Physics 121, Sections 9, 10, 11, and 12 Lecture 7 Today's Topics Homework 3: Due Friday Sept 23@ 6: 00PM Ch.3:#64,75,and81 Ch4:#4,8,21,25,36,and40 Chapter 4: Motion in 2-D Projectile motion Relative velocity More examples of FBD's Physics 121: Lecture 7, Pg 1
Physics 121: Lecture 7, Pg 1 Physics 121, Sections 9, 10, 11, and 12 Lecture 7 Today’s Topics: Homework 3: Due Friday Sept. 23 @ 6:00PM Ch.3: # 64, 75, and 81. Ch.4: # 4, 8, 21, 25, 36, and 40. Chapter 4: Motion in 2-D Projectile motion Relative velocity More examples of FBD’s
Typical questions (projectile motion; for given Vo and e) What is the maximum height the ball reaches(h)? P y: h=(vo sin 0)t-1/2 gt2 v=(Vo sin 0)-gt=0 at P 0 (Vo Sin 0)/g L How long does it take to reach maximum height? y (vo sin 0)/g Would the answers above be any different if the h projectile was moving only along y-axis(1-D motion with the initial velocity Vo sin(0)? (A) YES (B)NO(C)CANT TELL Vo sin(0)X Physics 121: Lecture 7, Pg 2
Physics 121: Lecture 7, Pg 2 Typical questions : (projectile motion; for given v0 and q) What is the maximum height the ball reaches (h) ? How long does it take to reach maximum height ? h = (v0 sin q) t - 1/2 g t2 v = (v0 sin q) - g t = 0 at P t = (v0 sin q) / g t = (v0 sin q) / g ! y : q h L y x v0 P Would the answers above be any different if the projectile was moving only along y-axis (1-D motion) with the initial velocity: v0 sin (q) ? ( A ) YES ( B ) NO ( C ) CAN’T TELL h y v0 sin(q) x P
Typical questions (projectile motion; for given vo and 0) What is the range of the ball (L)? h xo t=(vo cos 0)t 0 X How long does it take for ball to reach final point(P)? y: y=(vo sin 0)t/1/2 gt2=01 when at P [(Vo sin 0)-12gt]t=0 t=0 t=2(vo sin 0)/g Physics 121: Lecture 7, Pg 3
Physics 121: Lecture 7, Pg 3 Typical questions : (projectile motion; for given v0 and q) What is the range of the ball (L) ? How long does it take for ball to reach final point (P) ? q h L y x v0 P y = (v0 sin q) t - 1/2 g t2 = 0 ! when at P [ (v0 sin q) - 1/2 g t] t = 0 t = 0 ; t = 2 (v0 sin q) / g L = vx0 x : t = (v0 cos q) t y :
Problem 1 Suppose a projectile is aimed at a target at rest placed at the same height. at the time that the projectile leaves the cannon the target is released from rest and starts falling toward ground. Would the projectile miss or hit the target (A)MISS (B)HIT (C)CANT TELL PROJECTILE t=0 t=0 TARGET y Physics 121: Lecture 7, Pg 4
Physics 121: Lecture 7, Pg 4 Problem 1 Suppose a projectile is aimed at a target at rest placed at the same height. At the time that the projectile leaves the cannon the target is released from rest and starts falling toward ground. Would the projectile miss or hit the target ? t = t1 y x v0 t = 0 t = 0 TARGET PROJECTILE ( A ) MISS ( B ) HIT ( C ) CAN’T TELL
Problem 2 Suppose a projectile is aimed at a target at rest somewhere above the ground as shown in Fig below. At the same time that the projectile leaves the cannon the target falls toward ground. Would the projectile miss or hit the target? (A)MISS (B)HIT (C)CANT TELL t=0 TARGET t=t, t=0 PROJECTILE Physics 121: Lecture 7, Pg 5
Physics 121: Lecture 7, Pg 5 Problem 2 Suppose a projectile is aimed at a target at rest somewhere above the ground as shown in Fig. below. At the same time that the projectile leaves the cannon the target falls toward ground. Would the projectile miss or hit the target ? t = t1 q y x v0 t = 0 t = 0 TARGET PROJECTILE ( A ) MISS ( B ) HIT ( C ) CAN’T TELL
Inertial reference frames A Reference Frame is the place you measure from It's where you nail down your (x,y, z) axes An Inertial Reference Frame(IRF)is one that is not accelerating We will consider only IRF's in this course Valid IRF's can have fixed velocities with respect to each other More about this later when we discuss forces For now, just remember that we can make measurements from different vantage points Physics 121: Lecture 7, Pg 6
