Kepler's third law, p^2 is a^3, means that the square of the total time period of a planet's revolution the sun is directly proportional to the cube of its mean distance from the Sun.
What is Kepler's law ?The orbits of planets around the Sun are described by Kepler's laws of planetary motion, which he published between 1609 and 1619.
A planet's orbit is an ellipse with the sun at one of its foci. Equal areas are covered by the position vector r(t) from the sun to the planet in an equal amount of time. The semi-major axis of an orbital planet's semi-major period of revolution around the sun is proportional to the cube of that semi-major period's length.
They were essential in the discovery of dark matter in the Milky Way and have been used to forecast the orbits of several objects, including comets and asteroids.
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A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized.
y = 0 + 1x + 2x2 +
where
y = traffic flow in vehicles per hour
x = vehicle speed in miles per hour
The following data were collected during rush hour for six highways leading out of the city.
Traffic Flow (y) Vehicle Speed (x)
1,257 35
1,330 45
1,226 35
1,336 50
1,350 55
1,124 25
Enter negative values as negative, if necessary.
Show the estimated regression equation (to 3 decimals, if necessary).
= + x + x2
What is the value of the coefficient of determination (to 3 decimals)? Note: report R2 between 0 and 1.
What is the value of the F test statistic (to 2 decimals)?
What is the p-value?
Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6
Using = .01, what is your conclusion?
SelectConclude a curvilinear relationship exists for traffic flow and speedCannot conclude a curvilinear relationship exists for traffic flow and speedItem 7
Predict the traffic flow in vehicles per hour for a speed of 39 miles per hour (to the nearest whole number).
A highway department is studying the relationship between traffic flow and speed. Traffic flow is the movement of individual drivers and vehicles between two points, as well as their interactions with one another.the value of the coefficient of determination is R− sq = 0.984
Speed is one of the basic parameters of traffic flow, and the two representations of speed are time mean speed and space mean speed. Enter data in excel. Make new column for values x2.,Now click on Data->Data Analysis and select regresion. In y data range, give range of y values. In x data range, give range of x and x2 values. Click ok.
From the above output:
The estimated regression equation is: y = 612.223+26.215x0.233.x
The coefficient of determination is: R− sq = 0.984
The F test statistic is: F= 90.14
The exact p-value is 0.0021. Therefore, correct option is: less than 0.01.
Can conclude a curvilinear relationship exists for traffic flow and speed because p-value is very small.
When x = 39
y =612.223 + 26.215(39)-0.233(39)2: 1280.58= 1281
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in the figure, if the tension in string 1 is 135 n and the tension in string 2 is 220 n, what is the mass of the object shown?
The mass of the object will be 20 kg
What would be the mass of object shown?First, create a free-body diagram for the item and label it. I've included a drawing I made that depicts all the relevant forces at work on the object.
The tension forces (T1 and T2), their x and y components, and the weight force are shown on the free-body diagram (w).
In order to apply this angle later in the issue to determine the object's mass using Newton's Second Law, we want to start by determining the angle theta ().
By utilizing the knowledge that there are no imbalanced horizontal forces acting on the item and that the net force is zero, we can determine the angle.
This implies that T1 sin(40) = T2 sin(). Create an equation with them equal to one another and find the angle. The tension forces are provided as T1 = 34 N and T2 = 24 N.
T1 sin(40) equals T2 sin().
220 * sin() = 135 * sin(40).
To determine sin(), multiply 135 by sin(40) and divide the result by 220.
0.3944378513 = sin(Θ)
Consider both sides of the equation's inverse sine.
Θ = sin⁻¹(0.3944378513) (0.3944378513)
Θ = 23.2309189°
Now that we have the angle, we can utilize it to construct a mass-related equation according to Newton's Second Law.
We are aware that the object is subject to a weight force that is applied downward and is equal to mg (mass divided by the gravitational acceleration).
The two tension forces' x-components are the two forces pushing upward on the item.
Since the item is not moving vertically, we may infer that the net force must be zero (F = ma, and since there is no acceleration, F = 0 N).
The forces acting in the y-direction added together will equal zero. We can construct the following equation by making the upward direction positive and the descending way negative:
F is equal to T1 cos(40) plus T2 cos(23.2309189) - mg = 0.
Weight force (mg) should be added to both sides of the equation.
T2 cos(23.2309189) + T1 cos(40) = mg
Change T1 to 135 and T2 to 220.
