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Work and Energy - Detailed Help

Assignment WE7: Energy Conservation

Objectives:

The student should be able to identify the basic principles of and the conditions required for energy conservation.

The student should be able to apply the principles of energy conservation to a variety of physical situations.

Reading:

The Physics Classroom - Work, Energy and Power Unit, Lesson 2, Part b

	Some forces are categorized as conservative forces (or internal forces) while others are categorized as non-conservative forces (or external forces). Which of the following forces are generally categorized as conservative (or internal) forces?
	Definition of Conservative Force: All the different types of forces which could do work upon an object can be categorized as either conservative or non-conservative forces. A conservative force is a type of force which serves to transform an object's energy between kinetic and potential. When only conservative forces do work upon an object, the energy of the object changes forms (KE to PE or vice versa) without changing the total amount of mechanical energy.
	There are two forces commonly discussed in MOP questions which serve as conservative forces - gravity and spring. The force of gravity, when it does work, serves to change gravitational potential energy into kinetic energy or vice versa. The spring force, when it does work, serves to change elastic potential energy into kinetic energy or vice versa. All other forces are regarded as non-conservative forces which serve to change the total amount of mechanical energy.
	What types of forces are internal (i.e., conservative) and what types are external (i.e., non-conservative)?

	If the only forces doing work upon an object are conservative (or internal) forces, then the total mechanical energy of the object will ____. If the only forces doing work upon an object are non-conservative (or external) forces, then the total mechanical energy of the object will ____.
	Definition of Conservative Force: All the different types of forces which could do work upon an object can be categorized as either conservative or non-conservative forces. A conservative force is a type of force which serves to transform an object's energy between kinetic and potential. When only conservative forces do work upon an object, the energy of the object changes forms (KE to PE or vice versa) without changing the total amount of mechanical energy.
	Definition of Non-conservative Force: All the different types of forces which could do work upon an object can be categorized as either conservative or non-conservative forces. A non-conservative force is a type of force which changes the total amount of mechanical energy possessed by an object. When non-conservative forces do work upon an object, the total amount of mechanical energy changes.
	What is the relationship between the type of force doing work and whether or not mechanical energy is conserved?

	In order for an object to conserve its total mechanical energy it is absolutely necessary that ____. List all that apply ... .
	Work - Mechanical Energy Relationships: If non-conservative forces do net work upon an object, then the total mechanical energy of that object is changed. The sum of the kinetic and potential energies will change as work is done upon the object.
	Definition of Conservative Force: All the different types of forces which could do work upon an object can be categorized as either conservative or non-conservative forces. A conservative force is a type of force which serves to transform an object's energy between kinetic and potential. Definition of Non-conservative Force: All the different types of forces which could do work upon an object can be categorized as either conservative or non-conservative forces. A non-conservative force is a type of force which changes the total amount of mechanical energy possessed by an object.
	The role of conservative forces (when doing work) is to change the form of energy possessed by an object; kinetic energy is changed into potential energy or vice versa. The role of non-conservative forces (when doing work) is to change the total amount of mechanical energy possessed by an object. In order for mechanical energy to be conserved, it is essential that the total amount of work done by non-conservative forces is zero.
	What condition(s) is (are) necessary in order for the total mechanical energy of an object to be conserved? What is the relationship between the type of force doing work and whether or not mechanical energy is conserved?

	If the total mechanical energy of an object is conserved, then ____. List all that apply ... .
	Definition of Total Mechanical Energy: The total mechanical energy possessed by an object is the sum of its kinetic energy and potential energy.
	Often times an object moves in such a manner as to conserve its total mechanical energy. The kinetic energy and the potential energy may individually change, yet the sum of these two forms of energy (the total amount of mechanical energy) remains a constant value. If the sum is the same amount at every location along the object's path, then total mechanical energy is said to be conserved.
	What is meant when it is said that the total mechanical energy of an object is conserved? What is meant by total mechanical energy?

	An object starts at rest from a height of 40 meters. It's total amount of mechanical energy is 400 Joules. The object begins a free-falling motion; there is no air resistance. When it has fallen to a height of one-fourth of its original height, its potential energy will be ____ Joules and its total amount of mechanical energy will be ____ Joules. (Note: Your numbers are randomly selected and likely different from the numbers listed here.)
	Work - Mechanical Energy Relationships: If non-conservative forces do net work upon an object, then the total mechanical energy of that object is changed. The sum of the kinetic and potential energies will change as work is done upon the object. If non-conservative forces do NOT do net work, then the total mechanical energy will be conserved.
	Definition of Potential Energy: Potential energy is the energy stored in an object due to its position. The most common type of potential energy - gravitational potential energy - is the energy stored in an object due to its vertical position relative to the ground or some zero level.
	The potential energy is the energy stored in an object due to its vertical position above (or below) the ground or some zero level. The amount of kinetic energy (PE) possessed by an object depends upon its mass (m) and its height (h). The formula for calculating the potential energy is PE = m • g • h where g is the acceleration of gravity (9.8 m/s/s on Earth)
	The object is said to be in free-fall. The only force acting AND doing work upon the object is gravity. Gravity is a conservative force and so the total amount of mechanical energy is conserved. It is the same at every point during its fall as it is initially. See Physics Rules section above. Potential energy is the stored energy of position. In the case of the falling object, its height (i.e., vertical position above the ground) is decreasing. In fact, it decreases to one-fourth its original value. The object starts at rest, so there is no kinetic energy in the initial state. The initial potential energy is the same as the total amount of energy. Once the object has fallen to one-fourth its original height, its potential energy is one fourth its original value. See Formula Fix section above.
	What variables effect the potential energy of an object and in what way does the amount of potential energy depend upon the object's height? What condition(s) is (are) necessary in order for the total mechanical energy of an object to be conserved? How can mechanical energy conservation be used to predict the amount of kinetic or potential energy of an object in any given state of its motion?

