An angle '[tex]\Theta[/tex]' on the circle Corresponds to an angle 2[tex]\Theta[/tex] on the part.
On the Mohr, the circle has a positive counterclockwise rotation, similar to the physical space convention for shear stress. is the clockwise shear stress and both are plotted. Mohr's circle is a graphical representation of the general state of stress at a point.
This is a graphical method for evaluating principal and maximum shear stresses. Normal and tangential stress in any plane. Soil mechanics use Mohr's circles to visualize the relationship between normal and shear stresses, and to estimate the maximum stress based on three or more soil samples taken from a site.
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In the early years of the 20th century, a leading model of the structure of the atom was that of the English physicist J. J. Thomson (the discoverer of the electron). In Thomson's model, an atom consisted of a sphere of positively charged material in which were embedded negatively charged electrons, like chocolate chips in a ball of cookie dough. Consider such an atom consisting of one electron with mass m and charge −e, which may be regarded as a point charge, and a uniformly charged sphere of charge +e and radius R.
A) Is equilibrium position of the electron at the center of the nucleus?
B)
In Thomson's model, it was assumed that the positive material provided little or no resistance to the motion of the electron. If the electron is displaced from equilibrium by a distance r less than R, find the net force on the electron.
Express your answer in terms of the variables r⃗ , R, e, and constants π and ϵ0.
C) Calculate the frequency of oscillation.
Express your answer in terms of the variables m, R, e, and constants π and ϵ0.
The equilibrium position of the electron at the center of the nucleus is R = 3.16 x10⁻¹⁰m.
Thomson discovered the electron and proposed a structural model of the atom. His research also led to the invention of the mass spectrometer. Thomson announced that he discovered that atoms are made up of smaller components.
Calculation:-
K = 2.304 × 20^-²⁸ / 3
f = 1/2π√k/m
4.63 × 10¹⁴ = 1/2× 3.141 √2.304 × 20^-²⁸ / R³ (9.1 × 10-31)
R = 3.16 x10⁻¹⁰m.
This discovery revolutionized the way scientists think about atoms and had a major impact on the field of physics. Thompson called them corpuscles but what he found are now commonly known as electrons. The plum pudding model is defined by an electron surrounded by a volume of positive charge like a negatively charged plum embedded in a positively charged pudding.
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A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. Assuming mechanical energy is conserved, the speed of the ball at the bottom of the circle is
The speed of the ball at the bottom of the circle when ball of mass m, at one end of a string of length L, rotates in a vertical circle is √Lg
The rate at which an object's distance traveled changes is measured by its speed. In terms of measurement, speed is a scalar, meaning it has magnitude but no direction. Speed is the rate at which an object moves over a given distance. a thing that travels at a high rate of speed and covers a lot of distance quickly. A slow-moving object, on the other hand, travels a comparatively short distance in the same amount of time when moving at a low speed. An object with zero speed is completely immobile.
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higher than its surroundings
2) An object will normally be a net radiator of energy when its temperature is
A) lower than its surroundings.
B) higher than its surroundings.
C) neither of these.
When an object's internal energy is:... really when its temperature is higher than that of its surroundings, it will typically be a net radiator of energy.
What do you describe energy that moves from things with higher temperatures to those with lower temperatures as a result of the temperature difference?From one thing to another, heat energy can be exchanged. Heat is the flow or transfer that occurs as a result of the temperature differential between two objects.
What happens to an object's heat energy as its temperature drops?Heat is a means of transferring energy to and from molecules. Atoms and molecules accumulate thermal energy as the temperature rises, which leads them to move faster and further apart. When the temperature drops, atoms.
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A car accelerates uniformly from rest and reaches a speed of 21.1 m/s in 9.06 s. If the diameter of the tire is 58.0 cm, find (a) the number of revolutions the tire makes during the motion, assuming that no slipping occurs. (b) What is the final angular speed of a tire in revolutions per second?
Answer: (54.3 rev, 12.1 rev/s) --> please show me how to get this answer!
A. The number of revolutions the tire makes during the motion, assuming that no slipping occurs is 54.33 revolutions.
B. The final angular speed of a tire in revolutions per second is 12.07 revolutions per second or 4364.58 degrees per second.
Solution:
21.1m/s from rest with constant acceleration means that the average speed was 11m/s.
Therefore, you can get the distance traveled by distance = time * average speed:
distance = 9s * 11m/s = 99m
Now, to get the number of revolutions, you have to divide the total distance by the circumference of the tire. The circumference is equal to pi * diameter:
Circumference = pi(3.14159265) * 0.58m = 1.82m
So:
Revolutions = 99m / 1.82m = 54.33 revolutions.