220 * cos(23.2309189) + 135 * cos(40) = mg
On Earth, the gravitational acceleration is 9.8 m/s2. To find the object's mass, m, solve the problem using this number as a substitute.
220 * cos(65.59058699) + 135 * cos(40) = m (9.8)
Analyze the equation's left side.
194.30766 = 9.8m
M = 19.829, multiply both sides of the equation by 9.8.
Since the problem provides us with the tension forces as two significant values, round this to two.
m ≈ 20 kg
The object in the image weighs about 20 kg.
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what size equipment grounding conductor would be required for a copper conductor with an overcurrent protection device rated at 70 amperes?
Size of 12 AWG would be required for a copper conductor with an overcurrent protection device rated at 70 amperes
What is a conductor ?A substance or material that allows electricity to flow through it is referred to as an electrical conductor. When voltage is applied to a conductor, electrical charge carriers, typically electrons or ions, move easily from atom to atom.
The components or elements that permit electricity to flow through them are known as conductors. Conductors also permit the passage of heat through them. Animals, the Earth, copper, and the human body are all examples of conductors. A powerful conductor, the human body.
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Two identical speakers in the same orientation produce waves of the same wavelength that are in phase. At a point midway between the speakers, you would expect to hear.
Two identical speakers in the same orientation produce waves of the same wavelength that are in phase. At a point midway between the speakers, you would expect to hear louder due constructive interference took place.
While destructive interference can result in the complete cancellation of the contributing waves, constructive interference causes an increase in the amplitude of the sum wave. The "speaker and baffle" experiment, which uses a small loudspeaker and a large, square wooden sheet with a circular hole the same size as the speaker, is an intriguing demonstration of both sound interference and diffraction. When music is played through the loudspeaker, out-of-phase sound waves from the speaker's front and back diffract into the surrounding area. Particularly at very low frequencies, where the wavelength is longest and the diffraction is therefore greatest, the two waves interfere destructively and cancel one another.
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based on relative bond strengths, classify these reactions as endothermic (energy absorbed) or exothermic (energy released). AB+C --> AC+B
A+ BC --> AB + C
A2+C2 --> 2AC
B2+C2 --> 2BC
A2+B2 --> 2AB
Strongest Bond
A-B
A-A
B-B
C-C
B-C
A-C
Weakest Bond
Reactions that are Exothermic and Endothermic These emit energy in the form of heat, cold, light, sound, or vibration.
What distinguishes endothermic from exothermic reactions?The endothermic process is a term used to describe a reaction in which the system takes up heat from its environment.A reaction that is exothermic is the opposite of one that is endothermic. It emits energy onto its surroundings as heat or light.Chemical processes referred to as endothermic reactions occur when the reactants take in heat energy from their surroundings to create products.An exothermic reaction is one in which energy is given off as heat or light.In the same way that a stronger relationship releases more energy when it is established, a stronger bond also requires more energy to break.Because A-B is a strong connection that requires more energy to break than AC, which forms a weak bond and releases very little energy, the reaction is comparatively endothermic because more energy is taken in than released.As part of the reaction [rmA 2 + rmC 2] longrightarrow{{}}2{\rm{AC}}\] This reaction is endothermic because the A-C bond is weaker than the A-A and C-C bonds.To learn more about Exothermic and Endothermic Reaction refer to:
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PHYSICS HELP!!! 100POINTS !!! PLUS BRAINIEST IF CORRECT!!!
Three masses are arranged in the (x, y) plane
as shown.
What is the magnitude of the resulting
force on the 2 kg mass at the origin? The
value of the universal gravitational constant
is 6.6726 × 10−11 N · m2
/kg2
.
Answer in units of N.
The magnitude of the force of gravity that is acting on the objects is 1.33 × 10^−10 N.
What is the force that acts on the bodies?We know that the gravitational force is an attractive force that acts on all the objects that do exist in the universe. Thus, once body lies within the gravitational field of the earth this force of gravity can be said to act on the object. We have in the question two objects that are positioned on the cartesian coordinates as shown. The distance between the objects is 2 m.
Using the formula;
F = Gm1m2/r^2
F = gravitational force
G = gravitational constant
m1 and m2 = masses of the objects
r = distance of separation
Then we have;
F = 6.6726 × 10^−11 * 4 * 2/(2)^2
F = 1.33 × 10^−10 N
Thus the attractive force has a magnitude of 1.33 × 10^−10 N.
