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PHSX213 class • I hope you had a good weekend. – I spent a lot of Friday evening annoyed that my car seems to obey Newton’s 1st Law when I was turning on an icy corner ! • HW1 is due now. • Questions from last time ? (1-d kinematics) • Many of you are now signed up for the online access – please do this as soon as you can. – HW2 is available (only available with eGradePlus access) – Submissions • Kinematics in 2-d (Chapter 4) – Projectile motion – Uniform Circular Motion Mon. Jan. 31st 1 Position vector for a particle Mon. Jan. 31st 2 Reading Quiz Mon. Jan. 31st 3 A ball is thrown upward at a 45° angle. In the absence of air resistance, the ball follows a A. tangential curve. B. parabolic curve. C. sine curve. D. linear curve. Mon. Jan. 31st 4 A ball is thrown upward at a 45° angle. In the absence of air resistance, the ball follows a A. tangential curve. B. parabolic curve. C. sine curve. D. linear curve. Mon. Jan. 31st 5 Check-Point 0 You are throwing a ball straight up in the air. At the highest point, the ball’s A. velocity and acceleration are zero. B. velocity is nonzero but its acceleration is zero. C. acceleration is nonzero, but its velocity is zero. D. velocity and acceleration are both nonzero. Mon. Jan. 31st 6 Check-Point 0 You are throwing a ball straight up in the air. At the highest point, the ball’s A. velocity and acceleration are zero. B. velocity is nonzero but its acceleration is zero. C. acceleration is nonzero, but its velocity is zero. D. velocity and acceleration are both nonzero. Mon. Jan. 31st The ball reaches its highest point when its velocity is zero. The acceleration due to gravity is constant and never zero. 7 Check-Point 1 A person standing at the edge of a cliff throws one ball straight up and another ball straight down at the same initial speed. Neglecting air resistance, the ball to hit the ground below the cliff with the greater speed is the one initially thrown : A. upward. B. downward. C. neither—they both hit at the same speed. Mon. Jan. 31st 8 Check-Point 1 A person standing at the edge of a cliff throws one ball straight up and another ball straight down at the same initial speed. Neglecting air resistance, the ball to hit the ground below the cliff with the greater speed is the one initially thrown : On its descent, an object with initial velocity, v, has a velocity of –v, when it A. upward. reaches the height from B. downward. which it was thrown C. neither—they both hit at the same speed. Mon. Jan. 31st 9 Kinematics: General Case (3-D) • Reference frame – Origin, (x, y, z)-axes • • • • r→= ^ ^ ^ Position Vector, xi+yj+zk Displacement, ≡ D → r =→ r2 – → r1 → → Instantaneous Velocity, v ≡ d r /dt → → → 2 Instantaneous Acceleration, a ≡ d v/dt ≡ d r /dt2 Mon. Jan. 31st 10 Let’s look in more detail at what this 3-D stuff means Mon. Jan. 31st 11 Projectile Motion • (Neglect air resistance) • Launch a projectile at angle, q0, to the horizontal, and with initial speed, v0 • Horizontal component of the velocity, vx , experiences NO acceleration (ie. ax = 0). • Vertical component of the velocity, vy , has acceleration due to gravity (ie. ay = -g ). • Projectile motion can be analyzed by considering the horizontal and vertical as independent of each other. • Range = horizontal distance R. Mon. Jan. 31st 12 Check-Point 2 Consider the situation depicted here. A gun is accurately aimed at a dangerous criminal hanging from the gutter of a building. The target is well within the gun’s range, but the instant the gun is fired and the bullet moves with a speed vo, the criminal lets go and drops to the ground. What happens? The bullet : • 1. hits the criminal regardless of the value of vo. • 2. hits the criminal only if vo is large enough. • 3. misses the criminal. Mon. Jan. 31st 13 Check-Point 2 Consider the situation depicted here. A gun is accurately aimed at a dangerous criminal hanging from the gutter of a building. The target is well within the gun’s range, but the instant the gun is fired and the bullet moves with a speed vo, the criminal lets go and drops to the ground. What happens? The bullet : • 1. hits the criminal regardless of the value of vo. • 2. hits the criminal only if vo is large enough. • 3. misses the criminal. Why don’t you convince yourself for next time. Mon. Jan. 31st 14 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 passes beneath the coconut. C. the bullet hits the coconut. D. A situation similar to this wasn’t discussed in Chapter 4. Mon. Jan. 31st 15 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 passes beneath the coconut. C. the bullet hits the coconut. D. A situation similar to this wasn’t discussed in Chapter 4. Mon. Jan. 31st 16 Projectile Demo • Car on track with steel ball. Mon. Jan. 31st 17 Projectile Problems • Projectile (eg. punted football) launched with speed, v0, at launch angle, q. • Time to reach its highest point ? • Coordinates of highest point ? • Time to hit ground ? • Range ? • Velocity components just before landing ? • What launch conditions for maximum range ? Mon. Jan. 31st 18 Check-Point 3 A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship gets hit first? A. A B. B C. both at the same time D. need more information Mon. Jan. 31st 19 Check-Point 3 A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship gets hit first? A. A B. B C. both at the same time D. need more information Mon. Jan. 31st The time a projectile spends in the air is twice the time taken to fall from its maximum height. 20 Uniform Circular Motion • An object traveling with constant speed in a circular path IS accelerating (because the velocity is not constant) • The centripetal acceleration is given by : • a = v2/r • Period, T, and revolution frequency definitions. Mon. Jan. 31st 21 Centripetal acceleration derivation • Note the MINUS sign. Mon. Jan. 31st 22 On Wednesday • Relative Motion (end of chapter 4) • Start Newton’s Laws (chapter 5) Mon. Jan. 31st 23