1. FIRST Handback quizzes Homework discussion, and talking about cars and hills with a video. Next time: HW turn in HW FOR NEXT TIME: The one titled homework. Answers are in this PPT posted online.

2. LETS GET STARTED Today will discuss forces at angles, and the idea of net force. So you will: Understand how X and Y forces affect each other indirectly. Set up net force equations for things at angles Look at difficult conceptual situations involving forces and motion.

3. DO YOU GET NEWTONS 3 RD LAW?

4. If we are looking at the amount of force of B on A compared to A on B, we know… They are ALWAYS the same, DIFFERENT DIRECTION. And the more INERTIA one has, the LESS it will change its current motion from the force.

5. LETS MAKE SURE…DEMO IT

6. FORCES AT ANGLES AGAIN A force on a surface will mean that the angled force will have an effect on the normal force. You use Sin and Cos to find the X and Y parts of the force If there are other forces in the Y direction, then the normal force does NOT equal the weight

7. LETS DO ONE You pull a cat again at an angle. There is friction opposing your pull. 1) Draw a FBD and then another with the X and Y components Cat Weight Weight: Force of Earth on the cat Fn Fn: Force of ground on cat Ff Ff: Force of ground on cat Pull in X Pull: Force of person on the cat Pull in Y Pull X: Force of person on the cat horizontally Pull Y Force of person on the cat vertically Pull

8. QUESTIONS 1) Which is larger, the normal force or the weight? The weight, since the cat is in equilibrium in Y. And the weight is balanced by the normal force AND the Y pull. Cat Weight Weight: Force of Earth on the cat Fn Fn: Force of ground on cat Ff Ff: Force of ground on cat Pull in X Pull in Y Pull X: Force of person on the cat horizontally Pull Y Force of person on the cat vertically

9. QUESTIONS 2) If you pull at a larger angle, will the weight or the normal force change? The weight will NOT, since it’s the Earths pull on the cat. The normal force WILL, since you are still in equilibrium in Y, your larger pull in Y will decrease the normal force needed from the table. In other words… Cat Weight Weight: Force of Earth on the cat Fn Fn: Force of ground on cat Ff Ff: Force of ground on cat Pull in X Pull in Y Pull X: Force of person on the cat horizontally Pull Y Force of person on the cat vertically

10. QUESTIONS 3) If the cat was moving at a constant velocity, would increasing the angle change the friction? YES! Since friction depends on normal force (F f = µF normal ) then more of a Y pull will decrease the normal force, resulting in less friction In other words… Cat Weight Weight: Force of Earth on the cat Fn Fn: Force of ground on cat Ff Ff: Force of ground on cat Pull in X Pull in Y Pull X: Force of person on the cat horizontally Pull Y Force of person on the cat vertically

11. QUESTIONS 4) Say that the coefficient of friction is µ k and pulled at angle θ. Lets create 2 nd Law equations for X and Y X: Lets say the acceleration will be with the pull (my guess) so +. There is an imbalance then. X: F 1x – F f = imbalance Y: No imbalance, call down – Y: -Weight + F Normal = equilibrium Cat Weight Weight: Force of Earth on the cat Fn Fn: Force of ground on cat Ff Ff: Force of ground on cat Pull in X Pull in Y Pull X: Force of person on the cat horizontally Pull Y Force of person on the cat vertically

12. QUESTIONS X: F 1x – F f = imbalance X : F 1 Cosθ – µF normal = ma Y: -Weight + F Normal = equilibrium Y: -mg + F Normal = 0

13. SUMMARY When changing the angle of a force on a surface, the normal force changes. Which changes the friction as well. A downward push results in MORE normal force, an upward push results in LESS normal force. Friction is the coefficient of friction times the normal force. Use static for non-moving, kinetic for moving

17. DEMO OF THAT…NUTZ

18. LETS TRY A FEW AP PROBLEMS Alone, with a formula sheet. Just the first, please.

21. W HAT THIS R EINFORCED Static friction used to get things to move. Friction cannot make things speed up, so if friction is a larger force AND will cause a speed up, we have issues. We needed to solve for the normal force using Y info to put in X

22. Lets use our knowledge to define a term….

25. WHAT THIS REINFORCED 25: Increasing the angle in this case is taking the burden of the weight off the normal force, so it decreases. 26: Increasing the angle will result in less forward force, which will lead to a smaller acceleration.

26. Draw the FBD from 40.

28. Now its different….What words have changed everything?

31. The 3 Y forces are added together. 2 are negative because they are opposite the imbalance direction.