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

• 1. W independent of path.

W depends only on initial and final positions.

• 2. If the particle moves

back to the same point, W=0.

• 3. Examples: Gravity

(weight), spring, gravitational attraction.

Non‐conservative forces

• 1. W not only depends on

initial and final positions, it also depends on the path.

• 2. W0 even if the particle

moves back to the same point.

• 3. Examples: friction.

Potential energy

i forces ve conservati

• Non

i forces ve Conservati i forces ve conservati

• Non

U i forces ve Conservati i forces ve conservati

• Non

i forces ve Conservati i i i f

F by done Work U K F by done Work U F by done Work F by done Work K F by done Work F by done Work F by done Work K K K                      

      

                



Work – Kinetic Energy Theorem U is called the potential energy.

) y (y mg W

i f 

 

Potential Energy Case 1b: Gravity

y

mg

Calculation is path independent

x yf yi i f Only if upward is positive i f i

mgy U ) y (y mg U U W U

i f i f

        

(upward is positive)

L (natural length) x F= -kx Extension x=0 x F= -kx Compression

Potential Energy Case 2: Spring

) x k(x 2 1 W

2 i 2 f 

 

Calculation is path independent

2 2 i 2 f i f

kx 2 1 U ) x k(x 2 1 U U W U         

         

i f

r 1 r 1 GMm W

Calculation is path independent

Potential Energy Case 3: Gravitational force

M f i rf ri m

r GMm U r 1 r 1 GMm U U W U

i f i f

                  

Conservation of energy

F ve conservati

• non

by done Work ) U U ( ) K (K

• r

F ve conservati

• non

by done Work U K

i i i f i f 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.