Draw vector strokes (straight lines without arrowheads) in the diagram to the right that show what an object travelling in a counter clockwise circle looks like when it is doing the following.
How do you refer to a straight line?To indicate that a line has no "wobbles" anywhere along its length, it is sometimes called a long line or, more quaintly, a right line (Casey 1893). Even though lines are fundamentally one-dimensional shapes, they can still be found incorporated into higher dimensional areas.
The following equation is used to determine the acceleration in each scenario: a = v2/R. A = (3.70)2/(1.30) = 10.53 m/s2 is the speed at the top of the loop. A = (7.10)2/(1.30) = 38.78 m/s2 is the speed of the loop's bottom. Always use Fnet = m•a to calculate the net force. Fnet equals 1 kg times 10.53 m/s2 or 12.6 N just at bottom of the loop. Fnet equals 1.20 kg multiplied by 38.78 m/s2 to equal 46.5 N just at bottom of the loop. The formula mg, where g is equal to 9.8 m/s2, is always used to calculate the force of gravity.
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fill in the blank. research questions about the time course of cognition are better addressed using methods like___, whereas questions about the anatomy of cognition are better addressed using methods like___.
research questions about the time course of cognition are better addressed using methods like ERPs, whereas questions about the anatomy of cognition are better addressed using methods like fMRI.
What is ERPs and fMRI?The primary goal of an ERP system is to improve organisational efficiency by managing and improving how corporate resources are used.These systems are of three types, on-premises, cloud-based, and hybrid. It depends on the organization adopting ERP software to choose a suitable type for its business needs and operations to improve its productivity.
The fMRI magnet converts tissues into a visualizable state, and radio frequency pulses offer the signalling information required to distinguish them. The computer assembles the information from the radio frequency pulses into a manner that anyone who can read a weather map will recognise.
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newton's law with friction (force on angle) determine the acceleration of the system depicted below.
Therefore, no acceleration will occur until the frictional force exceeds the Driving Force (F), which in this case is gravity. The equation would then indicate a negative acceleration, which would not actually occur. Friction is a reactive force rather than an active one.
What is the best method for resolving forces to compute acceleration including friction on horizontal and incline planes?When you resolve, set your axes to be perpendicular and parallel to the surface rather than necessary vertical and horizontal axes.
As the item on the surface neither sinks into it nor accelerates away from it, the forces perpendicular to the surface will add up to zero.
The total of the forces acting parallel to the surface may be used to calculate the acceleration using the formula F=ma.
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determine the length of a hex head bolt for the following application: mounting hole size: 0.875 inch, mounting thickness including foot: 1.500 inches, plain washer thickness: 0.102 inch, lock washer thickness: 0.188 inch.
The minimum length of the bolt required is 2.665 inches, plus an additional length for the hex head.
The length of a hex head bolt for a specific application can be determined by adding up the thicknesses of the different components that make up the assembly. In this case, the components include the mounting hole, the mounting thickness including the foot, the plain washer, and the lock washer.
The mounting hole size is 0.875 inches, which is the distance between the surfaces being connected. The mounting thickness including the foot is 1.500 inches, which represents the thickness of the material to which the bolt will be attached.
The plain washer thickness is 0.102 inches, which is added to ensure even distribution of pressure on the mounting surface and to prevent damage to the surface during tightening. The lock washer thickness is 0.188 inches, which is added to prevent the bolt from loosening over time.
In total, the thicknesses of these components are 0.875 + 1.500 + 0.102 + 0.188 = 2.665 inches. Therefore, the minimum length of the hex head bolt required for this application is 2.665 inches.
It is important to note that this length does not include the length of the hex head itself. In most cases, an additional 0.25 to 0.375 inches is required for the length of the hex head.
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A circuit contains two resistors linked in parallel; each resistor has a resistance of 20 Ω . What is the circuit's total resistance?
The resultant resistance of the resistor combination is 10 Ω.
