Physics
Work Done
Work done is a measure of the energy transferred when a force acts on an object and causes it to move. It is calculated by multiplying the force applied by the distance over which the force is exerted. In physics, work done is a crucial concept for understanding the transfer and transformation of energy in various systems.
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12 Key excerpts on "Work Done"
- David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Similarly, if you decelerate the object to a lesser speed by applying a force, you decrease the kinetic energy of the object. We account for these changes in kinetic energy by saying that your force has transferred energy to the object from yourself or from the object to yourself. In such a transfer of energy via a force, work W is said to be done on the object by the force. More formally, we define work as follows. Work W is energy transferred to or from an object by means of a force acting on the object. Energy transferred to the object is positive work, and energy transferred from the object is negative work. ‘Work’, then, is transferred energy; ‘doing work’ is the act of transferring the energy. Work has the same units as energy (the SI unit is joule) and is a scalar quantity (it has no associated direction). The term transfer can be misleading. It does not mean that anything material flows into or out of the object; that is, the transfer is not like a flow of water. Rather, it is like the electronic transfer of money between two bank accounts: the number in one account goes up while the number in the other account goes down, with nothing material passing between the two accounts. Note that we are not concerned here with the common meaning of the word ‘work’, which implies that any physical or mental labour is work. For example, if you push hard against a wall, you tire because of the continuously repeated muscle contractions that are required, and you are, in the common sense, working. However, such effort does not cause an energy transfer to or from the wall and thus is not Work Done on the wall as defined here. To avoid confusion in this chapter, we shall use the symbol W only for work and shall represent a weight with its equivalent mg. Work and kinetic energy Calculating work with the force component along the displacement FIGURE 7.1 A constant force F directed at angle to the displacement d of a bead on a wire accelerates the bead along the wire.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Energy transferred to the object is positive work, and from the object, negative work. ● The Work Done on a particle by a constant force F → during displacement d → is W = Fd cos ϕ = F → · d → (work, constant force), in which ϕ is the constant angle between the directions of F → and d → . ● Only the component of F → that is along the displace- ment d → can do work on the object. ● When two or more forces act on an object, their net work is the sum of the individual works done by the forces, which is also equal to the work that would be done on the object by the net force F → net of those forces. ● For a particle, a change ΔK in the kinetic energy equals the net work W done on the particle: ΔK = K f − K i = W (work – kinetic energy theorem), in which K i is the initial kinetic energy of the particle and K f is the kinetic energy after the work is done. The equa- tion rearranged gives us K f = K i + W. Learning Objectives Key Ideas “Work,” then, is transferred energy; “doing work” is the act of transferring the energy. Work has the same units as energy and is a scalar quantity. The term transfer can be misleading. It does not mean that anything mate- rial flows into or out of the object; that is, the transfer is not like a flow of water. Rather, it is like the electronic transfer of money between two bank accounts: The number in one account goes up while the number in the other account goes down, with nothing material passing between the two accounts. Note that we are not concerned here with the common meaning of the word “work,” which implies that any physical or mental labor is work. For example, if you push hard against a wall, you tire because of the continuously repeated muscle contractions that are required, and you are, in the common sense, work- ing. However, such effort does not cause an energy transfer to or from the wall and thus is not Work Done on the wall as defined here.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
* In such a case, the work W is defined as the magnitude F of the force times the magnitude s of the displacement: W = Fs. The Work Done to push a car is the same whether the car is moved north to south or east to west, provided that the amount of force used and the distance moved are the same. Since work does not convey directional information, it is a scalar quantity. FIGURE 6.1 Work is done when a force F pushes a car through a displacement s. F F s The equation W = Fs indicates that the unit of work is the unit of force times the unit of distance, or the newton ⋅ metre in SI units. One newton ⋅ metre is referred to as a joule (J) (rhymes with ‘cool’), in honour of James Joule (1818–1889) and his research into the nature of work, energy, and heat. Table 6.1 summarises the units for work in several systems of measurement. TABLE 6.1 Units of measurement for work System Force × Distance = Work SI newton (N) metre (m) joule (J) CGS dyne (dyn) centimetre (cm) erg BE pound (lb) foot (ft) foot ⋅ pound (ft ⋅ lb) The definition of work as W = Fs does have one surprising feature: If the distance s is zero, the work is zero, even if a force is applied. Pushing on an immovable object, such as a brick wall, may tire your muscles, but there is no Work Done of the type we are discussing. In physics, the idea of work is intimately tied up with the idea of motion. If the object does not move, the force acting on the object does no work. Often, the force and displacement do not point in the same direction. For instance, figure 6.2a shows a suitcase‐on‐wheels being pulled to the right by a force that is applied along the handle. The force is directed at an angle relative to the displacement. In such a case, only the component of the force along the displacement is used in defining work. As figure 6.2b shows, this component is F cos , and it appears in the general definition below.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