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assume that the market for beef is perfectly competitive and in equilibrium. which of the following would most likely result in an increase in both the equilibrium price and the equilibrium quantity of beef?
The equilibrium price and the equilibrium amount of beef will both rise in response to a decline in the supply of beef.
How to explain this reduction in beef supply?When supply and demand, as well as financial forces, are in balance, there is economic equilibrium, and the values of economic variables do not change in the absence of external influences.
When supply and demand are in balance, the number of people who want to purchase an item determines the demand. This cycle has a number of variables, and if it continues to rise, the last minimal cost can enable a person to purchase an item. For instance, if you purchase ice cream every day and the price keeps rising, even if it is only by a cent, this ongoing rise in price could result in the last cent becoming an obstacle.
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An electron is accelerated through 2,400 V from rest and then enters a region where there is a uniform 1.70-T magnetic field. What are (a.) the maximum and (b.) minimum magnitudes of the magnetic force acting on this electron?
The magnetic force operating on this electron has a maximum value of 79.02 x 10^-13 N; its minimum magnitude is zero when the electron goes in the magnetic field's direction.
The total of all forces exerted on an object is referred to as the magnitude of the force. A crucial physics measurement is calculating the magnitudes of forces. Regardless of the direction in which it works, a force's "magnitude" is its "size" or "strength."
The magnetic field, which is the region around a magnet that exerts a magnetic force and is caused by moving electric charges, surrounds an electric charge similarly to how an electric field does the same for an electric charge. A visual representation of magnetic fields is made using magnetic field lines.
Let v represent the velocity an electron gains in an electric field.
Charge is applied with a potential difference of V q = 1/2 m v2 V. q, m denotes charge mass, and v denotes acquired velocity.
2400 x 1.6 x 10^-19 =0.5 x 9.1 x 10^31 x v2, where v2 = 844 x 10^12 v and v = 29.05 x 10^6 m/s.
When an electron moves perpendicular to the magnetic field, the strongest force is applied to it.
Maximum force = Bqv, where B is the magnetic field, q is the charge on the electron, and v is the electron's velocity, resulting in a force of 1.7 x 1.6 x 10^-19 x 29.05 x 10^6 = 79.02 x 10^-13 N.
When an electron moves in the magnetic field's direction, the minimum force is zero.
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how can you experience a black body in practice?
We can easily experience black body in practical.
What is black body?
A black body or blackbody is the an idealized physical of the body that absorbs all to the incident of a electromagnetic radiation, regardless of frequency or angle of incidence. The probability is a name "black body" is given because it is absorbs all colors of light. A black body also emits the black-body radiation.
A body which completely absorbs all heat radiation incident on it is called perfectly black body. A perfectly black body can not be realised in practice but materials like Platinum black or Lamp black come close to being ideal black bodies. Such materials absorbs 96% to 85% of the incident radiations.
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From a scientific perspective, which of the following statements about life elsewhere in the universe is best supported by current evidence?
the government has evidence (which it is not releasing) that there is at least one other intelligent life form on a planet orbiting another star
we only have evidence that life exists around three other stars
while we have evidence of the building blocks of life elsewhere in the universe, we have no definite evidence about life around other stars at this time
there is no evidence for intelligent life anywhere, even on Earth
we have good evidence that life exists on many planets around other stars
while we have evidence of the building blocks of life elsewhere in the universe, we have no definite evidence about life around other stars at this time
The first statement describes better how life is possible elsewhere other than on earth.
The James Webb Space Telescope, launched in 2021, could get the primary glimpses: the mix of gases in the atmospheres of Earth-sized exoplanets. Webb, or a similar spacecraft within the destiny, ought to pick up symptoms of an environment like our personal – oxygen, carbon dioxide, methane. A sturdy indication of life.
In the new article led by using Jim inexperienced, the company's chief scientist, a NASA institution gives a pattern scale to apply as a starting point for discussions amongst absolutely everyone who could use it, together with scientists and communicators. They envision a scale knowledgeable with the aid of many years of experience in astrobiology, an area that probes the origins of life on the earth and opportunities of living someplace else.
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how large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg ? neglect the buoyant force on the cargo volume itself.
Mass of w load is 876.71 kg. According to which the weight of the liquid that is being propelled away from a body equals the force applied to that body.