What is resistor?A resistor is an electrical component that controls or restricts how much electrical current can pass across a circuit in an electronic device. A specified voltage can be supplied via resistors to an active device like a transistor.
Resistance of each resistor is = 20 Ω
The resistors are connected parallelly.
Hence, the resultant resistance of the resistor combination = (20 ||20) Ω
= (20 × 20) ÷ (20 + 20) Ω
= 10 Ω.
Therefore, the resultant resistance of the resistor combination is 10 Ω.
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1.
Mechanical advantage is expressed in newtons squared.
True or false ?
Mechanical advantage has no unit, Hence, the statement that Mechanical advantage is expressed in newtons squared is False.
What is a mechanical advantage?A primary machine's mechanical advantage quantifies how much work goes into it and is used to manipulate the load. In other words, it is the ratio of a machine's input to output work. It has no units because it is the ratio of two identical quantities.
Mathematically, mechanical advantage = load/effort or work output/ work input
The higher the mechanical advantage of a machine, the more efficient will be the machine.
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following are the results of a sieve analysis. draw a particle-size distribution curve and determine cu
In order to plot each sieve % on the distribution curve, you must divide the entire mass of the sample material by the weight that was either retained or that passed thru every sieve.
What does the sieving method's particulate size distribution mean?As the asymmetric energy sieve method directly provides weight distribution, sieve methodology provides sieve diameter, which is determined as the micrometer of the globe that passes through the sieve aperture. By using the sieve process, particles of sizes between 50 and 1500 m are estimated.
Which two forms of particle size estimation are there?Adaptive mien scattering and laser particulate analyzers are two of the primary categories of particle size analyzers. Particles in solutions are measured by dynamic light diffracted analyzers between 0.6 nm and For particle in a substance that are between 10 nm and 3 mm in size, analyzers are utilized.
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Required information Problem 11.009 - Slowing car - DEPENDENT MULTI-PART PROBLEM - ASSIGN ALL PARTS NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. The brakes of a car are applied, causing it to slow down at a rate of 18 ft/s2. The car stops at 300 ft. 300 ft Problem 11.009.a - Slowing car: constant deceleration and distance traveled Determine how fast the car was traveling immediately before the brakes were applied. (You must provide an answer before moving to the next part.) The speed of the car immediately before the brakes were applied was ft/s. Problem 11.009.b - Slowing car: constant deceleration and elapsed time Determine the time required for the car to stop. The time required for the car to stop is S.
The acceleration is 7m/s².
For Part a, we can use the equation of motion for constant acceleration:
v f = v_0 + a x t
where v f is the final velocity, v_0 is the initial velocity, a is the acceleration, and t is the time. Since the final velocity is 0, we can write:
t = -v 0 / a
Next, we can use the distance formula:
d = v_0 x t + 0.5 x a x t²
where d is the distance traveled. Plugging in the value of t from the previous equation, we get:
d = v_0 x (-v_0 / a) + 0.5 x a x (-v_0 / a)²
d = -v_0² / 2a
Now, we can solve for v_0 using the value of d:
v_0 = (2 x a x d) = (2 x 18 x 300)= 102.9 feet/s
For Part b, we can use the equation for t from Part a:
t = -v_0 / a = -102.9 / 18 = 5.71 s
Acceleration is the rate of change of velocity of an object over time. It is a vector quantity with units of meters per second squared (m/s²) in the SI system. Acceleration can be caused by various factors such as force, changes in velocity, and changes in direction. Positive acceleration indicates that the velocity of an object is increasing, while negative acceleration indicates that the velocity is decreasing. In a uniform acceleration, the velocity of an object changes by an equal amount over equal time intervals.
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a block of mass m1 is at rest on a long frictionless table, one end of which is terminated in a wall. another block of mass m2 is placed between the first block and the wall and set in motion to the left with constant speed v2i. assuming that all collisions are completely elastic, find the value of m2 for which both blocks move with the same velocity after m2 has collided once with m1 and once with the wall. assume the wall to have infinite mass.
