Physics
Conservative and Non Conservative Forces
Conservative forces are those that do work that is independent of the path taken, such as gravity or electrostatic forces. Non-conservative forces, on the other hand, do work that depends on the path taken, like friction or air resistance. The work done by conservative forces can be recovered, while the work done by non-conservative forces cannot.
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11 Key excerpts on "Conservative and Non Conservative Forces"
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Later, we will encounter others, such as the elastic force of a spring and the electrical force of electri- cally charged particles. With each conservative force we will associate a potential energy, as we have already done in the gravitational case (see Equation 6.5). For other conser- vative forces, however, the algebraic form of the potential energy will differ from that in Equation 6.5. Not all forces are conservative. A force is nonconservative if the work it does on an object moving between two points depends on the path of the motion between the points. The kinetic frictional force is one example of a nonconservative force. When an object slides over a surface and kinetic friction is present, the frictional force points opposite to the sliding motion and does negative work. Between any two points, greater amounts of work are done over longer paths between the points, so that the work depends on the choice of path. Thus, the kinetic frictional force is nonconservative. Air resistance is another nonconservative force. The concept of potential energy is not defined for a nonconservative force. For a closed path, the total work done by a nonconservative force is not zero as it is for a conservative force. In Figure6.14, for instance, a frictional force would oppose the motion and slow down the car. Unlike gravity, friction would do negative work on the car throughout the entire trip, on both the up and down parts of the motion. Assuming that the car makes it back to the starting point, the car would have less kinetic energy than it had originally. Table6.2 gives some examples of conservative and nonconservative forces. In normal situations, conservative forces (such as gravity) and nonconservative forces (such as friction and air resistance) act simultaneously on an object.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
For other conservative forces, however, the algebraic form of the potential energy will differ from that in Equation 6.5. Not all forces are conservative. A force is nonconservative if the work it does on an object moving between two points depends on the path of the motion between the points. The kinetic frictional force is one example of a nonconservative force. When an object slides over a surface and kinetic friction is present, the frictional force points opposite to the sliding motion and does negative work. Between any two points, greater amounts of work are done over longer paths between the points, so that the work depends on the choice of path. Thus, the kinetic frictional force is nonconservative. Air resistance is another nonconservative force. The concept of potential energy is not defined for a nonconservative force. For a closed path, the total work done by a nonconservative force is not zero as it is for a conservative force. In Figure 6.13, for instance, a frictional force would oppose the motion and slow down the car. Unlike gravity, friction would do negative work on the car throughout the entire trip, on both the up and down parts of the motion. Assuming that the car makes it back to the starting point, the car would have less kinetic energy than it had originally. Table 6.2 gives some examples of conservative and nonconservative forces. In normal situations, conservative forces (such as gravity) and nonconservative forces (such as friction and air resistance) act simultaneously on an object. Therefore, we write the Start Figure 6.13 A roller coaster track is an example of a closed path. Table 6.2 Some Conservative and Nonconservative Forces Conservative Forces Gravitational force (Ch. 4) Elastic spring force (Ch. 10) Electric force (Ch. 18, 19) Nonconservative Forces Static and kinetic frictional forces Air resistance Tension Normal force Propulsion force of a rocket
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Therefore, consistent with version 2 of the definition of a conservative force, W gravity = 0 J for a closed path. The gravitational force is our first example of a conservative force. Later, we will encounter others, such as the elastic force of a spring and the electrical force of electrically charged par- ticles. With each conservative force we will associate a potential energy, as we have already done in the gravitational case (see Equation 6.5). For other conservative forces, however, the algebraic form of the potential energy will differ from that in Equation 6.5. Not all forces are conservative. A force is nonconservative if the work it does on an object moving between two points depends on the path of the motion between the points. The kinetic frictional force is one example of a nonconservative force. When an object slides over a surface and kinetic friction is present, the frictional force points opposite to the sliding motion and does negative work. Between any two points, greater amounts of work are done over longer paths between the points, so that the work depends on the choice of path. Thus, the kinetic frictional force is nonconservative. Air resistance is another nonconservative force. The concept of poten- tial energy is not defined for a nonconservative force. For a closed path, the total work done by a nonconservative force is not zero as it is for a conservative force. In Figure 6.14, for instance, a frictional force would oppose the motion and slow down the car. Unlike gravity, friction would do negative work on the car throughout the entire trip, on both the up and down parts of the motion. Assuming that the car makes it back to the starting point, the car would have less kinetic energy than it had originally. Table 6.2 gives some examples of conservative and nonconservative forces. Start FIGURE 6.14 A roller coaster track is an example of a closed path.