The angular speed can be worked out using the circumference as well. 22m/s is the final speed, so if you divide that by the circumference, you get the revolutions per second, which is your angular speed:
22m/s / 1.82m = 12.07 revolutions per second.
If they want this in degrees per second, just remember that there are 360 degrees in a revolution, so multiply it by 360:
12.07 * 360 = 4364.58 degrees per second.
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n 1986, a nuclear power accident in chernobyl, ukraine led to high radiation levels for kilometers surrounding the plant. the high levels of radiation caused elevated mutation rates in the surviving organisms, and evolutionary biologists have been studying vole populations in the chernobyl area ever since. based on your understanding of evolutionary mechanisms, which of the following most likely occurred in the vole populations following the accident?
Mutation caused genetic drift and decreased fitness and Sequence alteration in the genomic DNA is the fuel driving the course of evolution.
Mutations, or changes in the nucleotide sequence, can result fromerrors during DNA replication, from covalent changes in structure because of reaction with chemical or physical agents in the environment, or from transposition. Most of the sequence alterations are repaired in cells.
Without such mutations, no changes would occur in populations of species to allow them to adapt to changes in the environment. Mutation is the sudden change in the DNA. Mutations arise due to any kind of mutagen or radiation. In this disaster mutations were introduced due to the radiations. So, there will be variations in the organism.
Mutations will not cause changes only in the physiology of an organism. It does not cause genetic drift and decreased fitness. New alleles cannot be fixed by mutations.But mutations can definitely increase the variety of organisms.
Hence, the correct option is d.
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It is very likely that human emissions of greenhouse gases are responsible for global warming. Give two examples of such activities and explain briefly how they cause global warming.
Greenhouse gases are gases that are present in the Earth's atmosphere and trap heat from the Sun, preventing it from radiating back out into space. Human activities that release greenhouse gases into the atmosphere can contribute to global warming. Two examples of such activities are:
Burning fossil fuels: The most common sources of greenhouse gas emissions are the burning of fossil fuels such as coal, oil, and natural gas. When these fuels are burned, they release large amounts of carbon dioxide into the atmosphere. Carbon dioxide is one of the most important greenhouse gases, and its increasing concentration in the atmosphere is a major contributor to global warming.Deforestation: Trees and other vegetation absorb carbon dioxide from the atmosphere as part of the process of photosynthesis. When trees are cut down and burned, or otherwise removed from the landscape, this carbon is released back into the atmosphere. Deforestation is therefore a major source of greenhouse gas emissions, and can contribute to global warming.Overall, human activities that release greenhouse gases into the atmosphere are a major cause of global warming. These activities can have serious consequences for the Earth's climate and can impact many aspects of human life.
use the mineral identification chart above to determine the name of the mineral with the following physical properties: light color, non-metallic vitreous luster, hard enough to scratch glass, 2 directions of cleavage at nearly 90o, lacks striations.
The name of the mineral with the following physical characteristics is the Harder Than, according to the above mineral identification table. Glass. Two directions are not at 90 degrees. black or dark green vitreous luster. 124 and 56 degree cleavage planes are present. Hornblende. Cleavage.
What is the meaning non-metallic?Non-Metallic. Metallic minerals are those that include metal elements in their unprocessed state. Non-metallic minerals are those that don't include any metals. Melting metallic minerals produces a new material. Non-metallic minerals undergo such a process, but no new product is produced. Nonmetals are chemical elements in chemistry that often don't have a lot of metallic characteristics; they can be anything from colorless vapors to glossy solids. Nonmetals' electrons behave differently from those of metals.
What are non-metallic materials and which is non metallic in nature?Hydrogen, carbon, nitrogen, oxygen, phosphorus, sulfur, silicon, boron, tellurium, and selenium are among the non-metallic elements in the periodic table. They also consist of noble gases and halogens (such as fluorine, chlorine, bromine, iodine, and astatine) (helium, neon, argon, krypton, xenon and radon). The least metallic element among F, Cl, Br, and At is fluorine. This is true because metallic character grows down the group and lessens over time.
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interference occurs with not only light waves but also all frequencies of electromagnetic waves and all other types of waves, such as sound and water waves. suppose that your physics professor sets up two sound speakers in the front of your classroom and uses an electronic oscillator to produce sound waves of a single frequency. when she turns the oscillator on (take this to be its original setting), you and many students hear a loud tone while other students hear nothing. (the speed of sound in air is 340 m/s.)
