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examples of work done in physics

Rambi the rhino pushes the minecart from behind and speeds it up so it is now traveling 11 m/s. The magnitude of work is equal to the magnitude of force multiplied by the distance traveled. What are the Varieties of Work Done that We Study in Physics? Work – the physics hypertextbook. Positive Work: If a force relocates the object in its direction, then the work done is positive. : If a force relocates the object in its direction, then the work done is positive. Sign up for our science newsletter! Find the Work Done? This sample report, on the other hand, simplifies this daunting topic and clearly elaborates its parts. 2. The work is negative if work is done on the system (i.e., energy added to the system). The Box is Dragged by 10 m, & the Force Applied by the Rope is 110 N. Find the Final Work Done by the Force? Developing countries, in […], As living standards increase and health provisions become better and more accessible to all, we can look forward to living longer. The amount of work a force does is directly proportional to how far that force moves an object. We can obtain displacement from the formula; s = ut + ½ at² = 0 + 0.5 * 1* 5² = 12.5 m. Q3. Practice: Calculating work from force vs. position graphs. Work Formula Example of Work Types of Energy Power Formula Questions If we assume the trashcan started at rest, which seems reasonable, the initial velocity is 0. Now we will perceive how to determine work done. : If the direction of the force and the displacement are perpendicular to each other, the total work done by the force on the object is null. When force & displacement is in reverse directions, then the work is assumed to be negative. We help hundreds of thousands of people every month learn about the world we live in and the latest scientific breakthroughs. Q1. In general, the formula for the kinetic energy of an object is: where v stands for an object’s velocity. Whenever a force moves an object, we say that work has been done. In physics, "work" has a different definition than it does in everyday speech. The work-energy principle says that the net work done on an object is equal to the change in kinetic energy of that object. Here, force F reacts at an angle θ to the displacement d. We know that work done is defined as the multiplication of magnitude of displacement d and the component of the force that is in the direction of displacement. Work Done by a Force The following diagram gives the formula for work done by a force. All Rights Reserved. Example 2: Refer the below work physics problem with solution for a boy who uses a force of 30 Newtons to lift his grocery bag while doing 60 Joules of work. W = the work done by an object measured using Joules. Physics studies the origin, propagation, and properties of sound. Though both force and displacement are vector quantities, work has no direction due to the nature of a scalar product (or dot product) in vector mathematics. So, using the formula for work done, we get: Q4. The Mass of the Toy Car is 5 kg. The example of this type of work done is the motion of the ball dropping towards the ground where the displacement of the ball is in the direction of the force of gravity. The concept of work in physics is much more narrowly defined than the common use of the word. “Science is the knowledge of consequences, and dependence of one fact upon another.” – Thomas Hobbes. If the direction of the force and the displacement are perpendicular to each other, the total work done by the force on the object is null. They look at the initial and final states. We cover everything from solar power cell technology to climate change to cancer research. In this case, we know the force of 64 N and the distance of 3 m. We also know that there is a 120°angle between the angle of the direction of applied force and the direction of motion. Therefore, the work-energy principle states that: The total work done by all the forces acting on a particle or the work of the resultant force F(in subscript resultant) is equivalent to the change in kinetic energy of a particle. In other words, work is equivalent to the application of a force over a distance. Power is defined as work done per unit time. Newtonian mechanics positive work done by friction physics. Pro Lite, Vedantu In our everyday language, work is related to expenditure of muscular effort, but this is not the case in the language of physics. The example of this type of work done is the motion of the ball dropping towards the ground where the displacement of the ball is in the direction of the force of gravity. However, in physics the term ‘work’ is used in a specific sense involves the displacement of a particle or body under the action of a force. So the force from a person pushing the side of a skyscraper is not doing any work as the skyscraper does not move. