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Lecture 7 : Introduction to Physics PHY101

Lecture 7 : Introduction to Physics PHY101. Chapter 2: Free Fall (2.6) Graphical Analysis of Velocity and Acceleration (2.7) Chapter 3: Equations of Kinematics for Constant Acceleration in 2 Dim. (3.1, 3.2) Projectile Motion (3.3). Summary of Lecture 6.

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Lecture 7 : Introduction to Physics PHY101

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  1. Lecture 7: Introduction to PhysicsPHY101 Chapter 2: Free Fall (2.6) • Graphical Analysis of Velocity and Acceleration (2.7) Chapter 3: • Equations of Kinematics for Constant Acceleration in 2 Dim. (3.1, 3.2) Projectile Motion (3.3)

  2. Summary of Lecture 6 • equations with constant acceleration (t0=0): • x = v0t + 1/2 at2 • v = at • v2 = v02 + 2a x • free fall: ay = -g = -9.80 m/s2 • y = y0 + v0yt - 1/2 gt2 • vy = v0y - gt • vy2 = v0y2 - 2gy

  3. Correct: v2 = v02 -2gy v0 Dennis Carmen v0 H vA vB Concept Question Dennis and Carmen are standing on the edge of a cliff. Dennis throws a basketball vertically upward, and at the same time Carmen throws a basketball vertically downward with the same initial speed. You are standing below the cliff observing this strange behavior. Whose ball is moving fastest when it hits the ground? 1. Dennis' ball2. Carmen's ball3. Same

  4. Free Fall - Symmetry • At a given displacement along the path of motion the magnitude of the upward velocity is equal the magnitude of the downward velocity and they point in opposite directions: vup = - vdown

  5. Kinematics in Two DimensionsConstant Acceleration Consider an object which moves in the (x,y) plane from the initial position r0, at time t0 with velocity v0, with constant acceleration. • position: your coordinates (just r=(x,y) in 2-D) • displacement: r = r-r0change of position • velocity: rate of change of position • average : r/t • instantaneous: lim t->0r/t • acceleration: rate of change of velocity • average: v/t • instantaneous: lim t->0v/t Same concepts as in one dimension ! Equations of kinematics are derived for the x and y components separately. Same equations as in one dimension !

  6. Equations of Kinematics in 2 Dim.

  7. ABC Eqs. of Kinematics in 2 Dim. • The motions along the x and y directions are completely independent. They only share a common time. • Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth (B) swims perpendicular to the flow, Ann (A) swims upstream, and Carly (C) swims downstream. Which swimmer wins the race? A) Ann B) Beth C) Carly Time to get across = width of river / y-component of velocity correct

  8. Projectile Motion A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land ? 1. Forward of the center of the car 2. At the center of the car 3. Backward of the center of the car correct

  9. Kinematics of Projectile Motion (t0=0) • x direction : motion with constant velocity => ax = 0 x = x0 + v0xt vx = v0x • y direction : free fall => ay = - g = -9.80 m/s y = y0 + v0y t - 1/2 g t2 vy = v0y – g t vy2 = v0y2 – 2 g (y-y0)

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