1. Physics 151 Week 11 Day 2 Topics: Forces, Apparent Weight, & Friction  Energy  Dot Produce  Work  Conservation of Energy with Work  Work-Energy Theorem  Momentum  Conservation of Momentum  Collisions  1-D Collisions  2-D Collisions  Work and Impulse

2. Exam 2 comments: Once exams are graded, I will make score adjustments as needed if the class average is below normal for this class due to time pressure. However, in this class, you will be time limited on midterms What can you do? Make sure you know and understand key concepts so you can apply them quickly and correctly Practice doing homework problems with good solutions for time => this week, take 30 minutes, next week 25 minutes, next 20 minutes Read through the exam in the first minutes. Identify which parts you can do quickly and well to maximize points Don’t rush. It’s better to do three parts well, then four parts badly If you don’t have time to finish a problem, tell me what you would do if you had more time. More correct detail => more points

3. Course Grading Slide 4-19 Every students’ overall score will be calculated two ways 1.As stated in the syllabus 2.By Exams only 2 best midterm scores30% each Final Exam Score40% Total100% The higher overall score will be used to calculate your grade. Note, over 95% of the time, syllabus grading will result in the higher score. Homework scores correlate strongly with exam performance.

4. Dot Product Slide 4-19 Dot product or scalar product is a way of multiplying two vectors to get a scalar result Dot products can be calculated either independent of a coordinate system where is the angle between the two vectors Note that in this case the sign of the dot product only depends on the angle Or in component form

5. Dot Product: Example 1 Dot produce or scalar product is a way of multiplying two vectors to get a scalar result Dot products can be calculated either independent of a coordinate system where is the angle between the two vectors Vector A has a magnitude of 4 units Vector B has a magnitude of 3 units Angle between them = 60 degrees

6. Dot Product: Example 2 Slide 4-19 Dot product or scalar product is a way of multiplying two vectors to get a scalar result Dot products in component form Let and So

7. Example 3 Using a dot product to find angle Slide 4-19 We know 2 ways to calculate the dot product Put these two equations for dot product = to each other

8. Work Definition of Work (in physics) For constant Force Like all energy terms, work is a scalar Work is the overall effect of a force applied over a displacement. We can talk about the work done by any force or the work done by the net force. For non-constant force Work = area under F x vs. x graph Note that work can be positive or negative sign depends on cosine of angle between the vectors

9. Choosing the System Slide 10-16

10. Work by an External Force Slide 4-19 Conservation of Energy Equation KE i + PE gi +Pe si +  E sys = KE f + PE gf + Pe sf +  E th  E sys = W ext where W ext = work done by external forces  E th = - W friction

11. Sign of Work Questions Slide 10-23 Answer these questions: For each of the forces, in the force diagrams below, the work done by that force is (A) positive, (B) negative, (C) zero (D) Can’t tell

12. In terms of the initial and final total momenta: The Law of Conservation of Momentum In terms of components: Slide 9-18 P f = P i 

13. Slide 9-19

14. Summary Slide 9-30

15. Elastic and Inelastic Collisions Momentum is always conserved in collisions and explosions. Elastic collision => momentum & mechanical energy are conserved Inelastic collision => momentum conserved, mechanical energy is not Mechanical Energy = KE +  PE In an elastic collision, both objects return to their original state (no change in shape, no deformation) momentum & mechanical energy are conserved In an inelastic collision, one or both objects deform and change shape. Some mechanical energy goes into changing the objects shape and is transformed into  E thermal Inelastic collision => momentum conserved, mechanical energy is not

16. Inelastic Collisions First, we’ll consider perfectly inelastic collisions: A perfectly inelastic collision results whenever the two objects move off at a common final velocity. Momentum is always conserved in collisions and explosions. Inelastic collision => momentum conserved, mechanical energy is not

17. Elastic Collisions In an elastic collision, both momentum and mechanical energy are conserved

19. Summary