Suppose exactly 6.95 g of each reactant is taken and the following details are given by A and B then 6.95 g of A is equivalent to 6.95/molar mass of A moles of A. 6.95 g of B is equivalent to 6.95/molar mass of B moles of B.
How much extra reagent will still be present once the limiting reactant has been used up?To determine which reactant is limiting, we need to compare the amount of each reactant to the stoichiometry of the reaction.
The stoichiometry of the reaction is 1:2 for reactants A and B, respectively.
Therefore, if we have 6.95 g of A and 6.95 g of B, we can calculate the ratio of A to B to determine which reactant is limiting.
6.95 g of A is equivalent to 6.95/molar mass of A moles of A.
6.95 g of B is equivalent to 6.95/molar mass of B moles of B.
Comparing the moles of A and moles of B, we can see that A is limiting, as there is less A than required by the stoichiometry of the reaction.
To determine the mass of the excess reagent (B) that will remain after the limiting reactant (A) is consumed, we need to calculate the moles of B that are in excess.
We can calculate the moles of B that are used up by the reaction (based on the stoichiometry of the reaction) and subtract this from the total moles of B that were initially present.
The remaining moles of B can then be converted back into grams to find the mass of B that will remain.
Using the above method, the mass of the B remaining after A is consumed can be calculated.
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A solid sphere rolls along a horizontal, smooth surface at a constant linear speed without slipping.
What is the ratio between the rotational kinetic energy about the center of the sphere and the sphere’s total kinetic energy?
1. None of these
2. [tex]\frac{3}{5}[/tex]
3. [tex]\frac{3}{7}[/tex]
4. [tex]\frac{2}{5}[/tex]
5. [tex]\frac{7}{2}[/tex]
6. [tex]\frac{2}{7}[/tex]
7. [tex]\frac{5}{3}[/tex]
Answer:
6. 2/7
Explanation:
It's true
find the minimum height h that will allow a solid cylinder of mass m and radius rcyl to loop the loop of radius rloop .
The minimum height h that will allow a solid cylinder of mass m and radius h = rloop + (m * g) / (2 * π * rcyl)
What is the acceleration due to gravity? The acceleration due to gravity is the rate at which an object accelerates when freely falling in a vacuum. This acceleration is caused by the gravitational attraction between two massive objects. It is usually denoted by the symbol ‘g’ and its magnitude is 9.8 m/s2 near the Earth’s surface.The magnitude of the acceleration due to gravity changes with the distance from the center of the Earth. The acceleration due to gravity decreases with the increase in the distance from the center of the Earth. This is because the force of gravity decreases with the increase in the distance. At the Earth’s surface, the acceleration due to gravity is usually taken as 9.8 m/s2. The acceleration due to gravity is directly proportional to the mass of the object.The acceleration due to gravity is an important factor in the calculation of the force of gravity, the weight of an object, the time taken for an object to fall, and other important parameters. It is also used in calculating the trajectory of a projectile. The acceleration due to gravity is also used to calculate the escape velocity of a rocket and the speed with which a satellite orbits the Earth.To learn more about acceleration due to gravity refer to:
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Can anyone help me on this question please?
(a) The x and y component of 6 N are 4.8 N and 3.6 N respectively.
(b) The magnitude of the resultant of the three forces is 1 N.
What is the direction of the forces?
The direction of the forces is calculated as follows;
θ = arc tan ( Vy / Vx )
θ = arc tan ( 3 / 4 )
θ = 36.87 ⁰
The x and y component of 6 N is calculated as follows;
Fx = 6 cos (36.87 ) = 4.8 N
Fy = 6 x sin ( 36.87 ) = 3.6 N
The sum of all the x component of the three forces = -4 N + 4.8 N = 0.8 N
The sum of all the y component of the three forces = -3 N + 3.6 N = 0.6 N
The resultant force is calculated as follows;
F = √ ( 0.6² + 0.8² )
F = 1 N
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Explorer 35 took 11.5 hours to orbit the Moon. Use this period, and the semimajor axis of Explorer 35's orbit, to find the Moon's mass in kilograms (kg). Choose the answer that is closest to your calculated value. O 5 x 10^21 kg O 5 x 10^22 kg O 5 x 10^23 kg O 5 x 10^24 kg
The orbit of the Moon by exploration 35 took 11.5 hours. The mass of the moon is 5 x 1022 kg.
