a particle undergoes three successive displacements in a plane, as follows: , 4.00 m southwest; then , 5.00 m east; and finally , 6.00 m in a direction 60.0° north of east. choose a coordinate system with the y axis pointing north and the x axis pointing east. what are (a) the x component and (b) the y component of ? what are (c) the x component and (d) the y component of ? what are (e) the x component and (f) the y component of ? next, consider the net displacement of the particle for the three successive displacements. what are (g) the x component, (h) the y component, (i) the magnitude, and (j) the direction of the net displacement? if the particle is to return directly to the starting point, (k) how far and (l) in what direction should it move?

Answers

Answer 1

let east is the positive x direction

north is the positive y direction

for the net displacement

d = 4 * (- cos(45) i - j * sin(45)) + 5 i + 6 * (cos(60) i + j * sin(60))

d = 5.17 i + 2.37 j

for the return vector

d = - 5.17 i - 2.37 j

d = sqrt(5.17^2 + 2.37^2) at arctan(2.37/5.17) degree south of west

d =  5.69 m at 24.6 degree south of west  

the return vector is 5.69 m at 24.6 degree south of west  

displacement is defined as the change in position of an object from one point to another in a straight line with direction

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Related Questions

in a single-slit experiment, a beam of monochromatic light of wavelength 693 nm passes through a single slit of width 19.0 m. the diffraction pattern is displayed on a screen that is 2.15 m away. what is the distance between the third dark fringe and the center of the diffraction pattern? give your answer in cm.

Answers

The distance between the third dark fringe and the center of the diffraction pattern is 1.05 cm. The diffraction pattern is displayed on a screen that is 2.15 m away. We need to find the distance between the third dark fringe and the center of the diffraction pattern.

To solve this problem, we can use the formula for the position of the dark fringes:

y = mλL/d

where y is the distance from the center of the pattern to the \(m^{th}\) dark fringe, λ is the wavelength of the light, L is the distance between the slit and the screen, d is the width of the slit, and m is the order of the fringe.

Plugging in the values given in the problem, we get:
y = 3 × 693 × 10⁻⁹ × 2.15 / 19.0 = 1.05 × 10⁻³ m

Converting to centimeters, we get:
y = 1.05 × 10⁻¹ cm

Therefore, the distance between the third dark fringe and the center of the diffraction pattern is 1.05 cm.

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WORK ENERGY & POWER CROSSWORD

NEED HELP ASAP

WORK ENERGY & POWER CROSSWORDNEED HELP ASAP

Answers

To complete the energy crossword puzzle, fix the meanings with the relevant definitions provided. For instance,

2. The four sources of all energy are Electricity, renewables, fossils, and nuclear power.

4. It is impossible for any machine to be 100% efficient

5. The name sometimes given to the sum of potential and kinetic energy is Mechanical energy.

How to fill a crossword puzzle

To fill a crossword puzzle, you have to follow the clues provided in the text. For example, the first clue shows that the word or words for box 2 are or are related to the four sources of all energy.

Also, the word in the 4th box will be impossible because it is impossible for any machine to be 100% efficient.

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In context of nepal it is better to use energy like solar power .why?

Answers

Answer:

Nepal is one of the least developed countries. Solar power is well-founded than electricity. It's better to use solar power because it's a clean resource, the sun provides more energy than we will ever need.

Explanation:

How much heat energy is given out when 500g of steam at 100 degrees celcius condenses to water at 100 degrees celcius

Answers

Explanation:

How much thermal energy is released when 500g of steam at 100° C condenses into water and cools to 50°C

Givens: m=0.5 kg

t = 50

c = 2.010

Qtotal = Q1 + Q2

Qtotal = QmcΔt + mLv

Qtotal = (0.5kg)(2.010)(50) + (0.5)(2.3*10^6)

Qtotal = 1.15 * 10^6

The book says that the answer is 1.3*10^6?

What did I do wrong here?

What makes astronomers believe that mars once had rivers and running water?