After a collision, the center of mass velocity of this system of two balls with masses m1 and m2 and velocities v1 and v2 is ( m1 v1 + m2 v2 ) / ( m1 + m2 ).
What is the momentum law of motion?Momentum is the force needed to stop an item moving at a certain speed in a given amount of time. It is calculated by multiplying an object's mass by its velocity. The sum of the individual momenta determines the overall momentum for any array of many objects.
p = m.v
p = Momentum
m = Mass
v = Velocity
For ball 1,
m = m1
v = v1
p1 = m1 v1
For ball 2,
m = m2
v = v2
p2 = m2 v2
Center of mass velocity = Total momentum / Total mass
Total momentum is = p1 + p2
Total mass is= m1 + m2
Center of mass velocity is= ( p1 + p2 ) / ( m1 + m2 )
Center of mass velocity is= ( m1 v1 + m2 v2 ) / ( m1 + m2 )
Therefore, center of mass velocity of this system of two balls is
Center of mass velocity = ( m1 v1 + m2 v2 ) / ( m1 + m2 ).
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The systematic ways in which our ethics are limited in ways we are not even aware of ourselves is called _______________
The systematic ways in which our ethics are limited in ways we are not even aware of ourselves is called implicit bias.
Implicit bias refers to the unconscious attitudes, beliefs, and stereotypes that influence our thoughts and actions in ways we are not even aware of. This type of bias is often a result of cultural and societal conditioning, and it can impact our decision-making processes and behavior even when we consciously believe that we are being fair and objective. Implicit bias can affect all aspects of our lives, from our personal relationships to our professional practices, and it is a significant factor in perpetuating discrimination and inequality. Understanding and recognizing implicit bias is crucial for promoting equality and fairness in society, and for developing more equitable and just ethical practices.
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two stones are thrown vertically upward from the ground, one with three times the initial speed of the other. assume free fall.
Stone speed is equal to three times stone speed if the stones are the same size. The stone will touch the earth in 10/3s, or 3.3 seconds because gravity will affect both stones equally during the fall.
When a stone is thrown vertically upward, what two forces are at work on the object?Gravitational force acts downhill when a stone is propelled vertically, while muscular force or an applied force acts upward.
Why does a stone being hurled vertically upward lose speed?Gravity tries to pull the stone down when it is thrown vertically upward, slowing down its motion. After a period, the velocity falls to zero as a result of this persistent downward drag.
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What would the power (Watts) be for a speaker if it draws 3.0 Amps of current when connected to a 12.0 Volt source?
The power of Speaker can be calculated by
[tex]P=V.i\\P=(12).(3)\\P=36W[/tex]
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a ball is thrown directly downward with an initial speed of 7.70 m/s, from a height of 29.9 m. after what time interval does it strike the ground
The ball strikes the ground after 2.46 seconds.
The time interval can be calculated using the following equation:
t = [tex]\frac{2h}{g}[/tex]
where h is the height from which the ball was thrown (29.9 m), g is the acceleration due to gravity (9.8 m/s), and t is the time interval.
Substituting the values, we get:
t = (2 x 29.9 / 9.8) = (59.8 / 9.8) = [tex]\sqrt{6.1}[/tex] = 2.46s
So, the ball strikes the ground after 2.46 seconds.
Time is a continuous progression of events that occur in a linear sequence. It is a measure of the duration between two events and is an essential aspect of our lives. Time is fundamental to our understanding of the world and our place in it, as it allows us to track the passing of days, seasons, and years. It is an intangible concept that is difficult to define but is central to our experiences of the world. Time is an essential component of physics, as it is used to measure the duration of physical events and the speed of processes. Time is often described as the fourth dimension and is related to space and matter, as well as energy and momentum.
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The hot glowing surfaces of stars emit energy in the form of electromagnetic radiation. It is a good approximation to assume that the emissivity e is equal to 1 for these surfaces.