How does an orbit work?A route that a space-bound object follows around another is known as an orbit. The hemisphere, extraocular musculature, nerves, blood arteries, the conjunctiva apparatus, including adipocytes are all housed within the bony orbits of the skull. The globe is shielded by each orbit, and the supporting tissues enable three-dimensional movement.
What triggers an orbit to occur?A planet or moon's forward speed in space and the gravitational pull of another body located in space, including a big planet or star, are perfectly balanced to form orbits. High Orbit around earth, medium Orbital spaceflight, and low Orbital maneuvers are the three main categories of Earth orbits.
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The orbit of the Moon by exploration 35 took 11.5 hours. The mass of the moon is 5 x 1022 kg.
How does an orbit work?A route that a space-bound object follows around another is known as an orbit. The hemisphere, extraocular musculature, nerves, blood arteries, the conjunctiva apparatus, including adipocytes are all housed within the bony orbits of the skull. The globe is shielded by each orbit, and the supporting tissues enable three-dimensional movement.
where T is the period of the orbit, a is the semimajor axis of the orbit, G is the gravitational constant, M is the mass of the star (in this case, the Moon), and m is the mass of the planet (in this case, Explorer 35).
We know[tex]T = 11.5 hours = 11.5 hours * 3600 s/hour = 42000 s[/tex], and the semimajor axis of Explorer 35's orbit is the average distance from the Moon to Explorer 35, which we'll call d. The mass of Explorer 35 is much smaller than the mass of the Moon, so we can approximate it as 0.
Plugging in the values and solving for M, we find:
[tex]M = 4 * π^2 * d^3 / (G * T^2) = 4 * π^2 * d^3 / (G * 42000^2) = 4 * π^2 * d^3 / (6.67430 * 10^-11 m^3/kg * 42000^2)[/tex]
Since we don't know the value of d, we can't find an exact value for M, but we can use it to determine which of the given answers is closest to the calculated value.
Based on the given answer choices, the closest value to [tex]M is 5 * 10^22 kg.[/tex]
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if the planetary albedo is 30 percent, this means that the amount of energy reflected back to space is 30 percent.
Yes, it is true to say that a planet with an albedo of 30% will reflect 30% of its energy back into space.
What is planetary albedo?The planetary albedo is the percentage of incoming solar energy that Earth scatters back into space. The processes that control the magnitude, distribution, and variability of this reflected energy are fundamental to the Earth's energy balance and have a significant impact on both climate and climate change. The earth's planetary albedo is the proportion of radiant energy that is reflected back into space. The atmospheric component accounts for 88% of the observed global average planetary albedo. Because the atmosphere reduces the surface's impact on planetary albedo by a factor of about three, surface reflection has a relatively small impact on it.Here,
Yes, it is true that a planet's albedo of 30% indicates that 30% of the energy it receives is reflected back into space.
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a 60 kg man is going to use an elevator that will transport him upwards with an acceleration of 2 m/s². What is the force exerted by the floor of the elevator under the feet of that man?
The force is [tex]\bold{120 \: N}[/tex].
Step by step explanation:Newton's 2nd LawNewton's Second Law states that the resultant force acting on a body is equal to the product of the mass of this body times the acceleration it acquires.
We represent Newton's 2nd Law with the following formula:
[tex]\boxed{\bold{{F=m~ \cdot~a}}}[/tex]
Solution of the exercise:
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\displaystyle\text{$\mathrm{ \bold{F}= \bold{m}~ \cdot~ \bold{a}\left\{\begin{matrix}\displaystyle\text{$ \rm{ \bold F=? \: \bold{N}}$}\\\displaystyle\text{$\rm \bold{{m=60kg}}$}\\\ \: \displaystyle\text{$\rm{ \bold{a=2 m/s^{2} }}$} \end{matrix}\right.}$}\\\\\\\\ \: \displaystyle\text{$\rm{ \bold{F=60~\cdot~2}}$}\\\\\\\\ \boxed{\displaystyle\text{$\rm{ \bold{F=120~N.} }$}}\end{gathered} \end{gathered}\end{gathered}[/tex]
∴ The force is [tex]\bold{120 \: N}[/tex].
Answer: Therefore, the force exerted by the elevator floor under that man's feet is 120 Newtons.
Explanation:
A 60 kg man is going to use an elevator that will transport him upwards with an acceleration of 2 m/s². What is the force exerted by the floor of the elevator under the feet of that man?
Data:
m = 60 kg
a = 2 m/s²
F = ?