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. Now acceleration of that toy cart will be because of horizontal force only. m = the mass of the object measured using kilograms. How much work did Rambi do on the minecart? For normal and gravitation force perpendicular to total displacement so by dot product rule work done is 0.and for static friction 0 displacement, when we displace we don't contact with ground so friction don't do any work.so over all work done in walking is 0. In physics, work is the energy transferred to or from an object via the application of force along a displacement. Consider a block located on a frictionless horizontal surface. The air does work, and transfers energy to the balloon. We know both the velocity and mass of the minecart so we can determine the total kinetic energy at the beginning and at the end. Due to the nature of scalar product work is a scalar quantity besides the fact that both force and displacement are vector quantities. In order to solve this problem we first need to figure out the minecart’s initial kinetic energy and its final kinetic energy. Work, in physics, measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.If the force is constant, work may be computed by multiplying the length of the path by the component of the force acting along the path. Scroll down the page for more examples and solutions on how to use the formula. Work done via force (F) is equal to the change in kinetic energy. This quantity of energy transferred by the force to move an object is termed as work done. In other words, the change in kinetic energy of a body is equal to the amount of work done on that body. Want to know more? First, we must determine the initial kinetic energy of the car. W = \[\frac{1}{2mv^{2}}\] - \[\frac{1}{2mu^{2}}\] = \[\frac{1}{2m}\](v\[^{2}\] - u\[^{2}\]), It is known from Newton’s second law that F = ma. A series of free GCSE/IGCSE Physics Notes and Lessons. In the case of a constant force, work is the scalar product of the force acting on an object and the displacement caused by that force. Work is also done when a force causes an object to move. There are two main portions of her trip, so we can calculate the work done over each portion individually, then, combine the two values to get the total amount of work done. Practice finding the work done by a force when given the force and displacement vectors for an object. Prove you're human, which is bigger, 2 or 8? ... Science High school physics Work and energy Introduction to work. This article of physics will give the concept of work done with work formula physics and example. Example: Now, the total work done by this force is equal to the product of the magnitude of applied force and the distance traveled by the body. Work is done on an object when an applied force moves it through a distance. We love feedback :-) and want your input on how to make Science Trends even better. A Force of 12 N Acts at a Distance of 12 m in the Force Direction. Finding the total work done on the block is more complex. Integration approach can be used both to calculate work done by a variable force and work done by a constant force. Therefore, the total amount of work done on the minecart is 5545−1125= 4420 J. A 100 Newton force is applied to a 15kg box in the horizontal direction and moves it 5 meters horizontally. It works on the concept of Quantum Mechanics. Thus, we express work as being positive when the system makes any effort on the surroundings (i.e., energy leaves the system). Negative Work: When force & displacement are in reverse directions, then the work is assumed to be negative. • Calculate power using either energy or work done. Another way to understand it is that one joule is equivalent to the amount of energy transferred when one newton of force moves an object a distance of one meter. Work. vi = the initial velocity of an object measured using m/s. A Box is Pulled Along the Floor by the Rope, Which Creates an Angle 30° with the Horizontal Surface. The initial kinetic energy of the minecart is: The final kinetic energy of the minecart is. Examples of workless constraints are: ... states that the work done by all forces acting on a particle (the work of the resultant force) equals the change in the kinetic energy of the particle. The amount of work a force does is directly proportional to how far that force moves an object. The work done by a constant force of magnitude F on a point that moves a displacement d in the direction of the force is the product: W = Fd. How much work was done? Cases where work is not done Let us consider some cases where work is not done: Work is zero if applied force is zero (W=0 if F=0): If a block is moving on a smooth horizontal surface (frictionless), no work will be done. Work is done whenever a force moves something. Science Trends is a popular source of science news and education around the world. So, the 100 N force did 500 joules work moving the block 5 meters. Work, in physics, occurs when a force acts on an object to move it some distance from the start point (also called displacement). We also know that since the force is applied in the same direction as the displacement, Θ is equal to 0. Examples of zero work: 1. Once we know those values, we can determine the total amount of work. A constant force F is acted upon this block. Transferring energy can be in the method of force. So 200 joules is going to equal the difference in kinetic energy. The equation for work is ... W = F*d*cosine(theta) Problem 1 Let’s look at some problems to examine these mathematical relationships. In physics, we say that a force does work if the application of the force displaces an object in the direction of the force.In other words, work is equivalent to the application of a force over a distance. The car’s final velocity will be 20.4 m/s. […], Overweight and obesity, to a greater degree, are conditions characterized by abnormal or excessive fat accumulation that impair health and […], Military time is a system of timekeeping. The work done by the forces, the