Chapter 8 Potential Energy and Conservation of Energy

Conservative forces The net work done by a conservative force on a particle moving around any closed path is zero The net work done by a conservative force on a particle moving between two points does not depend on the path taken by the particle

Conservative forces: examples Gravity force Spring force

Potential energy For conservative forces we introduce a definition of potential energy U The change in potential energy of an object is being defined as being equal to the negative of the work done by conservative forces on the object Potential energy is associated with the arrangement of the system subject to conservative forces

Potential energy For 1D case A conservative force is associated with a potential energy There is a freedom in defining a potential energy: adding or subtracting a constant does not change the force In 3D

Gravitational potential energy For an upward direction the y axis

Chapter 8 Problem 8

Chapter 8 Problem 19

Elastic potential energy For a spring obeying the Hooke’s law

Conservation of mechanical energy Mechanical energy of an object is When a conservative force does work on the object In an isolated system, where only conservative forces cause energy changes, the kinetic and potential energies can change, but the mechanical energy cannot change

Work done by an external force Work is transferred to or from the system by means of an external force acting on that system The total energy of a system can change only by amounts of energy that are transferred to or from the system Power of energy transfer, average and intantaneous

Conservation of mechanical energy: pendulum

Pole vault Muscle energy becomes kinetic energy (x-direction)

Pole vault Kinetic energy becomes elastic potential energy

Pole vault Elastic energy becomes kinetic energy (y-direction)

Pole vault Kinetic energy becomes gravitational potential energy

Pole vault Gravitational potential energy becomes kinetic energy (y-direction)

Pole vault Kinetic energy energy becomes part elastic potential energy and part internal energy

Pole vault The ‘pole vault’ phenomenon is ubiquitous…

Potential energy curve

Potential energy curve: equilibrium points Unstable equilibrium Neutral equilibrium Stable equilibrium

Chapter 8 Problem 77

Answers to the even-numbered problems Chapter 8: Problem cm

Answers to the even-numbered problems Chapter 8: Problem 68 (a) −3.8 kJ; (b) 31 kN