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Questions and Answers
Which of the following statements about gravitational potential energy is true?
Which of the following statements about gravitational potential energy is true?
If an object is moving under the influence of only conservative forces, which of the following is true about its total mechanical energy?
If an object is moving under the influence of only conservative forces, which of the following is true about its total mechanical energy?
When solving a problem involving gravitational potential energy, the choice of the reference level:
When solving a problem involving gravitational potential energy, the choice of the reference level:
In the context of conservation of mechanical energy, what does it mean for a physical quantity to be conserved?
In the context of conservation of mechanical energy, what does it mean for a physical quantity to be conserved?
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If an object is moving under the influence of both conservative and nonconservative forces, which of the following statements is true?
If an object is moving under the influence of both conservative and nonconservative forces, which of the following statements is true?
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In the work-energy theorem extended to include potential energy, $W_c + W_{nc} = \Delta KE$, what does $W_c$ represent?
In the work-energy theorem extended to include potential energy, $W_c + W_{nc} = \Delta KE$, what does $W_c$ represent?
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In a system where gravitational potential energy and kinetic energy are the only forms of mechanical energy present, what is the relationship between the total mechanical energy at two different points in the system's motion?
In a system where gravitational potential energy and kinetic energy are the only forms of mechanical energy present, what is the relationship between the total mechanical energy at two different points in the system's motion?
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When solving a problem involving the conservation of mechanical energy, what is the significance of selecting a reference level for gravitational potential energy?
When solving a problem involving the conservation of mechanical energy, what is the significance of selecting a reference level for gravitational potential energy?
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If a non-conservative force, such as friction, is present in a system, which principle should be applied instead of the conservation of mechanical energy?
If a non-conservative force, such as friction, is present in a system, which principle should be applied instead of the conservation of mechanical energy?
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In a problem involving the conservation of mechanical energy, if the initial and final positions of an object are given, what additional information is typically needed to solve for the unknown quantity?
In a problem involving the conservation of mechanical energy, if the initial and final positions of an object are given, what additional information is typically needed to solve for the unknown quantity?
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What is the potential energy function associated with a compressed or stretched spring?
What is the potential energy function associated with a compressed or stretched spring?
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Which of the following equations correctly represents the conservation of mechanical energy for a system that includes a spring?
Which of the following equations correctly represents the conservation of mechanical energy for a system that includes a spring?
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If a nonconservative force acts on a system, what happens to the total mechanical energy of the system?
If a nonconservative force acts on a system, what happens to the total mechanical energy of the system?
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In a problem involving the conservation of mechanical energy, what is the significance of identifying the 'system' and the 'body of interest'?
In a problem involving the conservation of mechanical energy, what is the significance of identifying the 'system' and the 'body of interest'?
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In the context of energy transfer, what is the significance of the center of mass?
In the context of energy transfer, what is the significance of the center of mass?
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If the work done by a variable force acting on an object is represented by the area under the graph of force versus displacement, what does the area above the x-axis represent?
If the work done by a variable force acting on an object is represented by the area under the graph of force versus displacement, what does the area above the x-axis represent?
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In the context of energy transfer, what is the primary mechanism by which energy is transferred through electrical transmission?
In the context of energy transfer, what is the primary mechanism by which energy is transferred through electrical transmission?
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Which of the following statements about the reference level for potential energy is correct?
Which of the following statements about the reference level for potential energy is correct?
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If a system experiences a net positive work done by nonconservative forces, what can be concluded about the energy transfer?
If a system experiences a net positive work done by nonconservative forces, what can be concluded about the energy transfer?
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In the context of energy transfer, what is the primary mechanism by which energy is transferred through electromagnetic radiation?
In the context of energy transfer, what is the primary mechanism by which energy is transferred through electromagnetic radiation?
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If a spring is slowly stretched from its equilibrium position to a maximum displacement, what can be said about the work done by the force?
If a spring is slowly stretched from its equilibrium position to a maximum displacement, what can be said about the work done by the force?
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In the context of energy transfer, what is the primary mechanism by which energy is transferred through heat?
In the context of energy transfer, what is the primary mechanism by which energy is transferred through heat?
