Physics 111: Elementary Mechanics

1
Physics 111 Elementary Mechanics Lecture 7

• Carsten Denker
• NJIT Physics Department
• Center for SolarTerrestrial Research

2
Introduction

• Potential Energy and Conservation of Energy
• Conservative Forces
• Gravitational and Elastic Potential Energy
• Conservation of (Mechanical) Energy
• Potential Energy Curve
• External Forces

3
Work and Potential Energy
Potential Energy
General Form
Gravitational Potential Energy
Elastic Potential Energy
4
(Non-)Conservative Forces

• The system consists of two or more objects.
• A force acts between a particlelike object in
  the system and the rest of the system.
• When the system configuration changes, the force
  does work W1 on the particlelike object,
  transferring energy between the kinetic energy K
  of the object and some other form of energy of
  the system.
• When the configuration change is reversed, the
  force reverses the energy transfer, doing work W2
  in the process.
• W1 W2 ? conservative force

5
Path Independence of Conservative Forces

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

6
Conservation of Mechanical Energy
Mechanical Energy
Conservation of Mechanical Energy
In an isolated system where only conservative
forces cause energy changes, the kinetic and
potential energy can change, but their sum, the
mechanical energy Emec of the system, cannot
change.
7
Potential Energy Curve
1D Motion

• Turning Points
• Equilibrium Points
• Neutral Equilibrium
• Unstable Equilibrium
• Stable Equilibrium

A plot of U(x), the potential energy function of
a system containing a particle confined to move
along the x axis. There is no friction, so
mechanical energy is conserved.
8
Conservation of Energy

• The total energy of a system can change only by
  amounts of energy that are transferred to or from
  the system.
• The total energy E of an isolated system cannot
  change.

Thermal Energy/Friction