physics Chapter 4 Lecture a strategic approach randall d. knight FOR SCIENTISTS AND ENGINEERS Chapter 4_Lecture1 THIRD EDITION
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1 Chapter 4 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight Chapter 4_Lecture1 1
2 Chapter 4 Kinematics in 2D: Projectile Motion (Sec. 4.2) Which fountain soars out the farthest? Chapter Goal: To learn how to solve problems about motion in a plane. Human males can throw more than 3X faster than adult male chimps. Why? How? Read Slinging our way to the top of the foodchain posted on the course website. Chapter 4_Lecture1 2 Slide 4-2
3 Two Dimensional Kinematics (Sec 4.1) Trajectory - Picture or movie of the object s motion in real space Basic Equations: These equations of motion are extremely simple, but their application can be tricky! Do not confuse these graphs with trajectories! Chapter 4_Lecture1 3
4 We also learned about Vector Components! Like Conceptual Question 4.1 at end of chapter 4 This acceleration will cause the particle to a. Speed up and curve upward b. Speed up and curve downward c. Slow down and curve upward d. Slow down and curve downward e. Move to the right and down f. Reverse direction Chapter 4_Lecture1 4
5 Key Point: Change in Velocity vector results in Acceleration!! Sec 4.1 Extending velocity to multiple dimensions: an acceleration may change the magnitude and/or direction of the velocity! Chapter 4_Lecture1 5
6 Chapter 4 Projectile Motion Example of 2D Kinematics Sec 4.2 Chapter 4_Lecture1 6 Slide 4-4
7 Projectile Motion continued Sec 4.2 Baseballs, tennis balls, Olympic divers, etc. all exhibit projectile motion. A projectile is an object that moves in two dimensions under the influence of only gravity. Projectile motion extends the idea of free-fall motion to include a horizontal component of velocity. Air resistance is neglected. Projectiles in two dimensions follow a parabolic trajectory as shown in the photo. Chapter 4_Lecture1 7 Slide 4-44
8 Remember?? Position vs. Time Graphs for Projectile Motion Sec 4.2 Shown is the motion diagram of a basketball, with 0.5 s intervals between frames. x-motion vs. t y-motion vs. t x y t Chapter 4_Lecture1 8 t
9 ! Kinematics in 2D thrown ball Sec 4.2 Vector Components Note! Neglecting air resistance, 1) v x stays the same throughout! 2) velocity is not zero anywhere! 3) acceleration is not zero anywhere! 4) <inal velocity is same as initial Chapter 4_Lecture1 9
10 Projectile Motion (Sec 4.2) The start of a projectile s motion is called the launch. The angle θ of the initial velocity v 0 above the x-axis is called the launch angle. The initial velocity vector can be broken into components. where v 0 is the initial speed. Chapter 4_Lecture1 10Slide 4-45
11 Projectile motion and Vector components Sec 4.2 The thrown ball Note! Neglecting air resistance, 1) v x stays the same throughout! 2) velocity is not zero anywhere! 3) acceleration is not zero anywhere! 4) <inal velocity is same as initial! Chapter 4_Lecture1 11
12 Constant Acceleration (2D case) Sec 4.2 Note: Your author writes I will write x-motion y-motion For projectiles: a x = 0, a y = g downward Chapter 4_Lecture1 12
13 Whiteboard Problem 4.1 (Sec. 4.2) A heavy ball is launched exactly horizontally at height h above a horizontal field. At the exact instant that the ball is launched, a second ball is simply dropped from height h. Calculate the time taken by each ball to hit the ground in terms of h and other known constants. Which ball hits the ground first? Chapter 4_Lecture1 13Slide 4-52
14 Conceptual Question 4.2 (Fig in book) Sec 4.2 A hunter points his rifle directly at a coconut that he wishes to shoot off a tree. It so happens that the coconut falls from the tree at the exact instant the hunter pulls the trigger. Consequently, A. The bullet passes above the coconut. B. The bullet hits the coconut. C. The bullet passes beneath the coconut. D. This wasn t discussed in Chapter 4. Chapter 4_Lecture1 14 Slide 4-9
15 Reasoning About Projectile Motion (Sec 4.2) A hunter in the jungle wants to shoot down a coconut that is hanging from the branch of a tree. He points his arrow directly at the coconut, but the coconut falls from the branch at the exact instant the hunter shoots the arrow. Does the arrow hit the coconut? Without gravity, the arrow would follow a straight line. Because of gravity, the arrow at time t has fallen a distance ½gt 2 below this line. The separation grows as ½gt 2, giving the trajectory its parabolic shape. Chapter 4_Lecture1 15 Slide 4-57
16 Reasoning About Projectile Motion (Sec 4.2) A hunter in the jungle wants to shoot down a coconut that is hanging from the branch of a tree. He points his arrow directly at the coconut, but the coconut falls from the branch at the exact instant the hunter shoots the arrow. Does the arrow hit the coconut? Had the coconut stayed on the tree, the arrow would have curved under its target as gravity causes it to fall a distance ½gt 2 below the straight line. But ½gt 2 is also the distance the coconut falls while the arrow is in flight. So yes, the arrow hits the coconut! Chapter 4_Lecture1 16 Slide 4-58
17 Conceptual Question 4.3 (Sec 4.2) Projectiles 1 and 2 are launched over level ground with the same speed but at different angles. Which hits the ground first? Ignore air resistance. A. Projectile 1 hits first. B. Projectile 2 hits first. C. They hit at the same time. D. There s not enough information to tell. Chapter 4_Lecture1 17 Slide 4-61
18 Conceptual Question 4.4 (Sec 4.2) Projectiles 1 and 2 are launched over level ground with different speeds and at different angles. Which hits the ground first? Ignore air resistance. A. Projectile 1 hits first. B. Projectile 2 hits first. C. They hit at the same time. D. There s not enough information to tell. Chapter 4_Lecture1 18 Slide 4-63
19 Whiteboard Problem 4.2 A batted ball is launched at 45 0 and just clears a fence 15 m higher than the launch point and 20 m away. a) Find the launch speed and time required for the ball to reach the fence. b) Is the ball on the way up or down when it clears the fence? Chapter 4_Lecture1 19
20 Whiteboard Problem 4.3 A punter kicks a football such that it leaves his foot at a speed of 22 m/s at an angle of 40 0 with respect to the ground. The returner has positioned himself 60 m from the kicker. How fast (average speed) must the returner run to catch the ball before it hits the ground? Chapter 4_Lecture1 20
21 Whiteboard Problem 4.4: Challenge problem An archer standing on a 15 0 slope shoots an arrow 20 0 above the horizontal, as shown. How far down the slope does the arrow hit if it is shot with a speed of 50 m/s from 1.75 m above the ground? Chapter 4_Lecture1 21
22 Discuss Challenge problem In one contest at the county fair, seen below, a spring-loaded plunger launches a ball at a speed of 3.0 m/s from one corner of a smooth, flat board that is tilted at a 20 o angle. To win, you must make the ball hit a small target at the adjacent corner, 2.50m away. At what angle should you tilt the ball launcher? Chapter 4_Lecture1 22
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