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Study Notes
Nonconservative Forces
- Examples of nonconservative forces include kinetic friction, air drag, and propulsive forces.
- Friction depends on the path and is a nonconservative force because the work required is less on a shorter path than on a longer path.
Work-Energy Theorem
- The theorem can be expressed in terms of the work done by both conservative forces (Wc) and nonconservative forces (Wnc): Wc + Wnc = ΔKE.
Potential Energy
- Potential energy is associated with the position of an object within a system.
- It is a property of the system, not the object.
- A system is a collection of objects interacting via forces or processes that are internal to the system.
- For every conservative force, a potential energy function can be found.
- Evaluating the difference of the function at any two points in an object's path gives the negative of the work done by the force between those two points.
Gravitational Potential Energy
- Gravitational potential energy is the energy associated with the relative position of an object in space near the Earth's surface.
- It is the potential energy of the earth-object system.
- The work done by the gravitational force between two points can be calculated using the equation: PE = mgy.
- Units of potential energy are the same as those of work and kinetic energy: Joule (J).
Reference Levels for Gravitational Potential Energy
- A location where the gravitational potential energy is zero must be chosen for each problem.
- The choice is arbitrary, but once the position is chosen, it must remain fixed for the entire problem.
- A convenient location for the zero reference height is often the Earth's surface.
Conservation of Mechanical Energy
- To say a physical quantity is conserved means that the numerical value of the quantity remains constant throughout any physical process.
- The total mechanical energy of a system remains constant in any isolated system of objects interacting only through conservative forces.
- Total mechanical energy is the sum of the kinetic and potential energies in the system.
Problem Solving with Conservation of Energy
- Define the system and include all interacting bodies.
- Verify the absence of nonconservative forces.
- Select the location of zero gravitational potential energy.
- Select the body of interest and identify two points.
- Apply the conservation of energy equation to the system.
- Identify the unknown quantity of interest and substitute values.
Work-Energy with Nonconservative Forces
- If nonconservative forces are present, the full Work-Energy Theorem must be used instead of the equation for Conservation of Energy.
- Do not include both work done by gravity and gravitational potential energy.
- Often techniques from previous chapters will need to be employed.
Potential Energy Stored in a Spring
- The force used in stretching or compressing a spring is a conservative force.
- The force can be calculated using Hooke's Law: Fs = -kx.
- Elastic potential energy is related to the work required to compress a spring from its equilibrium position to some final position.
- Spring potential energy can be transformed into kinetic energy of the block.
Work-Energy Theorem Including a Spring
- The work-energy theorem can be extended to include potential energy: Wnc = (KEf – KEi) + (PEgf – PEgi) + (PEsf – PEsi).
- The PE of the spring is added to both sides of the conservation of energy equation.
Conservation of Energy Including a Spring
- An extended form of conservation of mechanical energy can be used: Wnc = 0.
- The same problem-solving strategies apply, and the equilibrium position of the spring must be defined.
Nonconservative Forces with Energy Considerations
- When nonconservative forces are present, the total mechanical energy of the system is not constant.
- The work done by all nonconservative forces acting on parts of a system equals the change in the mechanical energy of the system.
Transferring Energy
- Energy can be transferred by work, heat, mechanical waves, electrical transmission, and electromagnetic radiation.
- Energy can cross a boundary or be transformed into a form of non-mechanical energy such as thermal energy.
Power
- Power is defined as the rate of energy transfer.
- SI units of power are Watts (W).
- Instantaneous power can be calculated using the equation: P = Fv.
- Power units can be defined in terms of units of work or energy: kilowatt hours (kWh) are often used in electric bills.
Center of Mass
- The center of mass is the point in the body at which all the mass may be considered to be concentrated.
- When using mechanical energy, the change in potential energy is related to the change in height of the center of mass.
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Description
Test your knowledge on nonconservative forces like kinetic friction and air drag, as well as the work-energy theorem and potential energy. Explore how these forces affect the work required along different paths and their impact on the kinetic energy changes. Understand the relationship between conservative forces, nonconservative forces, and the change in kinetic energy.