Answers

Astronomers believe that mars once had rivers and running water images from orbiting spacecraft reveal ancient channels that resembles drive up river beds on earth.

Astronomers are scientists who study celestial objects and phenomena, such as stars, planets, galaxies, and black holes. They use a variety of tools and techniques to observe and measure these objects, including telescopes, cameras, spectrographs, and computer simulations.

Astronomers seek to understand the fundamental properties and behavior of the universe, such as its origins, evolution, and composition. They also explore the possibility of life beyond our own planet and the potential for space exploration and colonization. To pursue their research, astronomers often collaborate with other scientists in related fields, such as physics, chemistry, and computer science. They also work closely with engineers and technicians to develop and improve the instruments and equipment used in their observations.

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If a sample of a radioactive isotope has a half-life of 1 year, how much of the original sample will be left at the end of the second year?

Answers

Answer:

1/4 of the original

Explanation:

That would be TWO half lives:

1/2  * 1/2   = 1/4   <======= 1/4 would be left

Water breaks down into
hydrogen and oxygen.

Answers

Electrolysis is the process of using electricity to split water into hydrogen and oxygen. This reaction takes place in a unit called an electrolyzer.

The diffusion of inanimate forms of energy was vital to the accelerated development of the modern world. The industry is completely dependent on the techniques of extracting energy from nature. The development of energy sources or the lack of them determined the fate of countries. Those that were able to develop and exploit them led the industrialization process, those that did not invest in the energy sector became technologically lagging countries.

Discuss about:

a) the evolution of the main energy matrices after the industrial revolution (main sources of energy);

b) The social and environmental consequences of these energy sources;

c) relate energy development and degree of industrial development.

Answers

The evolution of energy matrices, the social and environmental consequences of energy sources, and the relationship between energy development and industrial development are critical aspects of understanding the interplay between energy and the modern world. Balancing the need for energy with sustainability and minimizing environmental impacts is a key challenge for societies today.

a) The evolution of the main energy matrices after the industrial revolution:

The industrial revolution marked a significant shift in the sources of energy used to power the growing industries and societies. Prior to the industrial revolution, human and animal labor, along with limited use of water and wind power, were the primary sources of energy. However, with the advent of steam engines and mechanization, there was a need for more abundant and efficient sources of energy.

Coal: Coal became the dominant energy source during the early stages of the industrial revolution. It provided the necessary fuel for steam engines and played a crucial role in powering factories, railways, and steamships.

Oil: The discovery and commercialization of oil in the late 19th century revolutionized the energy landscape. Oil became a major source of energy for transportation, as it fueled the internal combustion engines of automobiles, trucks, and airplanes.

Natural Gas: With the expansion of oil drilling, natural gas also emerged as an important energy source. It is used for heating, electricity generation, and as a feedstock for various industrial processes.

Nuclear Energy: The development of nuclear power in the mid-20th century introduced a new source of energy. Nuclear reactors harness the energy released from nuclear fission reactions to generate electricity.

Renewable Energy: In recent decades, there has been a growing emphasis on renewable energy sources such as solar, wind, hydroelectric, and geothermal power. These sources offer sustainable alternatives to fossil fuels, with lower environmental impact and the potential for long-term energy security.

b) The social and environmental consequences of these energy sources:

Each energy source has its own social and environmental consequences:

Fossil Fuels: The burning of fossil fuels, such as coal, oil, and natural gas, releases greenhouse gases and contributes to climate change. Extraction of fossil fuels can lead to habitat destruction, water pollution, and health hazards for workers and nearby communities.

Nuclear Energy: While nuclear energy does not produce greenhouse gas emissions during operation, it presents risks associated with accidents, radioactive waste disposal, and potential weaponization of nuclear materials. Public safety concerns and environmental risks have led to debates over the use of nuclear power.

