The boat will cost a total of 287.7 feet.
Using calculus, we can find that the equation for the velocity of the boat at any given time is[tex]v(t) = 90e^(-0.1t)[/tex]. We can then integrate this equation to find the total distance the boat travels while coasting.
Integrating v(t) from t=0 to t=s, where s is the time it takes for the boat to slow to 30 ft/s, we get:
[tex]∫(0 to s) 90e^(-0.1t) dt = 900(-e^(-0.1s) + 1)[/tex]
We know that at s seconds, [tex]v(s) = 30 ft/s[/tex], so we can solve for s:
30 = 90e^(-0.1s)
s ≈ 6.848 seconds
Substituting this value of s into our previous equation, we get:
[tex]900(-e^(-0.1(6.848)) + 1) ≈ 287.7 feet[/tex]
Therefore, the boat will coast a total of 287.7 feet before coming to a complete stop.
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what total force will cause an object with a mass of 10kg to gain 5 meters per second every second?
The total force required to cause an object with a mass of 10 kg to gain 5 meters per second every second is 50 newtons. To calculate the force required to cause this acceleration, we simply applied Newton's second law of motion here.
The force required to cause an object with a mass of 10 kg to accelerate at a rate of 5 meters per second every second can be calculated using Newton's second law of motion, which states that the force F required to accelerate an object of mass m at a rate of a is given by:
F = m * a
In this case, the acceleration a is 5 meters per second every second. Substituting m = 10 kg and a = 5 meters per second every second into the above equation, we get:
F = 10 kg * 5 meters per second every second
= 50 newtons
Therefore, the total force required to cause an object with a mass of 10 kg to gain 5 meters per second every second is 50 newtons.
The force required to cause an object to accelerate depends on its mass and the rate of acceleration. The mass of an object is a measure of its resistance to changes in motion, while the rate of acceleration is a measure of how much the object's velocity changes per unit of time. Newton's second law of motion, which relates force, mass, and acceleration, is one of the fundamental laws of physics and is used to understand and predict the motion of objects under the influence of forces.
In this case, we were given the mass of the object, which is 10 kg, and the rate of acceleration, which is 5 meters per second every second. To calculate the force required to cause this acceleration, we simply applied Newton's second law of motion, which states that the force required to accelerate an object is equal to the product of its mass and acceleration.
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urn on Path. Dots will now trail your skater in the style of a motion diagram. Equal time intervals exist between each new dot’s creation.
When are the dots furthest apart along the path? What does this indicate?
The dots are furthest apart along the path when the speed of the skater is the greatest.
This is because the dots represent the position of the skater at equal time intervals, and when the skater is moving faster, the position change between each dot will be greater, resulting in the dots being further apart.This indicates that the skater is experiencing a period of acceleration. The dots being further apart means that the position change of the skater over a given period of time is greater, which can only happen if the skater is experiencing a change in velocity, i.e., acceleration.Conversely, when the dots are closer together, it indicates that the skater is moving slower and experiencing little to no acceleration. Therefore, by analyzing the dots' spacing, one can infer the skater's motion's acceleration and deceleration phases.To know more about speed visit:
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a 1.1 kw-hr dryer is used for .5 hours every day. what would georgia power charge for 30 days if their going rate is 11 cents/kw-hr ?
Answer:
21
Explanation:
The Georgia power charge for 30 days when their going rate is 11 cents/kw-hr every day will be 108.9 watts.
Electric power is the rate at which electrical energy is transferred from an electric circuit. The SI unit of power is expressed in the watt, one watt is equal to one joule per second.
The amount of power rate for one minute = 1.1 × 11/100 = 1.1 × 0.11 = 0.121 watts
The amount of power rate for 30 minutes = 0.121 × 30 = 3.63 watts
The power rate for 30 days(a month) will be = 3.63 × 30 = 108.9 watts
Therefore, the power charge for 30 days (one month) is 108.9 watts.
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what is thermal boundary layer thicker than velocity boundary layer?
The thermal boundary layer is typically thicker than the velocity boundary layer due to the difference in the diffusion rates of heat and momentum.