The formula for Newton's second law is:
F = m × aWhere
F = forcem = massa = accelerationSince we must calculate the force, it is not necessary to solve the formula. We substitute data and solve, then
F = 60 kg × 2 m/s²
F = 120 Newton
Therefore, the force exerted by the elevator floor under that man's feet is 120 Newtons.
50% part (a) one night it snows so that the snow on the lawn has a uniform depth of 18.5 cm. what volume of snow is on the lawn, in cubic meters? v
The volume of snow on the lawn is 6331.625 cm³
What is volume?Volume is the area occupied inside the confines of an item in three dimensions. It is frequently known as the object's capacity. An object's capacity is expressed in terms of volume. The quantity of space filled by a three-dimensional object may also be used to describe volume. The basic equation for volume is length, width, and height, as opposed to the fundamental equation for the area of a rectangular shape, which is length, breadth, and height. For examples, one could use "depth" rather than "height."
The shape of the snow is assumed to be a cube
Therefore, the volume of the snow is the cube of its uniform depth.
Given that,
Uniform depth = 18.5 cm
Volume = (uniform depth)³
Volume = (18.5 cm)³
Volume = 6331.625 cm³
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a cyclist rides 6.99 km east, then 11.88 km in a direction 39.84 degrees west of north, then 7.43 km west.A. What is the magnitude of the total displacement, in km?B. What is the direction of the displacement, measured in degrees west of north?
The magnitude of the total displacement, in km, is 25.3 km, and the direction of the displacement, measured in degrees west of north, is 125.76 degrees.
A. The magnitude of the total displacement, in km, is 25.3 km. This is calculated by using the Pythagorean theorem, where a2 + b2 = c2. The first two legs of the displacement are a and b, where a = 6.99 and b = 11.88. So,
a2 + b2 = 6.992 + 11.882
= 162.42 + 140.24 = 302.66.
The square root of 302.66 is 17.36. The third leg of the displacement is c, where c = 7.43. So, the total displacement is 17.36 + 7.43 = 24.79 km. Rounding to the nearest tenth, the magnitude of the total displacement is 25.3 km.
B. The direction of the displacement, measured in degrees west of north, is 125.76 degrees. This is calculated by using the Law of Cosines, where c2 = a2 + b2 - 2ab cos(C). The sides of the triangle are a = 6.99, b = 11.88, and c = 7.43. The angle C is the direction of the displacement, so we can solve for C in terms of a, b
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identify the graph(s) below in which the slope of the line provides an estimate of the heritability value for a trait? A.The mean value for the parents and offspring combined B.The average of the offspring and the average of the parents C.It depends on what aspect of heritability is being measured D.One parent and one offspring
Option C: Depending on what element of heritability is being examined x is the mid-parent trait value and y is the offspring trait value.
How effectively genetic variations in humans explain variations in their attributes is determined by their heritability. In addition to mental illnesses like schizophrenia and autism spectrum disorder, traits can also include physical qualities like height, eye color, and IQ. How much of the variation in a particular characteristic may be ascribed to genetic variation is known as heritability, which is a statistical concept (represented by the symbol h2) in science. An estimate of a trait's heritability pertains to a single population in a single environment, and it can alter over time as conditions change.
Between 0 and 1 heritability estimates are given. A heritability close to zero means that environmental variables account for practically all of the variation in a characteristic among individuals.
The correct question is:
identify the graph(s) below in which the slope of the line provides an estimate of the heritability value for a trait?
A.The mean value for the parents and offspring combined
B.The average of the offspring and the average of the parents
C.It depends on what aspect of heritability is being measured
D.One parent and one offspring
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a 561-g ball is thrown at a speed of 34.2 m/s from the top of a 42.7-m high cliff. determine the impact speed of the ball when it strikes the ground. assume negligible air resistance.
The impact speed of the ball when it strikes the ground is 28.94 m/s. The ball is thrown at a speed of 34.2 m/s from the top of a 42.7-m high cliff.
Which equation entails conservation?The concept of linear momentum balancing is expressed by the momentum conservation equation. The Cauchy momentum equation and Cauchy's first law of motion are other names for this conservation equation.
What is the speed of impact?An object's impact velocity is the speed at which it strikes another object or the ground.