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Not all forces are conservative. A force is nonconservative if the work it does on an object moving between two points depends on the path of the motion between the points. The kinetic frictional force is one example of a nonconservative force. When an object slides over a surface and kinetic friction is present, the frictional force points opposite to the sliding motion and does negative work. Between any two points, greater amounts of work are done over longer paths between the points, so that the work depends on the choice of path. Thus, the kinetic frictional force is nonconservative. Air resistance is another nonconservative force. The concept of potential energy is not defined for a nonconservative force. For a closed path, the total work done by a nonconservative force is not zero as it is for a conservative force. In Figure 6.14, for instance, a frictional force would oppose the motion and slow down the car. Unlike gravity, friction would do negative work on the car throughout the entire trip, on both the up and down parts of the motion. Assuming that the car makes it back to the starting point, the car would have less kinetic energy than it had originally. Table 6.2 gives some examples of conservative and nonconservative forces. In normal situations, conservative forces (such as gravity) and nonconservative forces (such as friction and air resistance) act simultaneously on an object. Therefore, we write the work W done by the net external force as W 5 W c 1 W nc , where W c is the work done by the conservative forces and W nc is the work done by the nonconservative forces. According to the work–energy theorem, the work done by the net external force is equal to the change in the object’s kinetic energy, or W c 1 W nc 5 1 2 mv f 2 2 1 2 mv 0 2 .
eBook - PDF- Raymond Serway, Chris Vuille(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
This observation motivates the following definition of a conservative force: A force is conservative if the work it does moving an object between two points is the same no matter what path is taken. Nonconservative forces, as we’ve seen, don’t have this property. The work–energy theorem, Equation 5.7, can be rewritten in terms of the work done by conservative forces W c c and the work done by nonconservative forces c and the work done by nonconservative forces c W nc nc because the net work is because the net work is just the sum of these two: W nc nc 1 W c c 5 D KE [5.8] It turns out that conservative forces have another useful property: The work they do can be recast as something called potential energy, a quantity that depends only on the beginning and end points of a curve, not the path taken. 5.3 Gravitational Potential Energy An object with kinetic energy (energy of motion) can do work on another object, just like a moving hammer can drive a nail into a wall. A brick on a high shelf can also do work: it can fall off the shelf, accelerate downward, and hit a nail squarely, driving it into the floorboards. The brick is said to have potential energy associated y associated y with it, because from its location on the shelf it can potentially do work. Potential energy is a property of a system, rather than of a single object, because it’s due to the relative positions of interacting objects in the system, such as the position of the diver in Figure 5.11 relative to the Earth. In this topic we define a system as a collection of objects interacting via forces or other processes that are internal to the system. It turns out that potential energy is another way of looking at the work done by conservative forces. b Conservative force Figure 5.11 Because the gravity field is conservative, the diver regains as kinetic energy the work she did against gravity in climbing the ladder. Taking the frictionless slide gives the same result.
eBook - PDF- Robert Resnick, David Halliday, Kenneth S. Krane(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
If this total work is zero, we call the force a conservative force. If the total work for the round trip is not zero, we call the force a nonconser- vative force. The elastic restoring force (spring force) and gravity are two examples of conservative forces. Friction is an example of a nonconservative force. A second way to identify a force as conservative or non- conservative is based on a comparison of the work done when the object on which the force acts moves from one lo- cation to another by several different paths. For example, suppose you are moving packages of mass m from the base- ment to the first floor in a building that has several floors, each of height h. If you move a package directly from the basement to the first floor, the (conservative) gravitational force acting on the package does work W g mgh. If in- stead you first move it to the fifth floor (W g 5mgh) and then return it to the first floor (W g 4mgh), the total work done by gravity for the entire process is W g mgh, exactly the same as if you had carried the package directly. No matter how many intermediate stopping points or how many times you go back and forth over the same path, when you finally deliver the package to the first floor, the total work done by gravity between the original location of the package (the basement) and its final location (the first floor) will be mgh. On the other hand, consider the behavior of the noncon- servative frictional force for the system illustrated in Fig. 12-3 as the disk moves along two different paths from posi- 258 Chapter 12 / Energy 2: Potential Energy + kd 2 1 2 – kd 2 1 2 + kd 2 1 2 – kd 2 W= W= W= W= 1 2 (a) (b) (c) (d) (e) x x = 0 x = + d x = – d k m FIGURE 12-1. A block moves under the action of a spring force from (a) x d to (b) x 0, moving left, to (c) x d, to (d ) x 0, moving right, and (e) back to x d.