The thermal boundary layer is the region of fluid near a solid surface where the temperature of the fluid differs from the temperature of the solid surface.
The velocity boundary layer, on the other hand, is the region of fluid near a solid surface where the velocity of the fluid differs from the velocity of the solid surface.
The diffusion rate of heat is typically lower than the diffusion rate of momentum, meaning that heat takes longer to spread through a fluid than momentum does. As a result, the thermal boundary layer is typically thicker than the velocity boundary layer.
This difference in thickness is important in many engineering applications, such as the design of heat exchangers and the prediction of heat transfer rates. It is also important in the study of fluid dynamics, as the thickness of the thermal and velocity boundary layers can affect the behavior of the fluid flow.
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A 25.0 kg box of textbooks rests on a loading ramp that makes an angle α with the horizontal. The coefficient of kinetic friction is 0.250, and the coefficient of static friction is 0.350.
A) As α is increased, find the minimum angle at which the box starts to slip.
B）As this angle, find the acceleration once the box has begun to move
c) at this angle, how fast will the box be moving after it has slid a distance 4.7m along the loading ramp
(a) As σ is increased, The minimum angle will be "19.2°".
(b) The acceleration will be "0.91 m/s²"once the box has began to move.
(c) The speed will be "3 m/s" as the box slid a distance 4.7 m along the loading map.
According to the question,
Mass = 25.0 kg
Kinetic friction = 0.25
Coefficient of static friction = 0.35
(a) We know,
⇒ static friction = mg sine
⇒ mg cosine * u = mg sine
then,
tan A = u = 0.35
a = 19.2
Therefore, as α is increased, the minimum angle at which the box starts to slip is 19.2°.
(b) We know that:
Kinetic friction = mgCos19.2 * 0.25
= 2.31m
and,
Net force downwards = mgSin19.2 - mgCos19.2* 0.25
By substituting the values, we get
= m(3.22-2.31)
= 0.91m/s²
Therefore, As this angle, the acceleration once the box has begun to move at 0.91 m/s².
(c) since the box is sliding at a distance of 4.7 meter:
Thus,
The speed will be:
→ [tex]v^{2} - u^{2} + 2as[/tex]
[tex]0 + 2* 0.91* 5[/tex]
= 9.21
[tex]v = 3m/s[/tex]
Therefore, at this angle, at 3m/s will the box be moving after it has slid a distance 4.7m along the loading ramp
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Many mountain roads are built so that they zigzag up the mountain rather than go straight up toward the peak. Discuss the advantages of such a design from the viewpoint of energy conservation and power
Zigzagging mountain roads offer several advantages from the viewpoint of energy conservation and power: Reduced gradient. Improved traction. Reduced stress on the road. Easier construction
What advantages do Zigzagging mountain roads have?
Zigzagging mountain roads also known as switchbacks have several advantages with respect to energy conservation and power: Reduced gradient: Switchbacks allow the road to have a shallower gradient compared to a straight road, which reduces the amount of energy required to climb the mountain. This can save fuel for vehicles and reduce the physical exertion for hikers and cyclists. Improved traction: The zigzagging design provides better traction for vehicles and reduces the risk of skidding or slipping, especially in wet or icy conditions. Reduced stress on the road: A straight road up a steep mountain would experience higher stress and wear and tear, which could lead to damage or even collapse. Zigzagging the road reduces the stress and prolongs the road lifespan. Easier construction: Building a straight road up a steep mountain would require much more excavation and engineering work, making it a more expensive and time-consuming process. Zigzagging the road allows for easier and more efficient construction.
Overall, the switchback design of mountain roads is a more efficient and practical solution that conserves energy, improves safety, reduces stress on the road, and makes construction easier.
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what property of earthquakes does the richter scale measure?
The Richter scale measures the magnitude of an earthquake, which is a measure of the energy released by the seismic waves generated by the earthquake.
What is the measures ?Measures are the steps taken to achieve a desired outcome. They can be in the form of legislation, policies, regulations, practices, procedures, and processes. They are used to implement and enforce objectives, goals, and strategies, and can be both proactive and reactive. Measures can be utilized by governments, businesses, and individuals to ensure desired outcomes are achieved in a timely and cost-effective manner. Measures can also be used to monitor progress and evaluate the effectiveness of policies and procedures.
