Mon. Jan. 31st1 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 1 st 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. 31st2 Position vector for a particle

Mon. Jan. 31st3 Reading Quiz

Mon. Jan. 31st4 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. 31st5 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. 31st6 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. 31st7 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. The ball reaches its highest point when its velocity is zero. The acceleration due to gravity is constant and never zero.

Mon. Jan. 31st8 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. 31st9 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. On its descent, an object with initial velocity, v, has a velocity of –v, when it reaches the height from which it was thrown

Mon. Jan. 31st10 Kinematics: General Case (3-D) Reference frame –Origin, (x, y, z)-axes Position Vector, r = x i + y j + z k Displacement, ≡  r = r 2 – r 1 Instantaneous Velocity, v ≡ d r /dt Instantaneous Acceleration, a ≡ d v/dt ≡ d 2 r /dt 2 ^ ^ ^ → →→→ → → → →→

Mon. Jan. 31st11 Let’s look in more detail at what this 3-D stuff means

Mon. Jan. 31st12 Projectile Motion (Neglect air resistance) Launch a projectile at angle,  , to the horizontal, and with initial speed, v 0 Horizontal component of the velocity, v x, experiences NO acceleration (ie. a x = 0). Vertical component of the velocity, v y, has acceleration due to gravity (ie. a y = -g ). Projectile motion can be analyzed by considering the horizontal and vertical as independent of each other. Range = horizontal distance R.

Mon. Jan. 31st13 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 v o, the criminal lets go and drops to the ground. What happens? The bullet : 1. hits the criminal regardless of the value of v o. 2. hits the criminal only if v o is large enough. 3. misses the criminal.

Mon. Jan. 31st14 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 v o, the criminal lets go and drops to the ground. What happens? The bullet : 1. hits the criminal regardless of the value of v o. 2. hits the criminal only if v o is large enough. 3. misses the criminal. Why don’t you convince yourself for next time.

Mon. Jan. 31st15 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. 31st16 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. 31st17 Projectile Demo Car on track with steel ball.

Mon. Jan. 31st18 Projectile Problems Projectile (eg. punted football) launched with speed, v 0, at launch angle,  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. 31st19 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. 31st20 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 The time a projectile spends in the air is twice the time taken to fall from its maximum height.

Mon. Jan. 31st21 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 = v 2 /r Period, T, and revolution frequency definitions.

Mon. Jan. 31st22 Centripetal acceleration derivation Note the MINUS sign.

Mon. Jan. 31st23 On Wednesday Relative Motion (end of chapter 4) Start Newton’s Laws (chapter 5)