1. Forces & Newton’s Laws of Motion Chapter 4 (angles)

2. Sign Problems  Equilibrium-the state where all forces are balanced and acceleration is zero.  Includes both stationary and constant velocity cases.

3. Example #15  If the sign has a mass of 15kg, what is the tension in the string? What is the force the beam exerts on the sign? Assume equilibrium. One component at a time.

4. Set up equilibrium case FyFy FxFx FTFT 23 FgFg F beam

5. Equilibrium case for vertical

6. Equilibrium case for horizontal

7. Example #16  Find the tension in each rope. T1T1 T2T2

8. Break up Components F1F1 F2F2 F x1 F x2 F y1 F y2 FgFg

9. Horizontal Pieces  Since the sign isn’t accelerating horizontally, we can use: F x1 F x2 F y1 F y2 FgFg

10. Vertical Pieces  Since the sign isn’t accelerating vertically, we can use: F x1 F x2 F y1 F y2 FgFg

11. Putting the two together

12. Putting the two together cont.

14. Example #17 What is the tension in the cables that support the sign? Physics is Phun!! m = 1500 kg 40°

15. Example #18 – Angles with acceleration A sled of mass 30 kg is pulled with a force of 50 N at a 25 degree angle. IF the coefficient of friction between the runners and the snow is 0.1, what is the acceleration of the sled?

16. Example #19 A 50 kg boy is pushed on a 20 kg scooter with a force shown below at 20 degrees below the horizontal. What is the coefficient of friction that would keep the scooter from accelerating? F A =200 N

17. Example #20 A 50 kg girl is pushed on a 20 kg scooter with a force shown below at 20-degrees below the horizontal. What is the coefficient of friction that would keep the scooter accelerating at 1.5 m/sec 2 ? F A =200 N

18. Example #21 – Ramp Problem A crate slides down a 37 degree incline. What is the acceleration of the crate?

19. Example #22 A crate slides down a 35 degree incline. What is the acceleration of the crate if the coefficient of friction between the crate and the incline is 0.2?

20. Example #23 A skier is accelerating down a mountain that has a 30-degree incline at 4.0 m/sec 2. A)What is the coefficient of friction? B)How long does it take him to get to the bottom of the 0.5 km long mountain? C)How fast is he going by the time he reaches the bottom of the mountain assuming that he goes straight down without turns?

21. Example #24 A crate is sliding down an incline at constant speed. If the coefficient of friction is 0.45, at what angle is the incline?

22. What must  be for the second incline?