Application of Archimedes' principle?This is an application of Archimedes' principle, according to which the weight of the liquid that is being propelled away from a body equals the force applied to that body.Since B = g V, the load that the balloon can support is B - W structure - w load = 0 w load = B - W structure.The air density at T = 25oC is = 1.18 kg / m3, thus we can calculate w load = 1.18 9.8 4/3 7.153 - 930 9.8 w load = 17705,77 - 9114 w_ load = 8591.77 N, which translates to a mass of w load = m g m = w load / g m = 8591.77 / 9.8 m = 876.71 kg.
The complete question is,
Helium is used to fill spherical balloons, which have a radius of 7.15 meters. Given that the balloon's structure and skin weigh 930 kg, how much weight can it lift? Don't think about the bulk of the cargo itself being buoyant.
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a machine part has the shape of a solid uniform sphere of mass 230 g and diameter 2.70 cm . it is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 n at that point.
A machine part has the shape of a solid uniform sphere of mass 230 g and diameter 2.7 cm. The angular acceleration is 16.10 rad / s².
Given that, mass of the sphere is 230 g
diameter is 2.7 cm
Frictional force = 0.02N
Now, we need to calculate angular acceleration. We know the formula of torque as τ = f × r
I × α = f × r
Here, I is the moment of inertia of the sphere
2/5 m r² × α = f × r
α = 5 f /( 2 m r) = (5* 0.02) / (2 * 230 * 10⁻³ * 1.35 * 10⁻²)
α = 16.10 rad / s²
Thus, the angular acceleration is 16.10 rad / s².
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A 3.40 kg cylindrical rod of length 2.00 m is suspended from a horizontal bar so it is free to swing about that end. A solid sphere of mass 0.25 kg is thrown horizontally with a speed v1 = 13.0 m/s to hit the rod at the point A one-fifth of the way up from the bottom of the rod. The sphere bounces back horizontally with a speed v2 = 9.50 m/s, while the rod swings to the right through an angle theta before swinging back toward its original position. What is the angular velocity, in rad/s, of the rod immediately after the collision?
The angular velocity, in rad/s, of the rod of length 2.00 m is suspended from a horizontal bar so it is free to swing about that end immediately after the collision is 0.29 rad /s
p = m v
Initially,
p = 0.25 * 13
p = 3.25 kg m / s
Finally,
p = 0.25 * 9.5
p = 2.375 kg m / s
The point where the ball hits the rod,
r = 4 / 5 * 2
r = 1.6 m
Moment of inertia of a rod at a point,
I = Icm + M r²
I = M L² / 12 + M r²
I = ( ( 3.4 * 2² ) / 12 ) + ( 3.4 * 1.6² )
I = 1.13 + 3.7
I = 4.83 kg m²
According to law of conservation of angular momentum,
Initial momentum of ball + Initial momentum of rod = Final momentum of ball + Final momentum of rod
( 3.25 * 1.6 ) + 0 = ( 2.375 * 1.6 ) + 4.83 ω
4.83 ω = 5.2 - 3.8
ω = 1.4 / 4.83
ω = 0.29 rad / s
Therefore, the angular velocity, in rad/s, of the rod immediately after the collision is 0.29 rad /s
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Figure 1 of 1 > 00 E Part A Rank in order, from most positive to most negative, the potential energies U, to Ur of the six electric dipoles in the uniform electric field of (Figure 1). Rank the potential energies from largest to smallest. To rank items as equivalent, overlap them. Constants U The greatest potential energy The smallest potential energy The correct ranking cannot be determined.
An item has potential energy when it's miles in a state of affairs wherein, if its actions, the potential energy can drop because it profits kinetic electricity.
Potential energy due to the electric dipole is "Udipole = -P∈cosФ"; where P is dipole moment, ∈ electric, Ф is the angle made by the dipole. Therefore potential energies from largest to smallest are as follows; Ua > Uc > Uf = Ue > Ub >Ud
Potential energies may be defined as the potential for doing work that arises from function or configuration. inside the electrical case, a charge will exert a force on another rate, and the ability of electricity arises from any series of fees. the electrical ability, or voltage, is the distinction in capacity power according to unit rate among locations in an electric-powered area.
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What are the 3 types of wave motion?.
Surface waves, longitudinal waves, and transverse waves. Any wave in which the motion of the medium's particles is perpendicular to the wave's direction is referred to as a transverse wave.
Simple definition of wave motionWave motion refers to the movement of energy and momentum between two locations in a medium without the physical movement of any substance.