Renewable Energy: Renewable energy sources offer benefits in terms of reduced greenhouse gas emissions and environmental sustainability. However, their deployment may require land use changes, and some technologies (e.g., large-scale hydroelectric dams) can cause ecological disruptions and displacement of communities.

c) The relationship between energy development and degree of industrial development:

Energy development and industrial development are closely intertwined. The availability of affordable and reliable energy sources is crucial for driving industrialization and economic growth. Access to abundant energy resources enables countries to power their industries, expand transportation networks, and improve living standards.

Countries that have invested in the development and exploitation of energy sources have typically experienced accelerated industrialization and technological advancement. The ability to secure and utilize energy resources efficiently has been a determining factor in a country's competitiveness and economic prosperity.

Conversely, countries that lack access to energy sources or fail to invest in their energy sectors may face challenges in industrial development. Limited energy availability can constrain production capacities, limit access to modern technologies, and hinder economic progress.

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A grating with 250 grooves mm is used with an incandescent light source. Assume the visible spectrum to range in wavelength from 400nm to 700nm . In how many orders can one see (a) the entire visible speed

Answers

The number of orders that one can see the entire visible speed is 5 orders.

How to calculate the orders?

From the information given, it should be noted that the grating with 250 grooves mm is used and the visible spectrum range in wavelength from 400nm to 700nm. Therefore, the grating spacing will be:

d = (1.00 × 10^-4) / 250

d = 4000nm

Therefore, the number of times that are needed to complete the order will be the same as the number of orders which the long wavelength time will be visible. This will be:

= (4000 × sin 90°)/700

= 5.71

Therefore, the maximum orders will be 5.

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the unit of current, the ampere, is defined in terms of the force between currents. two 1.0-meter-long sections of very long wires a distance 2.0 m apart each carry a current of 1.0 a. part a what is the force between them? (if the force between two actual wires has this value, the current is defined to be exactly 1 a.) express your answer with the appropriate units. f

Answers

The force between the wires is 1*10⁻⁷T.

What is ampere?

The rate at which electrons flow or current flows across an electrical conductor is measured in amperes. An electrical charge of one coulomb (6.24 x 1018 charge carriers) per second that passes a particular place is represented by one ampere of current.

What is force?

A mass-containing object's change in velocity is referred to as a force when a push or pull is applied to it. A body can change its state of rest or motion when an external force acts on it. It is directed and has a magnitude.

The concepts required to solve the given problem is magnetic field due to a current carrying wire and force on a current carrying wire due to magnetic field.

Initially, determine the magnetic field at one wire due to other wire by using expression magnetic field due to a current carrying wire. Then, determine the force on the wire by using magnetic field, length of the wire and current in the wire.

The current carrying wire creates a magnetic field around the wire and the direction of magnetic field around the wire is known by using right hand rule.

The magnitude of magnetic field B due to a current carrying wire at distance r from the wire is given by following expression.

B=Here, I is the current, and μ₀ I/2πr

Here, I is the current, and

μ₀is the permeability.

The magnetic force F on a current carrying wire is given by following expression.

F= BIL

Here, L is the length of the wire.

Step: 1

The magnitude of magnetic field B due to a current carrying wire at distance r from the wire is given by following expression.

B= μ₀ I/2πr

Substitute 1.0 A for I, 2.0 for r, and

4πr*10⁻⁷ H/m

for  μ₀ in the above equation.

B= (4πr*10⁻⁷ H/m) (1.0A)/2πr(2.0m)

=1*10⁻⁷T

Explanation:

The direction of magnetic force on each wire is depends on the direction of current in the each wire. If the current direction of current is same in both wires then force is attractive and repulsive if the direction of current is opposite in both wires.

Therefore,  force between the wires is 1*10⁻⁷T.

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What is the electrical power when the current is 20 amps and the voltage is 15 volts? *


A. 1.33 watts

B. 300 watts

C. 35 watts


Objects in space appear to change position as they orbit the sun. What is this phenomenon called? *


A. Nebular theory

B. Stellar theory

C. Parallax


The moon lacks an atmosphere because its gravity is too STRONG and forces gas molecules into outer space. *


A. True

B. False


Heat pumps move heat from __________ to __________ areas & REQUIRES energy.