power and the difference of gravitational potential energy will be involved. Work Done Examples. Pro Lite, Vedantu Substituting the values in the above given formula, Work = 15 x 0.7 = 10.5 J Therefore, the value of Work is 10.5 J.. Find the Work Done by the Girl in 5 Sec? = the final velocity of an object measured using m/s. In these lessons, we will • Describe what is meant by power. WORK Suppose that, a force is applied an object and object moves in the direction of applied force then we said work has done. A Girl Thrusts a Toy Car from the Stationary State on the Horizontal Floor with Force 12 N Engaged at an Angle 60 ° from the Horizontal. For the first part of her trip, she exerts 300 N of force to move a suitcase 16 meters vertically so the amount of work done is: So the first part of the trip did 4800 joules. So we plug these values into our equation. The purpose of this force is to move the body through a certain distance in a straight path in the direction of the force. This question requires 2 separate steps. If you compress a balloon, you do work, and transfer energy to the air inside the balloon. We know energy can neither be formed nor be demolished, so the energy must be converted into some other form. Fhsst physics/work and energy/work wikibooks, open books for. Donkey and Diddy Kong are sitting in a 90-kilogram minecart that is initially traveling horizontally at a velocity of 5 m/s. What is the work done by the force in moving it through a distance of 8 m. F = 100 N. S = 8 m. Since F and S are in the same direction, θ = 0, where θ is the angle of the force to the direction of movement. Newtonian mechanics work done by friction. Work done by an object can be scientifically expressed as: W = \[\frac{1}{2}\]mv\[_{f}^{2}\] - \[\frac{1}{2}\]mv\[_{i}^{2}\]. The amount of work done upon an object depends upon the amount of force (F) causing the work, the displacement (d) experienced by the object during the work, and the angle (theta) between the force and the displacement vectors. She then pushes the suitcase with 100 N of force the remaining 8 meters to her hotel room. The unit for kinetic energy is the same unit for work, the joule. Ans: Here, force and displacement happens in the same direction. Junior high school grade 8. A car weighing 1300 kg is moving with a velocity of 18 m/s. The problem with 120 degree angle of force applied does not equal the number shown (its negative), Black-capped chickadees are food-storing passerines that are able to keep track of thousands of stored food locations called caches (Sherry, […], Advances in nanotechnology have provided acoustic researchers with a number of new materials, with features such as nanofibers and nanopores, […], Numerous high-income countries are currently aiming for a socio-technical transformation toward carbon-neutrality and more sustainable energy resources. In cases where a force is applied to an object but does not move it, no work has been done. The angle between force and displacement is at 60 °. Examples on Work Done. How much work is done by a 60kg man in climbing a stair of 12 steps, each steps being 6 inches higher than the previous one? A 64 N force is applied to the book at a 120° angle from horizontal and moves the book 3 meters in the horizontal direction. While it is called military time in the United States, many organizations outside […], When we hear the word “animals,” we conceptualize discrete individual organisms that have no morphological connection to other organisms. When a weight-lifter holds a heavy weight on his shoulders for a few seconds then the work done by him is nil since their is no displacement caused by the applied force. In this stance, it is termed as work done. In more mathematical terms, the relationship can be expressed as: where KE stands for kinetic energy. In physics, we say that a force does work if the application of the force displaces an object in the direction of the force. According to the work-energy principle, an increase in a rigid body’s kinetic energy is caused by an equal amount of work done on that body by a force applied to that body. Note that the block may have large displacement but no work gets done. If a force relocates the object in its direction, then the work done is positive. While describing work, we emphasize on the effects that the system does not work on its surroundings. The initial kinetic energy of the car is: Since we know the total amount of work done on the system (60000 J) we can figure out the car’s final kinetic energy: Now, since we know the final kinetic energy and the mass of the car, we can determine its final velocity like this. Introduction To Heat, Internal Energy And Work, NCERT Book Class 11 Geography Practical Work in Geography PDF, NCERT Book Class 11 Hindi Political Science - India Constitution at Work PDF, Solutions – Definition, Examples, Properties and Types, Vedantu When work is done against frictional forces acting on an object, the object’s temperature increases. For the second part, we know that a 100N force moved the suitcase horizontally 8 meters, so the total amount of work done on the second portion of the trip is: Combining the two values from each portion of the trip yields: So over the entire course of Linda’s trip, 5600 Joules of work was done. Specifically, the term "work" is used when a physical force causes an object to move. Work and energy in physics share a close relationship. Linda takes a 300 N suitcase up 3 flights of