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Write one word that means the time taken for a single vibration
Answer: d1ldo
Explanation:
How to find the length of an array in PHP?
To find the length of an array in PHP, you can use the count() function.
The count() function returns the number of elements in an array.
Here's an example:
$myArray = array("apple", "banana", "orange", "grape");
$length = count($myArray);
echo "The length of the array is " . $length;
In this example, we first define an array called $myArray with four elements. Then we use the count() function to find the length of the array and assign the result to a variable called $length. Finally, we use the echo statement to display the length of the array.
The output of this code will be:
The length of the array is 4
Note that the count() function can also be used to find the number of elements in an object or a variable with a countable value.
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how many oz in a 2 liter
A preferred 2-liter bottle contains 67.6 fluid ounces. of liquid. Assuming which you're using 8-ounce cups, you could have 8.45 glasses of a few issue liquid is inside the 2-liter bottle.
An ounce is a unit of measurement commonly used for weighing small amounts of mass or weight. It is equivalent to 28.35 grams or 1/16th of a pound. Ounces are commonly used to weigh food items, such as fruits, vegetables, and meats, as well as precious metals like gold and silver.
In the United States, ounces are also used to measure liquid volume, with one fluid ounce equaling approximately 30 milliliters. Ounces are divided into different types, including avoirdupois ounces and troy ounces. Avoirdupois ounces are used to measure most common items, while troy ounces are primarily used for precious metals like gold and silver.
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Complete question: -
How many oz does a 2 liter bottle hold?
What is 1.61 Blokz high index lenses?
1.61 Blokz high index lenses are a specific type of high index lens that is designed to block out harmful blue light from digital screens.
High index lenses are a type of prescription eyeglass lens that is made of a special type of plastic that is thinner and lighter than traditional plastic lenses. The term "high index" refers to the refractive index of the lens material, which is a measure of how efficiently it bends light. The higher the index, the thinner and lighter the lens can be.
1.61 Blokz, lenses have a refractive index of 1.61, which means they are thinner and lighter than traditional plastic lenses, and they also have a special coating that helps to filter out blue light. This can help to reduce eye strain and discomfort when using digital devices for extended periods of time.
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1. A charged particle moves from one point to another. What is the connection between the change in potential energy of the particle and the change in electric potential? A. The change in electric potential equals the change in potential energy. B. The change in electric potential is twice the change in potential energy. C. The change in electric potential is the change in potential energy times the charge D. The change in electric potential is the change in potential energy divided by the charge.
The connection between the change in potential energy of the particle and the change in electric potential is defined as "the change in electric potential is the change in potential energy divided by the charge". So, the correct answer is D.
The electric potential at a point in an electric field is defined as the electric potential energy per unit charge at that point. Therefore, the change in electric potential between two points is equal to the change in electric potential energy divided by the charge of the particle that is moving between those points.
As the charged particle moves from one point to another, its potential energy changes due to the work done by the electric field on the particle. The change in potential energy of the particle is equal to the work done by the electric field on the particle. Therefore, the change in potential energy divided by the charge of the particle is equal to the change in electric potential.
In summary, the change in electric potential between two points is equal to the change in potential energy divided by the charge of the particle that is moving between those points. Therefore, the correct answer is D - "The change in electric potential is the change in potential energy divided by the charge".
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A block of wood is floating with one half of its volume out of the water. Then it is pushed down so that it is completely underneath the water. Use your understanding of buoyant force and Archimedes' principle to determine what happens to the forces on the block of wood.
A. The buoyant force on the block is the same in the two cases because the weight per unit volume of the wood has not changed.
B. The buoyant force on the block is the same in the two cases because the weight per unit volume of the water is the same in each case.
C. The buoyant force on the block is greater when the block is completely submerged than it is when the block is floating.
D. The buoyant force on the block is greater when it is floating than when it is totally submerged.
E. The buoyant force on the block is the same in the two cases because the block loses weight as it is submerged.
In comparison to floating, the block experiences a stronger buoyant force when it is entirely submerged.