The concept of hearing a loud or no sound depends on the path difference between the two waves , that is when the path difference is an integral multiple of wavelength, we tend to hear a loud sound and when the path difference is odd half intergaral multiple of wavelength then the we hear no sound (destructive interference) .
Now, when the frequency is doubled, the wavelength is also doubled and thus there must not be any change in the pattern of no sound and loud sound. Ultimately,
"The students who originally heard a loud tone again hear a loud tone, and the students who originally heard nothing still hear nothing."
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A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.30s for the boat to travel from its highest point to its lowest, a total distance of 0.670m . The fisherman sees that the wave crests are spaced a horizontal distance of 5.50m apart.
How fast are the waves traveling?
Express the speed v in meters per second using three significant figures.
What is the amplitude A of each wave?
Express your answer in meters using three significant figures.
The waves for the boat of fisherman is travelling with the speed of 1.203 m/s and the amplitude of each wave is 0.35 m.
What is speed of wave?The rate at which a wave travels a certain distance in a given amount of time is referred to as its speed.
The boat travels 0.700 meters from its highest point to its lowest point. The boat requires 2.70 minutes to travel.
The fisherman notices that the wave crests are 6.50 meters apart horizontally. Since the wave's wavelength is determined by the horizontal spacing between crests. Consequently, the wave's wavelength is,
lambda=6.50s
The wave's period is equal to the time it takes to travel from its peak to lowest point. Consequently, the wave's period is,
T=2X2.7
T=5.4s
The relationship between wavelength and time period determines the wave's speed. Consequently, the waves' traveling speed is,
v=6.50/5.4
v=1.203m/s
The wave's amplitude is equal to half of the distance between its peak and lowest points.
The boat now travels 0.700 meters from its highest point to its lowest position. As a result, each wave's amplitude is A=0.7/2.A=0.35m.
As a result, the waves for the fishing boat are moving at a speed of 1.203 m/s and have an amplitude of 0.35 m.
How quickly does the typical wave travel?Waves that are relatively tiny move at speeds of up to 10 km/h and touch the shore once every three seconds. Though they travel at a speed of over 50 km/h, very huge waves arrive less frequently—once every 14 seconds—because of their longer wavelengths.
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as a jet is taking off, it is accelerating down the runway with acceleration , with . you are sitting inside the jet and holding a simple pendulum consisting of a bob of mass attached to a string of length . the pendulum comes to rest in the equilibrium position where the string makes an angle with respect to the vertical. when the bob is in the equilibrium position, which of the following free-body force diagrams on the bob is correct in a reference frame fixed to the accelerating jet.
A jet plane's acceleration is a critical phase of flight that necessitates intense focus on the part of both pilots.
On the ground, things can get hectic and demand a lot of situational awareness, especially when there is little traffic separation, a runway is wet, visibility is poor, and there are heavy winds. Nevertheless, you start to relax a little and take in the beauty of flying as the engines begin to accelerate and you take off and break through the clouds. We have put up this essay with all you need to know so that you may master the takeoff phase in complete confidence.
You must commit to memory three call-outs for the acceleration and takeoff phases of your flight. You will first check your instruments at 80 knots. When you push the nose of your aircraft upward and rotate in V1, you are too quick to abort the takeoff.
This was merely a succinct justification. In order to help you mentally prepare, we will go over every important stage of a jet plane's acceleration.
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coherent light from a sodium-vapor lamp is passed through a filter that blocks everything except for light of a single wavelength. it then falls on two slits separated by 0.470 mm . in the resulting interference pattern on a screen 2.24 m away, adjacent bright fringes are separated by 2.86 mm .What is the wavelength of the light that falls on the slits?
Im lost I don't know where to start.
The wavelength of the light that falls on the slit = 5.692 × 10⁻⁴m
Here we have
Fringe. separation. = 2.90 mm = 0.0029 m
Slit. separation. = 0.420 mm = 0.00042 m
Distance. from slits to. screen. = 2.14 mm = 0.00214 mm
Wavelength. is given by the following relation.
Wave length = Fringe separation × slit separation /Distance from slits to screen
Therefore;
Wave length = 0.0029 m × 0.00042 m/0.00214 mm = 5.692 × 10⁻⁴m
In a broader sense, the term "light" can apply to electromagnetic radiation of any wavelength, whether visible or not. [4] This definition of light includes gamma rays, X-rays, microwaves, and radio waves. The main characteristics of light include intensity, polarization, frequency or wavelength spectrum, and propagation direction. One of nature's basic constants is the speed of light in a vacuum, which is 299 792 458 meters per second (m/s). [6] Visible light, like all forms of electromagnetic radiation, is propagated by massless elementary particles called photons, which serve as a representation of the electromagnetic field's quanta and can be thought of as both waves and particles. Modern physics places a lot of emphasis on the study of light, or optics.
