Physics 1A

Lecture 7A

• 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)

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:

Example 7.4 A Block Pulled on a Rough Surface

• Find the speed of the block:

• Substitute numerical values: