_ Earth spins on its axis completing one rotation each day: Earth orbits around the Sun, completing one orbit each year: Earth's axis is tilted relative to its orbital plane. Earth has a satellite called the Moon, which rotates around Earth. Correct art B What is the June solstice? ANSWER: The time of the year when Earth's geographic North and South Poles are leaning in similar ways toward the Sun the time of the year when Earth's geographic North Pole is leaning most directly toward the Sun the time of the year when Earth's geographic North Pole is leaning most directly away from the Sun Correct art C How does the inclination of Earth's axis change over the course of a year? ANSWER:"
The following characteristics of Earth's relationship to the Sun explain the existence of Earth's seasons is:
Earth orbits around the Sun, completing one orbit each yearEarth spins on its axis completing one rotation each dayEarth's axis is tilted relative to its orbital plane.Earth's axis always points in the same direction relative to the stars.The tilt of the earth's axis creates the seasons. Throughout the year, different parts of the world receive the most direct sunlight. So when the North Pole tilts toward the Sun, it's summer in the Northern Hemisphere. And when the Antarctic tilts toward the Sun the northern hemisphere will be in winter.
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how will the momentum of the blocks after the collision compare to the momentum of the blocks before the collision? *
Momentum is conserved for any collision in an isolated system. Before and after the collision, the collection of items in the system had an equal amount of total momentum.
What does physics define as momentum?
Momentum is characterized as the intensity of a body's motion.
As momentum relies on both velocity and the direction of the body's motion, it is quantified by "mass velocity".
What is the connection between collision and momentum?
During collisions between objects, momentum is a relevant concept. The total momentum before a collision between two objects equals the total momentum after the impact (in the absence of external forces). The law of conservation of momentum is this. It holds true in every collision.
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Match each term with its definition.MorphemePhonemeGrammarSyntax1)smallest units of sound that carry meaning on their own2)smallest units of sound that make a difference in meaning3)combined set of rules that govern use of a particular language4)rules for forming speech sounds into phrases and sentences
All the terms are related to languages.
Morpheme - smallest units of sound that carry meaning on their own
Phoneme -smallest units of sound that make a difference in meaning
Grammar - a combined set of rules that govern the use of a particular language
Syntax - rules for forming speech sounds into phrases and sentences
The smallest linguistic unit capable of meaning modification is the phoneme.
Morphemes are divided into two distinct types, bases (or roots) and affixes.
Most people think of grammar as a set of rules that help us form sentences.It covers a variety of language-related topics, such as Parts of speech (verbs, adjectives, nouns, adverbs, prepositions, conjunctions, modifiers, etc.) Clauses (e.g. independent, dependent, compound) (e.g. independent, dependent, compound)
The sequence of grammatical elements like subjects, verbs, direct and indirect objects, etc. is determined by syntax in English.
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suppose you were to find all of the angles 8 at which two very narrow slits separated by a/2 would produce minimum. how would this set of angles be different from the set of angles given by your equation in part iii above?
This set of angles would be the angles at which destructive interference occurs, which is 180° apart from the angles at which constructive interference occurs.
What is Intensity?
The power transmitted per unit area is known as the intensity as well as flux of radiant energy.
Uses of Intensity
Intensity is most frequently used to describe the average power transfer above one period of the wave. Other situations where energy is transmitted can also be described in terms of intensity.
Hence, The set of angles given by the equation in Part III is the set of angles at which the maximum intensity of light is produced.
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This set of angles would be the angles at which destructive interference occurs, which is 180° apart from the angles at which constructive interference occurs.
What is Intensity?
The power transmitted per unit area is known as the intensity as well as flux of radiant energy.
Uses of Intensity
Intensity is most frequently used to describe the average power transfer above one period of the wave. Other situations where energy is transmitted can also be described in terms of intensity.
Hence, The set of angles given by the equation in Part III is the set of angles at which the maximum intensity of light is produced.
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A diverging lens has a focal length of magnitude 21.8 cm.
(a) Locate the images for each of the following object distances.
43.6 cm
distance cm
location ---Select--- in front of the lens behind the lens
21.8 cm
distance cm
location ---Select--- in front of the lens behind the lens
10.9 cm
distance cm
location ---Select--- in front of the lens behind the lens
(b) Is the image for the object at distance 43.6 real or virtual?
realvirtual
Is the image for the object at distance 21.8 real or virtual?
realvirtual
Is the image for the object at distance 10.9 real or virtual?
realvirtual
(c) Is the image for the object at distance 43.6 upright or inverted?
uprightinverted
Is the image for the object at distance 21.8 upright or inverted?
uprightinverted
Is the image for the object at distance 10.9 upright or inverted?
uprightinverted
(d) Find the magnification for the object at distance 43.6 cm.