Examples of wave motion and what it is.Wave Waves move when there is motion. A wave is characterized as a disruption brought on by the transmission of energy across space or a medium. Wave motion is exemplified by the motion of water ripples, sound waves, and light rays.
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complete the concept map to describe how electrical events at the neuromuscular junction result in the mechanical process of skeletal muscle fiber contraction.
The terminal end of a motor nerve and a muscle (skeletal, smooth, or cardiac) form the neuromuscular junction (NMJ), which is a synaptic connection.
It is the location where the action potential is sent from the nerve to the muscle. The NMJ is regarded as a cholinergic synaptic junction that serves as the link between motor neurons and fibers of skeletal muscle. The NMJ should transmit the impulses from the presynaptic motor neurons to the postsynaptic muscle fibers in order to maintain sustained skeletal muscle contraction.
The word "neuromuscular" refers to this process of transmitting the acetylcholine-dependent nerve impulse (action potential) from neuron to muscle. The NMJ, also known as the motor endplate, is made up of synaptic membranes on either side of the presynaptic and postsynaptic membranes.
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The squared period. T2 must be calculated in order to plot and obtain a numerical value for L vs. T. Gravity L vs. T2 Tension T2 vs. L. Tension T2 vs. L. Gravity
19.7 km distance far south of its starting point does the Robin land .
What distance?
The amount of space between two places or things is called distance.
It is a numerical qualitative measurement of how far apart objects or points are.
Sol-
Angle B = angle EAB =39°
BC= AB.COS B =21 COS 39°=16.3 km
CD = 36-16.32 =19.7 km
So south of stating point 19.7 km.
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What are the similarities between a leaf and a solar panel?.
A leaf and a solar panel both use the energy of the sun to function. The leaf uses the sun’s energy to produce food through photosynthesis, while the solar panel uses the sun’s energy to generate electricity.
Both processes require sunlight and the energy it produces to work. Additionally, both a leaf and a solar panel are reliant on the environment around them. A leaf needs sunlight, water, and other nutrients from the soil to survive, while a solar panel needs to be situated in an area with lots of direct sunlight and not a lot of shade to effectively produce energy. This means both are very dependent on their environment for their success.
Finally, both a leaf and a solar panel play an important role in the environment. Leaves are an essential part of the food chain, providing food for animals and oxygen for us to breathe. Solar panels are also important as they provide a clean, renewable source of energy that can help reduce our reliance on fossil fuels and the negative environmental impacts they have.
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What are the parts of rock cycle?.
The parts of rock cycle are -melting, cooling, eroding, compacting, or deforming. These are the physical changes by which rock undergoes during formation.
There are mainly three main types of rocks: sedimentary, igneous, and metamorphic. Each of these rocks are formed by undergoing physical changes.
Sedimentary Rocks
Sedimentary rocks are formed from pieces of already existing rock or organic material. Sedimentary rocks are further classified into three types of rocks listed as: clastic, organic (biological), and chemical.
Metamorphic Rocks
Metamorphic rocks are defined as those rocks that have been changed from their original form by immense heat or pressure.
When a rock with flat or elongated minerals is put under the immense pressure, the minerals line up in layers, creating the foliation.
Igneous Rocks
Igneous rocks are formed when the molten hot material cools and solidifies. There are different ways by which igneous rocks can be formed. When they formed inside of the earth, they are called intrusive, or plutonic, igneous rocks.
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twice each lunar month, all year long, these tides occur. whenever the moon, earth and sun are aligned, the gravitational pull of the sun to that of the moon causing tides.
True, twice each lunar month, all year long, these tides occur. whenever the moon, earth and sun are aligned, the gravitational pull of the sun to that of the moon causing tides.
When the Earth, Sun, and Moon align twice a month, their gravitational power combines to produce extremely high tides where the bulges occur, known as spring tides, Spring tides occur just after the full and new moons, when the sun, moon, and earth align. That is when the lunar and solar tides align and reinforce each other, resulting in a larger total tide. Neap tides occur when the moon is in its first or third quarter, forming a right angle with the sun, earth, and moon.
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When red light is directed normal to the surface of the soap film, the soap film appears black in reflected light. What is thinnest the film can be? let λ0 be the wavelength of red light in air.
The thinnest film of λ₀/2 can appear black in reflected light
.
What is distractive interference?When waves combine and totally cancel each other out, destructive interference occurs. Two waves must have the same amplitude travelling in opposing directions in order to interfere destructively.
