chap7

chap7 - MotioninTwo Dimensions: ProjectileMotion...

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Motion  in  Two   Dimensions: Projectile Motion Circular Motion Angular Speed Simple Harmonic Motion    Torque Center of Mass

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Projectile Motion A red marble is dropped off a cliff at the same time a black one is shot horizontally. At any point in time the marbles are at the same height, i.e., they’re falling down at the same rate, and they hit the ground at the same time. Gravity doesn’t care that the black ball is moving sideways; it pulls it downward just the same. Since gravity can’t affect horiz. motion, the black particle continues at a constant rate. With every unit of time, the marbles’ vertical speed increases, but their horiz. speed remains the same (ignoring air resistance). continued on next slide
Projectile Motion continued on next slide Gravity’s downward pull is independent of horiz. motion. So, the vertical acceleration of each marble is - g (for the whole trip), and the sideways acceleration of each is zero . (Gravity can’t pull sideways). Whatever horiz. velocity the black one had when shot is a constant throughout its trip. Only its vertical velocity changes. (A vertical force like gravity can only produce vertical acceleration.) 9.8 m/s 2 9.8 m/s 2 9.8 m/s 2

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Projectile Motion (cont.) continued on next slide t = 0 t = 1 t = 2 t = 3 t = 4 v y = 1 v y = 2 v y = 3 v y = 4 v y = 0 If after one unit of time the marbles have one unit of speed downward, then after two units of time they have two units of speed downward, etc. This follows directly from v f = v 0 + a t . Since v 0 = 0, downward speed is proportional to time. Note: The vectors shown are vertical components of velocity. The shot marble has a horizontal component too (not shown); the dropped one doesn’t.
Since the shot black marble experiences no horiz. forces (ignoring air), it undergoes no horiz. acceleration. Therefore, its horiz. velocity, doesn’t change. So, the horiz. vector has a constant magnitude, but the vertical vector gets longer. The resultant (the net velocity vector in blue) gets longer and points more downward with time. When t = 0, v = v x for the shot marble. v = v y for the dropped marble for the whole trip. Projectile Motion (cont.) continued on next slide v x = v v x v x v x v x v v v v y v y v y v y v y t = 0 t = 1 t = 2 t = 3 t = 4

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(cont.) The trajectory of any projectile is parabolic. (We’ll prove this later.) If its initial velocity vector is horizontal, as with the black marble, the launch site is at the vertex of the parabola. The velocity vector at any point in time is tangent to the parabolic trajectory. Moreover, velocity vectors are always tangent to the trajectory of any moving object, regardless of its shape. v
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This note was uploaded on 11/17/2011 for the course PHYS 121 taught by Professor Burgeson during the Fall '11 term at BYU.

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chap7 - MotioninTwo Dimensions: ProjectileMotion...

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