A. cold, hot

B. hot, cold

Answers

Answer:

The power is 300 watts.

Explanation:

Given that,

Current, I = 20 a

Voltage, V = 15 volts

The electrical power of any device is given by the product of current and voltage. It can be given by :

P = VI

So,

P = 15 × 20

= 300 W

So, the power is 300 watts.

ASAP A 1 kg ball is held motionless above the ground and then released. At impact, it was traveling at 5.50 m/s. How much potential energy did it
have before it was released?
O a
Ob
Oc
Od
5J
9.21
12.7J
15.1 J

ASAP A 1 kg ball is held motionless above the ground and then released. At impact, it was traveling at

Answers

If 1 kg ball is held motionless above the ground and then released. At impact, it was traveling at 5.50 m/s. The amount of the potential energy  it have before it was released is: D. 15.1 J.

How to find the potential energy ?

Potential energy is related to the height of an object and can be calculated using the equation:

PE = mgh

where :

m = mass of the object

g =  acceleration due to gravity (9.8 m/s^2)

h = height above the ground

Since the initial velocity of the ball is zero, the potential energy can be calculated as follows:

PE = 0.5 * m * v^2

where:
m = mass of the ball (1 kg)

v =  velocity at impact (5.50 m/s)

PE = 0.5 * 1 kg * (5.50 m/s)^2 = 15.1J

Therefore the ball had 15.1 J of potential energy before it was released.

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I WILL MARK BRAINLIEST!
A 0.040 kg dart is thrown with a momentum of +1.5 kg m/s at a dart board. The dart took 0.030 seconds to stop when it struck the board. What is the magnitude of the force the dart exerted on the board?
A)1.3 N
B) 15 N
C) 50 N
D) 60N

Answers

Answer:

Explanation:

The answer is C

The magnitude of the force the dart exerted on the board is 50 Newton.

What is force?

The definition of force in physics is: The push or pull on a mass-containing item changes its velocity.

An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. A spring balance can be used to calculate the Force. Newton is the SI unit of force.

Given parameters:

Mass of the dart: m= 0.040 kg.

Momentum of the dart: p = + 1.5 kg m/s.

Time required to stop = 0.030 seconds.

Hence, the magnitude of the force the dart exerted on the board is =

change in momentum/time

= (1.5 - 0.040×0)/0.030 Newton

= 50 Newton.

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the smooth and accurate execution of movement as conceived in the mind and executed by the body parts

Answers

The smooth and accurate execution of movement as conceived in the mind and executed by the body parts describes ; The central nervous system.

Although your question is incomplete an answer is provided which falls within the scope of your question

The human brain receives, interprets and transfer signals it deduces from the impulses it received to the various sense organs ( body parts ) for execution. and this process involves coordination within the nervous system.

The central nervous system is a category of the Nervous system of a human and it consists of the spinal cord and the human brain. and the peripheral nervous system

Hence we can conclude the smooth and accurate execution of movement as conceived in the mind and executed by the body parts describes, The central nervous system.

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the smooth and accurate execution of movement as conceived in the mind and executed by the body parts

Which one of these is not a physical charge

A melting and ice cube
B crushing a can
C chopping wood
D metal resting

Answers

Answer:

the answer is D metal resting

Explanation:

I just think that because if you treasure can that's physical charge by dropping where you create a physical charge melting and Ice Cube might be 1 but I feel like metal resting is more likely

Two point charges are placed at the following points on the x-axis. +2.0 C at
×=0, -3.0.C at 0.40m. Find the electric field strength at 1.20m?

Answers

The electric field strength at a distance of 1.20 m on the x-axis is -1.5 × 10⁴ N/C.

