physics 1a...conservative forces a conservative force is a force between members of a system that...
TRANSCRIPT
• Energy measures motion or potential for motion
• Energy is a scalar quantity
• Many processes in nature can be described as an exchange of different forms of energy
• Kinetic energy is the measure of motion
• Change in kinetic energy is done by work (Work−Kinetic Energy Theorem)
• The work by a conserved force can be stored into potential energy
Review of Last Lecture
Conservative Forces
A conservative force is a force between members of a system that causes no transformation of mechanical energy within the system
1. The work done by a conservative force on a particle moving through any closed path is zero
2. The work done by a conservative force on a
particle moving between any two points is independent of the path taken by the particle
Nonisolated System (Energy)
• In a nonisolated system:
– Energy crosses boundary of the system due to interaction with the environment
• For example, the work-kinetic energy theorem:
– Interaction of system with environment is work done by external force
– Quantity in system that changes is kinetic energy
Nonisolated System (Energy)
• Energy is conserved
• This means that energy cannot be created or destroyed
• If the total amount of energy in a system changes, it can only be due to the fact that energy has crossed the boundary of the system by some method of energy transfer
Nonisolated System (Energy)
• Mathematically, Esystem = ST
– Esystem is the total energy of the system
– T is the energy transferred across the system boundary
• Note: Twork = W and Theat = Q
• Others do not have standard symbols, so we use:
• TMW (mechanical waves)
• TMT (matter transfer)
• TET (electrical transmission)
• TER (electromagnetic radiation)
Nonisolated System (Energy)
• The primary mathematical representation of the energy analysis of a nonisolated system is
• If any of the terms on the right are zero, the system is
an isolated system
• The Work-Kinetic Energy Theorem (K = W) is a special case of the more general equation above
• W = work, Q = heat, T = transfer, MW = mechanical waves, MT = matter transfer, ET = electrical transmission, ER = electromagnetic radiation
Isolated System (Energy) • Isolated system: no energy crosses the system
boundary by any method
• Example: lifting a book in a gravitational field – System consists of the book and the Earth
– Mechanical energy:
• System is isolated, so
– Mechanical energy is conserved for isolated system
with no nonconservative forces acting
Combustion
Problem-Solving Strategy
1. Conceptualize - Study the physical situation carefully and form a mental representation of what is happening.
– As you become more proficient working energy problems, you will begin to be comfortable imagining the types of energy that are changing in the system.
2. Categorize - Define your system, which may consist of more than one object and may or may not include springs or other possibilities for storing potential energy.
• Determine if any energy transfers occur across the boundary of your system.
• If so, use the nonisolated system model:
Esystem = ST
• If not, use the isolated system model:
Esystem = 0
Problem-Solving Strategy
Categorize, cont.
– Determine whether any nonconservative forces are present within the system.
– If so, use the techniques of Sections 7.4 and 7.5.
– If not, use the principle of conservation of mechanical energy as outlined below.
Problem-Solving Strategy
3. Analyze - Choose configurations to represent the initial and final conditions of the system.
– For each object that changes elevation, select a reference position for the object that defines the zero configuration of gravitational potential energy for the system.
– For an object on a spring, the zero configuration for elastic potential energy is when the object is at its equilibrium position.
– If there is more than one conservative force, write an expression for the potential energy associated with each force.
Problem-Solving Strategy
Analyze , cont. – Write the total initial mechanical energy Ei of the
system for some configuration as the sum of the kinetic and potential energies associated with the configuration.
– Then write a similar expression for the total mechanical energy Ef of the system for the final configuration that is of interest.
– Because mechanical energy is conserved, equate the two total energies and solve for the quantity that is unknown.
Problem-Solving Strategy
4. Finalize - Make sure your results are consistent with your mental representation.
– Also make sure the values of your results are reasonable and consistent with connections to everyday experience.
Problem-Solving Strategy
Example 7.1 Ball in Free Fall
A ball of mass m is dropped from a height h above the ground.
(A) Neglecting air resistance, determine the speed of the ball when it is at a height y above the ground.
Example 7.1 Ball in Free Fall
– Apply the conservation of mechanical energy for the isolated system:
– Solve for the final velocity:
Example 7.1 Ball in Free Fall
(B) Determine the speed of the ball at y if at the instant of release it already has an initial upward speed vi at the initial altitude h.
• Apply the conservation of mechanical energy for the isolated system:
• Solve for the final velocity
• Nonisolated system in steady state: When the rate at which energy is entering the system is equal to the rate in which it is leaving
– Example: a home
Nonisolated System in Steady State (Energy)
• Example: the Earth-atmosphere system
• Energy is transferred through electromagnetic radiation
– Primary input radiation is from the Sun
– Primary output radiation is infrared radiation emitted from atmosphere and ground
• Ideally, transfers are balanced so Earth maintains a constant temperature
• In reality, transfers are not exactly balanced
– Earth is in quasi-steady state
Nonisolated System in Steady State (Energy)
Situations Involving Kinetic Friction
• When kinetic friction is involved in a problem, you must use a modification of the work-kinetic energy theorem
• Consider a book sliding on a table
• The change in kinetic energy is equal to the work done by all forces other than friction minus the energy associated with the friction force:
Situations Involving Kinetic Friction
• A friction force transformed kinetic energy in a system to internal energy
• The increase in internal energy of the system is equal to its decrease in kinetic energy:
For Next Time (FNT)
• Should be finished with Chapter 6
• Start reading Chapter 7
• Start homework for Chapter 7
• Quiz will cover material through this lecture
Example 7.4 A Block Pulled on a Rough Surface
A 6.0-kg block initially at rest is pulled to the right along a horizontal surface by a constant horizontal force of 12 N.
(A) Find the speed of the block after it has moved 3.0 m if the
surfaces in contact
have a coefficient of
kinetic friction of 0.15.
Example 7.4 A Block Pulled on a Rough Surface
• Find the work done on the system by the applied force:
• Apply the particle in equilibrium model to the block in the vertical direction:
• Find the magnitude of the friction force: