Find your group

1. Find your group • Take your seat • Be friendly

2. Announcements • Exam 1 Thursday (yes, already) • Standards covered: • DVA: Relate distance, velocity, and acceleration mathematically, graphically, and conceptually. • Vector ops: Carry out mathematical operations involving vectors: addition, subtraction, multiplication by a scalar, dot product, and cross product. • N1: Relate zero net force to constant velocity. • N2: Relate net force to acceleration. • Forces: Calculate and describe the magnitude and direction of the forces of gravity (weight), friction, support, and tension.

3. Announcements • Quiz ½ • Questions 2, 3, 4 evaluated Standard 1 (DVA) • Still need to fix if not all were correct • Mechanism TBA • I’m trying to figure how to post standards strandings

4. Projectile Motion Two independent dimensions

5. Objective • Describe and explain the motion of 2-D free fall.

6. What’s the point? • How do things move when they are thrown?

7. Free-Fall Trajectories • Only force is gravity (straight down) • Acceleration is straight down with magnitude g • No acceleration in horizontal direction • Vertical and horizontal components of velocity are independent

8. Handout Work • Determine the trajectory for a projectile dropped from rest. • Find the velocity at the end of each second. • Find the average velocity each second. • Find the displacement each second. • Plot the position at the end of each second. • Repeat until landing.

9. Handout Work Determine the trajectory for a projectile tossed at an angle. Find the velocity at the end of each second. Find the average velocity each second. Find the displacement each second. Plot the position at the end of each second. Repeat until landing.

10. Air Resistance (Drag) • Very complicated • Depends on airspeed: faster airspeed gives greater drag

11. Poll Question What happens to an object with zero net force acting on it? • It is motionless. • If it is moving, it soon stops. • It has a constant velocity. • It constantly accelerates. Hint: Remember Newton’s first law. Or Newton’s second law.

12. Initial Transition Terminal airspeed 0 0 < v < vT vT gravity mg mg mg drag 0 0 > drag > –mg –mg net force mg mg–drag > 0 mg–drag = 0 accel. g g > a > 0 0 v increasing maximum a v increasing a decreasing v constant a = 0 (Here, positive = downward, negative = upward) Falling through Air

13. Whiteboard Work For an object falling from rest to its terminal velocity: Sketch an acceleration-time graph. Sketch a velocity-time graph. Sketch a position-time graph.

14. Force Diagrams Forces on one object

15. Objective • Construct an object’s force diagram from its physical circumstances.

16. What’s the point? • How can we inventory an object’s forces? • How can we check that our model considers the correct forces?

17. Force diagrams • To find net force  acceleration • Analyze individual and net forces on a body • Analyze one body free from all others • Diagram covers only the body and the forces acting on it

18. Force Diagrams • Vector arrows directed outward from object • Indicate every force!

19. Think Question How many forces act on the anvil? zero net force

20. Think Question How many forces act on the table? zero net force

21. Combining Forces What are the forces on the anvil? Table? Free-body diagrams for them? zero net force

22. Anvil Support from table Its weight Net force ∑F = 0

23. Table support from ground its weight anvil’s weight Net force ∑F = 0

24. Whiteboard Work • Construct force diagrams for: • A rock falling to the surface of the moon • A crumpled wad of paper thrown horizontally • A passenger in a braking car • A box sliding down a ramp, slowing down

25. Reading for Next Time • Momentum: the “quantity of motion” • Big ideas: • Momentum is a vector • Momentum changes when a force acts for a time