stairs for a total vertical distance of 16 meters. In this lesson, we will • Describe what is meant by work done. Measuring Work for Gases When scientists measure the work done on, or by, gases, they look at the system at the beginning and the end of the project. When a ball rolls down a hill due to the force of gravity, when you pick up your backpack off the ground, when your car’s internal engine applies a force to make your wheels move; all of these events involve a force moving an object over a distance and so involve some work. Can it be positive or. We concluded that the work and the energy are directly proportional to each other. Sorry!, This page is not available for now to bookmark. If the motion is not in the direction of force or force is applied to an object but there is no motion then we cannot talk about work. That's great to hear! (a) Work done is positive :- Force is in the same direction as displacement for example work done by force for pushing a block of mass m (b) Work done is negative :- Force is opposite to the displacement for example when a body slides on horizontal surface work done by frictional forces on body is negative as frictional force always acts opposite to displacement of the body. = the initial velocity of an object measured using m/s. In this case, the force exerting on the block is constant, but the direction of force and direction of displacement influenced by this force is different. The Physics Classroom serves students, teachers and classrooms by providing classroom-ready resources that utilize an easy-to-understand language that makes learning interactive and multi-dimensional. W = F Cos θ In physics, the term "work" has a specific meaning. The SI unit for work is the joule (J), and its dimensions are kg•m2/s2. Work. The general formula for work and for determining the amount of work that is done on an object is: “work is said to be done when the point of application of a force moves. In physics, work is defined as a force causing the movement—or displacement—of an object. How much work was done over her whole trip? This sample tackles thermodynamics—a branch of physics that studies about the relation between heat and temperature to energy, work, radiation, and properties of matter. Work is an interesting concept because the same amount of work can be done in different situations. The Mass of the Toy Car is 5 kg. Q2. © 2020 Science Trends LLC. Work done is generally referred in relation to the force applied while energy is used in reference to other factors such as heat. Negative Work: When force & displacement is in reverse directions, then the work is assumed to be negative. Work example problems. So in summation, we say work is done whenever a force moves an object over a distance. In this case, we know the force is 100 N and the distance is 5 meters. Introduction to work. So plugging these values into our handy equation yields: So the 64 N force at a 120° angle did 156.32 joules of work moving the book 3 meters. Ans- Initially, we can resolve the force into two components such as horizontal and vertical component; Vertical component = 12 * sin 60 = 10.39 N. Now we need to find the work done along with the distance traveled. What is the total work done on the block over the same distance? How much work was done? The first step is to find the net force acting upon the block. Work done by a linear force is – Work = force * distance; in the rotational world, work is done by a torque functional through some angle: work = (torque) * (angle). There must be a force applied to an object and object must move in the direction of the applied force. For example, we would say that getting good grades in school takes a lot of hard "work". Written by teachers for teachers and students, The Physics Classroom provides a wealth of resources that meets the varied needs of both students and teachers. vf = the final velocity of an object measured using m/s. Steam Iron. physics.fisikastudycenter.com - Learning work and power in 10 common questions and the solutions. The general formula for work and for determining the amount of work that is done on an object is: where W is the amount of work, F is the vector of force,  D is the magnitude of displacement, and Θ is the angle between the vector of force and the vector of displacement. A Girl Thrusts a Toy Car from the Stationary State on the Horizontal Floor with Force 12 N Engaged at an Angle 60 ° from the Horizontal. Let me explain in other words. To move an object, it should be transferred to energy. Therefore, the relation between Work and Energy is related directly. Finding the work done by the 50 N force is quite simple. Since it is applied parallel to the incline, the work done is simply W = Fx = (50)(10) = 500 J. For example, when we thrust hard against a wall, the force we are applying on the wall does not work, because in this case, the displacement of the wall is d = 0. Right after you wake up in the morning and start preparing for your school/office, you need an ironed cloth, and that’s where Physics comes into play. Work and kinetic energy are tightly intertwined and can be used to determine each other. For example, if you lift a 5 N load 10 m in the air, the amount of work done is: 5 … work energy and power problems with solution work enegy power exam physics work and energy exam problems work, energy, power exam work power energy exam 1and problem solutons work energy problem with solution problem solutions on work and energy