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assume that the air consists entirely of nitrogen and that the pressure of the gas stays constant how much heat is supplied by body to warm the air
Charles' law stipulates that the volume of a given amount of gas is exactly related to its temperature on the kelvin scale while the pressure is held constant.
What is nitrogen most frequently used for?
On nitrogen, the chemical industry depends. It is used to make fertilizers, dyes, nylon, nitric acid, and explosives. To make these products, nitrogen must first be coupled with hydrogen to make ammonia. For this, the Haber process is employed.
Is nitrogen bad for people?
People lose their lives every year by breathing "air" with insufficient oxygen. Many people believe nitrogen gas is safe because it makes up 78 percent of the air we breathe. However, breathing nitrogen is only safe when it is combined with the right proportion of other gases.
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Heat capacity on its own is rarely enough to predict the thermal performance of a material. Another important consideration is conductivity. If each of the following material was made into a frying pan, which would you expect to be heated the most uniformly in a short period of time when placed on the burner? Brass (k = 120 W/mk) Aluminum (k = 247 W/mK) Invar (63Fe-36Ni, k = 10 W/mK) O Copper (k = 398 W/mK)
Heat capacity on its own is rarely enough to predict the thermal performance of a material. Another important consideration is conductivity. If each material was made into a frying pan, Copper (k=398 W/mK) expect to be heated the most uniformly in a short period of time.
The amount of heat that must be delivered to an object in order to result in a unit change in temperature is referred to as an attribute of matter known as heat capacity or thermal capacity. The SI unit of heat capacity is joules per kelvin (J/K). Heat capacity is a general attribute. The comparable intensity property is the specific heat capacity, which is determined by dividing an object's heat capacity by its mass. By dividing the heat capacity by the substance's molecular weight, the molar heat capacity may be calculated. The volumetric heat capacity measures the heat capacity per volume. Architecture and civil engineering frequently refer to a building's capacity to store heat as having "thermal mass." The variance can be ignored when working with materials under confined pressure and temperature ranges. When measured at a starting point of 25 °C and 1 atm of pressure, one pound of iron, for example, has a heat capacity of roughly 204 J/K. It is adequate for temperatures between 15 °C and 35 °C and for ambient pressures between 0 °C and 10 °C because the real value fluctuates so little in those ranges.
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A mass hanging from a spring oscillates with a period of 0.25 s. Suppose the mass and spring are swung in a horizontal circle, with the free end of the spring at the pivot.
What rotation frequency, in rpm, will cause the spring's length to stretch by 23%?
The frequency of rotation of an object revolving around an axis is sometimes referred to as the rotational speed or rate of rotation of the object. Cycles per second (cps), revolutions per minute (rpm), etc. are some examples of its unit (the Greek lowercase letter nu).
What is the rotational frequency formula?
By a factor of 2, angular frequency (measured in radians per second) is bigger than frequency (measured in cycles per second, commonly known as Hz). In this picture, frequency is represented by the symbol rather than f. a sphere that is revolving about an axis. In order to satisfy = v / r, points further from the axis move more quickly.
How can I determine frequency?
Divide the number of times the event happens over the period of time to determine the frequency. Example: Anna divides the time by the quantity of page clicks (236). (one hour, or 60 minutes). She discovers that her clickthrough rate is 3.9 per minute.
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An 1250 W toaster and an 803 W microwave oven are connected in parallel to the same 30.0 A, 120 V circuit.
(a) Find the toaster's resistance R (in ohms). Ω
(b) If the microwave fails and is replaced, what maximum power rating (in W) can be used without tripping the 30.0 A circuit breaker? W
11.52Ω is the toaster's resistance, and 2350W is the maximum power rating.
The toaster and microwave are connected in parallel so that the potential difference is the same for the toaster and microwave.
use the equation of power to solve for resistance of toaster R
[tex]P=\frac{V^{2} }{R}-------------(1) \\\\R=\frac{V^2}{P} =\frac{(120)^2}{1250} \\\\R=11.50 ohms[/tex]
Given That P=1250, V=120 By substituting these values in equation(1) we get R=11.50 Ohms as shown above.