3. Only the component of F → that is along the displacement d → can do work on the object. 4. When two or more forces act on an object, their net work is the sum of the individual works done by the forces, which is also equal to the work that would be done on the object by the net force F → net of those forces. 5. For a particle, a change ΔK in the kinetic energy equals the net work W done on the particle: ΔK = K f − K i = W (work–kinetic energy theorem), in which K i is the initial kinetic energy of the particle and K f is the kinetic energy after the work is done. The equation rearranged gives us K f = K i + W. LEARNING OBJECTIVES 7.2 Work and Kinetic Energy 149 Work If you accelerate an object to a greater speed by applying a force to the object, you increase the kinetic energy K (= 1 _ 2 mv 2 ) of the object. Similarly, if you decelerate the object to a lesser speed by applying a force, you decrease the kinetic energy of the object. We account for these changes in kinetic energy by saying that your force has transferred energy to the object from yourself or from the object to yourself. In such a transfer of energy via a force, work W is said to be done on the object by the force. More formally, we define work as follows: Work W is energy transferred to or from an object by means of a force acting on the object. Energy transferred to the object is positive work, and energy trans- ferred from the object is negative work. “Work,” then, is transferred energy; “doing work” is the act of transferring the energy. Work has the same units as energy and is a scalar quantity. The term transfer can be misleading. It does not mean that anything material flows into or out of the object; that is, the transfer is not like a flow of water. Rather, it is like the electronic transfer of money between two bank accounts: The number in one account goes up while the number in the other account goes down, with nothing material passing between the two accounts.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
6.1 Work Done by a Constant Force 159 as the magnitude F of the force times the magnitude s of the displacement: W = Fs. The Work Done to push a car is the same whether the car is moved north to south or east to west, provided that the amount of force used and the distance moved are the same. Since work does not convey directional information, it is a scalar quantity. The equation W = Fs indicates that the unit of work is the unit of force times the unit of distance, or the newton · meter in SI units. One newton · meter is referred to as a joule (J) (rhymes with “cool”), in honor of James Joule (1818–1889) and his research into the nature of work, energy, and heat. Table6.1 summarizes the units for work in several systems of measurement. TABLE 6.1 UnitsofMeasurementforWork System Force × Distance = Work SI newton (N) meter (m) joule (J) CGS dyne (dyn) centimeter (cm) erg BE pound (lb) foot (ft) foot · pound (ft · 1b) The definition of work as W = Fs does have one surprising feature: If the distance s is zero, the work is zero, even if a force is applied. Pushing on an immovable object, such as a brick wall, may tire your muscles, but there is no Work Done of the type we are discussing. In physics, the idea of work is intimately tied up with the idea of motion. If the object does not move, the force acting on the object does no work. Often, the force and displacement do not point in the same direction. For instance, Figure6.2a shows a suitcase-on-wheels being pulled to the right by a force that is applied along the handle. The force is directed at an angle θ relative to the displacement. In such a case, only the component of the force along the displacement is used in defining work.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Since work does not convey directional information, it is a scalar quantity. The equation W = Fs indicates that the unit of work is the unit of force times the unit of distance, or the newton · meter in SI units. One newton · meter is referred to *When discussing work, it is customary to use the symbol s → for the displacement, rather than x → or y → . F F s FIGURE 6.1 Work is done when a force F → pushes a car through a displacement s → . 6.1 Work Done by a Constant Force 145 as a joule (J) (rhymes with “cool”), in honor of James Joule (1818–1889) and his research into the nature of work, energy, and heat. Table 6.1 summarizes the units for work in several systems of measurement. The definition of work as W = Fs does have one surprising feature: If the distance s is zero, the work is zero, even if a force is applied. Pushing on an immovable object, such as a brick wall, may tire your muscles, but there is no Work Done of the type we are discussing. In physics, the idea of work is intimately tied up with the idea of motion. If the object does not move, the force acting on the object does no work. Often, the force and displacement do not point in the same direction. For instance, Figure 6.2a shows a suitcase-on-wheels being pulled to the right by a force that is applied along the handle. The force is directed at an angle relative to the displacement. In such a case, only the component of the force along the displacement is used in defining work. As Figure 6.2b shows, this compo- nent is F cos , and it appears in the general definition below: DEFINITION OF Work Done BY A CONSTANT* FORCE The Work Done on an object by a constant force F → is W = ( F cos θ ) s (6.1) where F is the magnitude of the force, s is the magnitude of the displacement, and is the angle between the force and the displacement. SI Unit of Work: newton · meter = joule (J) When the force points in the same direction as the displacement, then = 0°, and Equation 6.1 reduces to W = Fs.