The correct option is C.
How does buoyant force work?The buoyant force, which exerts upward pressure on completely or partially submerged objects, operates both ways. Its thrust upward is also known as an upthrust. The buoyant force on a body that is partially or entirely submerged in a fluid creates the impression that it is losing weight or becoming lighter.
What is Archimedes' guiding principle?A body submerged in a liquid, whether partially or entirely, will experience buoyant force, which is equal to the weight of the liquid the body displaces and acts upward at the centre of the fluid's mass.
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which of the following is the best example of Lawrence Kohlberg postconventional mortality
The best example is Preconventional Morality. The correct option is C.
What is Preconventional Morality?Preconventional morality is the first level of moral development in Lawrence Kohlberg's theory of moral development.
At this stage, individuals make decisions based on a desire to avoid punishment or gain rewards. They follow rules only to avoid punishment, and they have a self-centred view of the world.
According to my research on Lawrence Kohlberg's level of morality, I can say that the level being described is called Preconventional Morality based on the information provided within the question.
This is the first and second level of morality according to Kohlberg, and it focuses on obedience/reward, punishment, and self-interest. As stated in the question.
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The complete question is given below.
At which of Lawrence Kohlberg's levels of morality do people follow unvarying rules based on rewards and punishment?
a. Preconventional
b. Conventional
c.. Postconventional
d. Unconventional
A skateboarder on a ramp is accelerated by a nonzero net force. For each of the following statements, state whether it is always true, never true, or sometimes true.
Sometimes true.
For example, if a skateboarder is going down a ramp, the motion will be in the same direction as the net force. Conversely, when a skateboarder climbs a ramp, the direction of motion is opposite to the direction of net force. In general, there is no reason why the direction of motion should be in the same direction as the net force.
About net forceThe net force is defined as the sum of all the forces acting on an object.
Example,When you kick the ball, the ball takes off and moves through the air. At that time, there is a net force acting on the ball. When the ball begins to return to the ground and finally comes to rest, there is a net force acting on the ball as well.
Newton's Second Law says that "when a net force acts on an object, then the object must accelerate, that is, its velocity changes from second to second." By kicking the soccer ball for the first time, he speeds up, and when the soccer ball starts to slow down to a stop, he speeds up too.
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Storage that is wiped clean when power is cut off from a device is known as _____.
A. Volatile memory
B. Flash memory
C. Microprocessor
D. CPO-Chief privacy officer
Storage that is wiped clean when power is cut off from a device is known as Volatile memory. The correct answer A.
Volatile memory is a type of data storage that is wiped clean when power is cut off from a device. This type of memory is used in computers, servers, and other electronic devices to store data that needs to be accessed quickly or that needs to be retrieved quickly when power is cut off or the device is rebooted.
The main advantage of volatile memory is that it is faster than permanent storage, as it does not require any time to be written or read.
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When you increase the driving frequency of a wave on the string, does the wavelength decrease, increase, or stay the same? Select one: Increase Decrease Stay the same
When you increase the driving frequency of a wave on the string, the wavelength will decrease.
When you increase the driving frequency of a wave on a string, the wavelength of the wave will decrease. This is because the speed of the wave on the string is constant, so as the frequency increases, the wave must travel a shorter distance in one period. The wavelength is the distance between two consecutive points on the wave that are in phase (i.e. have the same displacement and velocity), so as the wave must travel a shorter distance in one period, the distance between two consecutive points on the wave that are in phase (i.e. the wavelength) will decrease.
Therefore, the correct answer is: Decrease.
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How do you calculate thermal conductivity from temperature?
You can calculate thermal conductivity by relating heat flux with it and using the formula: q = -λΔT/Δx.
Heat flux is the amount of heat energy transferred over an area per second, while thermal conductivity is the ability of a given material to conduct or transfer heat through it. Once the heat flux is known, you can easily calculate the thermal conductivity of a material. The two can be related as:
q = -λΔT/Δx, where:
q is the heat flux, λ is the thermal conductivity, ΔT is the temperature difference across the material, and Δx is the distance travelled by heat.