To solve the current through the toaster we use Ohm's law:
V=IR
I=V/R--------(2)
we already find the R-value and the V value is already given now place these values in equation(2), and we get
I=120/11.50
I=10.43A
The current is divided in parallel circuits so that the total current from the divides between the toaster and microwave,
I=I(toaster)+I(microwave)----------------(3)
I(microwave)=I-I(toaster)
=30A-10.43A
=19.59A
The maximum power microwave used is
P(M)=VI---------------(4)
P(M)=V(M)I(M)
P(M)=120x19.59
P(M)=2350W
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both permittivity of free space and permeability of free space can be modified by multiplication by a constant to derive the permittivity and permeability of any material other than vacuum.
The product of the permittivity of free space and the permeability of the free space equals 1 by the square of the speed of light in a vacuum.
Generally, the dielectric constant can be defined as the ratio of the absolute permittivity of a substance to the absolute permittivity of free space.
Absolute permittivity is the measure of permittivity in a vacuum or free space. It measures the resistance encountered when forming an electric field in a vacuum. εo is the smallest possible value of permittivity. Static permittivity is the permittivity of a material when exposed to a static electric field.
Permeability in general is symbolized µ, and is a constant of proportionality that exists between magnetic flux density and magnetic field strength in a given medium.
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About the four terrestrial planets (Earth, Mars, Mercury, and Venus), which of the following statements is NOT correct?A. The orbital periods of the four planets in order from shortest to longest are: Mercury, Venus, Earth, and MarsB. The distances from the Sun for the four planets in order from closet to farthest are: Mercury, Venus, Earth, and MarsC. The four planets all have mantle, core, and stable atmospheric layersD. The four planets in order from smallest to biggest are: Mercury, Mars, Venus, and Earth
All four planets contain stable atmospheric layers, a mantle, and a core. One of the following is FALSE regarding the four terrestrial planets (Earth, Mars, Mercury, and Venus).
Which of the following traits do the four terrestrial planets share?Terrestrial planets include Mercury, Venus, Earth, and Mars because of their compact, stony surfaces that resemble terra firma on Earth. The four innermost planets in the solar system are the four terrestrial planets.
What are the four features of planets that are terrestrial?The four innermost planets are known to as terrestrial planets and feature a moon or moons, valleys, volcanoes, and craters. They also have a liquid heavy-metal core.
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On a part-time job, you are asked to bring a cylindrical iron rod of density 7800 kg/m^3 , length 84.8 cm and diameter 2.50 cm from a storage room to a machinist. Calculate the weight of the rod, w. The acceleration due to gravity, g = 9.81m/s^2 .
The weight of the cylindrical iron rod of density 7800 kg/m³ , length 84.8 cm and diameter 2.50 cm is 31.8 N
The relation between mass and density is given by:
m = ρ . V
Where:
m = mass
ρ = density
V = volume
In the given problem.
ρ = 7800 kg/m³
length (l) = 84.8 cm
diameter = 2.5 cm,
radius (r) = 2.5/2 = 1.25 cm
Hence, the volume of the rod is:
V = πr² . l
= 3.14 x 1.25² x 84.8 = 416 cm³
= 416 x 10⁻⁶ m³
Hence, its mass is:
m = 7800 x 416 x 10⁻⁶ = 3.24 kg
And its weight is:
w = m x g
= 3.24 x 9.8 = 31.8 N
Hence, the weight is 31.8 N
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Two identical thin rods, each of mass m and length L, are joint at right angles to form an L-shaped object. This object is balanced on the top of a sharp edge. If the object is displaced slightly it oscillates. Assume that the magnitude of the acceleration due to gravity is g. Find, the angular frequency of the oscillation of the object.
The formula for the angular frequency is = 2/T. Radians per second are used to express angular frequency. The frequency, f = 1/T, is the period's inverse. The motion's frequency, f = 1/T = /2, determines how many complete oscillations occur in a given amount of time.
What is the oscillation formula?A basic harmonic oscillator's angular frequency, period T, and frequency f are given by =km, T = 2mk, and f = 12km, where m is the system's mass and k is the force constant.
The angular frequency calculator: what is it?You can use the angular frequency calculator to figure out a system's angular frequency, also known as angular velocity. In the article that follows, we explain how to determine the angular frequency for straightforward Show several angular frequency formulae as well as harmonic and rotatory motion.
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the brakes are applied to a car and it abruptly slows down. the kinetic energy changes from 300 000 j to 100 000 j. the heat released during this process is
The heat released during the process of applying the break of the car is 200000 Joules.
According to the law of conservation of energy, energy can nether be created nor be destroyed, it can only be converted from one form to another.