eBook - PDFWorkshop Physics Activity Guide Module 2
Mechanics II
- Priscilla W. Laws, David P. Jackson, Brett J. Pearson(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
c. Based on your answers above, try to make a guess as to how one might define work mathematically in this situation. Most people feel that the effort required to push something along the table depends on both the amount of force required to push the object and the distance the object moves. For such a motion, it would be reasonable to guess that the Work Done is the product of these two factors: “force times distance.” It turns out that this guess is essentially correct for this situation, although as we’ll see, there are a few subtleties to consider. Defining and Calculating Work in Simple Situations Although related, the definition of work in physics does not correspond directly to effort. We begin by looking at a very simple situation and thinking of work simply as force times distance. We will then see how such a definition is lacking. 10.2.3. Activity: A First Look at Defining Work a. Consider pushing a low-friction cart along a track (as we have done many times). Specifically, assume the cart begins at rest and you push it in the positive x-direction with a constant force of 5 N over a distance of 0.5 m and then release it. Describe what happens to the cart in this situation. How do the direction of force and the direction of the cart’s UNIT 10: WORK AND ENERGY 317 motion compare to each other? According to our simple definition of work (force times distance), how much work have you done? b. Now imagine the same cart is (still) moving in the positive x-direction and you push on it in the negative x-direction with a constant force of 5 N for a distance of 0.5 m. Describe what happens to the cart in this new situation. How do the direction of force and the direction of the cart’s motion compare to each other? According to our simple definition, how much work have you done this time? It should be clear that the physical response of the cart is quite different in these two situations, speeding up in the first case and slowing down in the second.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Since work does not convey directional information, it is a scalar quantity. The equation W 5 Fs indicates that the unit of work is the unit of force times the unit of distance, or the newton ? meter in SI units. One newton ? meter is referred to as a joule (J) (rhymes with “cool”), in honor of James Joule (1818–1889) and his research into the na- ture of work, energy, and heat. Table 6.1 (see next page) summarizes the units for work in several systems of measurement. The definition of work as W 5 Fs does have one surprising feature: If the distance s is zero, the work is zero, even if a force is applied. Pushing on an immovable object, such as a brick wall, may tire your muscles, but there is no Work Done of the type we are discussing. In physics, the idea of work is intimately tied up with the idea of motion. If the object does not move, the force acting on the object does no work. Often, the force and displacement do not point in the same direction. For instance, Figure 6.2a shows a suitcase-on-wheels being pulled to the right by a force that is applied along the handle. The force is directed at an angle u relative to the displacement. In such a case, only the component of the force along the displacement is used in defining work. *When discussing work, it is customary to use the symbol s B for the displacement, rather than x B or y B . F F s B B Figure 6.1 Work is done when a force F B pushes a car through a displacement s B . 142 © Oleksiy Maksymenko Photography/Alamy 6.1 | Work Done by a Constant Force 143 As Figure 6.2b shows, this component is F cos u, and it appears in the general definition below: Definition of Work Done by a Constant* Force The Work Done on an object by a constant force F B is W 5 (F cos u)s (6.1) where F is the magnitude of the force, s is the magnitude of the displacement, and u is the angle between the force and the displacement.
eBook - PDFEngineering Mechanics
Problems and Solutions
- Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel(Authors)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
13.1 Introduction In this chapter we will study two principles, i.e., the work and energy principle and the principle of conservation of energy. Earlier, we have used D’ Alembert’s principle to analyse the kinetic problems. The work and energy principle is another alternative method to analyse the kinetic problems. The basic difference in its application is that the work and energy principle is preferred when problems deal especially with velocity. However D’ Alembert’s principle is preferred when problems deal with acceleration. 13.2 Work Done by a Force Work is done by a force when a force displaces a particle by some displacement in its direction. It is a scalar quantity. Consider a particle of mass ‘m’ kg lying on a smooth horizontal surface as shown in Fig. 13.1. If the particle is pushed by a constant force ‘p’ by displacement ‘ d ’ then the Work Done is given by W = p × d Chapter 13 Work and Energy P P m P mg mg N N d Fig. 13.1 592 Engineering Mechanics However, if the particle is pushed for displacement ‘d’ by a constant force ‘p’ applied at an angle ‘α’ from the horizontal surface as shown in Fig. 13.2, the Work Done is given by W = Force in the direction of displacement × d W = p cos α × d If α = 0° then it belongs to the earlier case as discussed. If α = 90° then it shows that Work Done will be equal to zero as force is not causing displacement. For example consider Fig. 13.2, where normal reaction ‘N’ of mass ‘m’ is not producing displacement due to which Work Done by normal reaction will be zero. Work Done will be negative if force and displacement are opposite in direction. For example Work Done by frictional force is always negative. It is to be noted that force and displacement both are vector quantities but work is a scalar quantity. The unit of work is Nm or Joule in S.I. unit. 13.3 Work Done by a Variable Force Consider a particle displaced by variable force as shown in Fig. 13.3. P m P sin α mg mg N N d α P α P cos α P cos α P sin α Fig.