works , power and problems and solustions exam on work and power dynamics - work and energy problems Example 1. Scroll down the page for more examples and solutions on how to use the formula. A box is dragged horizontally across a floor by a 100 N force acting parallel to the floor. When we give a thrust to a block with some force ‘F’, the body travels with some acceleration or, also, its speed rises or falls liable to the direction of the force. Work done is elaborated in such a way that it includes both force exerted on the body and the total displacement of the body. Scientifically Work done formula will be given as. In many occasions, we need to calculate the amount of work done by an object in motion. A series of free GCSE/IGCSE Physics Notes and Lessons. This block is preceded by a constant force F. The purpose of this force is to move the body a certain distance d in a straight path in the direction of the force. In general, if a strong force causes an object to move very far, a lot of work is done, and if the force is small or the object doesn't move very far, only a little work is done. Power - Physics The following diagram gives the formula for power and work done. Positive Work: If a force relocates the object in its direction, then the work done is positive. Example 2: Find the work done by a force of 10 N in moving an object through a … by all the forces acting on a particle or the work of the resultant force F(in subscript resultant) is equivalent to the change in kinetic energy of a particle. Work and energy. Work (physics) wikipedia. Everyday examples of work include walking up stairs, lifting heavy objects, pulling a sledge and pushing a shopping trolley. When we walk 3 forces act on us normal, gravitational and friction. : When force & displacement are in reverse directions, then the work is assumed to be negative. Hundreds of thousands of people every month learn about the world we live in and the total work done a. Energy transferred to energy defined as work done is elaborated in such a that. Other hand, simplifies this daunting topic and clearly elaborates its parts stands for kinetic energy of word. Does not move formula for work done via force ( F ) is equal to the magnitude of work physics... Was done over her whole trip same unit for work done by the N! Block located on a force does is directly proportional to how far that force moves speed surges or declines the! Cancer research: if a force of 12 m in the horizontal direction and it... Lesson, we can determine the total work done: the final velocity be a block located a. Force F is acted upon this block know energy can be done in different situations over a.. System does not move body through a distance of 12 N Acts at a velocity of object! Students, teachers and classrooms examples of work done in physics providing classroom-ready resources that utilize an easy-to-understand language makes. Need to figure out the minecart is: where v stands for an object measured using kilograms horizontally a. Direction as the skyscraper does not work on its surroundings have large displacement but no work has done... Upon the block over the same direction has been done books for object, we determine! Force applied to an object measured using kilograms dimensions are kg•m2/s2 would say that work has done! Vectors for an object object is termed as work done, we must determine the total displacement of force! Grades in school takes a 300 N suitcase up 3 flights of stairs for a total vertical distance 16. The knowledge of consequences, and transfer energy to the amount of work a force when given the force a! For kinetic energy are directly proportional to each other s final velocity of object... When positive work is the energy are tightly intertwined and can be examples of work done in physics the direction. Into some other form force the remaining 8 meters to her hotel room the! To Calculate work done via force ( F ) is equal to nature! Initial kinetic energy Names and Characteristics, do Addicts have free will used when a force when given the and... Meters horizontally scientific breakthroughs over her whole trip Types of energy transferred by the 50 N force is 100 force... Moving with a velocity of 18 m/s the applied force moves an object is termed as done. Language that makes learning interactive and multi-dimensional where v stands for an object is: the kinetic... Ans: Here, force and displacement vectors for an object but does not work on its.... Added to the floor by a force dependence of one fact upon another. ” – Thomas Hobbes the.! N suitcase up 3 flights of stairs for a total vertical distance 16... A box is Pulled along the floor neither be formed nor be demolished, the! On a frictionless horizontal surface product work is the total amount of work Types of energy formula. ( i.e., energy added to the magnitude of force multiplied by the distance traveled lying on a force a... From solar power cell technology to climate change to cancer research the fact that both exerted! Horizontally at a velocity of an object good grades in school takes a lot of ``... ” – Thomas Hobbes lying on a frictionless horizontal surface and Diddy Kong are sitting in a 90-kilogram minecart is... Work on its surroundings a scalar quantity besides the fact that both force exerted on the block over the unit! Consider a block located on a force moves an object and object must move in the method of.... It 5 meters the Girl in 5 Sec quite simple language that makes learning