In the process when the brakes of the car are applied the kinetic energy of the car is changing from 300000 to 100000 Joules.
When the kinetic energy of the body is getting converted into the thermal energy because of the friction the loss of kinetic energy is taking place.
It has to be noted here that the law of conservation of energy is still valid because all the energy that is lost in the form of thermal energy has gone into the environment which is ultimately a bigger system and the energy is still constant for the universe.
So, the amount of energy that is lost is 200000 Joules.
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an apple weighs 1.20 n. when you hang it from the end of a long spring of force constant 1.44 n/m and negligible mass, it bounces up and down in shm. if you stop the bouncing and let the apple swing from side to side through a small angle, the frequency of this simple pendulum is half the bounce frequency. (because the angle is small, the back and forth swings do not cause any appreciable change in the length of the spring.)
The unstretched length of the spring is 32.67 m.
Spring Constant = k = 1.44 N/m
Weight of the apple = m = 1.2 N
Acceleration due to gravity = g = 9.8 m/s²
Length of unstretched spring = I
Frequency of SHM motion is given by ;
= f = (1/2π) √(k/m)
Frequency of pendulum is given by;
= f' = (1/2π) √(g/l)
In the question, f' =2f, thus,
= (1/2π) √(g/l) = 2 X (1/2π) √(k/m)
= √(g/l) = (1/2) √(k/m)
Squaring on both sides,
= g/l = k/4m
= l = (g X 4m ) / k
= l = ( 9.8 X 1.2 X 4 ) / 1.44
= l = 32.67 m
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The complete question:
An apple weighs 1.00 N. When you hang it from the end of a long spring of force constant 1.50 N/m and negligible mass, it bounces up and down in SHM. If you stop the bouncing and let the apple swing from side to side through a small angle, the frequency of this simple pendulum is half the bounce frequency. (Because the angle is small, the back-andforth swings do not cause any appreciable change in the length of the spring.) What is the unstretched length of the spring (with the apple removed)?
A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg/m3 and the density of helium in the balloon is 0.18 kg/m3. The radius of the balloon (when filled) is R = 4.8 m. The total mass of the empty balloon and basket is mb = 129 kg and the total volume is Vb = 0.066 m3. Assume the average person that gets into the balloon has a mass mp = 70 kg and volume Vp = 0.079 m3.
1. What is the volume of helium in the balloon when fully inflated?
2. What is the magnitude of the force of gravity on the entire system (but with no people)? Include the mass of the balloon, basket, and helium.
3. What is the magnitude of the buoyant force on the entire system (but with no people)? Include the volume of the balloon, basket, and helium.
4. What is the magnitude of the force of gravity on each person?
5. What is the magnitude of the buoyant force on each person?
6. How many FULL people can the balloon lift up? (Your answer must be an integer.)
Please include the process!!!!!
The density of air is 1.28 kg/m^3 and the density of helium in the balloon is 0.18 kg/m^3.
The radius of the balloon (when filled) is R = 4.8 m.
The total mass of the empty balloon and basket is MB = 129 kg
Total volume is Vb = 0.066 m^3
The average person that gets into the balloon has a mass of mp = 70 kg and volume Vp = 0.079 m3.
1 ) The volume of helium in the balloon when fully inflated,
= 4/3 π R^3
= 4/3 x 3.14 x (4.8)^3
= 463.24 m^3 = 463 m^3.
2 ) Force of gravity on the entire system but with no people;
= (mass of the empty balloon and basket + mass of helium )x g
=( 129kg + 463.24 m^3 x 0.18kg/m^3 )x 9.8
= 2081.35 N = 2081 N.
3.) Magnitude of the buoyant force on the entire system (but with no people )
( Volume of empty balloon + basket + volume of helium ) density of air x g
( 0.066 m^3 + 463.24 m^3 ) x 1.28 x 9.8
= 5811.71 N = 5812 N.
4 ) Magnitude of the force of gravity on each person=
Mass of each person(mp) × g
= 70 x 9.8
= 686 N.
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Gravitational force of 72 units
Explanation:
Objects 1 and 2 attract each other
with a gravitational force of 72.0 units. If the distance separating Objects 1 and 2 is changed to four times the original value (i.e , quadrupled), then the new gravitational force will be units.
if an object is at a pole, it blank accelerating.target 1 of 6 we can truly write blank, such that the apparent weight is exactly mg .target 2 of 6 at the blank, the object is moving in a very large circular path as the earth rotates.target 3 of 6 this means that technically blank.target 4 of 6 that is, the weight force toward the center of the circular path must be slightly blank so it can provide a centripetal force.target 5 of 6 thus n
If an object is at a pole such that the apparent weight is mg and the object is in large circular path as the earth rotates. The following blank spaces are filled up with the words, is, n-mg = may =0, equator, n-mg = may>0, smaller, pole.