Nature is home to a variety of fascinating wave phenomena that are not reducible to a single wave. We must look at the phenomenon of destructive interference based on the wave combination. We use the superposition principle, which states the following, to examine these:
The resulting wave function is the algebraic sum of the individual wave functions when two or more waves are passing through a medium.
The condition of distractive interference is: path difference = (m+1/2)λ₀ { where m = 0.1,2,3,.} and λ₀ is wavelength of light.
So, the thinnest film of λ₀/2 can appear black in reflected light.
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a contact lens is made of plastic with an index of refraction of 1.45. the lens has an outer radius of curvature of 2.04 cm and an inner radius of curvature of 2.60 cm. what is the focal length of the lens?
The focal length of the lens is 21.26 cm.
The radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the round arc which fine approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best suits an ordinary phase or combos thereof.
Calculation:-
1/f = (μ - 1)(1/R₁ - 1/R₂)
= (1.45 - 1)(1/2.04 - 1/2.6)
= 0.45 × 0.10
1/f = 0.047 cm
f = 1/0.047 cm
f = 21.26 cm.
The focal length of an optical system is a degree of the way strongly the system converges or diverges light; it is the inverse of the gadget's optical electricity. An effective focal period indicates that a device converges light, even as a negative focal duration indicates that the device diverges light.
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express the following relationship with an equation: the volume, v, of a sphere is directly proportional to the cube of its radius, r. use k as the proportionality coefficient.
If k is used as the proportionality coefficient, the relationship between volume v of a sphere and cube of its radius r is v = kr³.
If any two quantities are directly proportional to each other, a ∝ b, then the relation between a and b can be written as a = kb. This is because a and b are directly proportional to each other.
It is given that, volume of a sphere is directly proportional to the cube of its radius, v ∝ r³.
It can be written as v = kr³.
Hence, if k is used as the proportionality coefficient, the relationship between volume v of a sphere and cube of its radius r is v = kr³.
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Which of the answer choices best describes the structure and properties of ionic compounds?
Select all that apply.
Olonic compounds are best represented with the ball-and-stick model.
The bonds of ionic compounds are resistant to water's properties.
The structure of ionic compounds resembles a three-dimensional network.
Olonic compounds have high melting and boiling points.
A substance made up of both positive and negative ions is referred to as an ionic compound.
What is Ionic compound?A chemical molecule known as an ionic compound is made up of ions that are bound together by electrostatic forces, commonly known as ionic bonding. The molecule is neutral because it has both positively and negatively charged ions.Ionic compound characteristics include.Booking and high melting point.Use water to dissolve, not an organic solvent.when dissolved in water, conduct electricity.NaCl, NaI, and more examples come to mind.The ionic compound's structure and characteristics are described by the following:Ionic chemicals have a structure that resembles a three-dimensional network.Higher melting and boiling points are found in ionic substances.To Learn more About ionic compound refer to :
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g a solenoid 30.0 cm long and with a cross-sectional area of 0.600 cm2 contains 415 turns of wire and carries a current of 90.0 a.for related problem-solving tips and strategies, you may want to view a video tutor solution of storing energy in an inductor.
The total energy contained in the coil magnetic field is 0.161 J.
Given that, Length of the solenoid = 30 cm = 0.3 m
Area of cross section = 0.6 cm² = 0.6* 10⁻⁴ m²
Number of turns = 415
Current I = 90 A
Total energy contained in the coil magnetic field is given by the formula,
energy density × l ×A
Energy density is given by the formula, B²/2μ₀
The formula to find out magnetic field in the solenoid B = μ₀ ni = μ₀*N*i/L = 4π× 10⁻⁷* 415 * 90/ 0.3 = 0.15 T
Energy density = B²/2μ₀ = (0.15)²/2* 4π× 10⁻⁷ = 0.000895 × 10⁷ = 8.95× 10³ J/m³
Total energy contained in the coil magnetic field is 8.95× 10³ * 0.3 * 0.6× 10⁻⁴ = 0.161 J
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The magnitude of the drag force on a 20. 0-kg object is proportional to its speed. The object has a terminal velocity 80 m/s. What is the magnitude of the drag force on the object when it is falling with a speed 30 m/s?.
The drag force on the object is 73.5N.
What is drag force?