A) Find the radius RRigel of the star Rigel, the bright blue star in the constellation Orion that radiates energy at a rate of 2.7×1031W and has a surface temperature of 11,000 K. Assume that the star is spherical. Use σ=5.67×10−8W/m2⋅K4 for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.
The radius the star Rigel, a bright blue star in the constellation Orion that radiates energy at a rate of 2.7 × 10³¹ W and has a surface temperature of 11,000 K. (Assume that the star is spherical) = 5,422.17 km
To determine the radius of the star, we can apply the Stefan-Boltzmann law to determine the star output power.
Rigel emits radiation at a rate of 2.7 x 10²³ Watts
The power per unit area, according to the Stefan-equation, Boltzmann's is:
j = σT⁴
Where,
σ = (2[tex]\pi[/tex]⁵K⁴) / 15c²h³
T = temperature
σ = 5.670 x 10⁻⁸ Wm⁻²K⁻⁴
Hence,
The surface area of the star:
A = P / j
P = power ⇒ 2.7 × 10³¹
A = ( 2.7 × 10³¹) / (5.670 x 10⁻⁸) (11.000⁴)
= 3.52 x 10²³
The area = 4[tex]\pi[/tex]r²
3.52 x 10²³ = 4[tex]\pi[/tex]r²
r² = 2.58 x 10²²
r = 5,422.17 km
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you are hired by an optics manufacturer to design a high-precision mirror alignment system. the resolution for mirror displacements must be on the order of a few nanometers and these deflections must be driven by electrical voltages. which of the following materials properties would you consider most important when selecting a material for this system? you are hired by an optics manufacturer to design a high-precision mirror alignment system. the resolution for mirror displacements must be on the order of a few nanometers and these deflections must be driven by electrical voltages. which of the following materials properties would you consider most important when selecting a material for this system? thermal expansion coefficient electrical resistivity thermal conductivity piezoelectric coefficient
An optics manufacturer commissions you to create a highly accurate mirror alignment system. Mirror displacements must have a resolution of a few nanometers, and these
What is placement dis?
An volume or mass of a liquid (such as water) that is displaced by a lifting surface (such as a vessel) of equivalent weight is referred to as displacement: the distinction between an object's initial position and any subsequent positions additionally: the total volume that all of an internal combustion engine's pistons displace in this manner
Displacement activity: what is it?
furthermore, automobiles: Internal combustion engines' required amount so displaced by all of their pistons is referred to as displacement activity or displacement behavior. Numerous people have been displaced as a result of the war. shifts in the Earth's mantle soil shifting brought on by farming
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An experiment is performed using a sensitive ammeter attached to a length of conducting wire shaped into a coil. In the first trial, a bar magnet is quickly and repeatedly pushed into and pulled out of the space inside the coil. The reading on the ammeter indicates that the current is positive as the bar magnet moves forward into the coil. For the second trial, the connections between the ends of the coil of wire and the connections of the ammeter are reversed. The bar magnet is again quickly and repeatedly pushed into and pulled out of the space inside the coil. The reading on the ammeter shows that the current is again positive as the bar magnet moves forward into the coil. Which of the following is a correct claim about the second trial and indicates the Maxwell equation that provides the evidence? A. According to the Biot-Savart law, the poles of the magnet are aligned relative to the loop, the same as in the first trial. B According to Faraday's law, the poles of the magnet are aligned relative to the loop, the same as in the first trial. с According to Ampere's law, the poles of the magnet are aligned relative to the loop, the same as in the first trial. D According to Faraday's law, the poles of the magnet are reversed relative to the loop, as compared to the first trial.E According to Ampere's law, the poles of the magnet are reversed relative to the loop, as compared to the first trial.
According to Faraday's law, the poles of the magnet are reversed relative to the loop, as compared to the first trial. Option D
What is the Maxwell law of electromagnetism?The Maxwell laws of electromagnetism are a set of four equations that describe the behavior of electric and magnetic fields and their interaction with charged particles. These laws form the foundation of classical electromagnetism and predict the behavior of electromagnetic waves, including light. The laws are named after the Scottish physicist James Clerk Maxwell.