To find the electric field strength at a distance 1.20 m on the x-axis, we can use Coulomb's law:

\($$F=k\frac{q_1q_2}{r^2}$$\)

where F is the force between two charges, q1 and q2 are the magnitudes of the charges, r is the distance between the charges, and k is the Coulomb constant.For a single point charge q located at the origin of the x-axis, the electric field E at a distance r is given by:

\($$E=\frac{kq}{r^2}$$\)  where k is the Coulomb constant.

So, let's calculate the electric field due to each charge separately and then add them up:

For the +2.0 C charge at x = 0, the electric field at a distance of 1.20 m is:\($$E_1=\frac{kq_1}{r^2}=\frac{(9\times10^9)(2.0)}{(1.2)^2}N/C$$\)

For the -3.0 C charge at x = 0.40 m, the electric field at a distance of 1.20 m is:

\($$E_2=\frac{kq_2}{r^2}\)

\(=\frac{(9\times10^9)(-3.0)}{(1.20-0.40)^2}N/C$$\)

The negative sign indicates that the direction of the electric field is opposite to that of the positive charge at x = 0.

To find the net electric field, we add the two electric fields\(:$$E_{net}=E_1+E_2$$\)

Substituting the values of E1 and E2:

\($$E_{net}=\frac{(9\times10^9)(2.0)}{(1.2)^2}-\frac{(9\times10^9)(3.0)}{(0.8)^2}N/C$$E\)

net comes out to be -1.5×10⁴ N/C.

Therefore, the electric field strength at a distance of 1.20 m on the x-axis is -1.5 × 10⁴ N/C.

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You are in a room that has three switches and a closed door. The switches control three light bulbs on the other side of the door. Once you open the door, you may never touch the switches again. How can you definitively tell which switch is connected to each of the light bulbs?

Answers

Answer:

By watching in the door lock

Answer:

.-. you can flip a switch and look at the bottom or the top of the door and see if there’s a light of there isn’t then flip another one.

also the other chat that we were talking on got deleted

True or False? Index Fossils are used to help constrain the relative age of the rocks in an area?

Answers

The answer to this question is True

What is the best definition of luminous? A. A luminous object is an object that separates light.
B. A luminous object is an object that blocks light.
C. A luminous object is an object that gives off its own light.​

Answers

The best definition of a luminous object is that it gives off its own light. The correct option is C.

A luminous object is an entity that emits its own light, illuminating its surroundings. It generates and radiates light energy, making it visible in the absence of external light sources.

A. A luminous object is an object that separates light.

This statement is not true because separating light is not a characteristic of a luminous object. The term "luminous" refers to objects that emit light, not objects that separate or manipulate light.

B. A luminous object is an object that blocks light.

This statement is not true either because blocking light is the opposite of being luminous. Luminous objects emit light, while objects that block light are generally referred to as opaque.

C. A luminous object is an object that gives off its own light.

This statement is correct. Luminous objects are those that produce and emit their own light. They are capable of generating and radiating light energy. Examples of luminous objects include the Sun, light bulbs, stars, and fireflies.

Hence, The correct option is C. A luminous object is an object that gives off its own light.

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If car A is at 47 km/h and car B is at 62 km/h in the opposite direction,
what is the velocity of the car A relative to the car B?

Answers

Answer:

62+47=109

Explanation:

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please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

try finding on a website

Explanation:

lance bikes 15km east then 30 km north what is the distance he traveled and what is the magnitude of his displacement

Answers

Answer:

See below

Explanation:

Distance traveled = 15 + 30 = 45 km

Displacement (use Pythag theorem)

    15^2 + 30^2 = d^2      d = sqrt (1125) = 33.5 km

Adaline walks 2.0 miles north to school from her house. After school, she walks 2.0 miles south from the school to her house. What is her displacement?

0 miles
1.0 miles, north
2.0 miles, south
4.0 miles, north

Answers

0 miles

Explanation:

delta displacment=position end-position beginning

The displacement of Adaline if she walks 2.0 miles north to school from her house. After school, she walks 2.0 miles south from the school to her house is zero miles so, option A is correct.

What is displacement?