eBook - PDFWorkshop Physics Activity Guide Module 2
Mechanics II
- Priscilla W. Laws, David P. Jackson, Brett J. Pearson(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
2.0 m 3.0 kg 6.0 kg 11.6.2. Activity: A Completely Elastic Collision a. Determine the speed of box A at the bottom of the ramp just before it hits box B. Hint: Is mechanical energy conserved? b. Determine the velocities (x-components) of both boxes immediately after the collision. Which direction is each box traveling? c. What height does box A reach (as it travels back up the ramp) before coming momentarily to rest? 11.7 NON-CONSERVATIVE FORCES AND “LOST” ENERGY We have primarily focused our attention on situations involving only conser- vative forces. For each conservative force (such as gravity), we define a potential energy function according to ΔU g = −W g . However, such a definition is only possible when the associated force is conservative. For a non-conservative force, it turns out to be impossible to create a well-defined (i.e., single-valued) potential 372 WORKSHOP PHYSICS ACTIVITY GUIDE energy function. 10 In other words, there’s no such thing as potential energy for a non-conservative force, and therefore mechanical energy will not be conserved if such forces are present. We know that there are many situations in which mechanical energy is not conserved. For example, we have seen that sliding friction reduces kinetic energy, and there doesn’t appear to be any way of getting it back. So how do we incorporate non-conservative forces into our energy framework? Perhaps the simplest approach is to treat any non-conservative forces as external to the system. The revised work-energy principle of Eq. (11.3) can then be written as W nc = W ext net = ΔE mech (11.17) where W nc is the work done by non-conservative forces, and we have assumed that all of the conservative forces are handled by defining potential energy functions. Equation (11.17) shows that the work done by non-conservative forces on a system is equal to the change in mechanical energy of the system.
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)
Therefore, consistent with version 2 of the definition of a conservative force, W gravity = 0 J for a closed path. FIGURE 6.14 A roller coaster track is an example of a closed path. Start CHAPTER 6 Work and energy 155 The gravitational force is our first example of a conservative force. Later, we will encounter others, such as the elastic force of a spring and the electrical force of electrically charged particles. With each conservative force we will associate a potential energy, as we have already done in the gravitational case (see equation 6.5). For other conservative forces, however, the algebraic form of the potential energy will differ from that in equation 6.5. Not all forces are conservative. A force is nonconservative if the work it does on an object moving between two points depends on the path of the motion between the points. The kinetic frictional force is one example of a nonconservative force. When an object slides over a surface and kinetic friction is present, the frictional force points opposite to the sliding motion and does negative work. Between any two points, greater amounts of work are done over longer paths between the points, so that the work depends on the choice of path. Thus, the kinetic frictional force is nonconservative. Air resistance is another nonconservative force. The concept of potential energy is not defined for a nonconservative force. TABLE 6.2 Some conservative and nonconservative forces Conservative forces Gravitational force (ch. 4) Elastic spring force (ch. 10) Electric force (ch. 18, 19) Nonconservative forces Static and kinetic frictional forces Air resistance Tension Normal force Propulsion force of a rocket For a closed path, the total work done by a nonconservative force is not zero as it is for a conservative force. In figure 6.14, for instance, a frictional force would oppose the motion and slow down the car.
