Physics 102-002 Announcements

1. Physics 102-002Announcements • WebAssign – • Chapter 8 and 9 due Wednesday • Exam #2 corrections due Wednesday • Revised class schedule posted on website Picture: Trebuchet at Château des Baux, France

2. Class Schedule

3. Chapter 10Projectile and Satellite Motion (Not so much) • Projectile Motion • Projectiles Launched Horizontally • Projectiles Launched at an Angle

4. Projectile Motion • Projectile motion refers to the motion of an object projected into the air at an angle. A few examples include: • a soccer ball being kicked • a baseball being thrown • an athlete long jumping • fireworks • water fountains “Height” “Range” Projectile terminology Before Galileo, people thought projectiles followed a straight line until it lost its “impetus”, then fell to the earth. Galileo was the first to theorize that a projectile was influenced by 2 independent motions, the vertical motion influenced by the pull of gravity, and the horizontal motion which was uniform, consistent with the law of inertia.

5. Projectile Motion Without gravity, you could throw a rock and it would follow a straight line path at constant speed. But in the real world, if you throw a rock, it falls to the ground because of gravity. Since the vertical pull of gravity is the only force acting on the rock (if we neglect air resistance), this is a sign that the horizontal and vertical motions are independent. This figure shows both components. They change (or stay the same) independently of each other Projectile Motion Applet http://www.walter-fendt.de/ph11e/projectile.htm

6. Projectiles Launched Horizontally • When throwing a ball horizontally: • The horizontal component of the ball’s velocity doesn’t change as the falling ball moves forward. • The vertical component changes exactly in the same way as it would if the ball were dropped vertically. • The curved path is a combination of the uniform horizontal motion and the vertical acceleration due to gravity

7. Projectiles Launched Horizontally Whether an object is dropped vertically or launched horizontally, its rate of fall is the same. It has the same acceleration downward due to gravity. The projectile’s horizontal speed is constant (unless there’s air drag). At a given location on the earth and in the absence of air resistance, all objects fall with the same uniform acceleration. Thus, two objects of different sizes and weights, dropped from the same height, will hit the ground at the same time. An object is controlled by two independant motions. So an object projected horizontally will reach the ground in the same time as an object dropped vertically. No matter how large the horizontal velocity is, the downward pull of gravity is always the same.

8. Projectiles Launched Horizontally Newton’s first law applies: Without gravity, an object in motion will continue in motion with the same speed and in the same direction. With gravity, the object will fall below its “inertial” path. Gravity will cause a downward acceleration. No horizontal force is needed to maintain the cannonball’s horizontal motion … inertia does that. Physics Place Interactive Figures http://wps.aw.com/aw_hewitt_cp_10/0,10865,2370903-,00.html

9. Projectiles Launched at an Angle A projectile falls from ideal trajectory (the straight-line path that it would follow if there were no gravity) the same distance over time regardless of the launch angle. d = ½ gt2 Where d = the distance fallen d = ½ (10)t2 = 5t2 Water Balloons game http://library.thinkquest.org/2779/Balloon.html

10. Projectiles Launched at an Angle Remember: the horizontal component of the projectile’s velocity doesn’t have any affect on it’s vertical velocity. Animation: A projectile launched vertically in a vehicle moving at uniform speed will come down at the same spot that it was launched from! Notice how the vertical velocity changes as the projectile moves along the trajectory. It’s equal to zero at the apex. The horizontal velocity vector is always the same. A launch angle of 45 degrees gives the greatest range (if no air drag). Launching at a higher or lower angle gives a shorter range. There are always 2 angles that will give the same range, and they add to 90 degrees. Monkey zookeeper animation http://www.physicsclassroom.com/mmedia/vectors/mzng.html

11. Projectiles Launched at an Angle Air Drag has the effect of reducing the range and making the path of the projectile altered from the ideal “parabolic” shape. The projectile has the same deceleration going up as the acceleration it experiences going down. The speed it loses going up is the same as the speed it gains as it comes down. So, when it reaches it’s starting height, it has the same speed that it had when it was launched.

12. Question 1 If you toss a ball upward in a train moving at constant speed, it returns to its starting place. Will the ball do the same if the train is accelerating? A. Yes B. No

13. Question 1 Answer If you toss a ball upward in a train moving at constant speed, it returns to its starting place. Will the ball do the same if the train is accelerating? A. Yes B. No 

14. Question 2 When a rifle is being aimed at a distant target, the barrel should be lined up so that it points A. Slightly higher than the target • Exactly at the target • Slightly lower than the target

15. Question 1 Answer When a rifle is being aimed at a distant target, the barrel should be lined up so that it points A. Slightly higher than the target • Exactly at the target • Slightly lower than the target 