Physics 121: Lecture 7, Pg 6 Inertial Reference Frames: A Reference Frame is the place you measure from. It’s where you nail down your (x,y,z) axes! An Inertial Reference Frame (IRF) is one that is not accelerating. We will consider only IRF’s in this course. Valid IRF’s can have fixed velocities with respect to each other. More about this later when we discuss forces. For now, just remember that we can make measurements from different vantage points
Lecture AcT 1 Relative Motion Consider an airplane flying on a windy day A pilot wants to fly from New Haven to Bradley airport Having asked a friendly physics student, she knows that Bradley is 120 miles due north of New Haven and there is a wind blowing due east at 30 mph. She takes off from New Haven Airport at noon. Her plane has a compass and an air-speed indicator to help her navigate. she uses her compass at the start to aim her plane north, and her air speed indicator tells her she is traveling at 120 mph with respect to the air After one hour A) She is at Bradley B) She is due east of Bradley C) She is southeast of Bradley Physics 121: Lecture 7, Pg 7
Physics 121: Lecture 7, Pg 7 Lecture 7, ACT 1 Relative Motion Consider an airplane flying on a windy day. A pilot wants to fly from New Haven to Bradley airport. Having asked a friendly physics student, she knows that Bradley is 120 miles due north of New Haven and there is a wind blowing due east at 30 mph. She takes off from New Haven Airport at noon. Her plane has a compass and an air-speed indicator to help her navigate. She uses her compass at the start to aim her plane north, and her air speed indicator tells her she is traveling at 120 mph with respect to the air. After one hour, A) She is at Bradley B) She is due east of Bradley C) She is southeast of Bradley
Lecture 2 Relative Motion You are swimming across a 50m wide river in which the current moves at 1 m/s with respect to the shore. Your swimming speed is 2 m/s with respect to the water You swim across in such a way that your path is a straight perpendicular line across the river How many seconds does it take you to get across? a)50/2=25s b)50/1=50s c)50/3=29s m 1m/s d)50/√2=35s Physics 121: Lecture 7, Pg 8
Physics 121: Lecture 7, Pg 8 Lecture 7, ACT 2 Relative Motion You are swimming across a 50m wide river in which the current moves at 1 m/s with respect to the shore. Your swimming speed is 2 m/s with respect to the water. You swim across in such a way that your path is a straight perpendicular line across the river. How many seconds does it take you to get across? 2m/s 50m 1m/s a) 50 2 = 25s b) 50 1= 50s c) 50 3 = 29s d) 50 2 = 35s
Physics 121: Lecture 7, Pg 9
Physics 121: Lecture 7, Pg 9
Dynamics Isaac Newton (1642-1727) published Principia Mathematica in 1687. In this work, he proposed three " laws"of motion Law 1: An object subject to no external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame Law 2: For any object, FNET =2 F=ma Law 3: Forces occur in pairs: FAB =-FBA (For every action there is an equal and opposite reaction Physics 121: Lecture 7, Pg 10
Physics 121: Lecture 7, Pg 10 Dynamics Isaac Newton (1642 - 1727) published Principia Mathematica in 1687. In this work, he proposed three “laws” of motion: Law 1: An object subject to no external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame. Law 2: For any object, FNET = F = ma Law 3: Forces occur in pairs: FA ,B = - FB ,A (For every action there is an equal and opposite reaction.)