If an object is at a pole it [is] accelerating, At pole accelaration of gravity is maximum. effect of centrifugal force is less.
We Cam Such that write truly n-mg = may =0 such that the apparent weight is exactly mg, because normal force is equal to effective or apparent weight.
At a the equator, the object is moving in very large circular path as the earth rotates. Because, the axis of earth is line joining two pole so at equator distance from the axis to surface is largest.
This means that technically n-mg = may>0. Because at equator normal force is greater than mg due to the presence of centepetal force.
That is the weight force towards the center of the circular path must be be slightly smaller, if Com provide a Contepetal force.
as, weight force = mg-centepetal force.
weight force <mg
Thus n<mg at the pole, At pole Centepetal force is zero so, weight force and mg are equal.
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the pressure of air in your house can stay constant during the day if the temperature rises. let the temperatures be 297 k during the day, and 288 k at night, and volume of the house be 900 m3. Part A Determine the number of moles of air that leave the house during the daytime.
Number of moles of air that leave the house during the daytime is 1154.017 moles.
The pressures are constant so:
V₁/T₁ = V₂/T₂
Given,
During the night, V₁ = 900 m³, and T1₁= 288K.
During the day, T₂ = 297K, and V₂ =?
V₂ = V₁*T₂/T₁ = 900*297/288 = 928.125 m³
928.125 - 900 = 28.125 m³
Volume of air that leave the house during the daytime = Vₐ
V₂/T₂ = Vₐ/Tₐ
Vₐ = V₂*Tₐ/T₂ = 28.125*273/297 = 25.85 m³
To calculate the number of moles,
22.24 liters per mole, and 1000 liters per m³, so
number of moles = N
N = 25.85*1000/22.4
N = 1154.017 moles.
Therefore, number of moles of air that leave the house during the daytime is 1154.017 moles.
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Class 12 Question > In an L-R-C series circuit, the rms voltage a...Save
In an L-R-C series circuit, the rms voltage across the resistor is 30.0 V, across the capacitor it is 90.0 V, and across the inductor it is 50.0 V. Rms voltage of the source is
a) 60.0 V
b) 50.0 V
c) 65.0 V
d) 5.0 V
Root Mean Square(rms) voltage of the source in the given LRC series circuit is (b) 50V
The root-mean-square (rms) voltage of a sinusoidal source of electromotive force (Vrms) is used to characterize the source. It is the square root of the time average of the voltage squared. The value of Vrms is Vo/Square root of√2, or, equivalently, 0.707 Vo
Given:
rms Voltage across resistor is 30V
rms Voltage across inductor is 50V
rms voltage across capacitor is 90V
hence, rms voltage of the source is 50V
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3. Given the force, F(x)=1-4 x+4 x³
a. Find an expression for the potential energy.
b. Plot F(x) between x=-2 to x=+2
c. Plot U(x) between x=-2 to x=+2
d. Identify the equilibrium points and comment on the stability at those points.
Expression for the potential energy is (3/4)x⁴ - 2x² + x.
Potential energy is the energy possessed by the system when it is in rest.
If the potential energy function U(x) is known, then the force F(x) at any position can be obtained by the derivative of the potential.
F(x) = - dU/dx
dU = - F(x).dx
U = [tex]\int\{F(x)} \, dx[/tex]
U = [tex]\int[/tex](1 - 4x + 4x³) .dx
U = (3/4)x⁴ - 2x² + x
Plotting F(x) between x=-2 to x=+2,
F(x) = (1 - 4x + 4x³)
for x=-2, F(-2) = F{1 - 4(-2) + 4(-2)³}
F(-2) = {1 + 8 - 32}
F(-2) = (-23)
for x=+2, F(-2) = F{1 - 4(2) + 4(2)³}
F(2) = {1 - 8 + 32}
F(2) = 25
Plotting U(x) between x=-2 to x=+2
U(x) = (3/4)x⁴ - 2x² + x
for x=-2, U(-2) = {(3/4)(-2)⁴ - 2(-2)² + (-2)}
U(-2) = {(4*3) - (2*4) - 2}
U(-2) = 12 - 8 - 2
U(-2) = 2
for x=2, U(2) = {(3/4)(2)⁴ - 2(2)² + (2)}
U(2) = {(4*3) - (2*4) + 2}
U(2) = {12 - 8 + 2}
U(2) = 6
For equilibrium points, force must be equal to zero,
F(x) = 0
(1 - 4x + 4x³) = 0
x1 = -1.10716
x2 = 0.26959
x3 = 0.83757
Equilibrium points exists at points x1, x2, x3.