	A sledder effortlessly glides from position A across the snow to position B (as shown in the diagram below). Resistance forces are negligible. At position B, the total mechanical energy of the sledder is _____ Joules and the kinetic energy is ____ Joules.
	Work - Mechanical Energy Relationships: If non-conservative forces do net work upon an object, then the total mechanical energy of that object is changed. The sum of the kinetic and potential energies will change as work is done upon the object. If non-conservative forces do NOT do net work, then the total mechanical energy will be conserved.
	Definition of Total Mechanical Energy: The total mechanical energy possessed by an object is the sum of its kinetic energy and potential energy.
	The sledder is gliding effortlessly; resistance forces are negligible. The only forces doing work upon the sledder is the force of gravity. So the mechanical energy of the object is conserved. It is the same initially as finally. See Physics Rules section above. Mechanical energy takes two forms - kinetic and potential. The total amount of mechanical energy is simply the sum of these two amounts (see Define Help section above). At any given location along the path of the sledder, the total mechanical energy can be determined by adding the kinetic energy and the potential energy. If mechanical energy is said to be conserved, then the sum of the two forms - KE and PE - will be the same at any given location along the path of the sledder. If the total amount is known and the PE is known, the KE can be quite easily calculated.
	What condition(s) is (are) necessary in order for the total mechanical energy of an object to be conserved? How can mechanical energy conservation be used to predict the amount of kinetic or potential energy of an object in any given state of its motion?

	A roller coaster car coasts from position A to position B (as shown in the diagram below). Resistance forces are negligible. At position B, the total mechanical energy of the car is _____ Joules and the kinetic energy is ____ Joules.
	Work - Mechanical Energy Relationships: If non-conservative forces do net work upon an object, then the total mechanical energy of that object is changed. The sum of the kinetic and potential energies will change as work is done upon the object. If non-conservative forces do NOT do net work, then the total mechanical energy will be conserved.
	Definition of Total Mechanical Energy: The total mechanical energy possessed by an object is the sum of its kinetic energy and potential energy.
	The coaster car is coasting and resistance forces are negligible - gravity is the only force doing work upon it. So the mechanical energy of the coaster car is conserved. It is the same initially as finally. See Physics Rules section above. Mechanical energy takes two forms - kinetic and potential. The total amount of mechanical energy is simply the sum of these two amounts (see Define Help section above). At any given location along the path of the coaster car, the total mechanical energy can be determined by adding the kinetic energy and the potential energy. If mechanical energy is said to be conserved, then the sum of the two forms - KE and PE - will be the same at any given location along the path of the car. If the total amount is known and the PE is known, the KE can be quite easily calculated.
	What condition(s) is (are) necessary in order for the total mechanical energy of an object to be conserved? How can mechanical energy conservation be used to predict the amount of kinetic or potential energy of an object in any given state of its motion?

	Two objects of identical mass begin from rest at the same height at the top of two different hills - hill A and hill B. The hills are inclined at two different angles (see diagram). The objects are released from rest and slide to the bottom; resistance forces can be considered to be negligible. The object on top of hill ____ will have the greatest speed at the bottom of the incline.
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	An energy analysis is a simple means of making a prediction of which ball has the greatest speed at the bottom of the incline. The analysis would begin by comparing the total amount of mechanical energy of the two balls. Mechanical energy has two forms - kinetic energy (KE) and potential energy (PE). The kinetic energy depends on mass and speed. Initially, the balls have the same mass and the same speed. The potential energy (PE) depends on mass and height. Initially, the balls have the same mass and the same height. See Define Help section below. You can now make a comparison of the initial amount of mechanical energy of the two balls. Which has the most - A or B? Or are they both the same? We are told that resistance forces are negligible as the balls roll down the hill. The normal force does not do work on the balls since it acts at right angles to the motion. So the only force doing work is a conservative force - gravity. Since non-conservative forces are not doing work upon the balls; the mechanical energy (ME) of the balls is conserved. The total ME of the balls is the same at the bottom of the hill as it is at the top of the hill. See Physics Rules section below. You can now make a comparison of the final amount of mechanical energy of the two balls. Which has the most - A or B? Or are they both the same? Once the balls have reached the bottom of the hill (ground level), the PE is zero. All the mechanical energy possessed by the balls is in the form of KE. Since the two balls have the same ME at the top of the hill, they will also have have the same KE at the bottom of the hill. The KE is related to mass and speed. Each ball has the same mass, so the each ball will have the same speed.
	Work - Mechanical Energy Relationships: If non-conservative forces do net work upon an object, then the total mechanical energy of that object is changed. The sum of the kinetic and potential energies will change as work is done upon the object. If non-conservative forces do NOT do net work, then the total mechanical energy will be conserved.
	Definition of Kinetic Energy: Kinetic energy is the energy possessed by an object due to its motion. If an object is moving, then it has kinetic energy. The amount of kinetic energy depends on mass and speed. Definition of Potential Energy: Potential energy is the energy stored in an object due to its position. The most common type of potential energy - gravitational potential energy - is the energy stored in an object due to its vertical position relative to the ground or some zero level. The amount of gravitational potential energy depends upon mass and vertical height.
	What condition(s) is (are) necessary in order for the total mechanical energy of an object to be conserved? How can mechanical energy conservation be used to predict the amount of kinetic or potential energy of an object in any given state of its motion? How can one determine the speed of an object from energy information?