The impact speed of the ball,
[tex]v=\sqrt{2gh}[/tex]
Where,
v = impact speed (m/s)
g = acceleration due to gravity (9.81 m/s^2)
h = height of the cliff (42.7 m)
[tex]v=\sqrt{2*9.81*42.7}[/tex]
[tex]v=\sqrt{837.774}[/tex]
[tex]v=28.94 m/s[/tex]
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A truck of mass 500 kg moving at 4 m/s collides with another truck of mass 1500 kg moving in the same direction at 2 m/s.What is their common velocity just after the collision if they move off together?
2.5m/s is their common velocity just after the collision if they move off together.
What is common velocity?We refer to the objects as having a common final velocity because after an inelastic collision, the objects stick together. In place of being two distinct objects, they have combined to form one bigger object.
We have given the,
Mass of first truck , m₁ = 500kg
Speed of first truck, u₁ = 4m/s
Mass of second truck, m₂ = 1500kg
Speed of second truck, u₂ = 2m/s
Combined mass of both trucks, m = 1500 + 500 = 2000kg
Using the law of conservation of momentum,
m₁u₁ + m₂u₂ = mv
Combined velocity is,
500 × 4 + 1500 × 2 = 2000 × v
[tex]$\mathrm{ v = \frac{500 \times 4 + 1500 \times 2}{2000} }[/tex]
v = [tex]\dfrac{2000 + 3000}{2000}[/tex]
v = [tex]\dfrac{5000}{2000}[/tex] = 2.5m/s
Thus, 2.5m/s is their common velocity just after the collision if they move off together.
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Define the term "stability" from both a kinetic and a thermodynamic perspective. Give examples to show the differences in these concepts.
While kinetic stability is the stability of a system's greatest energy state, thermodynamic stability refers to the stability of the system's lowest energy state.
The thermodynamic perspective focuses on the amount of energy needed for chemical events to occur. The kinetic perspective, on the other hand, is concerned with the amount of time needed for the aforementioned phenomena to occur. When it comes to the stability of a compound, these viewpoints are complementary to one another: a system is said to be thermodynamically stable when it is found to be at its lowest energy level or in chemical equilibrium with its surroundings - the activation energy to change the system is high and the reaction does not happen spontaneously. A stable system will react much more slowly than an unstable one in terms of kinetics; similarly to thermodynamics, the reaction does not happen on its own.
Toluene nitration at 0 degrees celsius is an illustration of kinetic control in action. A direct reflection of the rate of product production is the distribution of the products (orto-, 61,5%; meta-, 1,5%; para-, 37,0%). It is feasible to comprehend the thermodynamic rule in another toluene reaction (the Friedel-Crafts alkalation) where the proportion of various products created over time reflects the greater stability of each product rather than the passage of time. Time controls how the reaction starts, and energy controls how the entire reaction works.
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the function d defined above shows the depth, in feet, of the water t hours after 12 a.m. in a certain harbor. which of the following presents the method for finding the instantaneous rate of change of the depth of the water, in feet per hour, at 6 a.m. ? responses
The instantaneous rate of change is the rate change at a single instant, and it is the same as the derivative value change at a specific point.
What is the instantaneous rate of change explained?The tangent line slope is the same as the instantaneous rate of change at a particular location on a graph.It has a curve slope, in other words.
B. D' (6) = 0 is the formula for calculating the instantaneous rate of change of the sea depth at 6 AM in feet per hour.
D (t) = 10 + 4.9 cos (pi/6 * t) is a function.
After 12 am, D is described above as the water's depth, measured in feet.
Which of the following demonstrates how to calculate the instantaneous rate of change in feet per hour for the water depth at 6 am?
Differentiate:
D'(t) is equal to -4.9 sin (t / 6) ( / 6
D'( 6 ) = -4.9 sin ( π ) ( π / 6 )
The fact that
sin ( π ) = 0
so D'( 6 ) = 0
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A 20.0-kg object has an eastward momentum of 120 kg m/s. The object encounters a
westward impulse of 40 N.s. What is the magnitude of the final momentum of the object?
8m/s the magnitude of the final momentum of the object
Describe momentum.
Momentum can be viewed as a body's "power" while it is moving, or the amount of force it can exert on another body. Momentum is measured by "mass velocity," which takes into account the fact that it depends on both the speed and direction of the body's motion.