Thermal conductivity of an object can also be illustrated as:
λ = (QL)/(AΔT), where:
λ is the thermal conductivity, A is the area of the surface, Q is the amount of heat transferred, L is the distance between two isothermal planes, and ΔT is the change in temperature.
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How does solar energy work? All energy must have a source; what is the source in this case? How do we take the power of the Sun and turn it into usable energy? What can we do with this energy?
Solar energy is a renewable and clean source of energy that has a wide range of applications and benefits for the environment and society.
Solar energy is the energy generated by the Sun's rays, which can be converted into usable energy using various technologies. The Sun is the source of solar energy, as it emits enormous amounts of energy through nuclear fusion reactions that take place in its core.
The process of generating usable energy from solar energy involves several steps:
Collecting solar energy: Solar panels or solar cells are used to collect solar energy. These devices are designed to capture the Sun's rays and convert them into direct current (DC) electricity.
Converting DC to AC: Since most electrical devices run on alternating current (AC), the DC electricity generated by the solar panels must be converted into AC. This is done using an inverter.
Distributing energy: The AC electricity produced by the solar panels is distributed to power electrical devices or is fed into the electrical grid.
There are several uses of solar energy. It can be used for:
Generating electricity: Solar power plants can be built to generate electricity on a large scale.
Heating water: Solar water heaters can be used to heat water for homes or businesses.
Heating buildings: Passive solar heating can be used to design buildings that are heated by the Sun's energy.
Cooking: Solar cookers can be used to cook food using the Sun's energy.
Providing light: Solar-powered lights can be used to provide lighting in areas where electricity is not available.
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The distance between the earth and the moon is approximately feet, and a rocket can travel there at a speed of about 1,540,000 ft/min. How long will it take the rocket ship to travel to the moon and back, in minutes? express your final answer in minutes and round to the nearest minute. Be sure to convert each number to scientific notation first, before performing any operations.
Be sure to convert each number to scientific notation first, before performing any operations ;50,000 min.
What is the notation ?Notation is a set of symbols or a system of symbols used to represent or communicate something. It is often used in mathematics and other sciences to represent formulas, equations, and concepts. Notation can also be used in music, literature, and other forms of communication. For example, musical notation is used to communicate the composition and performance of music, while literary notation is used to communicate the structure of a piece of writing. Notation can also be used to represent data or instructions in computer programming.
Distance to Moon = 3.84 x 10^8 ft
Speed = 1.54 x 10^6 ft/min
Time = (3.84 x 10^8 ft) / (1.54 x 10^6 ft/min) = 25,000 min
Time for round trip = 2 x 25,000 min = 50,000 min
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Be sure to convert each number to scientific notation first, before performing any operations ;50,000 min.
What is the notation ?A system of symbols is known as notation, and it is used to represent or communicate ideas. It is frequently used to express formulas, equations, and concepts in mathematics and other fields. Music, literature, and other kinds of communication can all use notation. For instance, literary notation is used to convey a piece of writing's structure, whereas musical notation is used to convey the composition and performance of music. In computer programming, notation can also be used to represent data or instructions.
Distance to Moon = [tex]3.84 \times 10^8 ft[/tex]
Speed = [tex]1.54 \times 10^6 ft/min[/tex]
Time = [tex]\frac{(3.84 \times 10^8 ft)}{ (1.54 \times 10^6 ft/min) } = 25,000 min[/tex]
Time for round trip = 2 x 25,000 min = 50,000 min
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An object is accelerated by a force of 100N. suddenly a second force of 100 N in the opposite direction is exerted on the object, so that the forces cancel. Why is it that the object will continue with same velocity it had before the second forces was applid?
Because according Newton's second law, When a second force of 100N is applied to the object, the net force is
Total F = 100N-100N, it's zero.
Therefore, the two forces cancel each other out and the net force is zero. Acceleration is also zero.
a = 0
About Newton's second lawNewton's Second Law tells us that an object can experience a change in speed due to a force. Reporting from the NASA Glenn Research Center, Newton's second law defines force equal to the change in momentum (mass times velocity) per change in time.