From the Faraday's law, we know that it is the relative motion between the coil and the magnet that induces current.
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three objects are brought close to each other, two at a time. when objects a and b are brought together, they repel. when objects b and c are brought together, they also repel. which of the following are true? (select all that apply.)
Since all three objects a, b and c repel one another, they possess charges of the same sign.
Assuming all three objects are conductors, the electric charge, either positive or negative, will be evenly distributed throughout the object.
Opposite charges attract each other, while same charges repel. Object a and b repel when they are brought together, which means that both objects have the same charge. This is the same case with object b and c. This means that all three objects possess the same charge.
The multiple choices are most probably these:
A. Objects a and c possess charges of the same sign.B. Objects a and c possess charges of opposite sign. C. All three objects possess charges of the same sign. D. One object is neutral.E. Additional experiments must be performed to determine the signs of the charges.Learn more about electric charges at https://brainly.com/question/874116.
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consider the action of the biceps when carrying a load of 8 kg with the forearm making an angle of 20
When carrying a load of 8 kg with the forearm making an angle of 20, the biceps muscle must exert a force to hold the forearm and its load in place.
The amount of force the biceps must exert depends on the lever arm of the load, which is the perpendicular distance between the line of action of the force and the axis of rotation.
The lever arm of the load in this case is the distance between the line of action of the load and the axis of rotation of the elbow joint. With a lever arm of 8 kg and an angle of 20 degrees, the biceps must exert a force of 16.47 Newtons.
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true/false. if the earth somehow got 3 times more mass than it has now, but stayed the same size, our weight would increase by a factor of 9.
F=GmMr2=kM, where G is your weight and m is the primordial mass of the earth. Where k=Gmr2 k = G m r 2, F = G m M r 2 Equals k M.
Has the mass of the Earth remained constant?Did you realize that the weight of the planet Earth is decreasing daily? In spite of the 40,000 tons of space dust that reach the surface of our planet every year, it is really becoming 50,000 tonnes lighter.
Does the planet's weight increase or decrease?The University of Guelph's Joanna O'Meara, a lecturer and associate head in the faculty of physics, argues why meteor showers actually cause the Earth to grow heavier. According to her, space dust, which includes meteor and asteroid debris, adds around 40,000 tonnes of weight to the earth each year.
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write the general antiderivative of the given rate of change function. (use c for the constant of integration.) the rate of change of dvd orders is given by s(m)
The general antiderivative of the rate of change function "the rate of change of DVD orders is given by s(m) = 600m + 5DVDs per month" is "DVD orders = 300m^2 + 5m + c", where c is the constant of integration.
The antiderivative of a function is the original function whose derivative is equal to the given rate of change function. To find the antiderivative of the rate of change function "the rate of change of DVD orders is given by s(m) = 600m + 5 DVDs per month", we need to integrate the function with respect to the independent variable m.
The antiderivative of the function s(m) = 600m is 300m^2 and the antiderivative of the constant 5 is 5m. Adding these two antiderivatives, we get the general antiderivative of the rate of change function:
DVD orders = 300m^2 + 5m + c
where c is the constant of integration and represents the arbitrary offset from the original function. To find the value of c, additional information or boundary conditions are required. This antiderivative represents the total number of DVD orders as a function of the number of months since the beginning of the year.
Complete question:
Write the general antiderivative of the given rate of change function.
DVD Orders The rate of change of DVD orders is given by
s(m) = 600m + 5DVDs per month
where m is the number of months since the beginning of the year.
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the pressure drop across a short hallowed plug placed in a circular tube through which a liquid is flowing through can be expressed as g
The pressure drop across a short, hallowed plug in a circular tube through which a liquid is flowing can be expressed as: ΔP = KΔv^2,
where ΔP denotes the pressure drop, Δv is the velocity change of the fluid and K is a constant of proportionality that depends on the geometrical parameters of the tube and the fluid properties.
