Physics
Force Energy
Force energy refers to the energy associated with an object's motion or position, which can result in the application of force to another object. It is a form of potential energy that is converted into kinetic energy when an object is in motion. In physics, force energy is a fundamental concept used to explain the behavior of objects in motion and at rest.
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9 Key excerpts on "Force Energy"
eBook - PDF- Richard C. Hill, Kirstie Plantenberg(Authors)
- 2013(Publication Date)
- SDC Publications(Publisher)
However, if we realize that the crate is in equilibrium, we know that the amount of work being put into the system has to equal the amount of work being taken out of the system. 1810.5 fk F U lb-ft Conceptual Dynamics Kinetics: Chapter 7 – Particle Work and Energy 7 - 16 7.2) KINETIC ENERGY 7.2.1) ENERGY Energy is defined as the capacity for doing work. It is, therefore, a scalar that has the same units as work and is directly related to work. Specifically, if a particle does work, its energy decreases by the amount of work it has performed. Conversely, if work is done on the particle, then its energy increases. Consider a block on the smooth level ground shown in Figure 7.2-1. Force P does positive work and increases the energy of the block by increasing its speed. This specific type of energy, the energy of motion, is referred to as kinetic energy. Energy is the capacity for doing work. Example 7.2-1 Consider a block being pushed along a smooth surface as shown in Figure 7.2-1. Answer the following questions. 1. The applied force P pushes the block causing the block to move, therefore, the force does work on the block. What is the work done by force P if the block travels through a distance of x? 2. The work done by the force on the block gets converted to ___________________. Conceptual Dynamics Kinetics: Chapter 7 – Particle Work and Energy 7 - 17 Example 7.2-1 continued 3. Using Newton’s second law (the equation of motion), determine the acceleration of the block. 4. Using the kinematic relationship adx vdv , determine the work done by force P on the block. 7.2.2) KINETIC ENERGY Kinetic energy is the energy due to an object’s motion. If a body has mass and is moving, then it has kinetic energy. The body's motion can be used to perform work. If a body is at rest, then it has no kinetic energy. The mathematical definition of kinetic energy is given by Equation 7.2-1.
eBook - PDF- Robert Resnick, David Halliday, Kenneth S. Krane(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
F B CHAPTER 11 CHAPTER 11 ENERGY 1: WORK AND KINETIC ENERGY W e have seen how Newton’s laws are useful in un- derstanding and analyzing a wide variety of problems in mechanics. In this and the following two chapters we consider a different approach based on one of the truly fundamental and universal concepts in physics: energy. There are many kinds of energy. In this chapter we consider one particular form — kinetic energy, the energy associated with a body because of its motion. We also introduce the concept of work, which is re- lated to kinetic energy through the work – energy theorem. This theorem, derived from Newton’s laws, pro- vides new and different insight into the behavior of mechanical systems. In Chapter 12 we introduce a sec- ond kind of energy — potential energy — and begin developing a conservation law for energy. In Chapter 13 we discuss energy in a more comprehensive way and generalize the law of conservation of energy, which is one of the most useful laws of physics. application moves through some distance, and one way to define the energy of a system is a measure of its capacity to do work. In the case of the wheelchair rider, he does work because he exerts a force as the wheelchair moves forward through some distance. For him to do work, he must ex- pend some of his supply of energy — that is, the chemical energy stored in his muscle fibers — which can be replen- ished from his body’s store of energy through resting and which ultimately comes from the food he eats. The energy stored in a system may take many forms: for example, chemical, electrical, gravitational, or mechanical. 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.