Newton's second law of motion states that a body's rate of momentum change is equal to the net force applied to it. In any inertial frame, momentum is a conserved quantity depending on the frame of reference, which means that if an enclosed system is not exposed to external influences, its total linear momentum is constant.
m = 20kg
Pi = 120kg m/s
J = 40Ns
ΔP = Pf - Pi
40 = Pf - 120
Pf = 160
Pf = m*vf
vf = 160/20 = 8m/s
Pi = m*vi
vi = 120/20 = 6m/s
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the temperature in a room at midnight is 22 c over the next 24 hours the temperature changes at a rate modeled by the fnction___
The temperature changes at a rate modeled by the fnction Change in temp in Celcius between midnight and 6:00am.
Which H(t)*dt interpretation is the most accurate?The temperature in a room at midnight is 22 c over the next 24 hours the temperature changes at a rate modeled by the fnction is The rate of temperature change is denoted by H(t). Therefore, if we integrate H(t), we will obtain the temperature change.Here are the facts:The difference in temperature between 6:00 AM (represented by the number 6) and midnight will be indicated (represented with the 0).The right answer is since it will indicate the change in temperature between midnight and six.The temperature changes at a rate modeled by the fnction Change in temp in Celcius between midnight and 6:00am.To learn more about temperature refer to:
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the p-wave shadow zone is larger than the s-wave shadow zone seismic waves follow curved paths through the interior of the earth p-waves travel more slowly in lower density materials liquids do not transmit s-waves. True or false?
All of the statements are True.
Give reasons to support your answer.The p-wave shadow zone is larger than the s-wave shadow zone because p-waves can travel through the Earth's core, while s-waves cannot. This means that the region where no p-waves are detected (the shadow zone) is larger than the region where no s-waves are detected.
Seismic waves do follow curved paths through the interior of the Earth. This is because the speed of seismic waves depends on the density and elastic properties of the material they are passing through, which vary at different depths and locations.
P-waves travel more slowly in lower density materials. This is because p-waves are compressional waves that are affected by the density of the material they are passing through. Lower density materials will have less resistance to compression, allowing the waves to travel more slowly.
Liquids do not transmit s-waves. This is because s-waves are transverse waves that require a solid medium to propagate. Liquids do not have the same level of shear strength as solids and therefore s-waves cannot pass through them.
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Estimate the moment of inertia of a bicycle wheel 68 cm in diameter. The rim and tire have a combined mass of 1.2kg . The mass of the hub can be ignored.
The moment of inertia of a 68 cm diameter bicycle wheel is 1387.2 kg.m². The rim and tire weigh 1.2kg together. The hub's mass is unimportant.
The moment of inertia of a hoop about an axis passing through its center is, I=mR²
I=mR²
I=m(D/2)²
I=mD²/4
I=(1.2kg)(68 cm(10⁻² m/1cm))²/4
I=1387.2 kg.m²
A body's resistance to having the speed of its rotation along an axis changed by the application of torque is quantified by the term "moment of inertia" in physics (turning force). The axis could be fixed or not fixed, internal or exterior. Nevertheless, the moment of inertia (I), which is always described in relation to that axis, is calculated as the total of the products produced by multiplying the mass of each particle of matter in a particular body by the square of that particle's distance from the axis. The moment of inertia can be compared to mass in linear motion when calculating the angular momentum of a rigid body.
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The half-life of Po-211 is approximately 500 ms (half a second). Without using the PhET model, sketch a pie graph indicating the number of undecayed P0-211 atoms for a reaction starting with 100 total atoms. o t= 0.55 t=1.0s te1.55 t=2s Now, simulate the decay of 100 pd 211 atoms by adding 100 atoms from the "Bucket o Polonium". Sketch what the pie graph looks like at the times shown. t=0.5s t=1.0s t=1.55 t=2s 3 Compare VOL prediction to the resulte that heened Hourcan aynlain any discronancies?
The pie graphs would show the number of undecayed Po-211 atoms in each case.
What is half life?Half life is defined as the time that it takes for half of the original value of some amount of a radioactive element to decay.
Given, half-life of Po-211 is 500 ms
At t = 0.5s (500 ms), 50 atoms of Po-211 will have decayed, leaving 50 atoms remaining.
And at t = 1.0s, 25 atoms of Po-211 will have decayed, leaving 25 atoms remaining ; At t = 1.55s, 12.5 atoms of Po-211 will have decayed, leaving 12.5 atoms remaining ; At t = 2s, 6.25 atoms of Po-211 will have decayed, leaving 6.25 atoms remaining.
So, the pie graphs would show the number of undecayed Po-211 atoms in each case.
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estimate the number of people in the world who are suffering from the common cold on any given day. (answers may vary. remember that a person suffers from a cold for about a week, and assume that the average person catches a cold twice a year. the population of earth is approximately six billion.)