What doe sthe above equation shows?The equation shows that the pressure drop is proportional to the square of the velocity change. The value of K can be determined experimentally or calculated using fluid dynamics models.
What causes pressure drop?The pressure drop is caused by various factors, including fluid viscosity, pipe roughness, diameter, and flow rate. The pressure drop across a pipeline is directly proportional to the fluid velocity.
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true/false. two competing models attempt to explain the motions and changing brightness of the planets: ptolemy's geocentric model and copernicus' heliocentric model. sort the characteristics according to whether they are part of the geocentric model, the heliocentric model, or both solar system models.
The geocentric model is a solar system model that places the Earth at the center and explains the motion of the planets through circular paths. The heliocentric model, on the other hand, places the Sun at the center and explains the motion of the planets through orbit around the Sun. The changing brightness of the planets is explained by their varying distances from either the Earth (geocentric model) or the Sun (heliocentric model).
True, two competing models were created to explain the motions and changing brightness of the planets. These were Ptolemy's geocentric model and Copernicus' heliocentric model. The geocentric model, as its name suggests, places the Earth at the center of the solar system and the planets, including the Sun, orbit around it. The heliocentric model, on the other hand, places the Sun at the center of the solar system and the planets, including Earth, orbit around it.
In the geocentric model, the planets move in circular paths called epicycles, which are superimposed on larger circular paths called deferents. The changing brightness of the planets is explained by their varying distances from the Earth.
The heliocentric model explains the motion of the planets as the result of their orbit around the Sun. The changing brightness of the planets is also explained by their varying distances from the Sun.
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geothermal energy is used to run large and complex power stations as well as small and relatively simple pumping systems. which of the following most accurately explains how geothermal energy is produced and utilized in these applications?
The statement that accurately explains how geothermal energy is produced and utilized is the one that says that geothermal energy uses the natural insulating power of Earth to create temperature differentials that are used to heat buildings in the winter and cool them in the summer.
Geothermal energy is the thermal or heat energy in the Earth's crust. It originates from the formation of the planet as well as from various materials' radioactive decay.
Geothermal energy has been used for thousands of years. Geothermal heating (using hot springs water for heating) has been used for pathing since Paleolithic times, while space heating has been existing since ancient Roman times. Recently, geothermal power is used to generate electricity as well.
Attached below is a picture of a power plant that utilizes geothermal energy, the Nesjavellir Power Plant.
Your question seems incomplete. The completed version is most likely as follows:
Geothermal energy is used to run large and complex power stations as well as small and relatively simple pumping systems. Which of the following most accurately explains how geothermal energy is produced and utilized in these applications?
Geothermal energy uses heat from the Sun to raise the Earth's surface temperatures to a point where these applications can heat homes and buildings.Geothermal energy uses heat from the Sun to create atmospheric temperature gradients, which in turn power turbines to generate electricity.Geothermal energy uses the natural insulating power of Earth to create temperature differentials that are used to heat buildings in the winter and cool them in the summer.Geothermal energy cannot be tapped directly from heat generated by volcanoes or other geologically active areas.Learn more about geothermal energy at https://brainly.com/question/1197584
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clcl express your answer in condensed form in order of increasing orbital energy as a string without blank space between orbitals. for example, [he]2s22p2[he]2s22p2 should be entered as [he]2s^22p^2.
The electron configuration of Cl (chlorine) is [Ne] 3s^2 3p^5. The order of increasing orbital energy would be 3s, 3p. So the answer would be: [Ne]3s^23p^5
The arrangement of electrons within an atom is referred to as the "electronic configuration of an atom." With the help of the Aufbau principle, a sequence of energy levels for the electrons in an atom can be filled up or built up. In German, the word "aufbau" implies "building up."
According to this idea, orbitals are filled in a sequence of increasing energy. The lowest energy level is filled first. The higher energy levels are then filled one by one. Because it is the most stable, the atom is said to be in its ground state, sometimes referred to as the normal state.