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
Potential energy for an ideal spring U(x) = 1 2 kx 2 + const. Work done by conservative force over a closed path W closed path = ∮ E → cons · d r → = 0 Condition for conservative force in two dimensions ⎛ ⎝ dF x dy ⎞ ⎠ = ⎛ ⎝ dF y dx ⎞ ⎠ Conservative force is the negative derivative of potential energy F l = − dU dl Conservation of energy with no non-conservative forces 0 = W nc, AB = Δ(K + U) AB = ΔE AB . SUMMARY 8.1 Potential Energy of a System • For a single-particle system, the difference of potential energy is the opposite of the work done by the forces acting on the particle as it moves from one position to another. • Since only differences of potential energy are physically meaningful, the zero of the potential energy function can be chosen at a convenient location. 386 Chapter 8 | Potential Energy and Conservation of Energy This OpenStax book is available for free at http://cnx.org/content/col12031/1.5 • The potential energies for Earth’s constant gravity, near its surface, and for a Hooke’s law force are linear and quadratic functions of position, respectively. 8.2 Conservative and Non-Conservative Forces • A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. • A non-conservative force is one for which the work done depends on the path. • For a conservative force, the infinitesimal work is an exact differential. This implies conditions on the derivatives of the force’s components. • The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction. 8.3 Conservation of Energy • A conserved quantity is a physical property that stays constant regardless of the path taken. • A form of the work-energy theorem says that the change in the mechanical energy of a particle equals the work done on it by non-conservative forces.
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
Plot velocity squared versus the distance traveled by the marble. What is the shape of each plot? If the shape is a straight line, the plot shows that the marble’s kinetic energy at the bottom is proportional to its potential energy at the release point. Figure 7.9 A marble rolls down a ruler, and its speed on the level surface is measured. 7.4 Conservative Forces and Potential Energy Potential Energy and Conservative Forces Work is done by a force, and some forces, such as weight, have special characteristics. A conservative force is one, like the gravitational force, for which work done by or against it depends only on the starting and ending points of a motion and not on the path taken. We can define a potential energy (PE) for any conservative force, just as we did for the gravitational force. For example, when you wind up a toy, an egg timer, or an old-fashioned watch, you do work against its spring and store energy in it. (We treat these springs as ideal, in that we assume there is no friction and no production of thermal energy.) This stored energy is recoverable as work, and it is useful to think of it as potential energy contained in the spring. Indeed, the reason that the spring has this characteristic is that its force is conservative. That is, a conservative force results in stored or potential energy. Gravitational potential energy is one example, as is the energy stored in a spring. We will also see how conservative forces are related to the conservation of energy. Potential Energy and Conservative Forces Potential energy is the energy a system has due to position, shape, or configuration. It is stored energy that is completely recoverable. A conservative force is one for which work done by or against it depends only on the starting and ending points of a motion and not on the path taken. We can define a potential energy (PE) for any conservative force.
- Jerry D. Wilson, Anthony J. Buffa, Bo Lou(Authors)
- 2022(Publication Date)
- CRC Press(Publisher)
Suppose an object initially has mechanical energy and that nonconservative forces do an amount of work W nc on it. Starting with the work-energy theorem, W K K K net o = = - Δ m k v ▲ FIGURE 5.21 Conservative force and the mechanical energy of a spring See Example 5.13 for description. 122 College Physics Essentials In general, the net work ( W net ) may be done by both conservative forces ( W c ) and nonconservative forces (W nc ), so W W K K c nc o + = - (5.12) But from Equation 5.10a, the work done by conservative forces is equal to W c = −ΔU = − ( U − U o ), so Equation 5.12 then becomes W K K U U K U K U nc o o o o ( ) = - + - = + - + ( ) ( ) Therefore, W E E E nc o = - = Δ (5.13) Hence, the work done by the nonconservative forces acting on a system is equal to the change in mechanical energy. Notice that for dissipative forces, E o > E. Thus, the change is negative, indi- cating a decrease in mechanical energy. This condition agrees in sign with W nc , which, for friction, would also be negative. Example 5.14 illustrates this concept. EXAMPLE 5.14: NONCONSERVATIVE FORCE – DOWNHILL RACER A skier with a mass of 80 kg starts from rest at the top of a slope and skis down from an elevation of 110 m (▶ Figure 5.23). The speed of the skier at the bottom of the slope is 20 m/s. (a) Show that the system is nonconservative. (b) How much work is done by the non- conservative force of friction? THINKING IT THROUGH. (a) If the system is nonconservative, then E o ≠ E, (actually here E < E o ), and these quantities can be computed. (b) The work cannot be determined from force-distance considerations, but W nc is equal to the difference in total energies (Equation 5.13). SOLUTION Given: m = 80 kg v o = 0 v = 20 m/s y o = 110 m Find: (a) Show that E is not conserved. (b) W nc (work done by friction) (a) If the system is conservative, the total mechanical energy is constant.
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