Physics 121, Sections 9, 10, 11, and 12 Lecture 5 Today's Topics Homework 2: Due Friday Sept 16@6: 00PM Ch.3:#2.11,18,20,25,32,36,46,50,and56 Chapter 3: Forces and motion along a line Motion with constant acceleration Falling objects Apparent weight Chapter 4: Motion in 2-D Vectors Kinematics Projectile motion Physics 121: Lecture 5, Pg 1
Physics 121: Lecture 5, Pg 1 Physics 121, Sections 9, 10, 11, and 12 Lecture 5 Today’s Topics: Homework 2: Due Friday Sept. 16 @ 6:00PM Ch.3: # 2, 11, 18, 20, 25, 32, 36, 46, 50, and 56. Chapter 3: Forces and motion along a line Motion with constant acceleration Falling objects Apparent weight Chapter 4: Motion in 2-D Vectors Kinematics Projectile motion
Recap: constant acceleration in 1-D For constant acceleration Xo +vot+at V=Vo+at a= const From which we know v=2a(x-X0) (Vo +v) Physics 121: Lecture 5, Pg 2
Physics 121: Lecture 5, Pg 2 Recap: constant acceleration in 1-D For constant acceleration: v v at 0 = + 2 0 0 at 2 1 x = x + v t + a = const From which we know: (v v) 2 1 v v v 2a(x x ) av 0 0 2 0 2 = + − = −
Lecture 5 ACT 1 1D Freefall Alice and Bill are standing at the top of a cliff of height H. Both throw a ball with initial speed vo. Alice straight down and Bill straight up. The speed of the balls when they hit the ground are va and vB respectively. Which of the following is true: (a va VB Alice Vol Bill 0 H B Physics 121: Lecture 5, Pg 3
Physics 121: Lecture 5, Pg 3 Lecture 5 ACT 1 1D Freefall Alice and Bill are standing at the top of a cliff of height H. Both throw a ball with initial speed v0 , Alice straight down and Bill straight up. The speed of the balls when they hit the ground are vA and vB respectively. v0 v0 Alice Bill H vA vB Which of the following is true: (a) vA vB
About air resistance When a body moves through a fluid A drag force due to friction take place Like friction, its direction is opposite to the motion This force increases dramatically with speed It is proportional to v2 Fa=bv2 For an object falling through air As gravity accelerates it, v increases When the magnitude of Fd equals the weight mg 》 Not net force→ y becomes constant The object has reached its terminal speed vt mg Physics 121: Lecture 5, Pg 4
Physics 121: Lecture 5, Pg 4 About Air resistance ? When a body moves through a fluid A drag force due to friction take place Like friction, its direction is opposite to the motion This force increases dramatically with speed It is proportional to v2 For an object falling through air As gravity accelerates it, v increases When the magnitude of Fd equals the weight mg »Not net force v becomes constant The object has reached its terminal speed vt Fd mg v
Air resistance When a body reaches V, Both forces are equal in magnitude F d but mg So the coefficient b is 79 mg And d =m t. e 6 0 The terminal speed v, varies mass, shape, size Feather: 0.5 m/s Raindrop 7m/s Skydiver: 50-60 m/s(spread-eagle Skydiver: 100 m/s diving) Physics 121: Lecture 5, Pg 5
Physics 121: Lecture 5, Pg 5 Air resistance When a body reaches vt Both forces are equal in magnitude So the coefficient b is And The terminal speed vt varies mass, shape, size Feather: 0.5 m/s Raindrop: 7 m/s Skydiver: 50-60 m/s (spread-eagle) Skydiver: 100 m/s (diving) Fd mg vt
Apparent weight The weight is read by a scale It is given by the magnitude of the normal force W′=|N|=N N >)The block pushes on the scale with a mg force equal but opposite to N(action reaction) The normal is found from the net force net=N+mg= ma If platform (and object+scale)is not accelerated Net force is zero N=-mg =,W=mg Physics 121: Lecture 5, Pg 6
Physics 121: Lecture 5, Pg 6 Apparent weight The weight is read by a scale It is given by the magnitude of the normal force »The block pushes on the scale with a force equal but opposite to N (actionreaction) If platform (and object+scale) is not accelerated Net force is zero N mg -N The normal is found from the net force a
Apparent weight N If the "elevator is accelerated a Net force≠0 net N+mg= ma g Choosing axis as illustrated N-mg=ma=>N=m(g +a) a Apparent weight is W′=m(g+a) N mg W>mg if a>0(upward): heavier W 0(downward): lighter N Physics 121: Lecture 5, Pg 7
Physics 121: Lecture 5, Pg 7 Apparent weight If the “elevator” is accelerated Net force 0 Choosing axis as illustrated a N mg Apparent weight is W’ >mg if a>0 (upward): “heavier” W’ 0 (downward): “lighter” a N mg -N
Chapter 4: Vectors In 1 dimension, we can specify direction with a or-sign In 2 or 3 dimensions, we need more than a sign to specify the direction of something To illustrate this, consider the position vector in 2 dimensions Example: Where is Boston? Choose origin at New York Boston Choose coordinate system Boston is 212 miles northeast of new york or New york Boston is 150 miles north and 150 miles east of new york Physics 121: Lecture 5, Pg 8
Physics 121: Lecture 5, Pg 8 Chapter 4: Vectors In 1 dimension, we can specify direction with a + or - sign. In 2 or 3 dimensions, we need more than a sign to specify the direction of something: To illustrate this, consider the position vector r in 2 dimensions. Example: Where is Boston? Choose origin at New York Choose coordinate system Boston is 212 miles northeast of New York or Boston is 150 miles north and 150 miles east of New York Boston New York r
Vectors There are two common ways of indicating that something is a vector quantity Boldface notation: A A=A Arrow notation: A Physics 121: Lecture 5, Pg 9
Physics 121: Lecture 5, Pg 9 Vectors... There are two common ways of indicating that something is a vector quantity: Boldface notation: A “Arrow” notation: A = A A
Vectors, definition A vector is composed of a magnitude and a direction examples: displacement, velocity, acceleration magnitude of A is designated Al usually carries units A vector has no particular position Two vectors are equal if their directions and magnitudes match A=C A≠B.B≠C Physics 121: Lecture 5, Pg 10
Physics 121: Lecture 5, Pg 10 Vectors: definition A vector is composed of a magnitude and a direction examples: displacement, velocity, acceleration magnitude of A is designated |A| usually carries units A vector has no particular position Two vectors are equal if their directions and magnitudes match. A B C A = C A = B, B = C