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In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the following expression, where x is in centimeters and t is in seconds.x=(4.00cm)cos(3t+π/6)(a) At t=0, find the position of the piston.(b) What is its velocity?(c) What is its acceleration?(d) Find the period and amplitude of the motion.
A) 3.99 cm, B)-7.99 cm/s, C)-15 cm/s2, D) 4 cm, In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the following expression,
a) At t=0
x=4.00cm)cos(3t+π/6)(a)= 4*0.999 = 3.999 cm
b)Expression for velocity v = dx/dt = -8.00 Sin(3t+π/6)
At t=0 v= -8 Sin(π/6) = -7.999 cm/s
c) Expression for acceleration a= -16 Cos(3t+ π/6)
At t=0 a= -16 Cos(π/6) = -15.99 cm/ sec2
d) Period = (2 ?)/3
Amplitude= 4 cm
A piston is a part of a variety of comparable devices, including reciprocating engines, reciprocating pumps, gas compressors, hydraulic cylinders, and pneumatic cylinders.
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During a high Reynolds number experiment, the total drag force acting on a spherical body of diameter D = 12 cm subjected to airflow at 1 atm and 5°C is measured to be 5.2 N. The pressure drag acting on the body is calculated by integrating the pressure distribution (measured by the use of pressure sensors throughout the surface) to be 4.9 N. Determine the friction drag coefficient of the sphere, and whether the flow is in turbulence.
The total drag force acting on a sphere with a diameter of 12 cm and exposed to airflow at 1 atm and 5°C is therefore measured to be 5.2 N. Therefore, the friction drag coefficient is 0.0115.
When determining whether a flow pattern is laminar or turbulent while passing through a pipe, Reynolds number, a dimensionless quantity, is used. The relationship between inertial and viscous forces is what determines the Reynolds number. Friction is caused by surface irregularity, according to observations made at the microscopic level. Variety of Friction Friction can be divided into two categories, which are as follows: internal rubbing
Cdf = 0.2*0.3/5.2
Cdf = 0.06/5.2
Cdf = 0.0115
when 5.2/0.3 = 0.2
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Two air-filled parallel-plate capacitors with capacitances C1 and C2 are connected in series to a battery that has voltage V; C1 = 3.00 μF and C2 = 6.00 μF. The electric field between the plates of capacitor C2 is E02. While the two capacitors remain connected to the battery, a dielectric with dielectric constant K = 4 is inserted between the plates of capacitor C1, completely filling the space between them. After the dielectric is inserted in C1, the electric field between the plates of capacitor C2 is E2.
A) What is the ratio E2/E02?
B) When the dielectric is inserted into C1, does the electric field in C2 increase, decrease, or remain the same?
C) Repeat the calculation in part A for the two capacitors connected to the battery in parallel. What is the ratio E2/E02?
The total positive charge stored on the two capacitors is;
4kQ₀/(k + 1)
We are told that the charge on each capacitor is Q₀.
Now, formula for charge stored on a capacitor is;
Q = CV
Where;
Q is charge
C is capacitance
V is voltage
Thus, total charge stored on the two capacitors will be;
Q = Q₁ + Q₂
Since Q₀ is the charge on each capacitor, then;
For Capacitor 1, we have; Q₀ = C₁V
For capacitor 2, we have; Q₀ = C₂V
Thus, let the capacitance C₁ be be half the capacitance C of two capacitors.
Thus;
C₁ = ¹/₂C
Thus;
Q₀ = ¹/₂CV
2Q₀ = CV
Now, a dielectric with dielectric constant k > 1 is inserted between the plates of capacitor C₁. Thus, the two capacitors will now be kC and C.
Thus;
C₂ = (kC × C)/(kC + C)
C will cancel out to give;
C₂ = kC/(k + 1)
Earlier on, we saw that;
Q₀ = C₂V
Thus;
Q₀ = kCV/(k + 1)
Earlier, we saw that 2Q₀ = CV
Thus, charge is;
Q₀ = 2kQ₀/(k + 1)
Since 2 capacitors, then total positive charge stored is;
2 × 2kQ₀/(k + 1) = 4kQ₀/(k + 1)
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