The electron configuration of an element describes how its electrons are distributed throughout its atomic orbitals. Atomic subshells that contain electrons are placed in a series, and the number of electrons that each one of them holds is indicated in superscript for all atomic electron configurations.
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A man exerts a horizontal force of 145 N on a crate with a mass of 31.2 kg.
Answer:
Below
Explanation:
If you can't overcome the force of friction....the crate will not move
so friction force = 145 N
Coeff of friction = Ff / Normal force = 145 / (31.2 * 9.81) = .47
A satellite of mass 2,000 kg is in an elliptical orbit about the Earth. When the satellite reaches point A, which is the closest point to the Earth, its orbital radius is 1.2x10'm and its orbital velocity is 7.1x 103 m/s. (Me = 6x1024 kg and Re = 6.4x10 m) a. Determine the total mechanical energy of the satellite at point A, assuming that the gravitational potential energy is zero at an infinite distance from the Earth. b. Determine the angular momentum of the satellite at point A. c. What is the minimum speed of the satellite at point A in order to escape from Earth? When the satellite reaches point B, which is the furthest point from the Earth, its orbital radius is 3.6x107m. d. Determine the speed of the satellite at point B.
A satellite of mass 2,000 kg is in an elliptical orbit about the Earth. When the satellite reaches point A, which is the closest point to the Earth, its orbital radius is 1.2x10'm and its orbital velocity is 7.1x 103 m/s. (Me = 6x1024 kg and Re = 6.4x10 m). So, the total mechanical energy of the satellite at point A is -0.6x10^13 J, assuming that the gravitational potential energy is zero at an infinite distance from the Earth.
The total mechanical energy (E) of an object in orbit is given by the equation E = kinetic energy (K) + potential energy (U).
At point A, the kinetic energy (K) is given by the equation K = (1/2)mv^2, where m is the mass of the satellite (2,000 kg) and v is its velocity (7.1x10^3 m/s).
The potential energy (U) is given by the equation U = -GMe/r, where G is the gravitational constant (6.67x10^-11 Nm^2/kg^2), Me is the mass of the Earth (6x10^24 kg), and r is the distance of the satellite from the Earth (1.2x10^6 m).
Substituting the values into the equations and solving, we get:
K = (1/2)(2,000 kg)(7.1x10^3 m/s)^2 = 3.0x10^13 J
U = -(6.67x10^-11 Nm^2/kg^2)(6x10^24 kg)/(1.2x10^6 m) = -3.6x10^13 J
E = K + U = 3.0x10^13 J + (-3.6x10^13 J) = -0.6x10^13 J
So, the total mechanical energy of the satellite at point A is -0.6x10^13 J, assuming that the gravitational potential energy is zero at an infinite distance from the Earth.
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114 Find two elements of R4 which belong to the span of the following vectors. Find an element of Rtwhich does nOt belong to their span. (Hint: Compute Ithe sum of the entries of each of the given vectors | Xi=lEI X [S_Um} 24 X=[}-2-2]'
The span of a set of vectors is the set of all linear combinations of those vectors. In this case, the set of vectors is:
X1 = [1, 2, 3, 4]
X2 = [2, 4, 6, 8]
Two elements in R4 that belong to the span of these vectors are:
a1X1 + a2X2 = [a1 + 2a2, 2a1 + 4a2, 3a1 + 6a2, 4a1 + 8a2]
So for example, if we choose a1 = 1 and a2 = -1, we get:
a1X1 + a2X2 = [1 - 2(-1), 2(1) - 4(-1), 3(1) - 6(-1), 4(1) - 8(-1)] = [3, 0, 9, -3]
Another example is if we choose a1 = 2 and a2 = -2, we get:
a1X1 + a2X2 = [2 - 2(-2), 2(2) - 4(-2), 3(2) - 6(-2), 4(2) - 8(-2)] = [6, 0, 18, -6]
To find an element of R4 that does not belong to the span of these vectors, we need to find a vector in R4 that cannot be expressed as a linear combination of X1 and X2. For example, the vector [1, 1, 1, 1] cannot be expressed as a linear combination of X1 and X2, so it does not belong to their span.