The number of people in the world who are suffering from the common cold on any given day is 230,136,986
The common cold, sometimes known as the cold, is an infectious viral disease of the upper respiratory tract that primarily affects the nasal, pharyngeal, sinus, and laryngeal respiratory mucosa. Less than two days after the virus has been exposed, signs and symptoms may start to manifest. These symptoms could include fever, headache, runny nose, sneezing, and coughing. However, certain symptoms can continue up to three weeks. Most people recover in seven to 10 days. Sometimes people with other health issues can get pneumonia.The majority of the more than 200 viral strains that have been linked to the common cold include rhinoviruses, coronaviruses, adenoviruses, and enteroviruses.
From given data, the probability for a person to suffer from a cold on any given day is
[tex]\frac{2\times7}{365}[/tex]= [tex]\frac{14}{365}[/tex]
Given there are 6 billion people, so [tex]6000000000\times\frac{14}{365}[/tex] = 230,136,986 people per day have a cold.
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when an object effected by gravity on earth is spinning in a non-vertical circle, there is a small angle between the spin of the object and the actual horizontal
For minor displacements, gravity has very little effect on an object's horizontal motion. This suggests that the spin and horizontal are at a little angle and that the horizontal velocity is constant.
Motion is defined as a change in an object's location with respect to time. A book tumbling off a table, water running from a faucet, rattling windows, etc. are examples of motion. In physics, a force is an effect that has the ability to change how an object moves. A mass-containing object's velocity or acceleration can be altered by a force (for example, moving from a condition of rest). Force can also be intuitively described as a push or a pull.
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The complete question is-
when an object effected by gravity on earth is spinning in a non-vertical circle, there is a small angle between the spin of the object and the actual horizontal, explain?
uppose that a slice of pizza at a temperature of 80 degrees has been placed inside a freezer, where the temperature is 2 degrees. if the pizza cools to 45 degrees in 1 hour, then its temperature after t hours is given by the equation:
The temperature after t hours is given by the equation T(t) is 2 + 78e-0.5955t
What is the temperature after t hours is given by the equation?That a piece of pizza that was 80 degrees at the time was put inside a freezer that was 2 degrees at the time. if the pizza cools to 45 degrees in 1 hour, then its temperature after t hours is given by the equation: dT/dt = k(T - 2
Put the variables apart: [1/(T-2)]
dT = kdt
Integrate the two sides as follows: ln l T-2 l = kt + C
ekt + C = l T - 2 l
T - 2 equals eCekt
To obtain T(t) = 2 + Cekt = temperature in t hours, rename eC to C.
2 + Cek(0) = 80 since T(0) = 80.
C = 78
T(t) = 2 + 78ekt
T(1) = 45, therefore 2 + 78ek = 45
78ek = 43
ek = 0.5512821
k = ln(0.5512821) = -0.5955
T(t) = 2 + 78e-0.5955t
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show that, in the limit that v is small, the relativistic kinetic energy reduces to the ordinary kinetic energy from newtonian classical mechanics,
Relativistic kinetic energy turns into classical kinetic energy when traveling at low speeds.Since it takes an endless amount of labor and energy to accelerate a mass to the speed of light, no object with mass can reach that speed.
At low speeds, what happens to relativistic kinetic energy? Relativistic kinetic energy turns into classical kinetic energy when traveling at low speeds.Since it takes an endless amount of labor and energy to accelerate a mass to the speed of light, no object with mass can reach that speed.Classical mechanics is subject to two constraints.First, the velocity of the objects must be substantially slower than the speed of light, v > c, in order to avoid relativistic mechanics.The bodies must also be suitably massive and/or energetic.Therefore, v by c is root 3 by 5, and v is root 3 by 5 times c, which is 0.35 c or 1.04 into 10 to the power 8 meters per second.Consequently, the velocity at which there is a 10% difference between the relativistic and newtonian formulations of kinetic energy is v = 0.35 c or 1.04 into 10 to the mute 8.To learn more about kinetic energy refer
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in designing subway trains and stations, engineers want to optimize the time and energy use between stations. a train can comfortably accelerate at 5 ft/s2 without causing its passengers to fall over. when coasting, the train will slow down at an acceleration of -2 ft/s2. the train begins at rest and must come to a complete stop at the destination. if two train stations are 2 miles apart, determine the fastest time that the train can arrive at the second station given the provided accelerations. also, determine the maximum velocity obtained. draw the a-t, v-t, and s-t graphs for the train. (122 s, 174 ft/s)
The fastest time that the train can arrive at the second station given the provided accelerations , the maximum velocity obtained 174 m/s
What is the maximum velocity obtained?Let t1 and t2 represent the time needed for acceleration a1 and deceleration a2.
the same since the ultimate velocity during acceleration and the beginning velocity during deceleration
a₁ t₁ = a₂ t₂
5t₁ = 2 t₂ ————————————————————— ( 1 ) ( 1 )
Acceleration distance equals half of a1t12.
