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Friday, September 9, 1998 Chapter 3 -- Projectile Motion Relative Motion Chapter 4 -- Newton’s Laws Force and Mass Think about the following two demonstrations Assume that the vertical component of the velocity is equal in both cases. Would the balls (a) Hit the ground simultaneously (b) The ball thrown vertically only hits first. (c) The ball thrown with both Vx and Vy hits first. Consult with Neighbors! After the ball leaves my hand, the ONLY acceleration it experiences (in the absence of air resistance) is that due to gravity! Gravity acts downward, affecting only the vertical component of the velocity, Vy. The horizontal component of the velocity... REMAINS UNCHANGED!!! (At least until the ball hits the ground!) Vx = constant H 0 x y y0 v0 y t gt 1 2 The bullet: In the absence of gravity, the bullet would arrive at the dot at time So y(t ) v0 y t H * * 2 x t v0 x * H x Without Gravity: y(t ) v0 y t H * * Now let’s put gravity back into the problem. How will this change things? Does the time it takes the bullet to travel the horizontal distance x change? H x Still true: x t v0 x * y(t ) v0 y t g(t ) H g(t ) * * 1 2 * 2 1 2 * 2 So, that tells us the position off the ground the bullet will be when it reaches the horizontal position of the criminal. Now, how far off the ground is the criminal? H x The criminal starts falling from a height H and falls until the bullet arrives at his horizontal position at x t v0 x * yc (t ) y0c v0 yct g(t ) H 0 g(t ) * 1 2 * * 2 yc (t ) H g(t ) * 1 2 * 2 1 2 * 2 No! We’re not talking about how fast you run from your folks when you learn mom’s made her favorite goulash for dinner! Think about two cars on the highway, one driving 50 mph and the other driving 60 mph. How fast does the faster car APPEAR to be travelling to a passenger in the slow car? 10 mph! What type of motion does the tennis ball appear to have to me? To you? To me: FREE FALL To you: Parabolic Motion As I walk at an angle to the wall in the front of the classroom, what is the speed of my shadow across the wall? That speed represents the “component” of my velocity that is parallel to the wall. It is often helpful in solving physics problems to look at the PROJECTIONS of vector quantities onto useful coordinate systems…(e.g. LAB last night)! y v vy vx x 1 2 x x0 v0t 2 at v v0 at Careful! These do NOT quite match the ones in the book! Newton’s Laws What is a force? What is mass? How are these quantities related to acceleration? Definition IV: “An impressed force is an action exerted upon a body in order, to change its state, either of rest, or of uniform motion in a right line.” Object sitting still Object moving with uniform velocity Law I: “Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.” Hmmm…I guess I had better IMPRESS you if I’m ever going to get you guys to START liking physics, eh??? Law I: “Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.” What does this really mean? We leave the room and return 10 minutes later. Where will the keys be? We leave again and return 10 minutes later. Where will the keys be? Unless there’s SOME outside force that acts upon the keys, they’re not going anywhere!! We’re in outer space…far away from or galaxy, or star... Our spaceship is moving with const toward the distant planet “GRADUAT The engines are off! What happens to our velocity? Nothing! We keep going... and going... and going... Nothing outlasts Physics 111 They keep going and going a