eBook - PDF- Stephen Lee(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
● The kinetic energy of a moving object 1 2 mass ( speed ) 2 . Potential energy is the energy which a body possesses because of its position. It may be thought of as stored energy which can be converted into kinetic or other forms of energy. You will meet this again on page 208. The energy of an object is usually changed when it is acted on by a force. When a force is applied to an object which moves in the direction of its line of action, the force is said to do work. For a constant force this is defined as follows. ● The work done by a constant force force distance moved in the direction of the force . The following examples illustrate how to use these ideas. A brick, initially at rest, is raised by a force averaging 40 N to a height 5 m above the ground where it is left stationary. How much work is done by the force? S OLUTION The work done by the force raising the brick is 40 5 200 J. Figure 9.1 Examples 9.2 and 9.3 show how the work done by a force can be related to the change in kinetic energy of an object. A train travelling on level ground is subject to a resisting force (from the brakes and air resistance) of 250 kN for a distance of 5 km. How much kinetic energy does the train lose? 5 m 40 N 202 AN INTRODUCTION TO MATHEMATICS FOR ENGINEERS : MECHANICS E XAMPLE 9.1 E XAMPLE 9.2 S OLUTION The forward force is 250 000 N. The work done by it is 250 000 5000 1 250 000 000 J. Hence 1 250 000 000 J of kinetic energy are gained by the train, in other words 1 250 000 000 J of kinetic energy are lost and the train slows down. This energy is converted to other forms such as heat and perhaps a little sound. A car of mass m kg is travelling at u ms 1 when the driver applies a constant driving force of F N. The ground is level and the road is straight and air resistance can be ignored. The speed of the car increases to v ms 1 in a period of t s over a distance of s m.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
force { Final KE { Initial KE This expression is the work–energy theorem. Its left side is the work W done by the net external force, whereas its right side involves the difference between two terms, each of which has the form 1 2 (mass)(speed) 2 . The quantity 1 2 (mass)(speed) 2 is called kinetic energy (KE) and plays a significant role in physics, as we will see in this chapter and later on in other chapters as well. DEFINITION OF KINETIC ENERGY The kinetic energy KE of an object with mass m and speed υ is given by KE = 1 2 mυ 2 (6.2) SI Unit of Kinetic Energy: joule (J) The SI unit of kinetic energy is the same as the unit for work, the joule. Kinetic energy, like work, is a scalar quantity. These are not surprising observations, because work and kinetic energy are closely related, as is clear from the following statement of the work–energy theorem. THE WORK–ENERGY THEOREM When a net external force does work W on an object, the kinetic energy of the object changes from its initial value of KE 0 to a final value of KE f , the difference between the two values being equal to the work: W = KE f − KE 0 = 1 2 mυ f 2 − 1 2 mυ 0 2 (6.3) } s v 0 v f Final kinetic energy = m f 2 _ 1 2 1 2 Initial kinetic energy = m 0 2 _ ΣF ΣF υ υ INTERACTIVE FIGURE 6.5 A constant net external force Σ F → acts over a displacement s → and does work on the plane. As a result of the work done, the plane’s kinetic energy changes. *For extra emphasis, the final speed is now represented by the symbol υ f , rather than υ. 6.2 The Work–Energy Theorem and Kinetic Energy 149 The work–energy theorem may be derived for any direction of the force relative to the displace- ment, not just the situation in Interactive Figure 6.5. In fact, the force may even vary from point to point along a path that is curved rather than straight, and the theorem remains valid.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
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 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. 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 Finding an Expression for Work Let us find an expression for work by considering a bead that can slide along a frictionless wire that is stretched along a horizontal x axis (Fig. 7.2.1). A con- stant force F → , directed at an angle ϕ to the wire, accelerates the bead along the wire. We can relate the force and the acceleration with Newton’s second law, written for components along the x axis: F x = ma x , (7.2.1) where m is the bead’s mass. As the bead moves through a displacement d → , the force changes the bead’s velocity from an initial value v → 0 to some other value v → .
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
Mechanical energy is the energy associated with the motion or position of macroscopic objects. On the other hand, the energy of the random motions of the atoms that make up these objects is called thermal energy, the energy stored in molecular bonds is called chemical energy, and the energy carried by light waves is called electromagnetic energy. One of the most important laws of physics is the law of conservation of energy. It states that the total amount of energy in the universe cannot change. If we measured the total energy of the universe today and then again in a month, a year, or a million years from now, we would find that the total energy has not changed. Here in Section 6.5 we investigate a special case of the law of conserva- tion of energy called the principle of the conservation of mechanical energy. Recall the work–energy theorem (Equation 6.2.1), W net = ΔK, which states that the net work done on an object W net is equal to the change in the object’s kinetic energy ΔK. We can distinguish between the work done by nonconservative forces W nc and the work done by conservative forces W c . The net work can now be written as the sum of the two: W nc + W c = ΔK Recall from Equation 6.4.1 that W c = −ΔU, so the work–energy theorem becomes W nc = ΔK + ΔU (6.5.1) Thus, if the work done by nonconservative forces is not zero, then the total mechanical energy changes. Example 6.5.1 illustrates the use of Equation 6.5.1. 6.5 CONSERVATION OF ENERGY Learning Objectives 164 | Chapter 6 Example 6.5.1 Calculating the Work Done by Air Resistance Jackie (mass 50.3 kg) has decided to try skydiving. In her first try, she jumps out of a plane that is moving horizontally at 43.0 m/s. After falling through a vertical drop of 513 m, she has reached “terminal velocity” and is moving straight down at a speed of 53.6 m/s.