= 1/2 x 5 x t₁² = 2.5 t₁²
Deceleration distance equals half of a2t22.
= 1/2 x 2 x t₂² = t₂²
Total distance travelled: 10560 feet, or 2 miles, or 2 x 1760 feet.
2.5 t₁² + t₂² = 10560
2.5 ( 2t₂ / 5 )² + t₂² = 10560
.4 t₂² + t₂² = 10560
1.4 t₂² = 10560
t₂ = 86.85 s
t₁ = 2t₂ / 5 = 34.75 s
t₁ + t₂ = 121.6 = 122 s
Time spent: 122 seconds.
maximum speed = a1t1
= 5 x 34.75 = 173.75 = 174 m/s
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the speed of light is approximately 1.86 x 10^7 kpmmhow long does it take light from the sun to reach earth
8 minutes and 20 second is the time it takes to reach earth.
What is speed of light and how long does it take light from the sun to reach earth?Around 1.86 x 107 kilometers per second, light travels at its speed. About 93,000,000 miles (150,000,000 kilometers) separate the sun from the Earth. Sunlight takes 8 minutes and 20 seconds to reach Earth.It is important to note that this distance is not fixed and it varies due to the elliptical shape of the Earth's orbit around the sun. The closest point of the Earth's orbit to the sun is called the perihelion and the farthest point is called the aphelion. At perihelion, the distance between the Earth and the Sun is about 147 million kilometers and at aphelion is about 152 million kilometers. This means that the time light takes to travel from the Sun to the Earth can vary by a few seconds.To learn more about speed of light refer:
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A ball is thrown upward with an initial velocity vo from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2 (where, m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith (maximum height) isA1√2γgtan−1(√2γgv0)B1√γgtan−1(√γgv0)C1√γgsin−1(√γgv0)D1√γgln(1+√γgv0)
B) 1√γg tan−1(√γ/g) v0 is the time taken by the ball to rise to its zenith (maximum height).
Why does drag force exist?As an outcome of collisions among moving objects and the molecules of a fluid like air or water, drag is a force that hinders or resists motion. Even though it inhibits motion like surface friction does, drag only occurs in flowing fluids. Drag is a force acting against the relative movement of any moving object with relative to a surrounding fluid in fluid dynamics. It is sometimes alluded to as fluid friction, air resistance, or another sort of friction.
-(g + γv^2) = dv/dt
=> -gdt = g/γ (dv/ (g/γ+v^2))
integration 0=>t ; vo => 0=>
=> -gt = -√g/γ tan^-1(vo/√gγ)
=> t= 1√γg tan−1(√γ/g) v0
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A ball is thrown upward with an initial velocity vo from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2 (where, m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith (maximum height) is
A) 1√2γg tan−1(√2γ/g) v0
B) 1√γg tan−1(√γ/g) v0
C) 1√γg sin−1(√γ/g) v0
D) 1√γg ln(1+√γ/g) v0
a mass is lifted from the ground to an altitude h1, requiring work w1. the work to lift an identical mass to an altitude h2 is w2. if h2 is twice h1, what is the ratio of w2 to w1? (note: assume that the force of gravity does not change between h1 and h2.)
The ratio requested is answer D.2:1 .In a gravitational field, g, the work required to raise a mass m to a height h is W = mgh.
What does the H in MGH stand for?In a gravitational field, g, the work required to raise a mass m to a height h is W = mgh.This is an illustration of how labor is defined simply as the result of multiplying a force (in this case, mg) by a distance (h in this case).If the height doubles, the amount of work required to lift the same amount of weight also doubles.Answer D is the ratio you asked.P.E. = mgh is the formula for gravitational force, where m is mass in kilograms, g is acceleration due to gravity (9.8 m/s2 at the earth's surface), and h is height in meters.To learn more about gravitational field refer
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You toss a marble straight upward. Which of the following statements best describes the motion of the marble at the point where it reaches its maximum height?
