Class 25: Potential energy and conservation of energy Conservative - PowerPoint PPT Presentation

Class 25: Potential energy and conservation of energy

Conservative and non ‐ conservative forces Conservative force Non ‐ conservative forces 1. W independent of path. 1. W not only depends on W depends only on initial initial and final positions, it and final positions. also depends on the path. 2. W  0 even if the particle 2. If the particle moves back to the same point, moves back to the same W=0. point. 3. Examples: Gravity 3. Examples: friction. (weight), spring, gravitational attraction.

Potential energy Work – Kinetic Energy Theorem       K K K Work done by F f i i i       Work done by F Work done by F i i Conservati ve Non - conservati ve forces forces         K Work done by F Work done by F i i                Conservati ve forces Non - conservati ve forces  U      U Work done by F i Conservati ve forces       K U Work done by F i Non - conservati ve forces U is called the potential energy.

Potential Energy Case 1b: Gravity y y f f f i i i y i mg x Only if upward is positive        U W U U mg (y y ) f i f i   f  W mg (y y )   U mgy i Calculation is path independent (upward is positive)

Potential Energy Case 2: Spring F= -kx Extension x x=0 L (natural length) F= -kx Compression x 1        2 2 1 U W U U k(x x )   f  2 2 f i f i W k(x x ) 2 i 2 1   2 U kx Calculation is path 2 independent

Potential Energy Case 3: Gravitational force f r f M r i m i     1 1 1 1               U W U U GMm   W GMm   f i   r r   r r f i f i GMm    U Calculation is path independent r

Conservation of energy       K U Work done by non - conservati ve F i i or       (K K ) ( U U ) Work done by non - conservati ve F f i f i i i Mechanical energy ( K + U) is said to be conserved if work done by non-conservative forces = 0.  K+  U = 0 if that is the case.