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

3. 2D case:

4. 2 or 3D cases: If or
then

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

6. 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

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

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

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

10. Initial E1=KE1+U1…

11. Final E2=KE2+U2

12. Then use or

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