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
142 Work and Energy 6 A new kind of farming—wind farming—is gaining popularity as the world turns to renew- able energy sources, due to heightened concerns over the environmental impact and the availability of nonrenewable sources. These wind turbines, part of the Thorntonbank off- shore wind farm located about 28 km off the Belgian coast, will eventually have an energy- producing capacity of 300 megawatts—enough to supply about 150,000 homes with their electricity needs. The concepts of energy, work, and power are explored in detail here in Chapter 6. v.schlichting/Shutterstock Work Done by a Constant Force | 143 6.1 Calculate the Work Done by a constant force. When someone is doing work, it usually means that they are engaged in an activity involving a mental or physical labor for the purpose of achieving a result. In physics, forces do work, and work has a very specific meaning that differs from its everyday meaning. To understand the physics definition of work, consider the situation in Animated Figure 6.1.1, where two identical blocks are initially at rest on a horizontal, frictionless surface and are acted upon by a force F . They are prevented from moving by stops. When the animation is run, the stops disappear and the blocks begin to move. Start the animation and watch carefully. 6.1 Work Done BY A CONSTANT FORCE Learning Objective The force F is horizontal in part (a), while it is directed at an angle θ above the horizontal in part (b). The forces act as each block is moved through the same displacement r Δ , as shown. Each force does work on the block as it moves. In the animation, the forces have the same magnitude, but less work is performed in part (b) than in part (a).
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Since work does not convey directional information, it is a scalar quantity. The equation W 5 Fs indicates that the unit of work is the unit of force times the unit of distance, or the newton ? meter in SI units. One newton ? meter is referred to as a joule (J) (rhymes with “cool”), in honor of James Joule (1818–1889) and his research into the na- ture of work, energy, and heat. Table 6.1 (see next page) summarizes the units for work in several systems of measurement. The definition of work as W 5 Fs does have one surprising feature: If the distance s is zero, the work is zero, even if a force is applied. Pushing on an immovable object, such as a brick wall, may tire your muscles, but there is no Work Done of the type we are discussing. In physics, the idea of work is intimately tied up with the idea of motion. If the object does not move, the force acting on the object does no work. Often, the force and displacement do not point in the same direction. For instance, Figure 6.2a shows a suitcase-on-wheels being pulled to the right by a force that is applied along the handle. The force is directed at an angle u relative to the displacement. In such a case, only the component of the force along the displacement is used in defining work. *When discussing work, it is customary to use the symbol s B for the displacement, rather than x B or y B . F F s B B Figure 6.1 Work is done when a force F B pushes a car through a displacement s B . 126 © Oleksiy Maksymenko Photography/Alamy 6.1 | Work Done by a Constant Force 127 As Figure 6.2b shows, this component is F cos u, and it appears in the general definition below: Definition of Work Done by a Constant* Force The Work Done on an object by a constant force F B is W 5 (F cos u)s (6.1) where F is the magnitude of the force, s is the magnitude of the displacement, and u is the angle between the force and the displacement.
eBook - PDF- Robert Resnick, David Halliday, Kenneth S. Krane(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
In this chapter we study the relationship between work and one particular type of energy — the energy of motion of a body, which we call kinetic energy. 11- 2 Work Done BY A CONSTANT FORCE Figure 11-2a shows a block of mass m being lifted through a vertical distance h by a winch that is turned by a motor. The block is raised at a constant velocity; since its acceleration is equal to zero, the net force acting on it is, by Newton’s sec- ond law, also equal to zero. The magnitude of the upward force exerted by the motor and winch must thus equal the magnitude of the downward force m due to gravity. In Fig. 11-2 b, a conveyor belt is operated by a motor to move an identical block a distance L up an incline that makes an angle with the horizontal. If the block moves at a constant velocity, the net force is again zero, and so the magnitude of the force up the incline exerted by the belt must equal the component of the weight mg sin that acts down the incline. In both cases, the final result is the same — the block has been raised a distance h. If we release the block and al- F B g B T B low it to fall, it will reach the ground with a certain speed v. We could use the falling block to accomplish some objec- tive, such as driving a spike into the ground or launching a projectile from a catapult. The outcome would be the same, no matter how the block was originally raised. Once the block has been raised, we can turn the two motors off and the block will remain in place. That is, it costs some fuel or electrical power to run the motors only to lift the block, not to hold it in place. The investment in this process is in the lifting, not in the holding. We define the work W done by a constant force that moves a body through a displacement in the direction of the force as the product of the magnitudes of the force and the displacement: (constant force, (11-1) In Fig. 11-2 a the motor exerts a force of magnitude T mg in moving the block a distance h.
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