The change in momentum produces an external force and causes an acceleration on the object. Not only causing an external force, the change in momentum also sometimes results in a change in direction. Remember momentum and acceleration are vector quantities.
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The rotational inertia of a pencil is greatest about an axis
A)along its length, where the lead is.
B)about its midpoint, like a propeller.
C)about its end, like a pendulum.
Answer:
I = M L^2 description of moment of inertia I
Only (B) and (C) are useful because L is very small along the length
(C) has the largest momejnt:
I = M L^2 / 3 for a thin rod about one end
(I = M L^2 / 12 for a rod about its midpoint)
What event will produce the greatest increase in the gravitational force between the two masses?.
The gravitational force between two masses depends on their masses and the distance between them.
What is gravitational force ?The gravitational pull between two masses is determined by their respective masses and their separation from one another. The biggest increase in gravitational force will result from moving the two masses closer together if the masses don't change. Therefore, a gravitational collapse or collision that brings the two masses together will result in the largest increase in the gravitational force between them.To know more about gravitational force , check out :
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An elevator suspended by a cable is descending at constant velocity. How many force vectors would be shown on a free-body diagram? Name them
When the elevator is descending at a constant speed, there are two forces at work on it. Both the weight of the elevator and the cable's tension are forces.
When the speed of a cable-supported elevator that is being suspended in the air is constant?A cable-hung elevator will experience zero change in velocity if it is descending at a steady speed. The net acceleration is therefore zero. The tension force (T) applied by the cable to the elevator is pulling it upward.
An elevator that is going downhill uses what kind of energy?The mechanical labour that moves the elevator up and down uses potential in the case of the elevator sinking. Note: The entire mechanical energy comprises a system in consideration is the sum of kinetic energy and potential energy.
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Which product forms from the synthesis reaction between strontium (Sr) and
sulfur (S)?
A. Sr₂S₂
B. SrS2
C. SrS
D. Sr₂S
The product form from the synthesis reaction between strontium (Sr) and sulfur (S) is SrS. Option C is the correct answer.
What is Strontium sulfide (SrS) compound?Strontium sulfide is the inorganic chemical compound. It has the formula SrS. It is a white solid. The compound is an intermediate in the conversion of strontium sulfate, the main strontium ore called celestite, to other more useful compounds.
Strontium sulfide is used in chemical research and as organic intermediates. It is also used as depilatory. It is also used as Isotope labelled enantiomer of Voriconazole (V760000), an antifungal agent and an ergosterol biosynthesis inhibitor.
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Place a lighted candle in front of a plane mirror. Try to see the flame of the candle in the mirror. It appears as if a similar candle is placed behind the mirror. The candle, which appears behind the mirror, is the image of the candle formed by the mirror. The candle itself is the object. Now move the candle to different positions in front of the mirror. Observe the image in each case.
1. How does the image appear in plane mirror?
2. What will be the size of the image?
3. What is reflection?
4. If the candle is placed 3 m away from a plane mirror, later moved one meter towards the mirror then the distance between the candle and its image will be
Answer:
1. The image in the plane mirror appears to be identical to the candle, but reversed from left to right.
2. The size of the image in the plane mirror will be the same as the size of the object (candle).
3. Reflection is the bouncing back of light rays when they encounter a surface, such as a mirror or any other shiny object.
4. The distance between the candle and its image in the plane mirror will remain the same, which is 3 meters.
what are electrical connectors
Answer:
CONNECTORS THAT BE ELECTRICAL AND CONNECT
Explanation:
IF YOU KNOW YOU KNOW HOW IT BE AND HOW IT IS AND WHY IT BE AND WHY IT IS
Electromagnetic radiation consists of particles called _________, each of which has a discrete amount, or quantum, of energy. However, since electromagnetic radiation also has wave properties, each particle is also characterized by a specific (usually expressed in nm) and frequency __________ (expressed in s-1).
The photons that make up electromagnetic radiation each have a distinct quantity of energy known as a quantum.