eBook - PDFWorkshop Physics Activity Guide Module 2
Mechanics II
- Priscilla W. Laws, David P. Jackson, Brett J. Pearson(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
Name Section Date UNIT 10: WORK AND ENERGY VIAVAL TOURS / Shutterstock A roller coaster presents a challenge for using Newton’s laws of motion to predict the position of the carts as a function of time. The slope of the track is continually changing; imagine trying to figure out the net force on each cart on a moment-by-moment basis as the carts go uphill, downhill, and even upside down. As opposed to Newton’s laws, the concepts of work and energy can be used to simplify the analysis of such complex motions. We will examine these powerful new concepts in Units 10 and 11. 314 WORKSHOP PHYSICS ACTIVITY GUIDE UNIT 10: WORK AND ENERGY OBJECTIVES 1. To extend the intuitive notion of work as relating to effort into a more formal mathematical definition of physical work. 2. To learn to use the definition of physical work to calculate the work done by a constant force or a force that depends on position. 3. To introduce the concept of power as the rate at which work is done. 4. To define the concept of kinetic energy and its relationship to the net work done on a point mass as embodied in the work-energy principle. 10.1 OVERVIEW Although we have seen that momentum is generally conserved in collisions, different outcomes are still possible. For example, two carts can collide and stick together, or they can bounce off each other after the collision. Two carts can even “explode” apart if you release a compressed spring between them. In this unit we will introduce two new concepts that are useful for studying the interactions just described—work and energy. We start by considering both intuitive and mathematical definitions of the work done on objects.
eBook - PDF- David Agmon, Paul Gluck;;;(Authors)
- 2009(Publication Date)
- WSPC(Publisher)
This statement will be later generalized to a many-particle system. We saw above that kinetic energy is not an invariant. By the same token, work too depends on the frame of reference. Nevertheless, the relation between the two quantities as expressed by the work-energy theorem holds in every frame of reference. We prove the theorem for a constant force and then generalize for the variable case. Let m and V be the mass and initial velocity of the body along the x-axis, respectively, and let a constant force F act on the body along x, causing it to acquire a final velocity V f . The acceleration of the body is F/m, so that V f 2 = V 2 + 2ax = V 2 + 2Fxlm. Multiplying both sides by mil gives Chapter 6 Work and Energy 181 Fx = W=mV f 2 /2-mV i 2 /2 = E kf -E ki =AE k When the force depends on x the work is given by (6.3), so that X X W= JF(x')dx'= jmadx' 0 0 Using a = dV/dt, changing the variable of integration from x to V and integrating between the limits V x and V f , we obtain X X jy V f ( riv' Vf 1 1 W if = madx'= m dx'= m dV = mVdV =-mV f 2 mV-Exercise A bead is given an initial velocity V 0 and slides along a frictionless stiff wire lying in a horizontal plane. Discuss the forces acting on the bead and the changes in its velocity in the course of its motion in terms of work and energy concepts. Example 3 Work-energy theorem and center of mass. Two identical blocks of mass m lying on a horizontal smooth table are connected by a light string passing over 3 pulleys, as shown here in a top view. The pulley on the right is movable by another string attached to it, the other two are fixed to the table. The right hand pulley is moved a distance S by a constant force F 0 . (a) Calculate the work done by F 0 . (b) What is the kinetic energy transferred to the system? (c) By how much is the center of mass (com) of the system displaced? Solution (a) Displacement is reckoned from the point of application of the force.
eBook - PDFEngineering Mechanics
Problems and Solutions
- Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel(Authors)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
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. 13.2 dx X Y Displacement Varying force, p Fig. 13.3 Work and Energy 593 If a particle is displaced by displacement dx under variable force p then the work done will be given by δW = p dx The total work done by a variable force will be given by W d x = ∫ p i.e., area under the curve provides the work done by variable force. 13.4 Energy Energy is the capacity of a body to conduct work. In other words it is equivalent to the work. It is also a scalar quantity like work. A particle can have various types of energies like electrical energy, chemical energy, heat energy and mechanical energy. Out of these energies only mechanical energy is considered in engineering mechanics which includes mainly kinetic energy (KE) and potential energy (PE). If a particle of mass ‘ m ’ is moving with a velocity ‘ v ’ at height ‘ h ’ then the kinetic energy of the particle is given by K E mv . . = 1 2 2 and the potential energy is given by P. E. = mgh 13.5 Work–Energy Principle Consider a particle of mass ‘ m ’ kg is moving on a smooth plane surface and a pushing force ‘ F ’ changes its velocity from initial velocity v 1 to final velocity v 2 as shown in Fig. 13.4. If the particle is infinitesimally displaced by displacement ‘ ds ’ during time ‘ dt ’ then the work done by pushing force will be given by δ δ w F ds w m a ds a dv dt = = = . . . where Substituting the value of a in equation (1), δ δ δ w m dv dt ds w m ds dt dv w m v dv = = = . . . . . . ..... (1)
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