Chapter 5: Work, Energy and Power

Work by One Force

Work due to multiple forces

Work due to multiple forces expanded

Joule

The unit of work and energy

scalar

Because work is equal to the dot product of the net force and the displacement vector, it is a \__________ whose magnitude and sign are determined by the component of the net force parallel to the direction of motion.

Work

the change in an object’s kinetic energy due to the action of a given force.

Work–kinetic energy theorem

Work–kinetic energy theorem

This is the first and most fundamental of a number of equations we will soon derive relating various types of work and energy. This theorem is a restatement of Newton’s laws, and it is always valid.

Energy

never created or destroyed; it merely changes form.

Conservative forces

Are involved in reversible energy conversions, where we can get our kinetic energy back.

Nonconservative forces

Are involved in irreversible energy conversions; though the total energy is always conserved, energy is converted to forms from which we cannot recover

Conservative forces

kinetic energy ⇒ potential energy ⇒ kinetic energy

Nonconservative forces

kinetic energy ⇒ sound, heat, etc. ⇒ cannot be easily recovered

General definition of a potential energy function

zero

Based on the above equation, when the starting and ending points of the motion are the same, the net work must always be \_________

Gravitational potential energy

Work done by gravitational force

spring constant

The proportionality constant k , called the \_____________ or force constant, is a property of the particular spring.

negative

The direction of the spring force is opposite the displacement, as indicated by the \______ sign.

restoring force

Because the force always tries to restore the spring to its relaxed state, whether it has been stretched or compressed, it is called a \_______________ .

Elastic Potential Energy

Work Done by Spring Force

general form of the energy conservation equation

Power

The rate at which a force does work on a system

Average power

Constant power

Watt

Unit of power

Turning Points

All the energy is potential energy, so the object is temporarily at rest.

Equilibrium Points

Points at which the force is zero

Stable equilibrium points

Points where, if the object is given a small nudge, it will remain close to the equilibrium point, oscillating within an “energy well”.

Unstable equilibrium points

Points where, if the object is given a small displacement, it will end up far away from the equilibrium point

Neutral equilibrium points

Points where the U(x) curve is completely flat, so if the particle is given a little nudge, it will continue to move with a constant velocity.