The overall modification of an object's location and direction of motion is referred to as displacement. Since displacement considers both the amount of the changing location and the direction of the motion, it is known as a vector quantity. There may be zero, positive, or negative displacement.

Given:

Adaline walks 2.0 miles north to school from her house. After school, she walks 2.0 miles south from the school to her house,

Calculate the displacement as shown below,

Displacement = Distance from house to school + Distance from school to house,

Displacement = 2 + (-2)  (North direction is taken as positive and south direction is taken as negative)

Displacement = 0 miles

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A light spring with force constant 3.70 N/m is compressed by 8.64 cm as it is held between a 0.261-kg block on the left and a 0.522-kg block on the right, both resting on a horizontal surface. The spring exerts a force on each block, tending to push them apart. The blocks are simultaneously released from rest. Find the acceleration with which each block starts to move, given that the coefficient of kinetic friction between each block and the surface is the following. (Let the coordinate system be positive to the right and negative to the left. Be sure to include the sign to indicate the direction of the acceleration.) (a) μ = 0 heavier block lighter block (b) μ = 0.110 heavier block lighter block (c) μ = 0.480 heavier block lighter block m/s² m/s² m/s² m/s² m/s² m/s²

Answers

The lighter block will also accelerate to the right with an acceleration of -0.82 m/s².

(a) μ = 0

The heavier block will accelerate to the right with an acceleration of:

a = F / m = k x / m = (3.70 N/m) (0.0864 m) / 0.261 kg = 1.22 m/s²

The lighter block will also accelerate to the right with an acceleration of 1.22 m/s².

(b) μ = 0.110

The heavier block will accelerate to the right with an acceleration of:

a = F - μk / m = k x / m - μk / m = (3.70 N/m) (0.0864 m) / 0.261 kg - (0.110)(0.261 kg)(9.80 m/s²) = 0.68 m/s²

The lighter block will not accelerate because the force of friction is greater than the force of the spring.

(c) μ = 0.480

The heavier block will accelerate to the right with an acceleration of:

a = F - μk / m = k x / m - μk / m = (3.70 N/m)(0.0864 m) / 0.261 kg - (0.480)(0.261 kg) (9.80 m/s²) = -0.82 m/s²

Therefore, the lighter block will also accelerate to the right with an acceleration of -0.82 m/s².

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I cannot find scince so can someone please help me out

I cannot find scince so can someone please help me out

Answers

The three statements which provide evidence of universe expansion that supports the Big Bang Theory include the following:

Galaxies are moving away from each other.The temperature of the universe is decreasing.An enormous amount of weak background radiation has been detected in the universe.

What is the Big Bang Theory?

The Big Bang Theory simply refers to an explanation that was given by astronomers to describe how the universe was formed, which describes a well-detailed information on how the universe started (its origin).

According to the Big Bang Theory, the whole universe stretched from a single point and then expanded to its present state and this is typically supported by the following evidence:

Red shift of galaxies due to Doppler effect.Cosmic background radiation.Decrease in the temperature of the universe.Universe is expanding.The movement of galaxies apart.Existence of quasars.

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Complete Question:

Which provides evidence of universe expansion that supports the Big Bang Theory? Select the three correct answers. (2 points)

An enormous amount of weak background radiation has been detected in the universe.

The temperature of the universe is decreasing.

The temperature of Cosmic Microwave Background radiation varies widely from one part of the universe to another

Galaxies are moving away from each other.

The universe is undergoing a cycle of contraction and expansion

The temperature of the universe is increasing.

Where in the galaxy are the most stars born?

Answers

Answer: Stars are formed in dust clouds and are found in most galaxies.

Explanation:

Answer: Stars form inside relatively dense concentrations of interstellar gas and dust known as molecular clouds.

Explanation:

physical sciences Practical test​

Answers

so ummmm what about ?

because I cant see any actual question?

a 72.9-kg base runner begins his slide into second base when moving at a speed of 3.93 m/s. the coefficient of friction between his clothes and earth is 0.693. he slides so that his speed is zero just as he reaches the base.(a)how much mechanical energy is lost due to friction acting on the runner?

