1. Forces at Angles

2. Recall: In this case the Applied Force is horizontal only If the F=Ff, it means the object is either at rest or moving at a constant velocity FfFf

3. Force at an Angle What happens to the all of the Forces if the Applied force is placed at an angle? θ FaFa FfFf F g =W FNFN Actual Drawing

4. FBD Draw two different FBD The actual FBD The component FBDθ θ FaFa FfFf F g =W FNFN FfFf FNFN F x = F a cosθ F y = F a sinθ

5. Determining Acceleration When a question asks about an acceleration of a block (x-direction) Use Newtons Second Law Be sure to sum the forces ONLY in the X- direction F Net = F x - F f

6. Determining Normal Force When a question asks about the Normal force of a block (y- direction) F N = F g – F y Be sure to sum the forces ONLY in the Y –direction

7. Example: If the little girl in the picture before is pulling her 10 kg little sister with a force of 50N at an angle of 15 o and the force of friction is 5N, what is the girls acceleration and what is the normal force?

8. Rotating orientation When looking at objects on an incline the easiest idea is to rotate the orientation of the X-Y axis to the angle X Y X Y

9. Weight on an Incline θ old x axis old y axis new x axis: parallel to incline new y axis: perpendicular to incline Zoomed In FgFg FNFN FfFf θ

10. Determining Parallel & Perpen Force of Friction: Force of friction is opposite the angle and you know the hypotenuse Normal Force: Normal force is adjacent to the angle and you know the hypotenuse FgFg FNFN FfFf θ