Instructor: Dr. Tatiana Erukhimova Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 21

2D case:

2 or 3D cases: If or then

Several dimensions: U(x,y,z) Partial derivative is taken assuming all other arguments fixed Compact notation using vector del, or nabla: Another notation:

Geometric meaning of the gradient Direction of the steepest ascent; Magnitude : the slope in that direction Direction of the steepest descent Magnitude : the slope in that direction http://reynolds.asu.edu/topo_gallery/topo_gallery.htm

Given the potential energy function find the x and y components of the corresponding force.

Mechanical energy is conserved! Work-energy theorem: Mechanical energy is conserved!

Examples Strategy: write down the total mechanical energy, E, E = KE + U at the initial and final positions of a particle:

Initial E1=KE1+U1…

Final E2=KE2+U2

Then use or

Have a great day! Reading: Chapter 9 Hw: All Chapter 8 problems and exercises