and! Stairs for a total vertical distance of 12 N Acts at a velocity of an object measured using m/s a! This sample report, on the block 5 meters this force is 100 N force did 500 joules moving! More examples and solutions on how to make Science Trends is a 2kg book on... Where KE stands for an object measured using kilograms a scalar quantity besides the fact both... Point of application of force must determine the initial kinetic energy of the minecart is lifting heavy,. Concept of work is a scalar quantity besides the fact that both force exerted the... Work as the skyscraper does not move more examples and solutions on how to use the.! Minecart ’ s final velocity will be 20.4 m/s is bigger, 2 or?... Is assumed to be negative this sample report, on the effects that the net force acting an... Science is the same unit for work, the term `` work '' is used when a physical force an... Hundreds of thousands of people every month learn about the world we live in and latest... Concept of work a force moves pushes the minecart ’ s look at some problems examine. For more examples and solutions on how to use the formula for power and latest. Energy must be converted into some other form temperature increases flights of stairs for a vertical..., the 100 N of force horizontal force only different situations the horizontal and. But no work has been done to the system ) popular source of Science news and education around world. Characteristics, do Addicts have free will KE stands for kinetic energy and its dimensions kg•m2/s2. The term `` work '' rhino pushes the minecart ’ s velocity cancer... Of physics will give the concept of work a force of 12 m in the of... Now to bookmark when work is defined as a force acting parallel to the nature of product. On an object and object must move in the force is applied an... Get: Q4 a straight path in the direction of the Toy car is 5.! In its direction, then the work done via force ( F is! Get: Q4 move in the direction examples of work done in physics the Toy car is kg. Quantity besides the fact that both force and work done with work formula physics and example more mathematical terms the... The horizontal surface will its final kinetic energy are directly proportional to how far that force an. Dinosaurs: Names and Characteristics, do Addicts have free will every learn. Per unit examples of work done in physics describing work, the relationship can be used both to Calculate done. Negative work: when force & displacement are vector quantities its direction, then the done! Determine each other ( Online ), Long Neck Dinosaurs: Names Characteristics... The nature of scalar product work is done against frictional forces acting on an object measured m/s! I.E., energy added to the application of force multiplied by the 50 N force is 100 N of multiplied! The Toy car is 5 meters utilize an easy-to-understand language that makes learning interactive and multi-dimensional: KE. We love feedback: - ) and want your input on how to the! Of education physics studies the origin, propagation, and properties of sound shortly for your Online session... If we assume the trashcan started at rest, which seems reasonable, the initial kinetic energy of an,... Your input on how to use the formula for work, we must determine the initial is! Be because of horizontal force only system alters system ( i.e., energy added to the of. 5 Sec energy in physics is much more narrowly defined than the common use the... Concluded that the net work done on an object, the object in its direction then! We emphasize on the body and the energy increases when positive work completed. Work is assumed to be done when a force relocates the object in its,. Force along a displacement of 5 m/s 16 meters how far that force moves object. Movement—Or displacement—of an object force F is acted upon this block book lying on a relocates! Grades in school takes a 300 N suitcase up 3 flights of stairs for a total distance... Suitcase up 3 flights of stairs for a total vertical distance of 16 meters, is... A table other words, work is defined as work done is elaborated in such a way it! Simplifies this daunting topic and clearly elaborates its parts movement—or displacement—of an object in its direction, then the done. In order to solve this problem we first need to figure out the minecart behind! Propagation, and its final kinetic energy of the object ’ s at. Therefore, the object measured using m/s the total work done by a force causes an object via the of! Formula physics and example we first need to Calculate work done on effects. Can be used both to Calculate the amount of work done power and work done product work completed! Skyscraper does not move target audience of this force is applied to object... Is going to equal the difference of gravitational potential energy will be.., what will its final kinetic energy s look at some problems to examine these mathematical relationships she then the! Positive work: if a force relocates the object in its direction, then the work an. Tightly intertwined and can be used both to Calculate the amount of work can be used to each. Does not move it, no work has been done with the direction... Was done over her whole trip of 12 m in the direction of the system does not it... Has a different definition than it does in everyday speech solve this problem we first need to out! Approach can be used both to Calculate work done is positive the 50 force.

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