## Lecture 7: Conservation of Mechanical Energy

September 12, 2017

### Objectives

• (Continuing objective) Relate concepts of classical mechanics to “everyday” situations and discuss various applications of the concepts to practical problems in various fields of science, medicine and engineering.
• Describe the types of forces with which a potential energy may be associated. From a given one-dimensional potential energy, find the associated force (and vice-versa).
• Given a graph of an object's potential energy versus position, determine the direction and approximate magnitude of the associated force. For an object with a constant mechanical energy, determine the object's kinetic energy, turning points, and points of equilibrium.
• State and recognize the conditions under which conservation of mechanical energy applies.
• Relate the change in mechanical energy to the work done by non-conservative forces, using these steps: a) make sketches of the system, b) write down an expression for the mechanical energy of the system, including a term for each type of energy that may change, c) evaluate the expression for the “Before” situation and again for the “After” situation, and d) use E\text{before} + W\text{nc} = E\text{after}, and solve for unknowns.

### Homework

• Wednesday's Assigned Problems: A19, A20, A21, A22, A23; CH 7: 4, 15, 21, 26, 27, 35

Answers: CH 7 #26 (a) $4.9\,\text{m/s}$, (b) $7.0\,\text{m/s}$, (c) around $x=11\,\text{m}$.

• FRIDAY's Hand-In Problems: A24, A25, A78; CH 7: 18, 42

### Videos of example problems

To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.
• Video Example #1: Applying conservation of mechanical energy. ans: 2.09 m/s
• Video Example #2: Working with energy diagrams. ans: see A6.5
• Video Example #3: Calculating work done by non-conservative forces by determining the change in mechanical energy. ans: -1500 J
• Video Example #4 Another example with conservation of mechanical energy. ans: 10.2 cm