Review of Free fall Motion: How Fast. Examples. Review of Vector Addition. Vector Addition

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1 Vector Addition Review of Vector Addition Tip - to - Tail Method of Vector Addition Steps for adding two vectors using the tip-to-tail method: Any vector can be replaced by two other vectors-one horizontal and one vertical W N C A B E 1) Draw the first vector (A) to scale, with its tail at the origin 2) Draw the second vector (B) also to scale, with its tail at the tip of the first vector W N C A B E W N B C A E S C = A + B 3) The resultant vector runs from the tail end of the first vector to the tip of the second vector. S C = A + B S C = A + B Examples Review of Free fall Motion: How Fast Object Dropped: v 0 =0 v f = gt A displacement A plus a displacement B is equal to C Force C is the same as forces A and B A velocity C is the same as velocities A and B 1

2 How Far? (Dropped -->) v 0 =0 Projectile Motion d= 1/2 g * t 2 d = 1/2 * g * t 2 d(1)=.5(-10m/s 2 )(1) 2 =-5m d(2)=.5(-10m/s 2 )(2) 2 =-20m d(3)=.5(-10m/s 2 )(3) 2 =-45m d(4)=.5(-10m/s 2 )(4) 2 =-80m An object may move in both the x and y directions simultaneously It moves in two dimensions The form of two dimensional motion we will deal with is called projectile motion Assumptions of Projectile Motion We may ignore air friction We may ignore the rotation of the earth With these assumptions, an object in projectile motion will follow a parabolic path 2

3 Projectile Motion Check Yourself 1. A baseball is batted at an angle into the air. If we neglect air drag, what is the ball's acceleration vertically? Horizontally? Horizontally Launched projectile 2. At what part of its trajectory does the baseball have minimum speed? Initially we consider object projected out horizontally y X direction: Object moves with constant velocity x=v x t x Y direction: y = 1/2 g * t 2 v yf =g t 3

4 Check Yourself At the instant a horizontally held rifle is fired over a level range, a bullet held at the side of the rifle is released and drops to the ground. Which bullet, the one fired downrange or the one dropped from rest, strikes the ground first? 4

5 Check Yourself The boy on the tower throws a ball 20 M downrange as shown in Figure What is his pitching speed? Throw a stone at any speed and one second later it will have fallen 5 M below where it would have been without gravity. 5

6 Why are orbiting Astronauts Weightless? Traveling at 8 km/s, how long will it take for this Satellite to go around earth? (Period) v=d/t D= 2πR t=t (Period) =9.8 m/s 2 =5105 s 5105 s x 1 min/60 s = 85 minutes 6

7 Elliptical orbit. An Earth satellite that has a speed somewhat greater than 8 km/s overshoots a circular orbit (a) and travels away from the Earth. Gravitation slows it to a point where it no longer moves farther from the Earth (b). It falls toward the Earth gaining the speed it lost in receding (c) and follows the same path as before in a repetitious cycle. Check Yourself The orbital path of a satellite is shown in the sketch. In which of the marked positions A through d does the satellite have the greatest speed? Lowest speed? 7

8 Kepler s Second Law A line drawn from the Sun to any planet will sweep out equal areas in equal times Area from A to B and C to D are the same Check Yourself 1. The orbital path of a satellite is shown in the sketch. In which marked positions A through D does the satellite have the greatest KE? Greatest PE? Greatest total energy? 2. Why does the force of gravity change the speed of a satellite when it is in an elliptical orbit, but not when it is in a circular orbit? 8

9 Escape Velocity If Superman tosses a ball 8 km/s horizontally from the top of a mountain high enough to be just above air drag (a), then about 90 minutes later he can turn around and catch it (neglecting the Earth's rotation). Tossed slightly faster (b), it will take an elliptical orbit and return in a slightly longer time. Tossed at more than 11.2 km/s (c), it will escape the Earth. Tossed at more than 42.5 km/s (d), it will escape the solar system. Review Questions 1.A friend claims that bullets fired by some high-powered rifles travel for many meters in a straight-line path before they start to fall. Another friend disputes this claim and states that all bullets from any rifle drop beneath a straightline path a vertical distance given by ½ gt 2 and that the curved path is apparent for low velocities and less apparent for high velocities. Now it's your turn: Will all bullets drop the same vertical distance in equal times? Explain. 2.For maximum range, a football should be punted at about 45 to the horizontal somewhat less due to air drag. But punts are often kicked at angles greater than 45. Can you think of a reason why? At which of the indicated positions does the satellite in elliptical orbit experience the greatest gravitational force? Have the greatest speed? The greatest velocity? The greatest momentum? The greatest kinetic energy? The greatest gravitational potential energy? The greatest total energy? The greatest angular momentum? The greatest acceleration? Which planets have a greater period than 1 Earth year, those closer to the sun than Earth or those farther from the sun than Earth? 9