Find the magnification for the object at distance 21.8 cm.
Find the magnification for the object at distance 10.9 c
A diverging lens has a focal length of magnitude 21.8 cm and the images are located behind the lens.
(a) u = -10.9 cm
1/v= 1/10.9 - 1/21.9
v= 21.8cm
Behind the lens.
(b) 1. Virtual
2. Virtual
3. Real
(c) m = v/u
1. Erect/ Upright
2. Upright
3. Inverted
(d) m = v/u
1. m = -43.6/-43.6 = 1. Magnification = 1.
2. infinity.
3. m = 21.8 / -10.9 = -2. Magnification = -2.
Therefore, these are the answers for above given question.
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In addition to science courses like physics and chemistry, what other types of courses are becoming increasingly relevant to space science careers?.
Structural engineering is the other course that are increasingly becoming relevant to space science careers
What are Space science careers ?Investigating how gravity affects the human body, building the telescopes of the future. providing accessible explanations of solar system discoveries. These are just a few examples of the projects that people involved in space exploration employment work on.
Learning how to repair space stations, aircraft, or even make space shuttles or items you'll need in space requires knowledge in civil engineering, which is the notion of designing large transportation projects.
Structural engineering is the other course that are increasingly becoming relevant to space science careers
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a solid conductor with radius a is supported by insulating disks on the axis of a conducting tube with inner radius b and outer radius c in the following figure. the central conductor and tube carry equal currents i in opposite directions. the currents are distributed uniformly over the cross sections of each conductor.
We can determine the magnetic field at two different distances from a system made up of two conductors using Ampere's law:
a) The system's magnetic field is:
b) The magnetic field for the system's exterior is b = 0.
Ampere's Rule.
According to Ampere's law, the magnetic field's dot product times a closed path is proportional to the current flowing through the path.
∫ B. ds = μ₀ I
Here, B is the magnetic field, S is the closed path, μ₀ is the vacuum permittivity, and I is the current where bold indicates vectors.
Ask about the magnetic fields within the two conductors (optional).
Fixing the associated circular path will cause I, the current that stops inside the path, to flow through the system.
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what is the power output, in watts, of the combined resistance when the motor is operating at full speed?
A watt is equivalent to an amp multiplied by a volt. All done! Therefore, watt = amp X volt. This equation is also sometimes written as W=A X V.
What does watt mean?The power unit is the watt. It refers to the quantity of energy required for a given object to operate as well as the rate during which energy is used up. A joule of energy (or one watt) is equal to one joule of electricity flowing for one second.
What distinguishes one watt from another?Watts, which are determined by multiplying Amps by Volts, are used to measure energy. As the wattage rises, the appliance produces more power and output. This is the amount of water that the hosepipe example would emit.
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if the moon rises around 3 a.m., its phase must be a) full. b) first quarter. c) third quarter. d) waning crescent. e) waxing crescent.
if the moon rises around 3 a.m., its phase must be Waning crescent .
What is meant by Waning crescent?The moon will look as a half moon, or third quarter moon, when the light level drops. The shadow cast by a third quarter moon will increase until it resembles a crescent form, which is known as a fading crescent.
A fading crescent moon has an illuminated area of less than 50% but is still growing.
You'll notice that the energy is waning as the moon begins to move back into the new phase, allowing you to calm down and devote more attention to your inner thoughts.
When the moon is transitioning from a full moon to a new moon, it is said to be in its declining phase. The declining moon, keep in mind sympathetic magick, is wonderful for banishing work, or cutting ,
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a 4 kg ball is thrown straight up in the air. what is the net force acting on the ball when it reaches its maximum height? g
A 4 kg ball is launched vertically into the air. The net force exerted on the ball at its highest point is 39.24N.
Given data
Ball mass m=4 kilogram
Gravitational acceleration is [tex]9.81 m/sec^{2}[/tex] , or g.
The location of the ball has no bearing on the net force applied to it in vertical projectile motion. As a result, the ball experiences a net downward force throughout its travel, and the size of this force is equal to the mass times the acceleration caused by gravity.
[tex]F_{net} = mg\\F= 4*9.81\\F= 39.24 N[/tex]
Therefore, the ball is subject to a net force of 39.24 N.
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the area of a typical eardrum is about 5.0 10-5 m2. (a) calculate the sound power (the energy per second) incident on an eardrum at the threshold of hearing
The sound power at the threshold of hearing is 5* 10⁻¹⁷ W.