The drag force (D) is the force that opposes the movement of a body through a fluid. It is the fluid's resistive force. Drag force on air resistance on the object is proportional to its speed:
[tex]F_{d} = kV[/tex]
where,
k = constant
We know, [tex]F =mg[/tex]
From above equations,
[tex]mg = kV[/tex]
[tex]\frac{mg}{V} = k[/tex]
[tex]\frac{20 * 9.8}{80} = k[/tex]
[tex]k = 2.45[/tex]
For drag force,
[tex]F_{d} = kV[/tex]
[tex]F_{d} = 2.45 * 30\\\\F_{d} = 73.5 N[/tex]
The drag force on the object is 73.5N.
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a 23.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rev/min. what centripetal force (in n) must she exert to stay on if she is 1.00 m from its center? (enter a number.) n(b) what centripetal force (in n) does she need to stay on an amusement park merry-go-round that rotates at 3.00 rev/min if she is 5.00 m from its center? (enter a number.) n(c) compare each force with her weight.
a. The centripetal force (in N) that she must exert to stay if she is 1.00 m from its center is 403.80 N.
b. The centripetal force (in N) required to stay on an amusement park carousel that is rotating at 3.00 rev/min if it is 5.00 m from its center is 11.30 N.
c. Comparison of each force with her weigh is 1.79 : 0.050
Centripetal forceUse formula:
Fc = m (rω )² / r
We have,
ω = 40.0 rev/min = 0.314 rad/s
So,
a. The centripetal force (in N) that she must exert to stay if she is 1.00 m from its center is:
Fc = m (rω )² / r
= 23.0 (1.00 x 4.19)² / 1.00
= 403.80 N
b. The centripetal force (in N) required to stay on an amusement park carousel that is rotating at 3.00 rev/min if it is 5.00 m from its center is
Fc = m (rω )² / r
ω = 3 rev/min = 0.314 rad/s
Fc = 23.0 (5.0 x 0.314)² / 5.0
= 11.30 N
c. Comparison of each force with her weight is:
W = m x g
So,
403.80/ (23.00 x 9.8)
= 1.79
11.30/ (23 x 9.8)
= 0.050
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What are the things that digital society can offer compared to the previous type of society?.
The things that digital society can offer compared to the previous type of society are mentioned below.
The things that digital society can offer compared to the previous type of society are increased rate of productivity and easier means to gain more knowledge. Also gaining information on what is happening on the other side of the world is received at a rapid speed.
A society in which everything runs on digital technology and electronic means and paperless is called as digital society. In the previous type of society paper is the norm and digital technology and electronic means are rare.
Therefore, the things that digital society can offer compared to the previous type of society are mentioned above.
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figure 10-35 shows three 0.0100 kg particles that have been v l glued to a rod of length l i 6.00 cm axis o and negligible mass. the assembly can rotate around a perpendicular axis through point 0 at the left
The percentage difference between these particles is 7.14%.
Calculation:-
Given mass = 0.100 kg
length of rod = 6 cm
I total = md² + m(2d)² + m(3d)²
if the Innermost one is removed then would only m92d)² = 13 md²
The percentage difference between these is
(13-14)/4 = 0.714% = 7.14%
For any planar body, the moment of inertia about any axis perpendicular to the plane is equal to the sum of the moments of inertia about any two perpendicular axes in the plane of the body that intersect the first axis in the plane. The axis of rotation is always perpendicular to the plane of motion. The sagittal plane divides the body into left and right sections, with axes on the left and right sides.
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elastic: based on the quantities you know are conserved in such collisions, derive the formulas for the final velocity of the carts in elastic collisions, (1) (1) and (2) (2). inelastic: based on what you know of totally inelastic collisions, derive the formula for the final velocity of the carts in inelastic collisions, (3) (3).
The derived formulas for the final velocity of the carts in elastic collisions are as follows:
Suppose you have a cart of mass m1 and velocity v1i colliding with a cart of mass m2 and velocity v2i, with motion confined to one dimension. If the collision is perfectly elastic, then both momentum and energy are conserved. in this case, the final velocities are:
Calculations;
v1f = (2m1/m1 + m2) × v1i - ( m1 - m2/m1+m2) × v2i .... (1)
v2f = (m1 - m2/m1 + m2) ×v1i + ( 2(m2)/ m1 + m2) × v2i .... (2)
If the collision is totally inelastic, then only momentum is conserved; energy is lost. in this case, the carts end up moving together with one common final velocity:
vf= (m1/ m1 + m2) × v1i + (m2/ m1 + m2) v2i .... (3)
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