What is the name of the electromagnetic radiation subatomic particles, each of which has a specific quantity of energy termed a?An electromagnetic wave makes up a photon, a small particle. They are both massless and chargeless. They can be compared to a small packet pure light energy. A quantum, or discrete packet comprising energy or matter, is an example.
Which of these devices measures the electromagnetic wave frequency?wavemeter: a tool for measuring the separation between subsequent wavefronts of an electromagnetic wave that are in phase. By measuring the wave's frequency, the decision is frequently made indirectly.
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A disk of mass m = 0.120 kg is attached to a lightweight, taut string which keeps it in circular motion, as shown in the figure below. A puck of mass m on a table is attached to a string that passes through a small hole in the table at point O. A hand holds the string taut below the table and pulls down with a force vector F. The puck moves counterclockwise with velocity vector vi in a circle of radius ri centered on the hole.
The disk slides on a horizontal table with negligible friction at speed vi = 80.0 cm/s, and the radius of its circular path is ri = 40.0 cm. The string passes a small hole in the table and is initially held in place. The string is then slowly pulled downward a distance of 18.0 cm. How much work (in J) is done on the disk?
Answer: [tex]W=\frac{1}{2}m[(\frac{v_ir_i}{r_i-y})^2-v_i^2)]\approx.089 J[/tex]
Givens:
m = 0.12 kg
vi = 0.8 m/s
ri = 0.4 m
y = 0.18m
Explanation:[tex]\\[/tex]
Note that the final radius subtracted by the distance pulled
[tex]r_f = r_i-y[/tex]Since angular momentum is conserved
[tex]L_i=L_f[/tex]
[tex]mv_ir_i=mv_fr_f[/tex]
[tex]mv_ir_i=mv_f(r_i-y)[/tex]
[tex]v_f = \frac{mv_ir_i}{m(r_i-y)}[/tex]
[tex]v_f = \frac{v_ir_i}{r_i-y}[/tex]
Work is the change in Kinetic Energy
[tex]W=KE_f-KE_i[/tex]
[tex]W=\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2[/tex]
[tex]W=\frac{1}{2}m(v_f^2-v_i^2)[/tex]
[tex]W=\frac{1}{2}m[(\frac{v_ir_i}{r_i-y})^2-v_i^2)]\approx.089 J[/tex]
GOOD LUCK ON THE WEBASSIGN
The work done on the disk is approximately -0.018 J. The negative sign indicates that work is done on the disk, reducing its mechanical energy.
Given:
Mass of the disk (m) = 0.120 kg
The initial speed of the disk (vi) = 80.0 cm/s = 0.8 m/s
Initial radius of the disk's circular path (ri) = 40.0 cm = 0.4 m
The distance the string is pulled downward (d) = 18.0 cm = 0.18 m
Calculate the initial mechanical energy (Ei) of the disk:
Ei = KE + PE
Ei = (1/2) × m × vi² + m × g × ri
= (1/2) × 0.120 × (0.8)² + 0.120 × 9.8 × 0.4 = 0.08544 J
Ef = KE + PE
Ef = (1/2) × m × vf² + m × g × rf
= (1/2) × 0.120 × (0)² + 0.120 × 9.8 × (0.4 + 0.18) = 0.06744 J
W = Ef - Ei
= 0.06744 J - 0.08544 J
= -0.018 J
Therefore, the work done on the disk is approximately -0.018 J. The negative sign indicates that work is done on the disk, reducing its mechanical energy.
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what is the origin and meaning of the word thermodynamics?
The word "thermodynamics" is derived from two Greek words "therme" meaning heat and "dynamic" meaning power. The word thermodynamics was first used in the late 19th century.
Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy, such as work, mechanical, chemical, and electrical energy. The term thermodynamics was first used in the scientific literature by Scottish physicist James Clerk Maxwell in 1871.
The concept of thermodynamics is based on the principle that energy cannot be created or destroyed, only transformed from one form to another. It also deals with the study of energy transfer, the laws of thermodynamics, and how these laws relate to the behavior of physical systems. This field has a wide range of applications, including the design of heat engines, the study of phase transitions, and the understanding of thermal and thermochemical processes.
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