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It has been proposed to use uranium carbide (UC) for the initial fuel in certain types of breeder reactors, with the uranium enriched to 25 w/o. The density of UC is 13.6 g/cm3 . The molecular weight of U-235 and U-238 are 235.0439 and 238.0508 respectively. (a) What is the atomic weight of the uranium? (b) What is the atomic density of U-235?
(a) The atomic weight of uranium can be calculated as a weighted average of the atomic weights of the isotopes U-235 and U-238, taking into account their natural abundances. The atomic weight of uranium is approximately 238.03 g/mol.
(b) To calculate the atomic density of U-235, we need to know the mass fraction (or weight fraction) of U-235 in uranium carbide fuel. Considering that uranium is enriched to 25 w/o U-235, the mass fraction of U-235 is 0.25. The atomic density of U-235 can then be calculated as follows:
atomic density = (mass fraction of U-235) * (UC density) / (atomic weight of U-235)
= (0.25) * (13.6 g/cm3) / (235.0439 g/mol)
= about 7.07 x 10^22 atoms/cm3
"Atomic" is a term that has many related but different meanings. In physics, "atom" refers to the smallest unit of an element that retains the chemical properties of that element. In computer science, "atomic" is used to describe an operation that is indivisible and cannot be stopped. This means that the operation was completed in its entirety or not at all.
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Which is the equation for a machine’s efficiency?(1 point)
The equation for a machine’s efficiency is = (output energy ÷ input energy) × 100%
What is efficiency ?Efficiency is the ability to achieve something or get a desired outcome without wasting resources, time, money, energy, or effort. In a broader sense, it is the capacity to carry out tasks effectively and efficiently.
It denotes the degree of performance that requires the fewest inputs to provide the greatest amount of output in more mathematical or scientific words.
Hence, mathematically, machine’s efficiency can be expressed as:
machine’s efficiency = (output energy ÷ input energy) × 100%
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A wheel of radius $a$ rolls along a horizontal straight line without slipping. Find parametric equations for the curve traced out by a point $P$ on a spoke of the wheel $b$ units from its center. As parameter, use the angle $\theta$ through which the wheel turns. The curve is called a trochoid, which is a cycloid when $b=a$
The position of point $P$ relative to the center of the wheel can be described as follows:
$x = a\theta - b\sin\theta$
$y = a - b\cos\theta$
$a$ is the radius of the wheel and $b$ is the distance of point $P$ from the center of the wheel. These equations define a trochoid. If $b = a$, then it becomes a cycloid.
About radiusThe radius is a circle is the line that connects the center point of the circle to a point on the circle. In a 3-dimensional sphere, the radius that connects the center of the ball to a point on the surface of the ball. The radius of a circle is half the diameter of the circle.
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the photograph below shows a girl pushing on a large stone sphere. the sphere has a mass of 8200 kg and a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water.
The time that will take the girl to rotate the sphere one time (the sphere has a mass of 8200 kg and a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water) starting from rest = 35.16 s
To determine the time it's take the girl to rotate, use the intertia formula:
I = ⅖ (m) (r²)
Where,
I = inertia
m = mass of the object (kg)
r = radius
Hence,
I = ⅖ (8200) (0.9)²
= 2657 kgm²
Determine the torque,
τ = (I)(α)
(30) (0.9) = (2657) α
α = 0.01016 rad/s²
Θ = ½(α) (t²)
2π rads = ½ (0.01016) (t²)
t =sqrt(4π 0.0106)
t = 35.16 s
The question is incomplete, it should be:
There is a girl pushing on a large stone sphere. The sphere has a mass of 8200 kgand a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water. Suppose that she pushes on the sphere tangent to its surface with a steady force of F = 30N and that the pressured water provides a frictionless support.1) How long will it take her to rotate the sphere one time, starting from rest?
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