Answers

The mechanical energy lost due to friction acting on the runner is 1095.7 J.

What is Energy?

Energy is a fundamental concept in physics that refers to the ability of a system to do work. In simpler terms, energy is the capacity of an object or system to perform work, move, or cause changes in matter.

To account for this, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy:

W = ΔK

where W is the work done on the runner by friction and ΔK is the change in the runner's kinetic energy.

The work done on the runner by friction is given by:

W = μkmgd

where μk is the coefficient of kinetic friction (0.693), d is the distance over which the runner slides (assumed to be the same as the distance between the bases, 15.24 m), and the other variables are as defined above.

W = (0.693)(72.9 kg)(9.81 m/\(s^{2}\))(15.24 m)

W = 1095.7 J

The change in the runner's kinetic energy is given by:

ΔK = \((1/2)mvf^{2}\) - \((1/2)mvi^{2}\)

where vf is the final speed of the runner (zero) and vi is the initial speed of the runner (3.93 m/s).

ΔK = (1/2)(72.9 kg)\((0 m/s)^{2}\) - \((1/2)(72.9 kg)(3.93 m/s)^{2}\)

ΔK = -1041.9 J

The negative sign indicates that the runner's kinetic energy has decreased, as expected.

Therefore, the actual mechanical energy lost due to friction is:

ΔE = W = 1095.7 J

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Work done by STATIC FRICTION is alwaysO positive,O negative, O perpendicular to the surface along the surface. O Zero.

Answers

The right answer is (d). Static friction can cause a system to do positive, negative, or even zero work.

Does static friction ever produce zero work?

At essence, static friction can also be active when a body is in equilibrium, when there is no movement and no static frictional work to be done.

Can static friction provide useful results?

This is because our force is opposed by the force of static friction. However, since the block stays there, there is no displacement. Therefore, friction produces no work. Friction can therefore produce positive, negative, or no work.

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A. It Implies That M Is Finitely Generated. B. It Implies That M Has Nonzero Elements Of Nonzero Order. C. When Every Non-Null Element Has Null . D. In The Case That The Ring R Is A Body. E. None Of The Above Alternatives Gives A
Which of the following alternatives give a true statement. Justify your answer.
A modulus M over a ring R has a finite basis:
a. It implies that M is finitely generated.
b. It implies that M has nonzero elements of nonzero order.
C. When every non-null element has null .
d. in the case that the ring R is a body.
e. None of the above alternatives gives a true statement.
Which of the following statements are true?
a. If a subset of a module generates that whole module, then the subset cannot be
empty.
b. Every submodule S of a module M verifies the inequality C. Two different subsets of M have to generate two different submodules of M.
d. If S generates a submodule N of the module M, then contains S.
e. Neither statement is true.

Answers

The correct answer is e. None of the above alternatives gives a true statement. None of the statements in options a, b, c, and d are true when it comes to a modulus M over a ring R having a finite basis.

When a modulus M can be formed entirely from a finite set of elements, the modulus M is said to be finitely generated. M's finite basis does not, however, automatically imply that M is finitely generated. A basis is a set of linearly independent elements, and it might not be enough to produce all of the components of the modulus.

According to the assertion in option b, M must include nonzero items of nonzero order if it has a finite basis. This is untrue, though. The smallest positive number k, such that the element raised to the power of k equals the identity element, is referred to as the order of an element.

According to option c, every non-null element in a modulus with a finite basis has a null. Nevertheless, this claim is likewise untrue. It is possible for a modulus with a finite basis to have non-null elements without a null element.

According to option d, a ring R is a body, or a field, and only then can a modulus have a finite basis. However, this assertion is also untrue. Even though the ring R is not a field, a modulus can nonetheless have a finite basis. None of the given alternatives provides a true statement about a modulus M over a ring R having a finite basis.

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