The sound power at the threshold of hearing:
Given that,
Area of the eardrum = 5* 10⁻⁵ m²
We know that, I = power/area
Threshold of hearing I = 1* 10⁻¹² W/m²
Form the above formula, we can write
Power = I* area = 1* 10⁻¹² * 5* 10⁻⁵ = 5* 10⁻¹⁷ W
The sound power incident on an eardrum at the threshold of pain is
We know that, I = power/area
Threshold of pain = 1 W
Power = I* area = 1* 5* 10⁻⁵ W
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Find its moment of inertia about an axis perpendicular to its plane and passing through the midpoint of the line connecting its two ends.
A) Moment of inertia about an axis passing through the point where the two segments meet : [tex]$I_A=\frac{1}{12} M L^2$[/tex]
B) Moment of inertia passing through the point where the midpoint of the line connects to its two ends: [tex]$I x=\frac{1}{3} M L^2$[/tex]
What is Moment of inertia?
The term "moment of inertia" refers to a physical quantity that quantifies a body's resistance to having its speed of rotation along an axis changed by the application of a torque (turning force). The axis might be internal or exterior, fixed or not.
A) The moment of inertia about an axis passing through the point where the two segments meet is [tex]$I_A=\frac{1}{12} M L^2$[/tex]given that the rod is bent at the center and distance from all the points to the axis remains the same, the moment of inertia about the center will remain the same.
B) Determine the moment of inertia about an axis passing through the point midpoint of the line which connects the two ends
First step: determine the distance between the ends ( d )
After applying Pythagoras theorem[tex]$\mathrm{d}=\frac{\sqrt{2}}{2} L$[/tex]
Next step : determine distance between the two axis [tex]$(\mathrm{x})$[/tex]
After applying Pythagoras theorem
[tex]\mathrm{x}=\frac{\sqrt{2}}{4} L$$[/tex]
Final step : Calculate the value of [tex]$\mathrm{I}_{\mathrm{x}}$[/tex]
applying Parallel Axis Theorem
[tex]$$I_x=I_8+M x^2$$[/tex]
[tex]$$\begin{aligned}& =\frac{1}{12} M L^2+\frac{1}{4} M L^2 \\& \therefore \quad I x=\frac{1}{3} M L^2 \\&\end{aligned}$$[/tex]
Hence we can conclude that Moment of inertia about an axis passing through the point where the two segments meet: [tex]$I_A=\frac{1}{12} M L^2$[/tex], Moment of inertia passing through the point where the midpoint of the line connects its two ends: [tex]$I x=\frac{1}{3} M L^2$[/tex]
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the mechanical advantage for a machine is defined as the output force divided by the input force. since the output force is typically greater than the input force, this value is normally greater than one. for an ideal machine, what would be another way of representing the mechanical advantage? the mechanical advantage for a machine is defined as the output force divided by the input force. since the output force is typically greater than the input force, this value is normally greater than one. for an ideal machine, what would be another way of representing the mechanical advantage? (output distance)/(input distance)
The mechanical advantage can also be represented as the ratio of output work divided by input work. This ratio is usually greater than one, indicating that the machine is doing more work than the input force is providing.
What is mechanical advantage?
The force amplified by using a device, mechanical device, or machine system is known as mechanical advantage. To achieve the desired output force amplification, the device trades off input troops against movement. The law of the lever serves as a model for this. Mechanisms are machine parts made to control forces and motion in this way. An ideal transmission system does not increase or decrease power. Consequently, the ideal machine is devoid of a power source, frictionless, and built from rigid materials that do not flex or wear.
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let a, b, c, and d be the vertices of a regular tetrahedron each of whose edges measures 1 meter. a bug, starting from vertex a, observes the following rule: at each vertex it chooses one of the three edges meeting at that vertex, each edge being equally likely to be chosen, and crawls along that edge to the vertex at its opposite end. let p
It picks one of the three edges that meet at each vertex, each of which has an equal chance of being chosen, and crawls along that edge to the vertex at its opposite end is p=182/729 and n is 182.
Let[tex]$V_k$[/tex] crawl exactly [tex]$k$[/tex] meters starting from vertex [tex]$V$[/tex] and ending at vertex A, where [tex]$V\in\{A,B,C,D\}$[/tex] and k is a positive integer. We wish to find [tex]$A_7.$[/tex]
Since the bug must crawl to vertex [tex]$B,C,$ or $D$[/tex]
on the first move, we have
[tex]where $S_k=A_k+B_k+C_k+D_k.$[/tex]
More generally, we get
[tex]\[A_{k+2}=A_k+2S_k. \qquad\qquad (\spadesuit)\]\[/tex]
The requested probability is
[tex]\[p=\frac{A_7}{3^7}=\frac{2(3)+2\left(3^3\right)+2\left(3^5\right)}[/tex]
[tex]{3^7}=\frac{2(1)+2\left(3^2\right)+2\left(3^4\right)}{3^6}=\frac{182}{729},\]from which $n=\boxed{182}.$[/tex]
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