2. Chapter 6: Motion in Two Dimensions TWO DIMENSIONAL MOTION

3. Trajectory After a projectile has been given an initial thrust, if you ignore air resistance, it moves through the air only under the force of gravity. Force of gravity is what causes it to curve downward. Its path through space is called its trajectory.

4. PROJECTILE MOTION What is a projectile? –Any object shot through the air How does it travel? –Follows a parabolic path Assume weight is the only force acting on it EQUATIONS OF MOTION will change…slightly

5. Range Equation If a projectile launches and lands from the same vertical height, we can find the distance traveled in the x by the following: R = v i 2 (sin 2  /g Notice the angle is doubled and the initial velocity is squared The unit for range is meters (m)

6. NEW EQUATIONS OF MOTION Y direction v f = (v i sin  ) - g t y = (v i sin  ) t - 1/2 gt 2 v f 2 = (v i sin  ) 2 - 2 g v f 2 = (v i sin  ) 2 - 2 g y X direction v f = v i x = v i (cos  ) t x = v i (cos  ) t

7. Projectiles launched at an angle… When a projectile is launched at an angle, the initial velocity has a vertical component as well as a horizontal component. Equations of motions change slightly…now we have to differentiate between x and y components.

8. Centripetal Acceleration “center seeking” The acceleration on an object to keep it traveling in a circular path The direction is always pointed towards the center, perpendicular to the velocity. ac=v2/rac=v2/r

9. Centripetal Force Force required to keep an object traveling in circular motion: F c = ma c = mv 2 /r Remove force, will travel in a straight line This is different than the “fictional” force of centrifugal force…which does not exist.

10. CENTRIPETAL LAB Materials –String/stopper –Stopwatch –Meter stick –Balance Procedures –Measure m, r, and t of the slowly, spinning block –Calculate v, a c, and F c. –Repeat using 2 different radii.

11. 51. 28.9 m 53. 3.2 m 56. 31 m, 212 m 58. 14.3 s, 497 m 60. 11.8 m/s 61. 9.65 m/s 2 ; 5937 N 62. 71 m/s 2, 500 N 65. 18 m/s 67. 1,470 m Ch6 Homework

12. PERIODIC MOTION Review hw problems What is periodic motion? Centripetal force is a “fictional” force pendulums(equation) circular motion

13. PENDULUM LAB Each group needs: –pendulum –stop watch –meter stick measure the difference in T for 5 different lengths of string use 10,20,30,40,50 cm lengths

14. Egg Drop Parachute Rules Nothing added to egg to improve its strength Raw, chicken eggs only Less than 1 m from egg bottom to parachute top Cannot be attached to anything on the ground or building (i.e. freefalling) Must fit through the “fire escape” (the window) Nothing attached to the egg to protect it…the egg must hit the ground first One throw per group

15. Eggcellent Parachute Project Procedures Ensure the parachute is working properly…make any adjustments Egg must be inspected before attaching to parachute (any cracks and/or rule violations) Attach egg to parachute Egg/parachute must be inspected again 1 person from each group will stay in the class to drop the egg/parachute Other group members will be in the courtyard After each drop, I will inspect the egg for damage