A) At its maximum height, the marble has a velocity of 9.8 m/s downward.
B)At its maximum height, the marble has an upward velocity for an infinitesimal (zero-length) amount of time.
C)At its maximum height, the marble has a velocity of zero for an infinitesimal (zero-length) amount of time
The motion of marble at its highest point is best described by the following statements: The stone has a downward acceleration of 9.8 m/s at its highest point.
How is velocity determined?You divide the amount by the time that it takes you travel this very same distance to calculate velocity, and then users add your directions to it. For instance, if you were traveling west and covered 50 miles in an hour, your speed would be 50 mph westward or 50 miles per hour.
What are some examples of velocity?Velocity can be defined as the rate that an object moves in a specific direction. like the pace of a car driving north on something like a highway or the pace of a rocket, for instance after launch, travels. Because the velocity vector is scalar, its absolute value magnitude will always equal the motion's speed.
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A car travels up a hill at a constant speed of 31 km/h and returns down the hill at a constant speed of 79 km/h. Calculate the average speed for the round trip.
The average car speed for one round trip on the hill is 45.54 km/hr
The car travels up a hill at the speed of 31 km/h
The car travels down the hill at the speed of 79 km/h
The average speed by the car can be found using the formula,
S = d/t
where s is the average speed
d is the total distance covered
t is the total time taken
The time taken by the car to up a hill is
t₁ = d /s₁
Let us substitute the known values,
t₁ = d / 32 x 2
= d / 64
The time taken by the car to reach the down of the hill is
t₂ = d/79 x 2
= d / 158
Thus, the average speed of the car is
S = d / (d/64 + d/158)
= 10112d / 222d
= 45.54 km/hr
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A dart is thrown horizontally at a speed of 12 m/s at the bull's-eye of a dartboard 2.7 m away. How far below the intended target does the dart hit
To solve this problem, we can use the equations of motion for projectile motion. Since the dart is thrown horizontally, we know that there is no vertical velocity and that the only acceleration acting on the dart is gravity, which is 9.8 m/s^2 downward.
The vertical motion of the dart can be described by the equation:
y = y0 + v0t + 0.5at^2
where y is the vertical position of the dart, y0 is the initial vertical position (which is 0 in this case), v0 is the initial vertical velocity (which is also 0), t is the time of flight, and a is the acceleration due to gravity.
To find the time of flight, we can use the horizontal motion of the dart, which is described by the equation:
x = x0 + v0t + 0.5at^2
where x is the horizontal position of the dart, x0 is the initial horizontal position (which is 0), v0 is the initial horizontal velocity (which is 12 m/s), and t is the time of flight.
We know that the horizontal position of the dart is 2.7 m, so we can substitute that into the equation and solve for t:
2.7 = 0 + 12t
t = 2.7/12 = 0.225 seconds
We can then substitute t and a into the vertical motion equation to find the vertical position of the dart:
y = 0 + 0 + 0.5(9.8)(0.225^2)
y = -0.061 m
So the dart hits 0.061 m below the intended target.
e potential energy associated with the force between two neutral atoms in a molecule can be modeled by the Lennard-Jones potential energy function:U(x) = 4ε[(σx)^(12)−(σx)^6] where x is the separation of the atoms. The function U(x) contains two parameters σ and ε that are determined from experiments. Sample values for the interaction between two atoms in a molecule areσ= 0.263 nm and ε= 1.51×10^(−22)J. (a) Make a plot of this function with x in units of 10^(−10)m and U(x) in units of 10^(−23)J.(b) Find the most likely distance between the two atoms.(c) Is this equilibrium point stable, unstable, or neutral?
a) To make a plot of the Lennard-Jones potential energy function, U(x) = 4ε[(σx)^(12)−(σx)^6], with x in units of 10^(-10)m and U(x) in units of 10^(-23)J, one can use the given values of σ and ε to plug into the equation and then plot the resulting values of U(x) against x.
What is e potential energy?To find the most likely distance between the two atoms, one can take the derivative of the potential energy function with respect to x, and set it equal to zero. This will give the position of minimum potential energy, or the equilibrium point, which corresponds to the most likely distance between the atoms.The nature of equilibrium point can be determined by looking at the second derivative of the potential energy function at that point. If the second derivative is positive, the equilibrium point is a stable one, if it is negative, it is an unstable one and if it is zero it is a neutral one.To learn more about e potential refer:
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